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206.Журнал Сибирского федерального университета. Сер. Техника и технологии №2 2011

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Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Журнал Сибирского федерального университета
2011
Journal of Siberian Federal University
4 (2)
Техника и технологии
Engineering & Technologies
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Editorial Advisory Board
Chairman:
Eugene A. Vaganov
Members:
Kirill S. Alexandrov
Josef J. Gitelzon
Vasily F. Shabanov
Andrey G. Degermendzhy
Valery L. Mironov
Gennady L. Pashkov
Vladimir V. Shaidurov
Veniamin S. Sokolov
CONTENTS / СОДЕРЖАНИЕ
Viktor V. Onufrienok and Anatoly M. Sazonov
Pilot Study of Isothermal Crystallization of Goethite from
Metastable Synthetic Pyrrhotite
? 123 ?
В.Г. Ломаев, С.С. Сердюк
)3*23*%??*%? ???2%!%????,? ?,%K,L-!??*%???????/. !3?
$ C!,%!,2?2?/L %KA?*2 ?? ?%??!?,?=?,, !??*%??2=????%L
C!%?/?????%?2, p%??,,
? 132 ?
Л.И. Худякова, О.В. Войлошников, Е.В. Кислов
o32, C%"/???, !=?,%?=???%?% C!,!%?%C%???%"=?,
C!,??!? q?"?!%-a=L*=???*%?% !3??%?% !=L%?=
?=
? 155 ?
К.Б. Бакин, О.Н. Симакова, П.В. Поляков,
Ю.Г. Михалев, Д.А. Симаков, А.О. Гусев
}??*2!%C!%"%??%?2? .??*2!%?,2%"-?3?C???,L ?,?2??/ NaFAlF3-CaF2-Al2O3
? 162 ?
Editorial Board:
Editor-in-Chief:
Mikhail I. Gladyshev
Founding Editor:
Vladimir I. Kolmakov
Managing Editor:
Olga F. Alexandrova
Executive Editor for Engineering &
Technologies:
Vitaly S. Biront
Л.Т. Денисова, О.В. Кучумова, В.М. Денисов,
Г.М. Зеер, И.В. Гриценко
j%?2=*2?%? "?=,?%??L?2",? !=?C?="%" Bi2O3-GeO2 c ?%?%2%?
, ??!?K!%?
? 170 ?
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???????????? ??????? ?.?. ?????????
????????? ? ?????? 19.04.2011 ?. ?????? 84x108/16. ???. ???. ?. 9,7.
??.-???. ?. 9,2. ?????? ???. ?????? ????????. ????? 1000 ???. ????? 3500.
?????????? ? ?? ??? ???. 660041 ??????????, ??. ?????????, 82a.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Editorial board for Engineering &
Technologies:
Yury D. Alashkevich
Viktor G. Anopchenko
Sergey M. Geraschenko
Gennadiy I. Gritsko
Lev V. Endjievsky
Sergey V. Kaverzin
Vladimir A. Kulagin
Sergey A. Mikhaylenko
Vladimir V. Moskvichev
Anatoli M. Sazonov
Vasiliy I. Panteleev
Sergey P. Pan?ko
Peter V. Polyakov
Viktor N. Timofeev
Galina A. Chiganova
Oleg Ostrovski
Harald Oye
Artem V. Khodyaev, Anatoliy P. Shevyrnogov,
Galina S. Vysotskaya and Olga S. Kozikova
Using Moving Variance Method to Detect Ocean Currents from
Space
? 179 ?
А.М. Сержантов, К.В. Лемберг
h?????%"=?,?
3C!="? ??%?%
?"?!."/?%*%?=?2%2?%?%
?,?*%*!,?2=??,???*%?% -=?%"!=?=2??
? 185 ?
С.Ю. Гуськов
p=?!=K%2*= ?=2??=2,???*%L ?%???, ??3?2=?%","???%?
C%"%!%2= ?3???,??%?% ???%C%?!3??,*= C?!?*,??%?% 2,C=
*?=??= 25 *m
? 193 ?
????????????? ? ??????????? ???
?? ? ??77-28-722 ?? 29.06.2007 ?.
М.В. Носков, К.В. Симонов, С.В. Кириллова
n???*= !,?*= , 3??!K= %2 ?="%????,L ?= %??%"? ????2*,.
??%???2"
? 200 ?
????? ???????? ? «???????? ??????? ????????????? ??????? ???????? ? ???????, ? ??????? ??????
???? ???????????? ???????? ??????? ?????????? ??????????? ??
????????? ?????? ??????? ??????? ?
????????? ????» (???????? 2010 ?.)
Ю.В. Удалова, А.И. Легалов, Н.Ю. Сиротинина
l?2%?/ %2?=?*, , "?!,-,*=?,, -3?*?,%?=???%-C%2%*%"/.
C=!=??????/. C!%?!=??
? 213 ?
К.В. Соловьева, А.И. Демченко,
Ю.Г. Новосельцев, А.Н. Шмарловский
l=2??=2,???*%? ?%???,!%"=?,? .??*2!,???*,. , 2?C?%"/.
C%??L C!, %??%?2%!%???L *%?2=*2?%L 2%????%L ?"=!*?
? 225 ?
К юбилею Александра Федоровича Шиманского
? 235 ?
К 85-летию Наиля Хайбулловича Загирова
? 237 ?
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 123-131
~~~
??? 548.6:549.322.21:549.521.5
Pilot Study of Isothermal Crystallization
of Goethite from Metastable Synthetic Pyrrhotite
Viktor V. Onufrienok* and Anatoly M. Sazonov
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
The crystal structure and the phase composition of synthesized pyrrhotite after its endurance in the
atmosphere of the Earth for 29 years at temperature about 20є? have been studied using the methods
of X-ray structural analysis. Pyrrhotite contained goethite which was absent in initial samples. The
analysis of the experimental facts allows to assume that goethite originated from pyrrhotite in a
metastable phase. The regularity of goethite formation depending on the percentage of troilite and
also on the sulphur and iron ratio in samples has been investigated. The diagram of goethite ? troilite
phase ratio has been constructed. The theoretical model of phase transition of pyrrhotite into goethite
is offered. Good conformity of the calculated curve of the goethite ? troilite phase ratio diagram with
the experimental one has been obtained. The calculations done in the offered model of secondary
quantization cohere well enough with the similar calculations done within the model of a molecular
field.
Keywords: pyrrhotite, goethite, crystal structure, phase composition, synthesis, metastable state.
Introduction
Nowadays the interest to the minerals containing the hydroxyl group (OH) in their structure
has increased significantly. Goethite FeO(HO), hydronium Fe (SO4) 2 (OH) 52H2O, parabutlerite Fe
(SO4) (OH) 2H2O etc. can serve as examples of such minerals. This interest can be explained by the
fact that their formation is supposed to be connected with hydrothermal metasomatic processes. Such
processes are widely developed in volcanic zones on dry land and in oceans. Studying of natural
minerals in such zones is actual from the point of view of theoretical and practical geology. It should
be noted that the oxidation processes of multi-component alloys have their own features [1]. Ocean
pools contain large volumes of valuable mineral resources. In particular, iron-manganese concretions
and sulphide accumulations with gold and platinoid admixtures in the formations of black smokers are
of practical interest. Necessity of detailed study of formation processes for such minerals is obvious,
however, they should be divided in, at least, two sections. The first section is studying minerals of ore
masses directly in the process of primary ores formation, which, as a rule, are in a metastable phase.
The second section of the research is studying the transformation of minerals during ores oxidation,
and transition of metastable minerals into the stable phase. One of the minerals being formed in
*
1
Corresponding author E-mail address: VOnufriynok@.sfu-kras.ru
© Siberian Federal University. All rights reserved
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
endogenic ores of igneous and hydrothermal deposits is pyrrhotite. It usually possesses varying nonstoichiometric composition, and its crystal structure contains cationic vacancies [2-4]. Distribution of
dot defects in the structure depends on free energy of the crystal. Therefore, transition into the stable
condition is diffusible and depends on time [5-7]. The processes of minerals transition (pyrrhotite in
particular) into the stable phase have not been investigated well enough yet. Experimental study of
minerals formation is complicated by the fact that usually it is a very long process in time. Theoretical
assumptions when applied can appear to be not absolutely correct. Therefore, long-term experiments,
during which transformations of minerals in isothermal conditions in the atmosphere of the Earth were
observed, represent indisputable interest.
Purpose of Work
We decided to try and experimentally study the metasomatic transformations of minerals as a
result of their ageing (29 years) in the atmosphere of the Earth on the example of metastable pyrrhotites
of different chemical and phase composition. At that we also tried to track possible pyrrhotite
transformation in a water- containing atmosphere into new minerals, the structure of which contains
water or group (OH). In the final part of the mineralogical experiment we tried to give the theoretical
explanation of revealed regularities in formation of balanced phase ratios in synthetic iron sulphide
samples at their isothermal ageing in the atmosphere of the Earth.
Samples
Samples with various sulphur and iron ratios S/Fe(?) were prepared using the method of dry
synthesis in vacuum at temperature 1000 °C. The estimated ratio varied within the range of 1.0 < ?
< 2.0. The samples were synthesized in 1979 [6] in the laboratory of the L.V. Kirenskogo Institute for
Physics (Krasnoyarsk, Russia).
The received samples were analysed on the DRON-3 diffractometer using X-ray radiation ?? (??).
The speed of diffractograms shooting equaled 1°/min in a continuous mode and 0.001 °?? in a discrete
mode. The filter of ? ? radiation from iron was used during diffractograms shooting.
The X-ray analysis of the samples showed that there are no compounds containing oxygen,
hydrogen or hydroxyl group (OH) in their crystal structure. The samples contained only pyrite FeS2 and
pyrrhotite FeSx of various compositions, defending on the sulphur and iron ratio. The results of study of
the phase composition and the crystal structure of phases of produced samples were published in 1982
[8]. Samples of sulphides of complex phase composition, varying in the qualitative and quantitative
ratio of their associations, were produced depending on quantitative iron and sulphur ratios in the
initial blend.
With the prevailing amount of iron (up to 50 % of Fe atoms) in the initial blend, the ferromagnetic
form ? ?Fe and the antiferromagnetic phase of iron sulphide were received. In the narrow range of
compositions containing ~50 % of Fe atoms, there is only one antiferromagnetic phase ? troilite
(Phase ?2). It has a hexagonal cell with the following parameters: ?=5.95 Е and ? =11.75Е. In the
range of 50 % to 48.08 % of Fe atoms there are two antiferromagnetic phases ? ?1 and ?2 , differing
in parameters of the unit cell. Phase ?1 has the structure of hexagonal low-temperature pyrrhotite
with the following unit cell parameters: ?=3.44 Е and ? =5.78Е. The percent ratio of ?2 and ?1 phases
in samples varies depending on iron concentration in the initial blend. In the system containing
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
48.08 to 47.51 % of Fe atoms, a homogeneous solid solution Fe-S-? (vacancy) is formed. With the
increase of sulphur content Phase ?1 is not formed, and only Phase ?2 exists in the range of 48.08 to
47.6 % Fe atoms. At that the unit cell parameters of this phase vary smoothly from ?=3.44 Е and
?=5.76 Е to ?=3.44 Е and ?=5.72 Е depending on the percent content of Fe in the initial blend. With
further increase of the sulphur content in the Fe-S system, ferromagnetic phase ?3 is formed, in
which the level of vacancy regulation in subbarrays depends on the composition, as nuclear gamma
resonance spectra showed. Phase ?3 is formed with Fe atoms concentration in the blend from 47.6
to 47.3 %.
Phase ?4 with a monoclinic structure and high intensity of magnetization (Is=19 Gs ·cm3 /g) is
crystallized together with Phase ?3 in the zone of Fe atoms concentration from 47.3 to 45.9 %, whereas
Phases ?1, ?2 , ?3 have a hexagonal structure.
With Fe atoms concentration in the blend below 45.9 %, the paramagnetic ?-phase with a facecentered cubic lattice was crystallized. Two phases ?4 and ? exist approximately till 34 % of Fe atoms
with gradual change of the relative content of these phases depending on the composition. Pure sulphur
exists simultaneously with ??phase with further increase of the sulphur content.
After synthesis the samples were maintained during 29 years at the room temperature (~ 20°?)
in atmospheric conditions. In 2008 X-ray structural study of the phase composition was carried out in
these samples in the laboratory of the Siberian Federal University (Krasnoyarsk, Russia).
Experiment Results
As a result of the analysis of the obtained X-ray difractograms it has been established that all
the samples contained compounds with the hydroxyl group (??) in the structure. These included
parabutlerite Fe(SO4)(OH)2H2O, goethite FeO(HO), czomolnokite Fe(SO4)(H2O), hydronium
Fe(SO4)2(OH)52H2O, rozenite Fe(SO4)4(H2O) and rhomboclase FeH(SO4)24(H2O). As was defi ned
earlier, synthesized samples initially contained pyrrhotite in a metastable phase only. At that it
was found out that the series of stable pyrrhotites did not contain phases with the hydroxyl group.
These are mineral phases of the following compositions: FeS, Fe9S11, Fe7S 8, Fe19S20, Fe10S11. The
results of the research allow to assume that metastable pyrrhotites in isothermal conditions of
modern atmosphere form compounds, the structure of which contains the hydroxyl group, and they
do not transform into stable phases of pyrrhotites with time. No compounds, in the structure of
which oxygen was present without hydrogen, were observed. For example, Fe?, Fe (S?4)2, Fe2?3
or Fe3?4.
As a result of the analysis of X-ray patterns it has been found out that for the last 29-year interval
of time pure iron has undergone no oxidation. In X-ray patterns where there was pure iron unreacted
during the experiment, no magnetite or other oxides of iron were found.
Earlier it was found out that the content of troilite with sulphides synthesis was increasing with the
increase of iron in the samples. The dependence of the percent troilite content on the sulphur and iron
ratio (S/Fe) in samples is given in Fig. 1. This dependence can be presented in the following way:
y=(1.96·106)·exp(-10.06·x) ,
where y corresponds to the percent troilite content in samples.
The phase composition of samples containing troilite is given in Table 1. It should be noted that
sulphur in a free state was excluded for calculation of phase percentage.
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
Fig. 1. Dependence of troilite percentage on the sulphur and iron (S/Fe) ratio in samples
Fig. 2. Dependence of goethite percentage on S/Fe ratio in samples
From the analysis of spectra we can assume that metastable pyrrhotites in conditions of impact of
the atmospheric water pass in due course into goethite. Possibly, pyrrhotite of intermediate composition
(for example, Fe0,98S) disintegrates into goethite and pyrrhotite with composition Fe0,95S.
Near stoichiometric FeS (S/Fe = 1.04) the content of goethite was maximal, and made 10.88 %.
At the increase of S/Fe ratio the goethite content exponentially fell down. For example, for ? = 1.105
it made already 6.62 %. The dependence of goethite percentage on S/Fe ratio in samples is given in
Fig. 2. This dependence is described by the formula:
y=216.1·exp(-3.1·x),
where y corresponds to goethite percentage in the samples.
The phase composition of samples containing goethite is given in Table 2.
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
Table 1 Phase composition of aged samples containing troilite
Sample No
Mineral Phases
1
2
3
4
5
6
7
S/Fe ratio in samples
1.00
1.010
1.022
1.124
1.125
1.131
1.380
Troilite (?2) ? FeS %
95.80
92.38
75.25
13.41
6.11
3.28
2.36
Pyrrhotite (?4) ? Fe7S8 %
1.14
7.62
11.82
86.52
70.11
96.34
30.38
Pyrrhotite (?1) ? Fe0.975S, %
2.75
-
12.93
-
-
-
-
Pyrite (?) ? FeS2 ,%
-
-
-
-
18.52
-
41.14
Czomolnokite ? Fe(SO4)(H2O), %
-
-
-
-
5.07
-
21.04
Goethite ? FeO(OH), %
-
-
-
-
-
-
3.73
Table 2 Phase composition of aged samples containing goethite
Sample No
Mineral Phases
1
2
3
4
5
6
7
S/Fe ratios in samples
1.039
1.105
1.134
1.158
1.380
1.571
1.741
Pyrrhotite (?4) ? Fe7S8, %
69.20
81.79
70.19
73.18
30.38
16.30
3.73
7.15
5.05
11.87
7.98
41.14
58.49
67.02
Czomolnokite ? Fe(SO4)(H2O), %
12.52
-
-
6.19
21.04
17.36
28.84
Goethite ? FeO(OH), %
11.13
6.62
8.34
3.65
3.73
2.93
0.40
Pyrite (?) -FeS2, %
The following question occurs: as the result of what does goethite disappear and troilite occur
in the samples under study? The authors think that troilite does not disappear and does not occur but
is present in samples from the moment of their synthesis in an unchanged state. This phase is stable.
Troilite is an extremely stable phase and does not decompose into iron and sulphur, even in the gaseous
state. Tests on troilite sputtering to the glass surface were carried out. The difractogram of the received
sample given in Fig. 3 testifies to the troilite composition of sputtered material as such.
Goethite percentage, according to the authors, depends on the content of metastable pyrrhotite
in initial samples. Metastable pyrrhotite as such under the impact of atmospheric water transforms to
goethite in time. There was maximum amount of pyrrhotite in the samples after synthesis with the S/
Fe ratio similar to troilite. The higher the sulphur to iron ratio, the higher percentage in initial samples
of iron sulphides in the stable phase state and, correspondingly, the least percentage of goethite in
samples after ageing in conditions of the impact of atmospheric air. This explains reduction of the
phase composition of goethite with the increase of the S/Fe ratio in the diagram (see Fig. 2).
The analysis of the phase structure and the description of other compounds (czomolnokite,
hydronium, rozenite, rhomboclase) containing (OH) in the structure, are beyond the topic of this work.
Mathematical Model of Phase Transformation
To explain the obtained experimental results the mathematical model of phase transformations is
offered.
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
Fig. 3 Reciprocal lattice received with the method of electronic diffraction of troilite sputtered to the glass
surface
Let us consider the unit cells in the crystal as some system of N identical cells. The distribution of
cells by different volumes can vary; therefore the statistics of cells should be Bose. In order to describe
the cells? power states it is necessary to enter operators of birth and destruction of a cell in some
individual volume p of the crystal lattice; at that comutative relations are fair for Bose operators:
>? , ? @
p
a G pq ; ap2
q
2
p
0 ; ap ap
n?p
where p is the number of individual volume of the crystal lattice.
Fourier image of the Green?s function
f
a p a g
і G pq
f
E
t e iEt
dt
where
G pq t iT t a p t a g 0 is the Green?s function, and
­1, t ! 0 Ѕ
ѕ,
Ї0, t 0ї
T (t ) ®
t is the variable of time
Hamiltonian describing power states can be written down in the form of:
H
¦H a a ¦V
p p p
p
n? n?
pq p q
p,q
where the first sum describes independent cells, and the second one ? their interaction.
If in some volume of the crystal the unit cell of a new phase was formed, then the energy of the
crystal will change with the ?p value.
Taking into consideration commutative relations of the operators after application of the spectral
theorem, we get the expression for the average value of the operator of the particles number:
a p a p
1
S
f
і f E Im
B
a p a g
f
E i?
dE
where f B stands for the Bose-Einstein function
# 128 #
§
f B ЁЁ H p ¦ V pq n q
q
©
·
ё,
ё
№
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
Let us introduce the following designations:
n?
n?
np
nq
This is the average number of cells of pyrrhotite corresponding to the composition FeSx and
goethite (? and ? correspondingly), falling to some individual volume of the crystal structure (i.e. n?
and n? are proportional to the concentration).
We receive the following system of equations:
nD
f B H JVn? ,
nE
f B H JVn? ,
where ?? = ?? = ?, and ? is the coordination number for unit cells.
In case of long-term ageing of samples the influence of temperature can be almost
excluded, and all processes in crystal structures can be considered as caused mainly by various
exchange interactions. This assumption in mathematical respect corresponds to the area of low
temperatures
H J Vn
?, ?
!! kT
Hence, we can write down:
nD
nE
exp(
H JVn?
exp(
H JVnD
kT
kT
);
).
The obtained exponential dependence of goethite concentration on the S/Fe ratio (that is
conditionally equivalent to pyrrhotite of FeSx structure) is in qualitative conformity with the
experimental results. The similar model can be applied to troilite at its formation.
Calculations on the basis of the offered quantum model of phases formation show that if the unit
cell of goethite was formed in some volume of the crystal, the energy of the crystal will change for
0.13 eV value and if the cell of troilite structure was formed, the energy should change for 17.5·103
eV value. The numerical values have been received as a result of comparison of the experimental
dependences presented above with theoretically received final formulas. From the calculations done it
follows that goethite can be easily formed from pyrrhotite while this process requires essentially less
energy than for troilite formation. Thus, troilite can be formed during synthesis only, and formation
of troilite from pyrrhotite is almost impossible in due course. Interaction of pyrrhotite ? goethite and
pyrrhotite ? troilite cells from the presented model equal to 10-2 eV and 0.3 eV correspondingly. This
can be explained by the fact that crystal structures of troilite and pyrrhotite in many respects are
identical. The crystal structure of goethite differs more sufficiently from the structure of pyrrhotite.
That fact that interaction of cells of related structures in the pyrrhotite ? troilite system significantly
exceeds interaction in the goethite ? pyrrhotite system does not cause any questions. In fact, power
connection of cells of related structures should be more significant than connection of structurally
different cells.
Interaction of cells in the crystal structure is defi ned, fi rst of all, by the integrals of exchange
interaction. The values of these integrals are calculated in the work within the frames of the
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Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
molecular field model, i.e. with another method of quantum mechanics. For pyrrhotite the crystal
structure of which in many respects is similar to the structure of pyrrhotite, they equal to 3.4 ·10 -2 eV
and 4.25·10 -2 eV, which corresponds to the values of exchange integrals inside the basic planes and
between them (i.e. along crystallographic axes ?a? and ?c? accordingly). The value of interaction of
basic troilite unit cells ? 30·10 -2 eV received in this work is in good conformity with the results of
quantum calculations using the method of a molecular field for pyrrhotite [2]. In fact, for calculations
done in this work the coordination number for the structure of pyrrhotite can be accepted as 8 (i.e.
the contribution of superexchange interaction was taken into account as well). Let us remind that
pyrrhotite possesses the crystal structure of NiAs type [3]. If the averaged value of the exchange
integral is multiplied by 8, we will receive the value of energy interaction of cells calculated in this
work using the method of secondary quantization (i.e. ? 30·10 -2 eV). Thus, the calculations of the
similar parameters in various works done using various methods are in good conformity with each
other.
One can give the following explanation to the phase transformation described above: hydrogen of
a polar water molecule is grasped by the cation vacancy of metastable pyrrhotite and diffuses into the
crystal structure, capturing oxygen as well, where new connections are formed transforming pyrrhotite
into goethite.
Conclusions
Inhomogeneity of the composition of sulphide phases with a various level of stoichiometry and
stability in synthesized samples and the dependence of troilite percentage (stable phase) on the sulphur
and iron ratio in the initial blend have been defined.
The dependence of goethite percentage on the sulphur and iron ratio in samples has been determined.
It was defined experimentally that goethite was formed as a result of isothermal transformation of
metastable pyrrhotite to goethite in atmospheric conditions, with the diffusion mechanism of exchange
reactions. Usually, the extremely slow diffusion process of metasomatic reactions (intra-crystal
diffusion is limited by first centimeters per million years) is assisted by almost instantaneous (from the
point of view of geological time perception) pyrrhotite replacement with goethite.
The quantum-mechanical model of pyrrhotite transition to goethite has been offered. Within
the frames of the offered model the calculations of power parameters of pyrrhotite ? goethite and
pyrrhotite ? troilite systems were done. The theoretical substantiation of transformation of metastable
pyrrhotite into goethite is given. The calculations carried out in the offered secondary quantization
model cohere well with the similar calculations done within the frames of the molecular field model in
the other work [1].
References
1. Biront V.S. Peculiarities of oxidation of three-component alloys on the basis of the iron-nickelcobalt system / Biront V.S., Drozdova T.N., Blokhin I.V., Lyndina E.N., Yakimov I.S., Ponamoreva S.V.,
Gusev A.O., Simakov D.A. // Magazine of the Siberian Federal University. Tekhnika i Tekhnologii
2(2009 2) pp.139-150
2. Onufrienok V.V. Metastable iron sulphides. News of the Russian Academy of Science of
Sulphurs./ Onufrienok V.V. // J. Inorganic materials. (2005) v.41 ( 6), p. 744.
# 130 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Viktor V. Onufrienok and Anatoly M. Sazonov. Pilot Study of Isothermal Crystallization of Goethite...
3. Koto K. The superstructure of the intermediate pyrrhotite./ Koto K., Morimoto N., Guybu A.
// Acta Cryst. (1975) v. ? 31, p. 2759
4. Novikov G.V. Mossbauer and X-Ray Studies of Relaxation Kinetics in Troilite-Pyrrhotite
Assemblies./ Novikov G.V., Egorov V.K., Sipavina L.B. // Physics and Chemistry of Minerals ( 1978)
v. 3, p. 82.
5. Ward J. C. The structure and properties of some iron sulphides./ Ward J. C. //Rev. Pure. Appl.
Chem. (1970) v. 20, p.175.
6. Zvegintsev A.G. The effect of conditions of synthesis on magnetic properties and crystal
structure of pyrrhotites. / Zvegintsev A.G., Onufrienok V.V. // IAGA Bulletin, Paris, (1981) 45, p. 245.
7. Mashukov A.V. The influence of the cation vacancies on the minerals formation process. /
Mashukov A.V., Onufrienok V.V., Mashukova A.E. // J. Geochimica et ?osmochimica acta (2008)
v.72S (12), ?. A601.
8. Onufrienok, V.V. The magnetic properties and crystal structure of ferric sulphide in the range
of the composition FeS ? FeS1.18./ Onufrienok, V.V., Zvegintsev, A. G. // News of the Russian Academy
of Science of Sulphurs. J. Inorganic materials (1982) v.18 (3), p. 366.
????????????????? ????????????
??????????????? ??????????? ??????
?? ??????????????? ?????????????? ?????????
?.?. ??????????, ?.?. ???????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
? ??????????????? ?????????? ????? ???????? ? ????????? ????? ? ??????? 29 ???
??? ??????????? ~20 є? ????????????? ???????? ???????????????????? ???????
??????????????? ????????? ? ??????? ?????? ????????. ???????????, ??? ??? ????????
?????, ??????? ???????????? ? ???????? ????????. ??? ??????????????? ? ???, ???
????? ??????????? ?? ?????????, ???????????? ? ?????????????? ??????? ?????????.
? ??????????? ?? ??????????? ???? ? ?????? ? ???????? ??????????? ??????????????
??????????? ??????. ????????? ????????? ??????????? ??? ????? ? ???????. ? ??????
?????????? ????????????? ?????? ???????? ???????? ????????? ? ?????. ???????? ???????
???????????? ????????? ?????? ????????? ???????? ??????????? ????? ? ??????? ?
?????????????????. ???????, ?????????????? ? ?????? ???????????? ?????? ??????????
???????????, ?????? ??????????? ? ???????????? ?????????, ???????????? ? ?????? ??????
????????????? ????.
???????? ?????: ???????, ????????, ?????, ??????????????? ?????????, ??????? ??????,
??????, ?????????????? ?????????.
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Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 132-154
~~~
??? 553.465+493 (571.51)
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???????????? ?????? ??? ????????????
??????????????? ?????????????? ??????
?.?. ???????, ?.?. ???????*
?
??? «???????»,
?????? 660049, ??????????, ??. ?. ??????, 62
?
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
???????????? ????????????? ??????-?????????????? ??? ???????????? ????? ??????
???????????? ?????, ????????? ?? ????? ???????????? ? ?????????????? ?????????? ?????
???????? ???????? ???????????? ??????????????? ?????????????? ??????. ?????????????
??????????? ? ?????????????????? ???? ??????????????? ??? ????????????
????????????. ?????? ???? ????????????? ???????????? ????? ?????? ?????????????
?????? ?????????????? 3,5 ?? ??? ?????? ?? 800 ?? 1400 ? ? ???????? ?? 200 ?. ????????
??? ???? ???: ????????? (?? ????????? ?????????? Nb2?5 ? 0,8 %) ? ?????????????? (??
????????? ?????????? ??? ? 3,0 %). ??????????? ?????? ???: ?????, ??????????, ???????,
??????????, ?????????, ?????????????, ????????????????, ?????????????, ????????,
?????????, ???????, ????????. ???????? ????????? ????????????????????????? ?????
??????????? ??? ? ?????????? ?? ?????? ??????? ?????????, ??????????????, ???????????,
?????????, ??????????, ???????? ?????????. ?????? ?????????????? ???, ???????????? ???
?? (2007 ?.) ??????????: 6639 ???. ? (???. ?2), ?????????? ?????? (???. ?.): 39,8 (??????????
0,6 %), ??? ? 486 ???. ? (?????????? 7,3 %).
????????????? ?????????????? ???????? ?????? ??????????????? ??????????????
?????? ? ???????????? ???? ???????? ??????? ?????????????? ???? ????? ???
??????? ?????????? ? ????????????? ?????? ? ?????????????? ????????, ??????? ?
???????????????? ???? ?? ?????????????? ? ???????????????? ???????? ? ?????????????
(???, ???? ?? ???, ?????????????????? ????????, ?. ??????????), ????????????????
???? ?? ??????????? ?????????????????? ???????????? (?????-?????????? ????????,
?. ????????????). ??????? ???????-????????????? ??????????? ???????? ?????????????
????????????? ?????????? ??????? ????????????? ??????? ? ?????????? ?????? 10
???. ???????? ??? ??????? ??? ????????? (??????????????) ???: ??? 33 (22) ???? ???.,
????????? ????????????? 35(25) ???? ???., ????? ?????????? 91(65) ???? ???. ??????????
????????????? ??????????? ???????? ?????? ??????????????? ???????????????
?????????????? ? ?????? ??????? ????? ? ??????? ????? ?????? ???????? ??? ???????
????????????? ????????????.
*
1
Corresponding author E-mail address: sssngpe@mail.ru
© Siberian Federal University. All rights reserved
# 132 #
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?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
???????? ?????: ???????????? ?????????????, ????????, ??????-?????????????? ????,
??????, ???????, ???????-????????????? ?????????? ????????, ????????????, ???????????????
??????????????.
??????????? ????????
? ??????? ????????? ??????????? ??????, ? ?????? ? ?? ???????, ?????? ????? ???????,
???????????? ??????? ?????????????? ?? ??????? ?????????, ??????? ????????????????? ?????????, ????????? ???????? ?????????? ? ????????? ????????????? ????????????, «?????»
??????????. ?????????????? ???????? ? ?????? ?????? ???????? ???? ? ???????????? ?????????? ??? ????????????????, ?????????? ????????, ???????, ?????????????? ???????, ????????????? ??? ????????????????????? ? ????????????? ??????????????, ???????????? ?
??????????????????? ?????? ???????????, ?????????????? ???????????, ???????????.
?????? ? ????????? ???????????? ????????? ????????? ????? ????????, ?????????????? ???????? ????? ??????? ????, ????? ??????????? ? ?????????????? ? ??????? ????????????? ??????????????. ??? ????? ?????????? ? ?????????? ????? ??????, ???????, ????.
???? ??????? ??????????, ? ???? ???????, ??????????? ??????.
??????? ???????????? ?????????????? ???????? (???) ? ?????? ??? ????????? 4 ????
????., ? ????????? ????? ????????, ??? ????????, ??? ? ???????, ?? 2004-2008 ??. ?????????
????? 10 % .
???????? ???????? ? ????????? ???-?????? ?????? ?? ??? ??????????-??? ????? ? ??????? (????? 80 % ???????? ????????????).. ?????-??? ? ??? ?????? ????????????? ?? ?????????????? ??? ??????????? 100 ???. ? (????? 90 % ????? ???? ?????????????? ???????? ??
??????? ?? ??????) [1-4].
? ????????? ????? ??? ? ?????? ? ???????? ????????????? ? ????? ??????. ?????????????? ?????????? ??????? ??????????? ? ??????? ???? ???? ?????????????? ?? 20 ???????? ?
??????? ???? ?????????. 247 ? ?????? ? ???????????? ??????????? ????????? ?????????????? ???, 744 ? ??????? ??? ??????????????? ?? ??? ????????????? ? ???????? ?????????????. ?? ??????????? ????????????? ???????? 25,4 ???. ? ???????????? ???????????, ??????????? 3100 ? ?????? ?????? ? 9500 ? ??????? ???. ?????????? ??????????? ????????
????, ?????????? ?? ?????????????? ????????? ??????????????, ??? ??????????? ?? ??????
? 10, ? ?? ??? ? 5 ??? ????? ??????, ??? ?? ???????? ?????????? ????????????, ?? ?????????
????????? ???????????? ?????? ????????, ????????, ??? ? ???????? ?????? ????????? ? ???
????????????? ?????.
???????? ???????????, ???????????? ?????? ??????? ? ?????????? ?? ??????? ??????????, ? ????????? ?? ???, ????? ???????? ???????????????????? ???????? ?????? ????????.
? ????????? ????? ????? ?????? ???????? ?????? ??????? ? ?????? ?? ?????????. ???????
??????????? ????????????, ? ?????? ???????????? ????????????? ???? ??????????? ?? ????
???????. ? 1991 ?. ? ???????????? ??????????? ? ?????? ????????? ?? ??????????? ????????????? ????? ??????????? ????????????, ? ?????????????? ????????????? ????????? ???????? ? ??????????. ??????? ????????????? ? ?????????? ??????????. ????? ???????, ???????????? ??????? ??? ? ?????? ? ???????????? ? ?????? ?????????? ????? 3 ???. ? ??? ???????
??????, ??????????????, 124 ? 90 ???. ? (Mineral Commodity Summaries, 2010).
# 133 #
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?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? ???????? ??? ??????????? ????????? ?????????????? ??????, ? ?????????,
??????????? ? ????????? ????? ?????, ?? ???????? ?????? ???????, ??? ?????????? ????
???? ??????????????????? ? ?????????? ????????????. ?????????????, ????? ?? ????????
????? ?????????????? ? ????????? ?????????? ????????. ??? ?????? ?????? ???? ?????? ??
?????? ???????????? ?????????? ?????? ?????? ??????????? ??? (????? 50 ???. ? ???????? ?????? 6,7 ???. ? ? 1990 ?.). ????????? ??????? ??? ????????? 3 ???? ???????????,
?????????? ????? ??????? ?? 34 % ? ?????? ????????? 2009 ?., ? 2010 ?. ?????????? ?? ??
?????????? ??? ?? 30 % .
?????? ??????????, ????????????? ???????? ??????? ????????, ?????????????? ????
????????? ????????? ?? ????????? ???.
? ??????? ????????? 20 ??? ??????????? ???? ?????????? ?????????????? ? ????????????
??? (??????, ???, ?????? ???) ? ?????? (???, ??????, ????????, ???). ????? ????????
??????????? ? ??????? ???????????? ???? ???????? ?????? ???. ??? ??? ??????? ????? ?????? ? ??? ??? ????? ??????????? ???????? ???????????? ??????????, ????? ????????????? ?
??????????? ???????? ?????????????? ?????. ????????????? ?? ???? ????? ?????? ?????????? ? ????? ?????????? ?????? ??? ??????? ???????? ????????????? ? ??????????????????
???????????? ??????.
???? ????? ?????????????, ??????????? ??????? ??? ??????????, ???????? ? ?????
???? ?????????? ?? ???? ??????????: ?? ?????? ? ????? ? ????????, ?? ??????????????
???????? ? ?????-??? ? ?????. ????????? ???????????? ?????? ?? 1 ? ???? ?????????????
????? ??????????? ? 17 ???. ???., ????????? 1 ? ???? ????????????? ?????-??? ?? ??????????? ???????? (???, ??????, ??????) ? ? 22 ???. ???.
???? ???????? ? ??????????? ??????????? ?????? ? ?????????????? ???????? ? ????????????? ??????????? ??????? ?? ?????? ?? ??????????????? ???????? ?????? ??????????????????? ???????? ? ?????? ????? ????????????????? ??????? ?? ?? ?????? ? ???????????.
?? ???????? ????????????? ????????????? ? ?????? ????? ??? ????????????? ??????
???????? ????? ????????? ??????????? ??????? ???????????? ? ?????????? ? ????????????. ????????? ??????????? ???????? ?? 1 ? ???? ???? ????????????? ?????????? 60 ? 20-25
???. ???. ??????????????. ???????? ??????????? ?????????????, ?????????????? ?? ???????? ?????? ?? ??????-?????? ?????? ? 400 ?? ?? ?????? ?????????? ? ? 1500 ?? ?? ????????
??????, ? ????????? ????? ?????????????. ??????? ???????????? ?????????????? ???????
??????????? ???????? ????????????. ? ????????? ????????? ? ???????????????? ?????????????? ????????? ??????????? ???????? ?? 1 ? ???? ??????????? ? 5 ? 8 ???. ???. ??? ????????? ?????? ???? ?????????? ??? ?????????? ????????????? ? ???????????? ????, ????????????? ????????? ????????????? ? ????????? ???????, ??????????? ????????????? ???
? ??????? ? ???????? ? ????????????? ???? ? ??????????????? ??????????? ?????????????
? ?????????? ???????. ??? ??????????? ????????????? ??????????? 1 ? ???? ?? ?????????
???????? ?? 6 ?? 10 ???. ???. ??? ????????????? ?? ????????? ???? ??????????? ???????, ?
?????????? ????? ? ?? ?????????.
????? ????????????? ??????-??????????????? ????????????? (???????????? ????, ??????????? ?????; ?????????? ?????? 59°27? ?.?., 99°54? ?.?.) ?????????? ? 100 ?? ? ?????? ??
??????????? ???. ?? ????? ? ?????? ???????? ?? ??????????? ??????? ????????? ????????
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?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
???. 1. ???????? ????? ?????? ????????????? ?????????????
??????? ?????????? (????????????? ????????????? ?? ? 203 ?? 22.02.1997 ?). ? ???? ??????? ??????????? ????????? ???? ????? ? ?????????? ? 570 ??? ?, ???? ? 1,1 ???? ?3. ? 14 ?? ?
?????? ?? ????????????? ??????? ????????? ????????????? ???????? «???????????» (?????????? ??????) ? ????????????? ???????? 41,2 ??? ? ? ??? ????????????? ??????? ???????? («?????????» ? «????»). ?? ???????????? ?. ?????? ? 100-150 ?? ???????? ????????????
?????? ?????????? ?????????????, ? 200 ?? ? ?????? ?? ??? ? ????????? ?????? ??????????
?????????????. ????????????? ????????? ???? ???????? ????? ????????? 300 ??? ?. (???. 1).
??????????? ??????????? ???????? ??????? ?????????? ???????, ?????? ?????, ? ?????????
????????-?????????? ?????????? ??????? ??? ?????????? ???? ???????? ??????? ???? ? ???????? ?????????????? ? ???????? ?????????????? ? ???????? ?????.
????????????? ?????????????? ???????? ?????? ??????????????? ??????????????
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?? ?????????????? ? ???????????????? ???????? ? ????????????? (???, ???? ?? ???,
?????????????????? ????????, ?. ??????????), ???????????????? ???? ?? ??????????? ?????????????????? ???????????? (?????-?????????? ????????, ?. ????????????). ???????? ??????
?????? ???????? ??????? ? ??????????? ?? ?????? ??????? ?????? ? ?????? ?????? ??????????,
?? ? ??????????? ??????????? ????????????? ? ???????????? ????????????? ? ??????????
???? ? ???? ?? ??????? ?????????????? ????????? [5-6].
????????????? ???????? ??????????? ??????? ??????
?????????? ?????? ????? (60?40 ??), ?????????? ???????????? ?????????????, ????????? ?? ????? ??????????? ????????? ????????? (???. 2). ? ????????????? ????????? ??
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????????, ???? ???????? ??????? ????????????? ?????????? ???????????? ?????. ? ????????
????? ???? ????????? ????????? ??????? ?????? ? ?????? ??????? ??????????? ? ??????????? ?????? ????? (???????????, ?????????????, ????????????, ???????????, ????????, ?????????????, ?????????? ? ?????????? ?????), ? ???????????? ??????? ?????? ??????? ????????????????? ???????????? ? ?????????????????? ???????????? ????????????? ? ????????
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???????? ? ?????? ??????? ????? 10-15°.
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???????? ??????????? ??????????? ( ????????-??????, ???????).
??????????? ??????????? ?????? ???????????? ??????? ? ??????? ????????? ? ??????????????? ?????????? (?????-?????), ????????????? ? ??????????????? ????????? ???????? ??????????? (?????? ?????) ??????????. ???????? ?????????????? ?????? ???????? ?
????? ?????????????, ?????- ? ????????????? ???.
?????????? ???????? ????????? ????? ?????????? ????????: ???????????? (?????)
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???????????? ????? ????????????? ????????, ?????????????? ??????? ???????? ?????????????????????? ?????????????? ???????, ????????????? ?? ?????? ???????????? ?????????? ??????- ? ?????????????????? ?????, ?? ??????? 3-4 ??. ??????????????, ??? ??????????????? ????, ??????????????? ???????????? ????????????? ????????? ???????? ???
?????????? ?????????, ???????? ?? ??????? 3,5 ??, ????? ????? ?????? ???????? 35-40 ??.
? ?????? ???? ????????????? ????????????? ???????? ????????? ????????????? ????????, ????? ???????????????? ? ?????????????? ? ????????? ?????. ? ????? ??? ?????
?????, ??????? ? ????????????. ??????? ??? ?????? ???????????? ? ???????? ????????,
??????????????? ??? ?????????????? ??????? ?????????? ????????? ??????????????? ?????????. ?? ?????????????? ? ????????????????? ?????? ???????? ??? ?????????? ?? ?????? ????? ?? 500 ? ? ?????.
? ???????? ?????????? ????????????? ???????? ?????????????? ??????????? ????????????? ????????, ??????????? ?????? ???? ????????? ? ?????????????? ?????????????.
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(??. ???. 2). ????????????? ??????????? ? ?????????????????? ???? ??????????????? ???
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????????.
????? ??????? ?? ???????? ????????????? ????????? 140 ??? ???., ? ??? ????? ??????
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? ???????? ????????????? ?????? ?.?. ??????, ?.?. ???????, ?.?. ? ?.?. ??????, ?.?. ?????????? (????????? ???), ?.?. ?????????, ?.?. ?????? (????????), ?.?. ????? (?????). ? 19992006 ??. ????????????? ????????????? ?????????? ?.?. ? ?.?. ???????, ?.?. ??????, ?.?. ??????, ?.?. ?????????? (????????), ?.?. ? ?.?. ??????? (??? «?????????? ????????», ???
«???????»), ?.?. ?????? (?? ?3), ?.?. ???????, ?.?. ???????? ? ?.?. ?????? (???? ?? ???),
?.?. ?????????, ?.?. ??????? (?????-?????????? ????????).
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??? ????????? ????? ????????, ??? ?? ?????????????????? ?????? ??????????? ????????????? ????????? ????? 1,5 ???? ???.
? 1993-1994 ??. ?? ????? ???? ???-93, ?????????? ?????????? ????? ? ?????????? ?????????? (???? ?? ???, ?. ??????????), ???? ????????? ????? ??????????? ?????????? ???
??? ?? ???????? ? ?????? ?????????? ????????? ?? ?????????????????????? ????????. ?????????? ?????? ? ?????????????? ???????? ??????????? ???? ??????????? ?????????????
????????? ?????????. ??????????? ????????????? ??????, ??????????? ?? ????????,
???????? ?????????????? ? ????? ? ????????????? ???????-????????????? ?????? ????????????? ?????????????.
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???-????????-??????????? ? ????????????? ????????.
????????????. ? ???????? ????????????? ?????????? ??????????? ??????? ???????
????????? ????????????, ???????????, ????????, ????????????? ???? ?????. ?????????? ??????? ?????, ???????????? ?? ?????????? ?????-????????? ???????, ?????????? 1290 ? 1250
??? ???.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (R 2 ??) ??????? ???????? ????? ???????????????? (??????? ???. ????????). ??? ???????????? ?????????? ? ????????????? ???????????? ? ?????????????? ????????? ? ??????? ?????????, ????????-????????? ? ??????????
???????. ???????? ????? ?????????, ???? ?????????????, ?????????????? ????????, ?????- ? ?????????????? ?????????, ?????-?????, ??????????-????? ???????. ???????? ?????
450-500 ?.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ( R 3 t r ) ???????????? ??????????, ???? ????????-??????????
???????? ???????????? ???????? ????????-???????? ????? ? ????????? ????? ? ????????????
???????????. ?????? ????? ? ???? ?????? (400-700 ?) ????????? ? ???????? ???????? ?? ?????????? ???????????? ?????. ???????? ????? 180-200 ?.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ( R 3 b r ) ???????? ?????? ??????? 800-900 ?, ??????????? ???? ??????????????? ??????????? ?????, ???????????? ????? ????? ???????????????? ????????-????????? ? ????????? ????????? ???????, ???????????, ?????????? ? ??????
??????????? ??? ????????? ? ?????????. ???????? ????? 100-300 ?.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ( R 3 m d ) ????????? ????????? ???????? ?????
? ??????? ?? ??????????? ? ??????-????????? ? ???-???????? ?????? ???????. ? ??????? ?????
????? ??????????? ?????????, ?????????????? ????????? ??????-??????, ?????? ?????. ???????? ????? 100-150 ?.
????? ???????? ?????????????????? ????????? ????????? 830 ? 1150 ?.
??????????? ??????. ??????? ???? ? ????????? ????????????? ????????????? ?????? ?????????????? ???????? ??????, ?????????????? ????????? ????????? ? ????????? ???????? ???????? (?? ?1), ? ??????????? (? ?1) ??????????? ?????????, ???? ???????
??????????????? ? ???????? ????? ???????????? ????????????????. ??????? ????? ????????? ????????? ?? ????????? ?????-????????? ??????? ??? ???????????????, ???????
???????? ???????? ?????????? ? ???????? 299,0±9,0?255,1±7,7 ??? ???, ??? ????????????
# 138 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? ?? ?????????? 219,7±6,6, ???????????? ? 260,1±7,8?183,3±5,3 ??? ???. ??? ???????, ??? ????????? ?? ???????????, ??? ? ?????????? ????????? ??????, ????????????
?????????? ???????????, ??? ??????????? ?????????? ??????????? ?????????? ? ????????
???, ? ????? ???????? ???????????????? ? ??????????????? ????????????? ????????? ?????.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ????????????? ??????????????? ???????????????? ??????????, ??????? ??????????? ???????? ?? ?? ???????? ?????????????? ?????. ??? ??? ?????????? ??????????? ?????????, ????????, ????????, ?????????, ?????? ?????????? ??????????
??????????, ?????????? ??????????????? ? ????????????, ????? ?????????? ?????????? ????????????, ? ????? ??????? ?????????? ??????? (0,77-2,63 %). ?????????? ????? ??????? (?? 1,3 ?? 5 ? 6 %) ????????? ??????? ?????? ? ???????? ??????????????. ?? ?????????
????????? ??????????????? ????????????? (Na2O+K 2O;Na2O/K 2O;al) ? ???????????? ? ??????????? ???????? ?????? ????????? ? ????????? ???????? ???????? ????????. ???????????
??????????? ???????? (????? ???? ????????) ???????? ???? ?? ?????? ????????????? ????????????. ???????? ??????? ???????????? ??? «???????» ??????, ??? ? ?????????? ?? ???????????. ??? ?????? ????????????? ????, ???? ????, ? ?????????????? ??????? ????????,
?????????????, ???????????? ????? ????????? ?? ?????? ?? ?????????? ????? ??????. ???????? ???, ??? ???????, ?? ????????? ?????????????? ????????, ???? ????????? ???? ?????????
?????? ??????? ????????????.
? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ??????? ????????????? ???? ?????????? ???????
(??????), ??????? ?????????? ? ?????????????? ????? ??????, ??? ??????????????? ?????????? ????????????, ???????? ????? ?????????????? ?? ?????????? ????? ???. ? ?????????? ??????? ?? ???????????? ?????? ???????? ? ?????????? ?????? ??????? ?????? ?????? ? ??????-????????????, ????-????????????, ??????? ? ?????. ?????????????? ?? ????
?????????? ?? ???????????.
? ? ? ? ? ? ? ? ? ? ? . ? ?????????? ????? ????????????? ?????? ???????????? ??? ???????
????????????? ???? ???????????? ? ????? ? ???????????. ???????????, ? ??????? ?? ???????? ????????, ??????????? ?? ????????, ?? ??? ????? ???????? ????????????? ????????? ???????? ?? ????????????, ????????????? ?????, ?????? ???????, ?????? ? ??????
????????, ?????????? ????? ??????????? ????????????, ?? ?????????? ?????-???? ?????
8-10 ???/?, ? ???????????? ???????????? ?????????????????? ??????????.
??????????? ???? ???????????? ??????????? ? ??????? ???. ????????, ????? ???????????? ????????????? ????? ? ??????????? ?????????, ?????? ???????? ? ??????????????
???????????, ???????? 2,5 ? 1,8 ??.
????? ???? ???????????? (1,9 ? 0,9 ??) ????????????? ?? ?????? ?????? ?????? ???. ????????, ????? ????? ??? ??????? ?????????, ????? ???????????? ????????????? ?????,
???????? ? ???????? ???????????, ??????? ??? ??????????.
?? ???????????? ???????, ?????????-??????????? ????????????, ? ????? ?? ????????? ?????? ?????????? ???????? ?? ????????????? ???????? ??? ?????????????????????????? ???? ????????????: ??????-?????????????? ? ??????????? ???????????,
?????????? ?????????????? ? ??????????? ??????????? ? ???? ????????????? ??????????????-???????????.
# 139 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
???????? ??????? ???? ???????????? ??????????????? ????????????
???????????? ????????????? ???????????? ?????? ????? ????????????. ? ??????????????? ????????? ??? ???????? ????????? ? ?????????? ????????, ??????? ?? ? ???????
??? ? ????????. ???? ???????????? ??????? ?? ???? ???????????? ? ?????????, ????????
?????????????? ???????, ??????????????? ????????????.
??????????????? ????? ???????????? ??????????? ????????? ??????????? ????????
????????? ??????????? ???????????? ????????????: ??????? ???????? (150-300 ?); ??????????? ????????????? ??????????? ?????????, ?????????? ???? ????????????? ????? ??????? ???????????? ???????????? ?????????? ????????? ????????? (????????? ????), ? ???????
?????????? ?????? ? ??????????? ?????? ? ????????; ??????????? ?????? ?????????? ?????????? ????????? ???????? ?????; ??????????????? ???????? ????????? ??????????? ???????????? ???????????? ?????????? ???????????? ?????? ?????? ??????? ? ???????????? Fe
? Mn.
??????? ???????????? ???????????? ??????????. ? ??? ???????? (????? ?????) ????????
??? ????: ?) ???? ?????????????, ?) ???? ????????????? ? ??????????? ??????????, ?) ????
????? ?????????? ? ??? (???????? ?????????).
??????? ???? ???????????? ?? ???????????? ???????????? ????????? ? ????? 16 ??2,
???????? ?? ????????? 300 ?, ??????????? ???????????? ? ???????? ????? ????????? ?????????. ?????? ? ??????? ??????? ???? ???????????? ?????? ????????.
???????? ???????????? ???????????? ????????? ?????????? ????????????? ? ??????????? ?????????? ?????? ? ????????, ?????????? ?? ???????? ???, ????? ????????????? ????? ?????????? ?????????-???????????? (?????? ? ???) ? ????????????? ???????????? 4-6.
???? ??? ? ???????? ?????? ???? ?????????????
??????????????? ???? ???? ???????????? ???????????? ?? ??????? ? ????????? ???????????? ?????????? ????? ???????? ???????????????:
????? ????????? ?? ??????????-????? ???????? ?? ?????-????? ? ??????, ???????
?????????-?????????? ???????? ???????? ?? ?????????? ?? ?? 10-15 ??. ?????? ????? ??????????????? ???????? ?????????, ??????????????, ??????? ???????? ???????? ?????????????,
???????? ????????????? ?????????? ?????????. ?????? ????? ?????????? ?????????? ?????
14 % ?????? ??????????????? ??? ????????????;
???? (?????????, ??????, ??????? ?????-?????? ?????, ?????? ??????????????? ??????),
??????? ?????????? ??????? ????? ?????????? ? ??????????? ?????, ????? ?????????????
??? ?????? ???????????? ???????????. ???????????? ????????? ???????? ? ???? ????????????? ?????? ?????????? ?????? ?????. ???? ?????????? ????? 42 % ?????? ???????????????
??? ????????????;
????? ????????, ?????? ??? ??????????, ?????? ??? ?????-?????, ???????????? ?? ???
????? ??????? ???????? ? ????? ?????? ??????????? ??????? ? ???????????? Fe ? Mn ???
????????? ?????????? ?????????? ????????? ? ??????????. ???????????? ????????? ????????. ?????? ?????????? ????? 44 % ?????? ??????????????? ??? ????????????.
?????????? ???? ???????????? ????????? ???????????, ??????????? ??? ? ?????? ????????? ?? ???? ????? ????????????.
# 140 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 3. ????? ?????????? ??????? ? ???????? ???????????? ?????????????. ??????? 1:10000.
1 ? ?????????????? ????, ????????? ?2; 2 ? ?????????????? ????, ????????? ?1; 3 ? ????????? ????,
????????? ?1; 4 ? ????????? ?????? ???????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
???. 4. ??????? ?? ?????? 3,5 ? 4,0. ??????????? ?????????????. ??????? 1:10000. 1-2 ? ??????? ???-
?????? ??? ?? ????????? ?????????? Nb2O5: 1 ? 0,4 %; 2 ? 0,8 %; 3-4 ? ??????? ?????????????? ??? ?????????: 3 ? ?2; 4 ? P1
?????? ???? ????????????? ????????????? ?????????????? ??? ?????? ??????? ????????????? ???? (???. 3, 4). ???????????? ?? ????????? ?????????? ??? ? 3,0 % ? ?????????????? ????? ? ?????????? ?????? ?????? 0,8 % ? ????????? ????? ?????? ???? ???????? ?????????????? ? ??????????? ?????-?? ????? 3,5 ??, ???????????? ?????? ?? 1600 ?. ?????? ????
????? ???????????? ?????????? ? ?????????? ?????? ????????? ? ????? ?????????? ???.
?????????????? ? ????????? ???? ?? ????? ????? ???????????? ?????????????? ?????? ? ?????????? ?? ?????? ???????????. ??????? ???????????? ????? ??????????????
???, ?????????????? ????? ??????? 3.5 ? 4.0, 400?600 ? ? ????? ? 200 ? ?? ???????. ?????
???? ????? ?????????? ??????? 7.0 ? 8.0 ????? ??????? ? ?????? ?? ?? ?????????????? 300
?, ? ?????? ?? ?????? 800 ? ? ?? ??????? ????????? ??? 100-200 ? ?? ?????? ??????????? ??
??????.
????????? ???? (?? ????????? ?????????? Nb2O5 ? 0,8 %) ? ????? ???????????? ?????????????? ????. ?? ????? ????? ??? ?? ???????????. ????? ???? ????????? ?????? ????????
???????-??????????? ???????????? ?? ?????? ??????????? ????????? ?????????????, ? ?????? ????????? ?????? ?????????????? ????. ???????????? ?????????? ??? ???????????????, ??? ? ?????????? ?????????? ?????????? ? ?????? ????? ???????????? (??) ???????????
???? ? ??????????? ??????????? ? ?????? ????????????? ?? ????????.
??????????? ?????? ??????????????? ??? ????????????
???????? ??????????? ???????????? ???????????? ?????? ?????????? ?? ????????????
???????. ?????????????? ???????????? ???????????? ??? ???????? ?????, ??????????, ???????, ??????????, ?????????. ?????????? ???????????? ????? ??????????????? ?????????:
?????????????, ????????????????, ?????????????, ?? ????????? ???????? ??????????? ???# 142 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??, ? ??? ??? ???? ??????? ??????????, ????????? ???????? ???????? ???????, ???????????
??? ???????????? ????????????. ???????? ?????? ?????? ???????????? ????????? ???????????, ?????????, ??????????.
??????????? ??????? ???????????? ?????? ? ?????? ?????? ? ?? ?????????? ?? ????
?????? ???????, ????????, ?????????? ? ???????? ???????? ??? ????????????? ???????????? ??????? ?????? ? ????????. ?? ???????? ????????????? ?????? ?????????? ??????????? ???? ?????????? ? ?????????, ?????????? ??????????????? ?????? ? ?????????????? ????????. ?????????????? ???????? ????????? ???? ??????????? ?????????????
?????????? ???????? ??????????? ??? ? ???????????, ?????????? ? ????????. ????? ????
?????????? ? ?????????????? ???????????? ???????? ? ??????????? ???????????? ???????????? ?????? ??????.
????? ?????? ? ??? ??? ????????????? ????????????? ???????????? ??????? ???????????? ????? ???????????? ??????????????????, ??????? ?????????? ? ??????????? ????????? ?? ? ??????????????? ??????? ????????, ??????, ???????, ??????, ???????, ????????,
????, ????????, ?????, ????.
??????????????? ?????????????? ???
? ????????? ????? ??????????????? ????????????? ???????? ??? ?????? ? ?????? ??????, ????? ??? ?? ??????? ??????????? ?????????? ???? ???????? ???????? ?? ??? ????????????.
???? ??????????????? ???????????? ??? ????????????? ????????????? ?????? ???????
? ????. 1.
??????? ??????? ? ????????
??????? ??????? ? ???????? ?????????????? ? ????????? ??? ????????????? ????????????? ???????? ?? ????????? ?????????, ????????????? ??????? ?? ???????? ??????? ? ??????????? ????? ??? «??????????????????», ?? ????????? ?? 01.01.2006 ?.
?? ???????????? ??????????? ???????????? ??? ????????? ??????????? ???????? ???
?????????????? ??? ????????????? ????????? ???????? ???????? ??????????:
? ???????? ?????????? ?? ????? ??????? ?????????????? ???????? 3 % ,
? ??????????? ???????? ??????? ????????? ? 4 ?, ??? ??????? ???????? ????????????
????????? ?????????????, ?????? 12;
? ???????????? ???????? ?????????????? ??? ? ?????? ???????? 5 ?;
? ??????? ???????? ??????? ????????? ?2 ??? ?????????????? ??? 100 ?.
?????? ???? ? ???????? ????? ????????????????? ?????????. ? ?????? ????? ??????? ??????? ???????? ??????? ???????????? ???????????? ??????? (????????????? ????????) ? ?????? ?????? ?? ??? ??????? (???. 3, 4).
?? ???????????? ????????????? ??? ????? ??????? ? ???????? ???????? ??? ?????????
???? ???: ????????? ? ??????????????. ?? ??????? 2,5 ? 1,5 ?? ????????????? ?????? ????????? ???, ??????????????? ? ?????????????? ???????????. ? ??????????? ?? ????? ??????????? ???? ?????????????? ???, ?????? ????????? ? ???????? ??????????? ? ??????? ???????
600 ? 400 ?.
# 143 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????? 1. ??????????????? ???????????? ??? ????????????? ?????????????
??
????, ???
?????
??????,
??? ?????
???-1
1987
???. 1, 2,
4, 8
??-3
1989
???. 16,
33-210 ?,
300 ??
??-4
1990
???. 3,
41-74 ?,
???. 19
69-111 ?,
???. 58
105-131 ?
??-5
1991
???. 59
53-70 ?
???. 62
12-28 ?
???????????,
??????????????
?????, ??????????
???????????
?????????????? ?????????
???????????
??????????????
???????????
??????????? ??????????? ???? ? ?????????? ????
?????????: ?????????? ??????????? ? ???????????
????????.
2,5 % Nb2O5, ??????????? ????? ??? ? ???????????
98
%
?
?????????????????
????????.
???
(??????) ??????????????????????????? ???????? ?????????? ??????
?????????
? ?????????? ?????? ? ??????? ??? 42:72 ????? ?????
????????
?????????? ??? ???????? ????????????????? ??????
????????????
? ??????????? 0,1-0,5 % ?????? ? 1,5-1,7 % ????????.
????????????
???????? ????, ?????????? 12,6 % ??? ? 7,3 % ???,
????? ??????? ?????? ??? ???????? ???????????
????????????? ? ??? ? ??????
???? (???????
??? ???????? ? ??? ??????????????? ????????? ???????
? ??.). ???????????????? ?????????? ? ?2?5 34,1 % ??? ??????????
56 %, ???????? ????????? ??????? ? 2,4 % Nb2O5 ?
?????????
??????????? 61,9 % ; ?????????????? ??????? ? 4,68 %
????????
????????????
??? ? ??????????? 80,9 %. ??????? ??????????? ???
????????????. Fe ? ?????????????????? ????????? ???????? ??????????
25,5 %, P2O5?12,4 %, ?????? ???????? ? ??????? -0,5 ?? ? 1,2 ???? ??? ???????
Nb2O5?0,88 %, ??? ? ??????? (??????? ???????) ?? 20 %
?1,89 %
1. ??????-?????? ????????????? ???????????? ???? ?
?????????? ????? ???, ???????????????? ???????????
????-???, ?????? ? Fe2?3 ? 55 %, P2O5?0,04 %, Nb2O5?0,85 % ; ?????????
????????? ? P2O5 20 %. ?????????? ???? ??????????? ?
(??????? ? ??.).
???? ???????????? ???????? ???????????? ?? ?????? 98 %.
2. ??????? ? ??????? ????????? ???????????? ????
????????????,
?
??????????
??????-?????????????-??????????
???????? ?
??????????? (Fe2?3 ? 61,5 %, ???? 7 %, Nb2O5?0,73 %,
?????????
????????.
P2O5?0,04 % ? ?????????? ????????? ? P2O5 30 %).
P2O5?6,56 %,
?????????? ???? ??????????? ? ???????? 98 %.
Nb2O5?0.72 %,
???????????? ?????????? ??????????? ???????????
? ??????????? ???????????? ????? ???????????
????6,72 %,
???; ??? ??????????????? ??? ????????? ????????
?????????? ??????? ???????????? ??????????? ??????
????????
?????????????
??????
?????
????
???????????????
??????????,
??????????
??????????????? ?????????? ???? ???????? ??????????
??????, ????????
(?????????????,
???????????,
???????????????,
(????????? ? ??.).
????????? ?????????). ??????????? ?????? ?
???? ????????????
??????????? ??????? ?????????????????, ? ???????????
????????????,
????????? ? ????????????????????? ????????. ???
???????? ?
???????????????? ?? ?????????-????????????? ???????
?????????
?????????? ????????? ???????????? ????????:
????????
? ????????? ??????? ??? ??????????? ? Nb2O5= 25 %,
?2?5 ? 5,6,
MnO=12,4 %, F2O3=59,4 %, ?2?5=0,1 % ;
Nb2O ? 1,20,
? ??????????, ?????????? 98 % ????? ???;
??? ? 4,70,
? ??????????? ?????????? ? ??????????? MnO=91,4 %
Y2O3 ? 0,19
?? ????????? ??????? ????? ???? ??????? Nb-Mn
?????????? ????? ? N2O5?2,31 %, Mn?50,5 %, ?2?5 ?
0,1 %, V2O5? 0,36 %
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????????? ????. 1
?? ?????? ????? ?????????? ????????????? ??????
???????? ?????????? ? ???? ?????? ??? ??????????
??????????
???????? ???????????, ?????????? ? ?????????
???? ?????
???????? ???? ? ????????? ??????? ? ????????.
????????? (???????)
???????? ??????? ???????? ? ???????????????
???-93
?????
???? ????????????
?????????? ????????, ? ??? ??????????? ???????????
1993
??????? 46, ????????????
????????? ? ????????? ?????? ? ????????? ??????????.
4, ??? 20 ??. F?2O3 ? 50 %,
????? ????????? ????????? ?????????? ????????
1998
P2O5 ?6 %,
??????????? (Nb+???) ????????????? ? 2,5 ????.
Nb2O5 ? 1,00 %
??????-??????????????? ???????????? ?????????? ?
??? ? 6 %
?????????? ???????? ?????????????? ? ?????????? ???
??????????????? ????????
1 ????????????????? ?????, ???????? ?????????
??? ?????????? ????????, ????????? ?????????,
??????????, ???? ?????????????:
?? ??? (???????). ? ??????-?????? ????????????? ???????????? ??????
?????? ? ??????????? 82-85 % ????? ? 87-88 % ?????????
???. 44, 47, Nb2O5?0,8 %,
??-6
??? ????? ?????????? ? ?????????? ??????????????
51, 54, 62, ????6,8 %,
1999
Fe ? 36 %,
???;
71, 74
Mn?7 %,
? ????????? ????????????? ??????????? ??????? ??????
P2O5?4,3 %.
??????????????? ?????????. ? ??????????? ???????? ?
5 % Nb2O5 ????? ????????? ??????? ??????????? Nb2O5
?????????? ?? 20 %.
?????? ???? ?????????????? ??? ??????????? ? ????? ????? ?????????????, ???????
???????? ????? ? ???????? ??????????? ? ????? ??????? 1000 ? 600 ?. ??????? ????? ??????????? ?????? ??? ??????? ? ?????? ???????. ???? ?? ????????? ??? ????????? ??? ???
???????? ????????? ?????????? ?????? ??????, ????????????? 0,8 % . ??? ?????????????
?????????????? ??? ????????? ???????? ????????? ?????????? 3 % ??????? ???. ??????????? ???????? ???????????, ???????????? ???????? ??? ??? ? ??????, ? ????????? ?????
?????????? 2,5 ? 3, ? ?????????????? ? 15 ? 20.
?????????? ??? ??? ?? ?1356 ?? 16.03.2007 ?. ?????????? ?????? ?????????? ?????????????? ??? ?? ???. ?2 ? ?????????? 6,6 ??? ?, ??? ??????? ?????????? Nb2O5 ? 0,60 % , ??? ?
7,32 % , Mn?2 ? 15,5 % , Fe???. ? 34,3 % .
????????? ?????????? ??????? ????????? ? ?????????????? ??? ?????????? ?? ??????????? ??????? ????? ? ?? ???????????? ??????????????? ?????????? ???????, ????????????
??? (????. 2).
????? ????, ? ?????????????? ????? ?? ????????? ?????? ??????????: ?????? (28,6 %),
???????? (6,9 %), ? ????????? ? ?????? (31,0 %), ???????? (4,6 %), ?????????? ????????? ??????? ?? ???????? ??????????? ? ????????? ? ??????? ?????? ?????????? ? ??????? 0,28 % .
?? ????????? ????? ??????? ? ?????????? ???????? ???????? ???????????? ????? ???, ?????????? ??????? ? ????????????. ? ????????? ????? ??? ??????????????? ????????? ????????? ?????????? ?????? ?????? 0,4 % , ? ?????????????? ????? ???????? ????????? ??????????
??????? ??? ?????????? 1 % , ????????? ???? ????? ??? ????? 220 ??? ?.
? ????????????? ?????????? ???????? ??? ??? ???????? ????????????? ??????????
??????? ????? ?? ???????????????? ???????????????? ????? ?? ????????? ??????????
# 145 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? 2. ?????? ? ??????? ????????? ? ?????????????? ???
??????????????
?2
??????
(???????),
???. ?
66,39
??????????????
?1
61629
0,34
6,18
209951
3809735
?????????
?1
101092
1,18
2,96
1197150
2997142
????
?????????
??????????, %
Nb2O5
???
?????? (???????), ?
Nb2O5
???
0,60
7,32
39834
485975
??? ? ??????? ?????????? ???????-??????????????? ???????. ?????????? ?????????? ???????????????? ?????????? ???????? ???????? ??????????? ? ????????, ??????, ???????, ??????? ? ? ????? ??????????? ?????????? ?????????????? ???? ??????????? ???.
? ?????????? ??????? ????????????? ??????????????? ?????????????????????????
?????, ????????????????? ????????????????? ?????? ? ????????? ???????? ? ????? ? ????.
? ????? ?????? ? ??????? ??????????? ???????? (82 %), ?????? (65 %), ?????? (88 %) ? ???????.
? ?????? ?????????? ??? ?????????? ?? ????? ??? ? 4 ???? ? ????????? 15-20 % . ??????????
??????????? ??????????????? ??????? ???? ???????? ?? ?????? ? ???? ????? ?????????????
????????? ? ?????????? ?????????, ??????????, ??????????? ? ????????? ?????????. ?????????????? ????? ???????????????? ?? ????????????????????? ????? ????? ??????? ????????????? ??????? ????????.
??????????? ???????????? ???????????????? ????????????
???????????? ????????????? ????????????? ? ?????????? ???????? ????????????
??? ??????????? ? ????? ??????, ??? ???????, ???????????? ? ????????????????????.
??????? ??? ???????? ?????????? ????????? ? ???????? ?????????????????, ??? ???????????? ??????? ?????????????????? ?? ????, ????????? ???????????? ? ??????? ??????????.
? ????? ????????????? ????????????? ? ????????????? ??????????? ?????????? ????????? ???? ????????, ?????????? ???????????? ????????????. ??? ?????? ? ???????? (?????? ???????), ??????, ?????????????? ??????? ? ??????? (?????? ??? ????? ????????????
??????? ???????). ????????????? ????? ?????? ???????? ???????????? ??????? ?????????? ??
?? ???? ?? ?????? 80 % ? ??????????? ???????? ????????????? ????????????? ??????????
?????????????.
?? ???????? ??????????? ??????????? ?????????????? ??????? ????????? ?? ??? ?????? ? ???????? ? ?????????. ? ?????? ???????? ?????? ?????? ???????? ??? ?????? ?????????? ? ?? ??????? ?? ???????. ? ?????? ????????? ?????? ? ??????? ?????????? ?? ??????? ??
???????, ??????? ?????????? ? ?? ????? ?? ???????, ? ????? ??????. ?????? ??????????????
??? ???? ????????????? ???????? ? ????. 3
???????? ?????????????? ??? ??????????? ?? ??????????? ? ?? ??????? ?????????????? ????????, ????? ???????????, ?? ???????? ???????? ??????????????, ? 100-200 ??? ??
???? ????, ??? ????? ????????????????. ?????? ???? ? ????????? ????????? 1 ?? ??? ????????????? ????????????? ? ??????? ????????? ? ?????????????? ??? (????. 4).
# 146 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? 3. ?????? ?????????????? ??? ????????????? ????
?????????????
?????-???, ?????
???????????,
??????????
???????
????????????
???
?????????????
???????????
???????????
??????????
??????-???????????????????? ?
???????????????
???????????,
????????????? ???? ?????????
???????
????????????
(?????????)
?????????
??????????, ????- ????????-?????????????
??????????????
????????????,
??????????????
????????-???????????
??????????????
????????-???????????????????,
??????????????
????????? ????
?????? ??? , % (???.)
???????
??????????
???????????
???, %
????????????
La-Nd
??????????????
Sm-Ho
????????????
Er-Lu
??????
3,5
97,5
1,90
0,1
0,5
0,58
97,85
2,12
0,02
0,01
0,21
21,7
22,4
10,70
45,2
0,23
64,9
11,0
2,6
21,5
5,9
90,03
5,03
0,73
4,21
3,71
94,16
3,48
0,36
2,0
1,75
91,84
4,74
0,48
2,94
Y
??????????. ? ????. 3-10 ??????? ????????? ?? ???????? (??????, ???, ???????) ? ???????????
?????????????? ???????? ??????? ? ??????? ?????????????? 0,7, 0,83, 0,56. ???? ???????? ????????? ?
??????????? ?????????????? ??? ?????? ?????? ? 1,43, ??? ? 1,2, ?????? ??????? ? 1,78.
? ?????? ?????? ???????? ?????????? ????? ?????????????? ???, ? ???????? ???????
???? 1 ?? ???, ?????? 0,8 ?? ?????????, ??? ?????????? ??? ?????????????? ??? ? 356 ???., ???
????????? ? 418 ???. (?? ????? 1 ????. ??? ? 30 ???.).
? 2002 ?. ? ????? ???? ?????????? ???????????? ????? ???????????????? ??? ???????????????????? ??????. ??? ????? ????????????? ? ???????? ???????? ??? ???? ???????????
?????????? 0,8 ? 0,9 ?? ?????? ????????? ??? ? ?????, ??? ????????????? ? ????????? ???????? ? 0,4 ? 0,7 [7].
??????????? ??????????????????? ??????????? ? ????????? 15 ??? ?????????? ??????????????? ???? ??????? ??? ? ??? ?? ?????????????? ???????. ?????? ????? «??????» ?????
? ????????? ?????? ???, ????????? ???????????. ? ????. 5 ????????? ???????? ? «????????»
????????? ????? ???????????? ? ????? ???. ???? ?? ??????? ????? ?? Metal Torg. Ru, ?????????? ????????, ????.
???????? ??????????? ?????? ?????? ????????????? ? ????????????? ?????, ??? ?? ???
??????????? ?????? ? ?????????. ? 2000 ?. ?????????? ?????? ???? ???????????? ????? ? ?????????? ???????? (????. 6). ?????????????, ??? ??? ????? ?????????????? ???????????? ?
1,6?2,7 ???? ????? ????? ?????????? ???????? ?????????? ? 6?10 ??? ??-?? ??????????????
????? ???? ???? ????????.
????????? ???????? ?????? ?? ?????? ???????????? ???, ?????????, ??????? (60-70 ? ?????? ?? 1 ? ?????) ????? ??????????? ??? ??????? ???????? ???????????? ?????? ?? 80-100 ???. ?.
# 147 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????? 4. ????????? ????????? 1 ?? ??? ????????????? ?????????????
????????? ???????
?????? ??????? ???, %
??????? ???? 1 ??,
? 1 ? ????, ????. ???
????. ???
?????????????? ????????? ?????????????? ?????????
(2004-2008)
????
????
????
????
6,4
32,39
27,84
2,073
1,782
???????
??????
?????
7,6
46,93
44,97
3,567
3,418
?????????
24,5
3,88
4,49
0,951
1,100
??????
26,5
10,96
14,54
2,904
3,853
???????
14,4
1,36
1,80
0,136
0,196
???????
410
0,34
0,48
1,394
1,968
?????????
25
1,08
1,47
0,270
0,368
??????
633
0,13
0,17
0,823
0,693
?????????
96,3
0,50
0,72
0,482
0,693
???????
140
0,07
0,10
0,098
0,140
?????
300
0,16
0,24
0,480
0,720
?????
1000
0,023
0,029
0,230
0,290
????????
150
0,15
0,18
0,225
0,270
???????
1500
0,028
0,027
0,420
0,405
??????
37,9
2,00
2,94
0,758
1,114
???????? ?????
94,16
91,84
9,50
10,15
????????? ?????
5,84
8,16
5,32
7,24
????? ????. ???
100
100
14,82
17,39
445
522
????? ???.
??????? 5. ???????? ????????????, ??? ? ??????? ????? ?????????????? ????????? (????. ???)
???????????? ?? ?????
????
?????,
???. ?
1996
64,0
2000
2002
???? 1 ?? ????? ?????,
???
??? ????.
???? ? ??????????? ???????, %
?????????
????????????,
? ???????????
???. ?
???????
????
?????
?????
9,1
582
77,0
7,9
608
2000/1996
20,3
-13,2
4,5
81,9
11,7
958
2002/2000
6,4
48,1
57,7
2004
85,0
11,6
986
2004/2002
3,8
-0,9
2,9
2006
102,5
14,6
1496
2006/2004
20,6
25,9
51,7
2008
104,2
22,9
2386
2008/2006
1,7
56,8
59,5
2008/1996
62,8
51,6
310,0
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????? 6. ??????? ???????????? ????? ? ?????????? ????????
????????????? ????????????
???????
MO
NB
????? ????? ????????,
???? ????.
F?
NI
FE
1990-1994
720
848
108
16
237,6
1995-1999
773
996
136
20
293,7
2000-2004
945
1184
131
36
411,1
2005-2009
1251
1339
200
54
625,5
NI
???????? ???-?? Ni,
Mo, Nb ?? 1 ? ?????
? ???????
MO
NB
NI
MO
NB
5,03
1,18
0,25
1180
150
22
6,63
1,35
0,32
1288
176
26
10,62
1,82
0,65
1253
139
38
31,00
12,0
2,16
1070
160
43
???????????
??????????, %
??????????? ?????????
???? 1 ?
???????,
???. ???.
??????????
?????????? ?
?????????????
???????, %
???????
??????? 7. ????????? ??????? ???????????? ???????? ?? ????????? ???? (?????????????????? 3,3 ??? ?)
??????,
???. ?
?????????,
???? ?
??? ???.
?????????, %
F?
31,0
0,85
26,4
9
871,2
7841
11,3
Mn
4,6
0,80
3,7
48
121,4
5829
8,4
Nb
0,83
0,80
0,66
1233
21,7
26879
38,7
V
0,16
0,70
0,11
1260
3,7
4657
6,7
???
2,50
0,70
1,75
418
57,8
24160
34,8
1075,8
69366
100
???????????
??????????, %
??????????? ?????????
???? 1 ?
???????,
???. ???.
??????????, %
?????????? ?
?????????????
???????, %
???????
??????? 8. ????????? ??????? ???????????? ???????? ?? ?????????????? ???? (??????????????????
2 ??? ?/???)
??????,
???. ?
?????????,
???? ?
??? ???.
?????????, %
F?
28,6
0,85
24,3
9
486,0
4374
9,9
Mn
6,9
0,80
5,5
48
110,0
5280
12,0
Nb
0,26
0,80
0,21
1233
4,2
5179
11,8
V
0,16
0,70
0,11
1260
2,2
2772
6,3
???
5,30
0,70
3,71
356
74,2
26450
60,0
676,6
44020
100
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? ???? ???????????? ????? ??? ? ?????????? ? ???????????????, ? ??????????????? ???????????? ? ???????????? ?? ?????????? ???????????, ?????????????? ? ????????????? ????????? ????????????? ???????? (????. 7-8).
??? ??????? ?? ????. 8, ????? 40 % ????????? ???????? ?????????? ??????, ????? 35 %
????????? ???????? ?? ???, ?????? ?? ????????? ???? ????? ???? ???????? 22 ???. ? ??????,
??? ? 10 ??? ?????? ????? ???????????? ?????? ? ???? ? ????????? ??? ??? ?????????????.
?????? ????????????? ?????????? ????? ????? ?????????????? ??????? ?????????? ????? 20 ???? ???. ????? ?????????? ??? ??????????? ??????? ??????????? ?????? ? ?????????
?????????? ???????????, ? ??????? ? ???????? ? ???????, ?? 100 % .
?? 2007 ?. ? ?????? ????????? 2008 ?. (????????????? ??????) ???????? ?????? ??????
?????? ?? ????? ?????? 40 ???. ? ?? ????? 63,9 ???? ??? ??? 23,5 ???? ???.
??????????????, ??? ????? ??????????, ??? ???????? ????????????? ?????????????, ????? ???? ?????????? ?? ????????????? ?????? ? ???????? ???? ?????-???????????? ???. ????? ??????, ????????? ????????????? ??? ???????? ??? ? ???????? ??????. ?????????
??????????? ???? ????? ? ??? ?? ????????? ???? ???????? 40 ???.?.
?? ??????? ?????, ????? ?????????? ? ???????????? ?????? ??? ??????? ?????????????????? 100 ???. ?. ?? ???? ???????? 83,7 ??? ????. ???. ?? ??????-????? ????????????? ???????? Ernst&Young (2005 ?.) ??????????? ? ??????????? ???????????? ? ?????? 85 ???
????. ???.
??????????????? ?????????? ??????????? ???????????? ??? ? ????????? ??????????????? ? ??????? ? ???????? ?????? ? ??????????????? ????? ????????? ???????? ????????????
??? ? ????? ?? 15-20 % . ???? ????? ???? ??????? ? ??????? ????????????? ???????? ? ????? ??????????? ??? ??????????? ? ???????????? ?????????? ??????????????? ????, ?????????????? ?????????????? ???????????, ????????????? ?????? ?????. ????? ???????????????
?????, ????????????????? ? ????? ??????? ?????????? ???, ??????????? ? ???????????????? ???? ??? ??????????????? ????????? ??? ????????????????????? ????????. ?????????????? ?????, ??? ?????????????, ??? ? ????????????????, ????? ??????? ???????????????? ??
??????????? ????????? ?????? ?? ??????? ??????????, ???????????? ??? ???????? ???????????? ???????????. ????? ???????????? ? ???????????? ??????????? ?????????? ???????????
???????????????? ?????? ??????????? ? ???????????? ??????? ?????? ?? ???.
? ????. 9 ????????? ???????-????????????? ?????????? ?????????? ???????? ????????
?????? ???????? ???????? ??????? ????????????? ???????????? ?????: ??????????? ?????????? ?????-????????????? ????????????? ? ????, ??????????? ?????-??????????, ???????????? ?????????????, ???????????? ???????????? ? ???????????? ????.
? ???????? ??????? ??? ????????? ????????? ???????? ?? ????????? ????????????????
???????????? ????????????????? ? ????????? ?????????????. ??? ?????????????, ????????? ??? 50 ???, ???????? ???????? ??? ???????????????, ????????????? ? ???????? ?????????????? ????????, ? ?? ?????? ?????????? ? ?????????????? ??????? ???????? ?? ?????
?????????????.
?????????? ????????????? ??????????? ???????? ??????? ?????? ??????? ?? ???????????? ???? ????????, ?????????? ??? ??????? ????, ??? ??????? ????????????? ????????????.
?????????? ????????, ??? ??? ???????? ????????? ??? ?? 10 ??? ?????? ????????????????
# 150 #
6000
3300
2000
2470
10844
15 ???
????????????, 2010 91193
(????????? ????)
10 ???
????????????, 2010
65811
(??????????????
10 ???
????)
5400
10 ???
93645
16 ???
???????????, ?u,
2008,
?????
???????????,
???????????, 2001
???????????,
?????, ???,
?????????, 2010
4000
9500
31365
26 ???
??????, 2009,
???????????
14000
???? ???.?.
1,35
???
74200 ?
(12365
???.. ???)
4 ??? ?
?????
2,1
1,32
1,33
Nb
21700 ?
(53350 ?.
?????. Nb)
280 ???. ?
1,46
1,32
1,27
????????
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?? ???????
?????
13000 ??
Au
24900 ?
???. Ni
9494 ?
??
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23677
19 ???
??????????
??? ???./
????????
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?????, 2009,
????????????
?????????????,
??????
??????? 9. ???????-????????????? ?????????? ???????? ?????????????
4087
??? ???.
44020
??? ???.
69366 ???
???.
7436 ???
???.
23794 ???
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18693 ???
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?????????
?????????
44553
10800 ???/? ??? ???.
14,6
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356
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1233 ???.
???/?
572
???/?
920
???. ???/?
1969 ???.
???/?
????
???????
?????????
3240
1324
8000
8879
658
655
1018
1 ? ????
3240 ???.
11720
???.
136
???. ???.
549 ???. ???.
327 ???. ???.
244 ???. ???.
1496 ???. ???.
1 ? ?????????
?????????????
??????????? ????, ???.
0,30
0,80
0,36
0,42
0,57
0,26
0,76
???????
?? 1 ???.
?????????,
???.
35,4
2,5
22,1
33,1
3,2
39,3
4,0
???,
???? ???.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
??????? 10. ????????? ???, ??????????? ?? 1 ? ???? ????????????? ????
????????? ???, ????. ???
???????????
?????????? ???, %
La-Nd
Sm-Ho
Er-Lu
?????-???
3,50
409,3
64,6
???????????
0,58
61,4
18,4
???????????
0,21
7,5
???????
0,23
??????????
?????????????
????????????
(?????????????? ????)
???????????? (?????????
????)
Y
?????
0,83
6,63
481,4
0,70
0,02
80,5
42,6
92,0
37,0
179,0
18,5
22,0
21,6
80,9
143,0
5,9
598,9
326,9
173,5
94,4
1193,5
3,71
352,3
118,8
50,3
28,1
549,5
1,75
177,7
78,8
24,9
19,5
300,9
????? ???????? 33 ???? ???. ??? ????????? ????????????? 35 ???? ???., ? ??? ??????????
?????????????? ??? ?????????????? 22 ? 25 ???? ???.
????? ?? ???????? ??????? ? ?????? ???????? ?????? ????????????? ?????????????
???????? ????????????? ??????, ???????????? ????????? ????? ???????? ????????? ??????
? ??????? ??? (5-8 %), ??? ????????????? ??????????? ?????? ??????????? ? ???? ? ?????
?????????????? ????? ?????? ?????????? ?????????. ??????? ??????????? ???? ?????????
???????? ? ????????? ???????????? ??? ?????????? 35-40 % , ??? ????? ????????? ?????
?????????? ??? ????????????? ??? ?? ????????? ??????? (????. 10).
??? ??????? ?? ????. 10, ???????? ????????????? ?? ????????? ??????????? ??? ???????? ???? ????????????? ?????-??? (481,4 ????. ??? ??? 14,4 ???. ???.), ??????? (1193,5
????. ??? ??? 35,8 ???. ???.) ? ?????????????? ???? ????????? (549,5 ????. ??? ??? 16,5
???. ???.). ???????? ?????????????? ???????????? ??? ????????? ????????????? ? 3-5 ???
????.
?? ???? ?????????????? ???????? ???????? ???????? ????????????? ????????????? ?????????? ????? ???????? ????????????, ?????????? ??????????? ? ????????? ?????????????? [5,6]. ??????? ?????????????? ???????? ??????? ??????? ? ???, ??? ????????? ????????????? ????????????? ??????????, ????? ???????? ????????, ?????? ? 50?70 ???. ? ????????
???, 4500 ? ????? ?????????????? ????????? ??????????? ??? ???????? ????????????? ?
????? ??????????? ? ?????????????.
? ?????? ? ?????? ?????????? ???????????? ?? ????? ???????????? ??????????? ??????. ??????? ????? (5 ??? ?) ??????????? ????????????, ????????????? ????, ???????????????
????? ??????? ????????, ???????? ? ????? ?? ?????????? ?????? ?????, ???????, ??????????????? ??????? ??????????. ??????? ??????? ???????????? ????? ?????????? ? ????????
?? ????????? ?????? ?????????? ????? 50 % .
????????, ??????????? ? ????. 10, ?????????? ??????? ??????????????? ? ??????? ????????? ???????? ??? ?????????? ????????????? ?????????????. ?????? ? ????????? ? ???????
????????? ???????????????? ??????????? ??? ?? ???????? ???????????. ???, ?????? ?????????? ???????-????????? ?????? ???????????? ????????????? (5 ??? ? ????) ? ?????????
# 152 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
?????????? ??????? ??????????? ? 60 ???? ???.. ????????? ??????? ????????????? ??????????? ? ???????????? ??????????? ??????? ?????????? 102 ???? ???., ??????? ????????????
??????????. ????????? ??????? ?????? ? ?????????? 20-30 ??? ? ???????? ???? ???????????
????????????? ? ??????? ??????? ??????????? ? 180 ???? ???.
????? ???????, ?????????? ????????????? ??????????? ???????? ?????? ??????????????? ??????????????? ?????????????? ? ?????? ??????? ????? ? ??????? ????? ?????? ???????? ??? ??????? ????????????? ????????????.
?????? ??????????
1. ?????, ?.?. ????????, ??????? ???????????? ? ???????????? ??????? ????? ????????????? ??? ???????????? ???????????? // ????????????? ????????. 1997. ? 11. ?.15-22.
2. ??????, ?.?. ??????????? ???????? ???????? ???? ??????????????? ??????????????
? ???????????? ????// ??????????? ??????? ??????. ????????? ? ??????????. ???????????
??????. ??????????? ??????? ????????????? ????. 2004, ?. 51-54.
3. ??????, ?.?., ???????, ?.?. ??????????????? ?????????????? ????????????? ???? ?
??????? ? XXI ??? // ???????? ? ?????? ????. 2003. ?6. ?. 23-25.
4. ???? ?????????????? ???????? ?????? /????????????? ?.?., ????????? ?.?., ?????
?.?., ?????? ?.?//??????????? ?????. ????? ???????-?????????????. ? 19. ?.: ????, 2006.
72 ?.
5. ??????, ?.?., ??????., ?.?., ??????????, ?.?. ??????????-???????? ???? ????????????? ????: ?????????????? ????????? // ??????????? ??????? ??????. 2000. ? 3. ?.13-27.
6. ??????, ?.?., ??????, ?.?., ?????????, ?.?. ? ??????????? ?????????????? ???????? ? ???????? ??????????-???????? ???? ??????? ??????????// ???????? ? ?????????????????? ??????? ??????????? ??????: ????????? ????????? ??????-???????????? ???????????. ??????????, 25-26 ?????? 2010 ?. ??????????: ???. ??? «????????????????????»,
2010. ?. 47-83.
7. ????????, ?.?. ?????????? ?????? ?????????????? ??? ? ??? ??????? ?? ?????? ?????????????: ???????. ????. ? ????. ????.- ???????. ????. ?.: ?????, 2002. 32 ?.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ??????. ???????????? ????????????? ??????-?????????????? ??? ? ???????????? ??????...
Chuktukon Deposit of the Niobium-Rare Earth Ores
is the Top Priority Asset for Modernization
of the Rare Metal Industry of Russia
Viktor G. Lomayeva and Sergey S. Serdyukb
?
?Geokomp? LLC,
62 K. Marx st., Krasnoyarsk, 660049 Russia
b
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia
Chuktukon deposit of the niobium-rare earth ores represents the mineral body, which due to its
qualitative and quantitative properties may become a key asset for modernization of the rare metal
industry of Russia. The deposit belongs to the ore-formational type of the rare metal crusts of the
carbonatite weathering. Ore zone of the deposit represents a thick blanket-like body having the length
of 3.5 km at the width from 800 to 1400 m and the thickness of up to 200 m. Two types of ores were
identified: the niobium ores (at the cut-off grade of Nb2?5 ? 0.8 %) and the rare earth ones (at the cutoff grade of the rare earth metals ? 3.0 %). Mineral composition of the ores: goethite, hydrogoethite,
hematite, psilomelane, pyrolusite, barium-pyrochlore, strontium-pyrochlore, cerium-pyrochlore,
pyrochlore, florencite, monazite, cerianite. The best treatment option is the pyro-hydrometallurgical
ore-processing scheme providing for the recovery of niobium, rare earth, manganese, phosphorus,
vanadium, iron commodity at different stages of the processing. Reserves of the rare earth ores,
approved by the State Committee for Reserves (GKZ) of the Russian Federation amount to: 6639 kt (?2
category), niobium pentoxide -39.8 kt (at the grade of 0.6 %), rare earth oxides ? 486 kt (at the grade
of 7.3 %).
Establishment of the rare earth industry center in the Krasnoyarsk Region has the following competitive
advantages: availability of the strategic raw material base required for the high technology ? deposits
of niobium and rare earth metals, availability of the scientific and production facilities able to perform
geological and process studies (Siberian Federal University, Institute of Chemistry and Chemical
Technology of the Siberian Branch of the Russian Academy of Sciences, exploration companies,
Krasnoyarsk), production facilities treating the slightly-radioactive concentrate (Integrated Mining
and Chemical Plant, Zheleznogorsk). Calculations of the technical-and-economic highlights of the
Chuktukon deposit?s developments demonstrate high efficiency of the project with the valuation
horizon of 10 years. Basic technical-and-economic highlights of the project for the niobium (rare
earth) ores: net present value ? 33 (22) billion rubles, budgetary efficiency ? 35(25) billion rubles,
volume of investments ? 91(65) billion rubles. Implementation of the Chuktukon mega-project will
allow Russia to modernize its rare metal industry and occupy the leading position on the world market
of rare metals.
Keywords: Chuktukon deposit, geology, niobium-rare earth ores, reserves, resources, technical-andeconomic highlights of development, modernization, rare metal industry.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 155-161
~~~
??? 330.15; 666.972
???? ????????? ?????????????
?????????????????? ?? ???????
??????-???????????? ??????? ??????
?.?. ????????a*,
?.?. ???????????a, ?.?. ???????
a
??????????? ???????? ?????????????????? ?? ??? ,
?????? 670047, ????-???, ??. ??????????, 6,
?
????????????? ???????? ?? ???,
?????? 670047, ????-???, ??. ??????????, 6? 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
??????????? ???? ????????? ????????????? ?????????????????? ??? ???????? ?????????????
???????? ??????????. ??????? ??????????? ????????????? ???????????????? ?????? ?????
????-???????????? ???????, ??????????? ????? ????????? ? ????????? ?????, ? ????????????
???????????? ??????????. ???????????? ???????????? ?????? ?????? ? ???????? ????????
? ??????? ??????????? ??? ???????????? ??????? ???????. ????????, ??? ?? ???????????
??????????????? ??? ?????? ?? ???????? ???????????? ????? ?? ????????? ?????.
?????????? ??????? ?????? ????? ????????? ??????-??????????? ??????????: ?????????
??? ?????? 28-32 ???, ??????? ????????? 2400-2600 ??/?3, ??????????? ?????????????
0,85-0,87, ??????????????? ? 50 ??????. ?????? ???????? ?????????? ??????????????????.
?????????? ?????? ????? ? ???????????? ???????? ?????? ???????? ???????? ????????????
??????? ???????????????? ???????????.
???????? ?????: ???????????? ??????????????????, ???????????????? ??????, ???????
?????, ?????? ?????-?????????? ???????????.
????????
? ?????? ???????????? ???????? ????????? ? ????????????? ?????? ???????????? ??????????? ??? ??????? ?????????? ????????? ????????. ?????? ??????? ?? ?????????????
?????????????????? ???????? ?????? ??????. ??? ?????? ???????????? ????? ???????????
??????? ?????????? ????????? ? ????????? ?????, ??????? ??????????? ?? ??????????,
? ?????????? ? ??????, ??????? ????????? ?????????? ????? ?? ???? ?????????? ?????????? ??????, ????????? ??? ????????????????????? ?????????????, ??????????? ??????????
???????, ????????????? ? ????????? ???, ?????????, ? ?????????????, ? ??????? ????? ????? ?? ??????????? ???????????. ?? ???? ?????? ???????? ?????????????? ??????????
70-80 % ?????? ???? ???????, ????? ??????? ???????????????? ?????? ???????? ????????
*
1
Corresponding author E-mail address: lkhud@binm.bscnet.ru
© Siberian Federal University. All rights reserved
# 155 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
?????. ? ???????? ??? ????????? ? ????????? ?????? ???????? ?????? ?????-??????????
??????????? ? ????????? ????????????? ???????????? ??????. ??? ???????? ???????? ????
???????? ?????????? ?????????, ???????? ??????-??????, ?????, ????????? ??????, ??????
? ????????.
???????? ??????????? ???????? ???????? ????????????? ??????? ?????-??????????
??????????? ???????? ????????? ??????????? ??????????. ?????????? ???? ????????? ????????????? ?????????????????? ??? ???????? ????????????? ???????? ?????????? ?? ??????? ??????-???????????? ??????? ??????.
?? ?????? ?????????? ??????? ? ??????-??????????? ?????? ???????? ??? ?????????????
?????????????, ??????? ???????????? ????????-???????? ? ??????????? ?????-?????????.
?? ???????????? ?????????????? ??????????? ?? ????????. ????????????? ????, ? ? ????????? ????? ????? ??? «?????????» ?????? ???????? ????????????? ????????????? [1, 2] ???????? ??????????? ???????? ? ?????????? ? ????????????? ?????? ??????????-????????
???? ??????. ??? ??? ??? ????????????? ??????????? ? ???????????????? ???????? ?? ??????? ??????? ??????????? ????????? ??????????, ??? ?? ???????????? ?????? ???? ????????? ?????????????????? ? ???????????? ?????????? ??????????, ?????????????? ????????
????- ? ???????????? ????????????, ?????????????????? ??????????? ????????????? ???????????? ????? ? ???????????? ?????????? ???????? ?????????.
? ????? ? ??????? ????????????????? ???????? ????????????? ????????-?????????
????????????? ?????? ??????? ???????????? ??????????????? ??????????? ? ???? ????????????? ???????. ???? ?? ??? ? ????-??????????? ??????, ??????????????? ? 8-12 ??
?? ????????????? ?????????????. ????-??????????? ?????-?????????-????????? ??????
????? ??????? 3,5?26 ?? ? ????????? ?? 56 ?36' ?. ?. ? 110 ? ?. ?. ? 60 ?? ? ?????? ?? ????
[3].
? ???????? ??????? ? 1959-1964 ? 1989-1994 ??. ????????? ????????-??????????? ????????
???????????? ?????-?????????? ?????????????, ? 2001-2002 ??. ? ????????-????????? ???????????? ?????????????????? ??????????????. «????????????????????» ????????? ?????????? ??????????? ????? ???????? ????????, ??????????????? ?????? ??????????? ????????.
? 2006 ?. ??? ???? ????????????? ?????-??????????????? ????????? ???? ?????? ???????? ??
??????? ?????? ??? ???????????? ???????????? ??????????. ?? ??? ?? ??? ???? ????????????
????? ???????.
??????? ??????? ???????? ??????????? ?????????? ???????????????? ?????? ?????
(???????, ???????????, ???????????, ?????????? ??????), ??????? ??? ?????????? ????????????? ????? ?????????? ? ???????. ????? ?????? ?????? ????? ??????????? ?? ??????
????????? ????. ???? ??????? ??????????? ?? ????????????? ??? ???????????? ????? ?????
???????.
???????? ?????????? ???????????? ??????? ?? ??????? ?????-??????? ????????????, ?
????????? ???????????????? ?????, ?????? ???????????? ????? ????? ????????? ??????
?????? ??????. ???, ?.?. ??????? ? ?.?. ?????????? ???????? ??????????? ?????????????
????? ?? ??????-??????????? ????? ? ???????? ???????????? ??????? ??????? [4-6]. ? ??????? ??? ??? ?????????? ?????? ?? ????????????? ????????? ????? ??????????????
????????????? ??? ????? ??? ????????? ????? ? ??????????? ??????? [7, 8].
# 156 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
???? ?????????? ???????? ?????? ?? ???????????? ?? ????????? ? ????????? ?????
????-???????????? ???????.
????????? ? ?????? ????????????
? ???????? ???????? ?????????? ???????????? ?????????????? ????? ?400?0 ??????????? ?????????? ??????, ????????? ?????? ??????? ????????, ????? ??????? ????????? ? ???????????????? ?????? ?????? ????-???????????? ???????, ?????????? ?????? ??????? ???????? ? ????. 1.
?? ?????????? ???????? ???????, ?????? ? ????? ???????????? ????? ??????????????
??????, ? ????????? ? ???????? ??????, ????????????? ??????????? ???????? ???????.
?????? ????-???????????? ??????? ????? ??????? ????????. ??? ?? 80-97 % ???????
?? ??????????? ?????????? ??????? ? ??????????? ??????????? ???? ????????? (1-2 %).
??????? ??????????? ????????????? ? ??????????. ???????? ? ????? (????????) ???????????? ????????????. ??????? ? ????????????? ?????????? ? ???????????? ????? ?????????????? ??????, ?? 80-85 % ????????? ?? ????????? ?????? ???????. ????? ????, ???
????? ? ????? ??????? ?? 5-10 % ??????????? ? ??????????????, 1-2 % ? ????????????.
?????????? ???????, ??????? ???????, ?? ????????? ??????????? (????????? ??? ?????????) ? ???????. ????????? ???????????? ? ?????????????? ?????????? ??? ???????????
?????.
??? ??????????? ???????????? ??????? ??????????? ????? ??? ???????? ??????????????? ??????, ??????? ???????, ??? ?? ??????????????? ??????, ??????? ? ?????????? ??????? ????? ????????? ?????? ???????: ???????, ??????????, ???????. ???? ????????, ???
?? ?????????????? ?????? ????? ???????????? ????? ?????? ????????? ??????: ?????????,
?????????????, ????????????. ? ??????? ??????? ???????? ????? ????????. ? ?????????? ??????????? ???????? ????????, ?????????, ???????.
??????? ??????? ??????????? ? ???????? ? ??????????? ??????? (???????? ???? 826793 ??????? ? ?????? ?? ??????? ?????? ????? ??? ???????????? ?????. ??????????? ????????) ?? ????????.
???? ????????? ???????????-????????????? ?????? ?????. ???????? ????????? ???????? ??????????? ?????????? ???????????? ????????????? ???? ??? ?????? ??????????
85,69 ??/??, ??? ??????? ? 107,89 ??/??, ??? ?????????? ? 131,69 ??/??. ?? ???????????? ??????????? ??????? ?? ????????? ??????????? ???????? ?????? 2.6.1.2523-09 ?????? ???????????? ????????????? (???-99/2009) ? ???????? ???? 8267-93 ????? ?????????????? ???
???? ????? ???????????? ?????.
??????? 1. ?????????? ?????? ???????????????? ?????, ????. %
??????
??????
?????
?????????
????????? ?????
SiO2
Al2O3
Fe2O3
FeO
CaO
MgO
Na2O
K 2O
Ni
39,70
37,40
40,60
38,40
1,80
1,25
12,00
2,10
0,42
3,10
1,11
2,93
10,70
12,60
9,45
9,95
0,81
0,40
5,57
0,46
43,83
40,81
28,60
43,20
0,12
0,14
0,57
0,05
0,07
0,02
0,04
0,03
0,165
0,218
0,084
0,156
# 157 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
?????? ???????????? ?? ?????? ?????????? ????????, ?? ? ?????? ????? ?????????????
???????????? ? ?????? ????????????? ?????????? ???????? ???????. ??? ?????????? ?????
??? ???????? ??????? ??????, ??????? ???????, ??? 68,4 % ????? ???????? ??????? ???????
0,63 ??. ?? ?????? ????????? (???=2,72) ? ??????? ??????? ?? ???? ? 0,63 ?? ????????? ?
?????? ??????? ??????. ?????????? ? ????? ?????????? ? ????????? ?????? ?????????? 5 %,
??? ?? ????????????? ??????????? ???? 8736-93 ?????? ??? ???????????? ?????. ???????????
????????. ??????? ????????? ?????????????? ??????????? ?????. ?????????? ????????????
???????? ? ????? ???????? ???? 8735-88 ?????? ??? ???????????? ?????. ?????? ??????????
????????? ? ???????? ?????????? ????????.
??? ?????????? ????? ???????? ????????? ???????? ??????????? ?????????? ???????????? ????????????? ???? ?????????? 94,45 ??/??, ??? ???????? ???? 8736-93 ????????????? ??????????? ??? ?????????? ? ?????????????.
??? ?????????? ??????-???????????? ????????? ?????? ????????????????? ???? 1018090 ???????. ?????? ??????????? ????????? ?? ??????????? ?????????, ???? 10060.1-95 ???????. ??????? ????? ??????????? ????????????????, ???? 12730-78 ???????. ?????? ??????????? ?????????, ?????????, ??????????????, ?????????? ? ????????????????????.
?????????? ? ?? ??????????
???? ??????????? ??????????? ????????????? ???????????????? ????? ? ???????? ???????? ? ??????? ??????????? ??? ????????? ??????? ??????? ??? ??????? ????????? ??????????? ???????? ???????? ?????? ? ??????????? ??????? ?? ?????????.
??? ???????? ??????? ????? ?? ???????????????? ????? ????-???????????? ???????
?? ??????????????? ???????? ???????? ?????? ???? ????????? ????????? ?? ???? ????? ?????: ?? ??????, ??????? ? ??????????. ????????? ????????, ??? ?????? ???? ????????? ?????
???????? ?????????? ???????? ??????-????????????? ????????????. ?? ????? ?????????
?????: ?? ?????????? ? 1200 ? 1400, ?? ??????????????? ? F150 ? F200. ????????? ?????
????????? ?????? ???? ????? ???????. ?????????? ??????? ???????? ?? ????????? ???????????????? ?????????? ????????. ?????? ?? ???????????????? ?????? ????? ????????????? ??
???????? ??????????? ??????????? ???? 8267-93 ??????? ? ?????? ?? ??????? ????? ???
???????????? ??????.
?????? ????? ???? ????? ? ??????? ??????? ????????? ?????? ?? ?????. ? ???????? ???????
??????????? ???????????? ????????? ????? ? ??????? ????????? ??=2,5 ? ????????? ?????
????-???????????? ??????? ? ??????? ????????? ??=2,72. ??????????? ???????? ?????? ??
???? ??????? ????????? 1-4 ?? ??? ??????????? ????? ????? ? ????? ????? ????????????,
?????? 0,4. ?????? ??????? ??? ??????? ??????? ?????? ??? ??????????. ? ???????? ?????????
???????????? ?????? ?? ??????? ??????????? ? ???? ?????????? ????? ? ?????? ? ?????? ??????????? ? ???? ?????????? ?????.
??????? ??????? ???? ???????? ? ??????? ??????????? ?? ????????? ???????. ???????????? ????????? ? ???????? 7 ? 28 ????? ?????????-???????????? ?????????. ?????????? ???????????? ? ????. 2.
?????????? ? ???? ????????????? ?????? ??????????, ??? ???????? ????? ?????????
?????????? ? ?????? 7 ????? ????????? ?????? (????? 50 %), ????? ????? ????????? ???????# 158 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
??????? 2. ???????????? ?????????? ???????? ?????? ? ??????????? ?? ???? ????????????
??? ???????? ???????????
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? ????????
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28 ?????
18,3
21,9
17,1
21,7
16,9
21,7
16,0
17,3
15,8
16,9
28,3
32,0
28,0
31,8
27,8
31,5
26,7
28,4
25,2
27,8
???? ? ????????? ????????????? ???????? ? 28 ?????? ????????? ? ?????????-???????????
????????.
??? ???????? ??????????? ????????? ??????? ?? ??????????? ?????????????? ???????.
????????? ??????? ?? ????? ?? ???????????????? ????? ???? ????????? ??????? ?? ???????????? ????? ????? ? ?????????? ?? ????????? ??????? ?? ????????? ????? ?? 4,1-6,0 %.
????????? ??????? ?? ????? ?? ?????? ????, ??? ?? ??????? ? ??????????. ????? ?????? ?????????? ????? ??????, ??? ? ???????? ???????? ??????????? ???????????? ??????.
?????? ??????????? ????? ????????? ??????? ?? ??????????? ?????????????? ???????.
?????? ?????????? ????? ?? ????????? ??????????? ????????? ?? ?????????.
??? ??????????? ??????????????? ?????????? ??????? ???????????? ????????????
??????? ?????????????-?????????? ????????, ??? ????????????? ????? ?? ???????????????
??????? F50, ??????????? ???????????? ?????? ??? ????????????? ? ???????????? ?????????????. ??? ???? ?????? ????????? ???????? ?? ????????? ? ???????????? ????????? 1,862,58 %.
?????????? ??????? ?????? ????? ????????? ??????-??????????? ??????????: ????????? ??? ?????? 28-32 ???, ??????? ????????? 2400-2600 ??/?3, ??????????? ????????????? 0,85-0,87, ??????????????? 50 ??????. ?????? ???????? ?????????? ??????????????????.
????????? ??????????????? ???????????? ?? ??????????? ????????????? ???????????????? ????? ????-???????????? ??????? ? ???????? ?????????????. ?????????? ??????????
??????????????? ? ????????????? ?????????? ???????????? ? ?????? ???????????.
??????????? ?????? ????? ? ? ????? ?????? ????????? ????????? ?????????? ??????????????? ?????????????? [9], ???????????? ?? ???-???????? ?????? ????????????? ????????????? ? ???????? ????????????? ???????. ?????????? ?????????? ? ???????????? ???????, ?????????? ??????????????, ??????-???????????? ????????, ???????? ? ????????????.
??????? ???? ???????? 1400?400 ?. ?????? ???????????? ?? ????????? ? ????????? ?????
???????? ???????????? ??????????? ????????????? ??? ????? ??? ???????????? ????????????
??????????.
# 159 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
??????
?? ??????? ??????-???????????? ??????? ?????? ???????? ??????????? ?????????????
????????? ????? ??? ???????????? ????? ????? ???????????? ??????????. ? ?????????? ??????????? ???????????? ???????? ??????? ?????? ?? ??????? ? ?????? ??????????? ?? ???????????????? ?????? ?????. ????????, ??? ??? ??????????? ????????? ??????? ?? ??????????? ?????????????? ???????. ?????? ?? ???????????????? ?????? ??????? ???????????????
?????????? ?????????? ?? ????????? ? ??????? ??????? ?? ????????? ????? ? ?????????
????? ? ???????????? ???????????? ??????? ??? ????????????? ? ???????? ??????????????,
? ?????????, ??? ???????????? ???????????? ??????, ?????????? ???????? ???????.
?????????? ????????????????? ????? ? ???????????? ???????????? ?????????? ???????? ??????? ????????????? ??????? ?? ???? ????????????? ??????? ????????? ? ?????????
?????, ? ??????? ????????? ???????????????? ??????. ??? ????? ???????? ?????????????
???????? ?? ?????????? ????? ?? ???? ???????????? ??????????, ????????????????? ???
??????. ??? ???? ??? ?????????? ????????????? ?? ????????? ??????????? ???????? ????????????? ????????????, ??? ???????? ?????????? ? ??????????? ???????????? ????? ? ?????????? ???????? ????????? ? ?????? ???????? ???????? ???????????? ??????? ???????????????? ????????????.
?????? ??????????? ?? ????????? ???? ??? ? 5.5.2 «????????? ????? ????? ?????????? ? ???????? ????????????????? ???????????????? ?? ??????? ?????-?????????? ??????????????».
?????? ??????????
1. ??????, ?.?., ???????, ?.?. ???????? ???????? ????????????? ????????-????????? ????????????? (???????? ???????????) // ????????? ? ????????? ???????. 2009. ? 4. ?. 33-39.
2. ??????????, ?.?., ????????, ?.?. ?????? ???????? «?????????» ? ????????? ???????
// ??????????? ??????? ??????. ????????? ? ??????????. 2006. ? 6. ?. 57-61.
3. ??????, ?.?. ????-??????????? ??????????? ??????. ????-???: ???????????? ??? ??
???, 1998. 265 ?.
4. ??????????, ?.?. ???????????? ????????? ?? ???? ????????? ??????: ???????. ???. ?
?-?? ????. ????. ???????, 1992. 35 ?.
5. ???????, ?.?. ??????????? ????????????? ???????????? ????? ? ????????. ?.: ???-??
?????????? ???????????? ?????, 1994. 268 ?.
6. ??????????, ?.?., ???????????, ?.?. ???????????? ????????? ?? ?????? ????????? ??????. ???.: ??????????, 2000. 198 ?.
7. ????? ?.?., ?????????? ?.?., ??????, ?.?., ??????, ?.?., ????????????? ?.?. ??????????? ????????????? ???????? ???????? ?????????????? ????????????? ???????? // ???????? ????????????? ????????????? ?????????? ? ???????????? ????? ????????? ??????? ?
?????????? ???????????? ? ??????????? ??????????. ????????????: ???. ???.?? ???, 2005.
?. 41-43.
8. ?????????????, ?.?., ??? ?.?., ??????????, ?.?., ???????, ?.?., ?????? ?.?., ?????????? ?.?. ??????????? ????????????? ????????? ????? ? ??????? ?????????? ???????? ???
# 160 #
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?.?. ????????, ?.?. ???????????? ???? ????????? ????????????? ??????????????????...
?????????????? ????????????? ??? ????????? ????????????? ????? ? ?????. ???????, 2002.
34 ?. ???. ? ?????? 12.07.2002. ? 1322 ? ? 2002.
9. ??????, ?.?. ????????? ?????-????????? ?????????? ? ???? ????????????? ????????????????? ????????????? ? ??? ??????? // ?????? ????????? ? ???????? ??????????? ????????? ??????????: ??????????-???????? ????????: ????????? ????????????? ????????????????? ??????????? ? ????????????? ????????. 20-24 ???? 2006 ?. ????-???: ???-??
??? ?? ???, 2006. ?. 24-27.
The Ways of Rational Nature Using Increasing
on Example of North Baikal ore Region
Lyudmila I. Khudyakovaa,
Oleg V. Voyloshnikova and Evgeniy V. Kislovb
a
Baikal Institute of Nature Using SD RAS,
6, Sahiyanovoy st., Ulan-Ude, 670047 Russia
b
Geological Institute SD RAS,
6a, Sahiyanovoy st., Ulan-Ude, 670047 Russia
The ways of rational nature using increasing during deposits development are considered. The
possibility of Ioko-Dovyren massif overburden and spoil Mg-Si rocks in building materials production
is studied. The using of these rocks as large and small filler at production of heavy concrete is offered.
It is shown that such concretes do not yield to traditional type on granite rubble by durability feature.
Got heavy concretes have following physics-technical factors: toughness at compression 28-32 MPA,
average density 2400-2600 kg/m3, water-resistance factor 0.85-0.87, frost-resistance ? 50 cycles.
The concretes are characterized by increased sulphate-resistance. The involvement of this rocks in
production will allow to solve the problems of the ecological clean enterprises mining creation.
Keywords: rational nature using, Mg-Si rocks, heavy concrete, spoil of mining enterprise.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 162-169
~~~
??? 669.713
?????????????????? ????????????-?????????
??????? NaF-AlF3-CaF2-Al2O3
?.?. ??????, ?.?. ?????????,
?.?. ????????, ?.?. ????????,
?.?. ????????, ?.?. ??????
?
????????? ??????????? ???????????
660041 ??????, ??????????, ??. ?????????, 79
?
??? «????? ???»,
?????? 660111, ??????????, ??. ?????????????, ?. 37, ???. 1 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
??????????? ?????????????? ????????? ?????????????????? ????????????-?????????
??????? Na3AlF6 -AlF3-5 ???. % ??F2 ? Al2O3 ??? ????????? ????????? ???????????? ?????????
(??=[NaF]/[AlF3]) ?? 1,2 ?? 2,0. ?? ?????? ????????????????? ?????? ???????? ?????????????
?????????, ??????????? ??????????? ?????????????????? ??????????? ????????????????????? ?? ??, ?????????? ??????????? ????????? ? ??????????? (?=f(??, [Al2O3], T)):
ln? =3,53986 + 15,6·10 -3·?? ? 14,99·10 -3·w(Al2O3) -3476,07/T,
??? ? ? ???????? ??????????????????, ??/??; ?? ? ???????? ??????????? ?????????; w(Al2O3) ?
?????????? ??????????? Al2O3, ??. %; T ? ???????????, ?.
???????? ?????: ??????????????????, ????????, ???????, ???????? ??????????? ?????????,
???????.
????????
?????????? ?????????? ????????????? ??????????????? («????????») ?????? ? ???????????? ???????? ?????? ?????????????? ???????????? ?? ??????????? ??????-??????????
??????? ????????? ????????? ? ?????????????????? ??????????????????? ????????? ? ?????
?????? ?????????? ?? ? ???????? ???????????.
?????????? ?? ????????? ???????? ??????? ??????????? ???????????, ???????????
????????? ???????? ???????? ???????? ?????? ? ???????????? ????? ??????????? ?????????? ????????? ???????????, ??? ????? ?????????? ????? ?? ???? [1]. ? ????????? ?????
??? ?????????? ?????? ? ???????, ????????????????? ?????????? ????????????-?????????
[2-6]. ??????-?????????? ???????? ????? ???????????? ???????? ?? ??????? [1].
????? ?? ????????? ??????-?????????? ??????? ???????????? ???????? ?? ??????????????????. ??????? ??? ?????????? ??????????????????? ??????????? ?????????? ?????, ???
???????? ?????????????????? ????????????-????????? ? ?? ???????? ? ????????????.
*
1
Corresponding author E-mail address: Simakov@rusal.com
© Siberian Federal University. All rights reserved
# 162 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
?????? ?? ???????????? ?????????????????? ??????????????????? ????????? ? ?????????? ?? ???????. ?????? ? ?????????? ??????? ????????? ????????? ??????? ????????????
???????????? ????, ??????????? ??????? ????????? ????????????? ?????????, ???????????
???????????? ????? ? ?????????????? ?????????, ?? ????????????? ? ????????? ? ??????
????? [2,3]. ??????????? ???????????? ????????, ? ??????? ????????? ???????????? ???????
?????????, ????? ????????????? ??? ??????? ?????? ????? ???????.
???????? [7] ????? ????????? ??? ??????? ??????????? ???????????? ? ?????, ?????????
?? ???? ? ????????????? ?G, ?????????? ???????? ?????? ? ????????????? ?L:
F
FL
1
3M
,
2 FG / F L
M
1 FG / F L
(1)
??? ? ? ???????? ???? ??????????? ???? ????, ??????? ???????????? ???
M
VG
,
VG VL
(2)
??? VG ? VL ? ????? ???? ? ????? ??????????????.
????????? (1) ??????????? ??????????, ???? ?????????? ???? ???????????? ????? ???????????? ??????????? ??????? (? ????? ?????? ??????? ?????????). ???? ?G/ ?L=0, ?? ????????? (1) ??????????? ????????? ???:
3
F
1
.
(3)
FL
2 /M 1
????? ?????? ???????? ????????????????? ???????????? ?????????????? ??????? ??????????? ????????? ?? ???????? ?????????????????? ??????????????????? ?????????????
????????? ??????? Na3AlF6-AlF3-5 ???. % ??F2 ? Al2O3. ????????????? ???? ???????????? ??????? ???, ??? ??? ???????????? ?? ?????? ?????? ?????????????? ?????? ??????? ? ????????, ??? ???????????? ??????? ????? ?????? ?????? ? ??????????? ?????, ?????? ???????
????????? ???????, ??????????, ??????.
???????? ????????????
??? ????????? ?????????????????? ??????????????????? ????????? ????????? ????????????????? ?????? ? ????? ????????????? ???????????, ???????????? ?? ???. 1.
?????? ??????? ?? ??????????? ??????? (1), ???? ??????????? ????????????? ??????????
(4) ? ??????? (5). ??? ????????????? ???????????? ?????????? ?????? (1) ? ?????????? ????????? 55 ?? ? ??????? 12 ??. ????????? ????????????? ?? ???????????? ??????? ???????
10 ??, ??????? 40 ?? ? ???????? 0,5 ??.
??? ??????????? ????????? ?? ?????????? ????????? ????? ??????????? ? ????? ??????????? ??????? ????????????? ????????? ??????? (5) c ????????? ???????? 40 ??, ?????????? ? ???????? ????????????????? (???????? ???????? ??????? 8 ??/c). ??????????? ?
?????? ?????????????? ???????????? ? ??????????????? ?????????? ???????-??????????
?????????? (11), ?????????? ? ?????????? ????? (9). ??????????? ? ?????????? ? ???? ???????, ??????????? ?? ??????????? ?????, ???? ???????? ?? ??????????? ??????????? ????? ??????????? ???????? (6-8). ??? ?????????? ????????? ??????? ???????? ????????????
?????????? ?? ????????? ? ????????? ????????? ???????? ?????? (2).
# 163 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
11
10
10
9
2
8
7
4
6
4
3
5
1
???. 1. ?????? ??? ??????????? ?????????????????? ?????????: 1 ? ?????????? ??????; 2 ? ????????
??????; 3 ? ??????????; 4 ? ???????????? ?????????; 5 ? ????????? ????????? ???????; 6,7,8 ?
?????????? ??????; 9 ? ?????????? ?????; 10 ? ???????? ???????????; 11 ? ?????????
????? ??????? ???????????? ?????????? ??????, ?????????? ?????????????? ???????????? ??????????? ???????, ???????? ? ???? ? ???????? ?????????. ????? ????, ??? ??????????
????????????, ? ???? ??????????????? ????????????? ???????, ?????????, ?????????? ? ?????????? ?????, ? ?????????. ??????? ???????????? ?????????? ? ??????? ????? ????????????. ????? ?????????? ????????? ??????????? ????????? ???? ????????? ????????????? ? ??
???????? ???????? ???????????? ?????????? ?????? K (4):
K = R·?,
(4)
??? R ? ???????????????????? ???????????, ??; ? ? ???????? ??????????????????, ??/??.
???????? ???????? ?????????????????? ??????????????????? ????????? ???????
Na3AlF6-AlF3-5 ???. % ??F2 ? Al2O3 ??? ?????????? ?????? ????????? ??? ???????????????
??????????? ???????????? ?? ????????? (5)[2]:
? = -3,662 ? 9,908·10 -2 ·?? -3,149·10 -2 ·w(Al2O3) + 4,972·10-3 ·?,
# 164 #
(5)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
??????? 1. ??????? ?????? ???? ????????? Worsley (?????????)
?????????? ???????, ???. %
+140 ???
-140 +100 ???
-100 +74 ???
-74 +45 ???
-45 ???
4,38
42,07
38,18
13,48
1,89
??? ? ? ???????? ??????????????????, ??/?? ; w(Al2O3) ? ?????????? Al2O3, ???. %; T ?
???????????, ?. ????????? ????????????? ??? 2,0????1,2, ? ????????? ????????? ??????????
Al2O3 ?? 0 ?? 6 ???. %, ? ??? ????????? ??? ???????????? ????????? ??????????? ??? ?????????
?? 45 K. ??????????? ????????????? ????????? ??? ???? ??????????? ????? 0,9985 [8].
????? ??????????? ????????? ?????? ? ??????? ????????? ??????? ????????? ????????
?????. ????? ?????? ??????? ????????? ???? ????????? ????????????? ??????????? ???
????????????? ??????????? ? ?? ???????? ???????? ???????????? ???????? ??????????????????.
?? ???? ????????????? ?? ???????????? ?????????????????? ????????? ????????????
???????? ???????????? ????? Worsley (?????????). ??? ??????????? ???????????????????
??????? ????????? ??? ???????? ??????? ?????? ??????? ?????? ???????, ?????????? ????????
???? ? ????. 1.
??? ????? ?? ?????? ????. 1, ???????? ????????? ? ????????? ????, ??? ??? ??????????
??????? -45 ??? ?????????? ????? 10 ???. % [3] ? ????? ???????? ?????????? ?????????????????? ?????? (?????????? ????????? ?????? 140 +45 ??? ????? 80 %).
????????????? ??????????? ?????????? ?? ?????????? ?????????, ??????? ??????? ?
??????? ????????????? AUTOLAB. ???????? ?????????? ??? ?????? ????????? ?????????? ??????????? ???? ?????? ??????? ?? ????????????????? ?????? ? ????????? ????, ???????????? ????? ???. ???????? ?? ?????? ????????? ?????? ?????? ??????????? ????, ???????
?????????? ? ????? ????????? ????????? [3].
?????????? ?????????? ?????? ? ????????????? ? ??????????????? ???????, ??????????? ???????? ??????? ? ????????? ?? 1 ??? ?? 0,1 ??, ????????? ??????? ??????????? ? ???????????????? ????????????? ??? ????????? ?? ??????? ????????.
????????????? ? ?????? ????????????? ??????????? ?????????????
??? ?????? ??????????? ?????????? ????????? ???? ???????? ???????????? ?????????????????? ????????????-????????? ???? ????????? ???????????? ?? ?????? 1? ????????
KCl ??? ????????? ?????????? ?????????. ??????? ??????? ????? ??? ??????, ?????? ???
??? ?????????????????? ?????????? ?????? ???????, ???????? ? ??? ?? ????????????, ???????
?????????. ?????????? ????????? ???????????? ? ????. 2 ? ?? ???. 2.
?? ????. 2 ? ???. 2 ?????, ??? ? ??????????? ?????????? ?????????? ?????? ????????
?????????????????? ????????? ??????????? ??????????? ???????. ?????????? (|?|) ????????
?, ???????????? ?? ????????? ????????? (3), ?? ????????????????? ?????? ?? ?????????
3,5 %. ????? ?????????? ????? ????????? ???, ??? ??????? ????????? ????? ????????? ?????? (????. 1) ? ??????? ?????????????? ?????, ???????? ?? ???????????. ?????? ?? ?????
# 165 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
??????? 2. ?????????? ????????? ?????????????????? ?????? ????????????-?????????
? ????., ?
297
?????????? ?????? Al2O3*, Al2O3**
???. %. ??. %
?·102, ??-1
28,6968
0
5
10
15
20
0
1,23
2,43
3,61
4,76
?????????????,
??
2,6126
2,6730
2,7406
2,8136
2,9058
????????
??????????????????,
??/??
????. ?? ????.
????.
(3)
0,1098
0,1098
0,1074
0,1078
0,1047
0,1059
0,1020
0,1040
0,0988
0,1022
|?|, %
0
0,43
1,12
1,97
3,46
??????????: * ? ?????????? Al2O3 ? ???????????-?????????; ** ? % ??????, ?????????? Al2O3,
?????????????? ? ??????????? ? ???? ?????????? ??????.
???. 2. ??????? ?????????? ??????????? ????????? ?? ?????????????????? 1? ???????? KCl: ????????
????? ? ????????????????? ??????????, ?????????? ????? ? ????????, ???????????? ?? ?????????
????????? (3)
????? ??????? ?????, ??? ????????? ???????? ????????? ? ?????????? ????????? ???????????
?????????????????? ????????????-?????????.
?????????? ????????????? ? ?? ??????????
????????? ?????????????????? ????????????-????????? ????????? ? ????????? Na3AlF6AlF3-5 ???. % ??F2 ? Al2O3 ? ????????? ?? ?? 1,2 ?? 2,0, ??? ????????? ?????????? ??????????? ????????? (?? 0 ?? 13,2 ??. %). ???????? ??????? ???????????? ??? ?????????? ??????
????????? ? ?? ?????????????????? ??? ??????????????? ???????????? ????????? ? ????. 3.
??? ??? ???????? ???? ???????? ?? ?????????, ?? ????? ???????, ??? ??????????? ? ????
???????????? ???????? ?? ??????????? ??????????? ? ??? ??? ??????? ?????????? ? ????????
# 166 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
??????? 3. ?????????????????? ???????? ??????????????????? ????????? ??????? Na3AlF6-AlF3-5
???. % ??F2 ? Al2O3
?.?.
??
Al2O3, ???. %
? ????., ?
?, ??/??[9]
1
2
6
1216
1,997
2
1,9
6
1201
1,932
3
1,8
6
1184
1,857
4
1,7
6
1163
1,763
5
1,6
6
1138
1,649
6
1,5
4
1112
1,592
7
1,4
4
1075
1,418
8
1,3
4
1030
1,204
9
1,2
3
1018
1,186
???. 3. ??????? ?????????? ??????????? ????????? ?? ?????????????????? ????????? Na3AlF6-AlF3-5
???. % ??F2 ? Al2O3 ??? ????????? ?? ?? 1,2 ?? 2,0: ???????? ????? ? ????????????????? ??????????;
?????????? ????? ? ????????, ???????????? ?? ????????? ????????? (3)
? ???? ?????????. ???????? ???? ??????????? ????????? ? ???????????-????????? ?????????? ?? ????????? (2). ???????? ????????? ????????? ????????? ?????? 4 ?/??3, ? ?????????
????????? ??? ?????????? ?????? ????????? ???????????? ?? ????????? (6), ??????????? ??
????????? ????????????????? ?????? ??? ???????? ??????????? ??????? [3]:
?= 2,802+0,2427 ·??-125,1·10 -4 ·w(Al2O3) ? 115·10 -5 ·?,
(6)
??? ? ? ?????????, ?/??3, w(Al2O3) ? ???????????? Al2O3, ???. %, ? ? ???????????, °?. ???????????
????????????? ????????? ??? ???? ??????????? ????? 0,95 [8].
# 167 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
?? ???. 3 ?????, ??? ??????????? ???????? ?????????????????? ?? ?????????? Al2O3 ?
????????? ????? ???????? ???????? ? ??????????? ?????????? ???????? ??? ???? ????????????? ??. ??? ?????????? ?????????? ??????????? Al2O3 ?? 1 ??. % ???????? ?????????????????? ? ??????? ????????? ?? 0,0215 ??/?? (??/??Al2O3= ? 0,0215).
?? ?????? ????????????????? ?????? ???????? ????????????? ????????? (7), ??????????? ??????????? ?????????????????? ??????????? ????????????-????????? ??????? Na3AlF6AlF3-5 ???. % ??F2 ? Al2O3 ?? ??, ?????????? ??????????? ????????? ? ??????????? (?=f(??,
[Al2O3], T)):
ln? =3,53986 + 1,56·10 -3·?? ? 14,99·10 -3·w(Al2O3) -3476,07/T,
(7)
??? ? ? ???????? ??????????????????, ??/??; ?? ? ???????? ??????????? ?????????; w(Al2O3) ?
?????????? Al2O3, ??. %; T ? ???????????, ?. ????????? (7) ????????????? ??? 2,0????1,2, ?
????????? ????????? ?????????? ??????????? Al2O3 ?? 0 ?? 13 ??. % ? ????????? ?????????? ??
1216 ?? 1018 ?. ??????????? ????????????? ????????? ??? ???? ??????????? ????? 0,998.
??????????? ????????????????? ? ???????????? ?? ?????????????? ????????? (7) ???????? ???????? ?????????????????? ?? ????????? 3,7 %, ??????? ?????????? ?????????? 1 %.
??????
1. ??????????? ???????? ??????????? ???????? ?????????????????? ?? ?????????? Al2O3
? ??????????????????? ??????????. ??? ?????????? ?????????? ??????????? Al2O3 ?? 1 ??. %
???????? ?????????????????? ? ??????? ????????? ?? 0,0215 ??/??.
2. ???????? ????????????? ?????????, ??????????? ??????????? ???????? ?????????????????? ????????????-????????? ??????? Na3AlF6-AlF3-5 ???. %. ??F2-Al2O3 ?? ??, ?????????? ????????? ? ??????????? (? = f(??, [Al2O3], T)). ??????????? ?????????????????
? ???????????? ?? ?????????????? ????????? (7) ???????? ???????? ?????????????????? ??
????????? 3,7 %, ??????? ?????????? ?????????? 1 %.
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
?????? ??????????
1. ???????, ?.?. ???????? ???????????? ??????????? ????????? ????????? ?? ?????????
????????? ? ????? ????????????????? ???????? ???-?????: ????. ? ????. ????. ????. ??????????, 2006. C. 177.
2. Brown, C.W. Laboratory experiments with low-temperature slurry-electrolyte
alumina reduction cells// Light metals, 2000. P. 391-396.
3. Sides, P.J. Phenomena and effects of electrolytic gas evolution// Modern aspects of
electrochemistry ? 18/ Plenum Press New York and London,1986. P.303-354.
4. Vogt, H. Gas-Evolving electrodes// Modern aspects of electrochemistry ? 6/ Plenum Press
New York and London,1983. P. 445-489.
5. ?????????????????? ????????? ??????? NaF-AlF3-CaF2-Al2O3 / ?.?. ?????, ?.?. ????????, ?.?. ???????, ?.?. ???????, ?.?. ???????, ?.?. ?????// ????????. 2009. ?6. ?. 19-27.
# 168 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????, ?.?. ????????. ?????????????????? ????????????-????????? ??????? NaF-AlF3-CaF2-Al2O3
6. ?????? ?.?., ???????, ?.?. ???????? ? ???????????? ???????? ????????????. ?: ???????????? ??? ??? «???», 2000. ?. 199.
7. Fletcher, D. Instrumental methods in electrochemistry. [Text]/ D. Fletcher, R. Greef, R. Peat ?
et al.// Horwood Publishing Ltd, Coll House, Westergate, Chichester, England, 2001. P. 445.
8. ??????????? ????????? ? ????????? ????????? ??????? NaF-AlF3-CaF2-Al2O3 / ?.?.
?????, ?.?. ???????, ?.?. ???????, ?.?. ????????, ?.?. ???????// ?????? ?????????? ???????????? ????????????. ??????? ? ??????????. 2008. ?1. ?. 47-57.
Electroconductivity Slurry-Electrolyte
of the Molten System NaF-AlF3-CaF2-Al2O3
Kirill B. Bakina, ?lga N. Simakovaa,
Peter V. Polyakova, Yurii G. Mikhaleva,
Dmytrii A. Simakovb and Alexandr O. Gusevb
a
Siberian Federal University,
79 Svobodny, Krasnoyarsk, 660041 Russia
b
RUSAL ETC Ltd, RUSAL,
37/1 Pogranichnikov, Krasnoyarsk, 660111 Russia
Electroconductivity ?f the molten system NaF-AlF3-Al2O3 with addition of 5 % wt.CaF2 at molar cryolite
ratio (CR) in the range of 1.2 to 2.0 was studied. Empirical equation describing electroconductivity of
the molten system Na3AlF6 -AlF3-5 % wt. ??F2-Al2O3 as a function of molar cryolite ratio, undissolved
alumina (Al2O3) content and temperature was derived on the basis of experimental data:
ln? =3,53986 + 1,56·10 -3·?? ? 14,99·10 -3·w(Al2O3) -3476,07/T,
where CR ? molar cryolite ratio, w (Al2O3) ? undissolved alumina content, % vol., T- temperature, K.
Keywords: Electroconductivity, range, addition, molar cryolite ratio, melt.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 170-178
~~~
??? 532.614+546.873
?????????? ?????????????? ?????????
Bi2O3-GeO2 c ??????? ? ????????
?.?. ????????, ?.?. ????????,
?.?. ???????*, ?.?. ????, ?.?. ????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
??????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 ? ??????? ? ????????
??????? ??????? ?????. ???????????, ??? ??? ???????? ?????????? ?????? ???????????
?? ???????, ????? ??? ?? ?????? ?????????? ??????????? ???? ??????????. ?? ???? ???????
??????? ???????-??????? ?????????????? ???????????? Au ? Ag ? ???????? ?????????.
???????? ?????: ??????????, ??????? ????, ???????, ??????, ???????, ?????? ??????? ?
????????.
????????
? ??????? ??????????? ??????? ?? ?????????? ??????? ? ?????????? ??????? Bi2O3-GeO2,
??? ??????? ? ???????? ? ??? ?????? ? ???????????? ????? ?????? ??????? [1-4]. ????????? ?
???????????? ???? ???????????? ??? ????????? ?? ??????? ? ??????????? ??????????????,
??? ? ???????? [5-8]. ????????, ??? ???????? ????? ????????? ??????? ?? ???????? ?????????? [8]. ???????????, ??? ???? ???????? ?????? ??????? ???????? ??????? ?? ????????? ??????????, ???????????? ??? ?? ?????????: Pt ? ???????; Au ? ?????????? ??? ??????????;
SiO2 ? ??????, ? ????????? ??????? ? ????????????. ????????? ???????? ?????? ????? ??
???????????? ?????? ????? ??????. ? ????????, ?????????? ? ?????? ?? Au, ??? ??????????,
? ?? ????? ??? ???????????? ?????? ?????? ??? ??????, ?????????? ? ?????????? ??????.
????????? ????????? ? ??????????? ???????????, ??????? ?????????? ?? ????? ??????? ??????. ???????? ??????? ??????????? ??????????? ? ???????, ?????????????? ? ?????? ?? Al2O3
? SiO2. ????????? ??????? ?????????? ??-?? ??????? ????? ?????? ? ??????? ????????. ??????? ???????????? ??????????? ?????????????? ????????? Bi2O3-GeO2 ? Au ? Ag ????????????
??? ????????????, ??? ? ??????? ???????.
???????????
????? ?? ?????????? Au ? Ag ?????????? Bi2O3-GeO2 ???? ?? ??????? ??? ??????????
??????? ??????? ? ????????. ?????????? ??????, ?????????? ????????????? Canon EOS 400
*
1
Corresponding author E-mail address: antluba@mail.ru
© Siberian Federal University. All rights reserved
# 170 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????? 1. ???? ???????? Bi2O3-GeO2 ?? ? ????? ??????????? ?????????????? ? ???????
0
??????
???? ???????? ?????
??????????? ??????????????
????-???????
5
??????
???????
10
??????
???????
?????????? GeO2, ???. %
???? ???????? ????????
15
?????????-?????????
????-???????
20
??????-??????
??????-???????
25
???????
??????-???????
30
???????
????-???????
32
???????
????-???????
35
???????
???????????
37
???????
???????????
?
?
?
?
???. 1. ??????????? ??????? ????? ?????????? ?? ??????????? ? ??????? (Bi2O3 ? GeO2) ? Au: ? ? Bi2O3;
? ? Bi2O3 +10 % GeO2; ? ? Bi12GeO20; ? ? Bi2O3 + 37 % GeO2
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
Digital, ???????????? ?? ?????????? ? ??????????? ?????????. ??? ????????????? ????????
???????????? Bi2O3 ? GeO2 ? ???, Au ? 99,99 ? Ag ? 99,99. ?????? ????????? ?????? ????????? ? ??????? ?????????? ???????????? ?????????? JEOL JSM 7001F ? ????????????????????
???????????? INCA Energy PentaFETx3.
?????????? ? ?? ??????????
???????????? ?? ??????????? ?????????????? ???????? ?????? ? ?????????? Bi2O3-GeO2,
?????????? 0, 5, 10, 15, 20, 25, 30, 32, 35 ? 37 ???. % GeO2, ????????? ? ??????????? ?? ???????
???????? ??? ? ???????????. ???????????, ??? ??? ??????????? ?? ??????? ????????? ???????
???? ?????????? ????????? ???????????? ???????? ????? ????? ???????? ??? ? ? ??????? 60
??? ?? ?????? ?????? ????????. ??? ????????? ??????? ??????? ??????????? ?? ??????????
Au ?????????? Bi2O3-GeO2. ? ???????? ??????? ?? ???. 1 ????????? ????????? ?????????? ??
?????????????? ?????? ? ???????. ??? ?????? ????????????? ???????? ????????? ????????
???????? ??????????? ? = f(T). ?? ???. 1 ???????, ??? ??? ????? ?????????? ????????. ???????? [9] ??? ??????????????? ? ?????????? ?????????????? ??????? ? ????????. ???????
????????? ??????????? ?????????? ??? ?????????? ????????? ? ???, ??? ??? ?????????
??????????? ???????????? ???????? ?????????????? ???????? ? ??????? ????? (??????????
???????, ??????????? ? ?.?.). ?????????????, ??? ??????? ????? ??????????? ?????????????? ?
Au ???????? ???? ???? (????. 1). ??? ????? ??????? ?????????????? ?????????? ??????????
??????? ? ??????? ??????? ? ????????.
?? ???. 2-4 ???????? ?????????????????? ??????? ?????????? ????????? ?????? ?????
???????? ? ???????. ?????, ??? ?? ???? ??????? ? ?????? ???????????? ?????? (??? ???? ??????-
???. 2. ???????? ?????? Bi2O3 ????? ??????????? ?????????????? ? ??????? ? ??????????????????
??????? ???????, ?????????, ?????? (?????????? ??3000)
# 172 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
???. 3. ???????? ????????? ????? ?????? 65 ???. % Bi2O3 ? 35 ???. % GeO2 ????? ???????????
?????????????? ? ??????? ? ?????????????????? ??????? ???????, ?????????, ???????? ? ??????
(?????????? ??3000)
??? ????????????? ???????? ????????? ???????? ??????????? ??????????). ????? ????????,
??? ?????? ? ?????? ????? ????? ?????????? ?????????????.
???????? ????????? ?????? ? ?????????? Bi 2O3-GeO2 ?????????????? ????????? ???????????. ?????? ????? ??????? ??? ????? ??????????? ????????? ???????? ??????? ????
?????????? 45? (???. 1 ?). ?????, ?? ???? ????? ???????????, ???????? ? ???????????.
???????? ??????? ?????????? ? ?????????? ??? ? > 1160 ?. ?? ?????? [10], ????????????? ???????????? ??????? ??????? ??????? ? ???????? ????????? ???????? ??????????
?????? ????????????????? ??????????? ????????????? ????????? ????? ??????????????? ??????. ? ?? ?? ????? ?????? ????? ?? ??????????, ? ????????????? ????????? ? ???
?????? ? ???? [10]. ? ?????? [11] ???????? ????????? ????????? ??????????? ???? ??
????????? ?????? ?????????? ???????? ??????????????? ??????? ????????? O2. ???????????? ???? ?? ??????? ??????????? ???????????? ???????? ?????? ?????? ????????, ???
??? ????? ????????? ?????? ?? ??????????? 470 ?. ??? ???? ??????????? ???????????
# 173 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
???. 4. ???????? ????????? ????? ?????? 95 ???. % Bi2O3 ? 5 ???. % GeO2 ????? ??????????? ??????????????
? ??????? ? ?????????????????? ??????? ???????, ?????????, ???????? ? ?????? (?????????? ??3000)
?????????????? ?????????? ?????????? ????????? ?? ??????????? ??????. ??? ?? ?????,
??? ??? 480 ? ?????????? ??????????? ?????????? ?????? ?????? ? ????????? ?????????
? ??????????????? ?????????????? ????????? ???????????. ???????, ??? ?????????? ????????????? ?????? ? ????????????? ????????? Bi 2O3-GeO2 ??????? ?? ??????? ????????
?????????:
C GeO , ???. %
0
5
30
32
35
CAu, ??. %
0,23
0,21
0,14
0,10
0,08
2
??? ??? ?????? ????????? ????????????, ??? ??????????? Au ? ???????? ?????????
Bi2O3-GeO2 ???? ?????????? ?? ???? ??????????? ??????? ? ???? ?? ????????? [5, 6], ????
???? ?????????? ???????????.
???????????? ??????????? ?????????????? Ag ? ?????????? Bi2O3-GeO2 ????????? ??? ?????????? 0, 5, 10, 20, 25, 30, 32, 35 ? 37 ???. % GeO2. ?? ???? ????????, ? ??????? ?? Au, ????????
# 174 #
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?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
???. 5. ???????? ?????????? ????????? ??????? Bi2O3 ? GeO2 ?? ??????? 1 ? 37 % ???. % GeO2; 2 ? 32 ???. %
GeO2; 3 ? Bi12GeO20; 4 ? 20 ???. % GeO2
? ??????????? 0, 5 ? 10 ???. % GeO2 ????? ???????? ????? ???????????, ? ??????? ???? ?? ???????????????. ?????? ?? Bi2O3 ????? ?????????? ?? Ag ????? ????-??????????? ???????. ????????
??????????? ???????????????? ??????? ??? ????? ????????? ?????????. ??????????? ?????? ???????, ??? ? ??? ?????????? (4,8 ± 0,2) ???. % Ag. ??????? ??????? ? ??????? Ag ? Bi2O3 ?????
???? ???????, ??? ??? ? ??????? Ag?Bi?O ????? ?????????????? ?????????? Ag5BiO4, Ag3BiO3,
Ag18BiO12, Ag25Bi3O18 [12]. ????? ????, ? ??????? Ag ? Bi2O3 ?? ??????? (??? ? ? ???????? ?????????????) ??? ??????????? 984 ? ?????????? ?????????, ????????? ? ??????? Bi2O3.
????????? ??????, ??????????? 5 ? 10 ???. % GeO2, ????? ???????? ???? ???? ? ???????
?? ??????-??????????. ???????? ???? ??????????? ? ????? ? ??????????? 20 ???. % GeO2,
??????? ??????????? ?? ???????? ?? ??????? ? ??????? 30 ?.
??? ?????????? Ag ????????? Bi2O3 + 25 ???. % GeO2 ????? ?????????? ????????????? ??
70 ?. ????????????? ????????????? ? ???????? ?????????? ????? ??????????. ??? ? ? ??????
???????? ? ??????????? 20 ???. % GeO2, ???? ????????? ????? ???????? ? ????-??????? ??
??????-??????????.
?????????? ?????????? ?????????? ? ???????? ????????? GeO2 ???????? ? ??????????
??? ???????? ?, ??? ? ??????? ?????????? (???. 5). ????????? ????? ???? ??????? ? ??????
???????? ????????? Bi2O3-GeO2 ??? ?????????? ???????????? GeO2 [2].
????????? ?????? Bi2O3-GeO2 ????? ??????????? ?????????????? ? Ag ? ?????????????????? ??????? ???????? ?? ???. 6-7. ?? ???? ?????? ???????, ??? ? ??????? ?? ?????? ??????? ?
??????? Bi2O3-GeO2 ????? ???????????? ?????????????.
??????????
??????? ?????????????? ???????? ????????? Bi2O3-GeO2 ? ??????? ??????? ? ????????.
???????????, ??? ?????????? ??????????? ??????? ???????? ? ???????? ?????????. ???????
?? ????????????? ????????? ? ???????? ?????????? ????????? ??? ????????? Bi2O3-GeO2. ?????? ????? ???????????? ??? ???? ?????, ?? ??? ?????????? ??????? ?????????? ?????? ????????.
# 175 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 6. ???????? ?????? ??????? 25 ???. % GeO2 ? 75 ???. % Bi2O3 ????? ??????????? ?????????????? ?
???????? ? ?????????????????? ??????? ???????, ?????????, ????????, ???????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
???. 7. ???????? ?????? ??????? 5 ???. % GeO2 ? 95 ???. % Bi2O3 ????? ??????????? ?????????????? ?
???????? ? ?????????????????? ??????? ???????, ?????????, ????????, ???????
?????? ??????????
1. ?????, ?.?. ?????????????? ????????? ? ???????? ???????????????? ???????? /
?.?. ?????. ? ?.: ???? ?????, 2003. ?163 ?.
2. ???????, ?.?. ????????????????? ?????????: ???????? ? ??????-?????????? ???????? / ?.?. ???????, ?.?. ?????????, ?.?. ???????, ?.?. ????????, ?.?. ???????, ?.?. ????????. ? ????????????: ??? ???, 2000. ? 527 ?.
3. ???????, ?.?. ???????? ? ??? ???????? / ?.?. ???????, ?.?. ???????, ?.?. ????????,
?.?. ???????????, ?.?. ???????. ? ????????????: ??? ???, 2002. ? 600 ?.
4. ???????, ?.?. ???????? ? ???????? ????????????? ??????? / ?.?. ???????, ?.?. ?????????, ?.?. ??????? ?.?. ????????, ?.?. ????????. ? ????????????: ??? ???, 1999. ? 499 ?.
5. ?????????????, ?.?. ?????????????? ??????? ? ?????????????? ?????????????????
???????? / ?.?. ????????????? // ??????????? ????. ? ?.?.?. ? ?.: ????, 1983. ? 24 ?.
# 177 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ????????, ?.?. ????????? ?????????? ?????????????? ????????? Bi2O3-GeO2 c ??????? ? ????????
6. ????????, ?.?. ????????????? Pt ? ????????? ??????? Bi2O3-?xOy, ??? ? ? Si, Ti, Ge, Zn,
Cd / ?.?. ????????, ?.?. ????????, ?.?. ????????? ? ??. / ???. ?? ????. ??????. ?????????. ?
1981. ? ?. 17. ? 4. ? ?. 663 ? 668.
7. ???????, ?.?. ???????????? ??????????? ?????????????? ????????? ?? ?????? ??????
??????? ? ???????? ????????? ? ???????? / ?.?. ???????, ?.?. ??????, ?.?. ???????? ? ??.
// ???. ?? ????. ???????. ?????????. ? 1991. ? ?. 27. ? 4. ? ?. 763 ? 765.
8. Lezal, D. Heavy metal oxide glasses: preparation and physical properties / D. Lezal, J. Pedlikova,
P. Kostka, J. Bludska, M. Poulain, J. Zavadil // J. Non-Cryst. Solids.- 2001. ? V. 294. ? P. 288 ? 295.
9. ????, ?.?. ??????-?????????? ?????? ?????????? ? ?????????? / ?.?. ????, ?.?. ???????.- ?.: ?????, 1976.- 232 ?.
10. ???????, ?.?. ??????????? ?????????????????? ?????? ? ???????? ?????????/
?.?. ???????, ?.?. ????, ?.?. ?????? // ???. ? 1965. ?. 39. ? ? 4. ?. 966?972.
11. ???????????, ?.?. ????????? ??????????? ?????????? ?????? ? ???????????? ???????
????????????? ??????????????? ????????????? ????????? ????????? ? ??????? ???????? ????? / ?.?. ????????????, ?.?. ??????, ?.?. ??????? // ????. ????. ??-??. ???. 2. ?????. ? 2007. ?
?. 48. ? ? 6. ? ?. 418 ? 426.
12. Assa,l J. Experimental phase diagram study and thermodynamic optimization of the Ag ?
Bi ? O system / J. Assal, B. Hallstedt, L.T. Gauckler // J. Am. Ceram. Soc. ? 1999. ? V. 82. ? ? 3. ?
P. 711 ? 715.
Contact Interaction of BI2O3-GEO2 Melts
with Gold and Silver
Liubov T. Denisova,
Oksana V. Kuchumova, Viktor M. Denisov,
Galina M. Zeer and Inessa V. Gricenko
Siberian Federal University,
79 Svobodny, Krasnoyarsk 660041 Russia
Contact interaction of Bi2O3-GeO2 melts with gold and silver was investigated by the sessile drop
method. It was found that these melts spread over the silver surface rather rapidly whereas equilibrium
wetting angles formed on gold. In all cases the melt-solid contact was followed by the dissolution of
gold and silver in the oxide melts.
Keywords: wetting, contact angle, melt, gold, silver, bismuth oxide, germanium oxide.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 179-184
~~~
??? 528.852.8
Using Moving Variance Method
to Detect Ocean Currents from Space
Artem V. Khodyaeva*, Anatoliy P. Shevyrnogova,
Galina S. Vysotskayab and Olga S. Kozikovaa
a
Institute of Biophysics, Siberian Branch
of Russian Academy of Sciences,
Russia 660036, Krasnoyarsk, Akademgorodok, 50/50
b
Institute of Computational Modeling, Siberian Branch
of Russian Academy of Sciences,
Russia 660036, Krasnoyarsk, Akademgorodok 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
This research based on using of moving variance method is directed on detection of global ocean
currents and other dynamic processes using multi satellite data. This method is based on the
statistical treatment of seasonal composites of sea surface temperature and phytoplankton pigments
concentration satellite imagery. Digital map of ocean currents and oceanic frontal features was
generated using moving variance method. Special software using IDL language for statistical
treatment was developed.
Keywords: global ocean currents, ocean color remote sensing, moving variance.
1. Introduction
Currents in the ocean can be observed using indirect signs. It can be changes of sea surface
temperature (SST) or phytoplankton. Another name for such signs is tracer agents. Tracer agents can
be detected by passive sensors in visible and infrared thermal channels. These tracers visualize ocean
currents in visible and infrared bands.
The NASA?s Sea-viewing Wide Field-of-view Sensor (SeaWiFS), Advanced Very High Resolution
Radiometer (AVHRR) and Moderate Resolution Imaging Spectroradiometer (MODIS) provide
images of such tracers. In order to detect ocean structure we should firstly understand the structure of
phytoplankton and SST fields.
In seminal worldwide survey of oceanic fronts, Legeskis (1978) demonstrated a variety of
SST fronts formed by vastly different physical processes. Shevyrnogov et al. have developed the
special scientific program named ?Chlorophyll in the bioshpere? and clearly shown the relation
between dynamics of phytoplankton and large- and small-scale hydrological structure of the
ocean.
*
1
Corresponding author E-mail address: artymail@mail.ru
© Siberian Federal University. All rights reserved
# 179 #
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Artem V. Khodyaev, Anatoliy P. Shevyrnogov? Using Moving Variance Method to Detect Ocean Currents from Space
Based on mathematical model Kartushinsky (2004) estimated the spatial and temporal ranges
of the SST frontal zones variation affected by the advection of currents, horizontal turbulent heat
exchange, and the radiation heat flow in separate parts of the ocean.
It is necessary to develop the image processing tool based on statistical treatment for allocation of
oceanic structures. C.A. Brown et al. [3] uses clustering and principal component analysis to define the
relationship between chlorophyll and ocean color. A. Turiel et al. [4] shown that the use of advanced
image processing tools as wavelet singularity analysis allows to characterize the oceanic circulation
patterns. Using statistical EOF analysis is it possible to explain the general seasonal cycle and quantify
interannual variability of chlorophyll-a [5].
2. Methods and data
In a manner analogous to method of Shevyrnogov et al., 1996 we use a ?moving variance? statistical
method to reveal global ocean structure features [6]. Moving variance or quasistationary areas method
is based on the statistical treatment of seasonal composites of satellite imagery. Quasistationary areas
it is areas with the same type of seasonal dynamics. It means that change of parameter (chl-a or sst) in
these areas occur equally.
The basis of the given approach is made by a box which moves on images and applies the following
algorithm.
Let Ak ,i , j ^am ,n | m i q, i q, n j q, j q` is a set of pixels in a square with centre (i, j) for
each season K. Dk,i,j is a standard deviation for Ak,i,j. Moving variance Vi,j at the point (i, j) is a mean
for D1,i,j, D2,i,j, D3,i,j, D4,i,j. For those areas where values change slowly values of moving variance are
insignificant but it sharply increases where seasonal dynamics varies. Depending on parameters of a
box areas with various spatial scales are allocated.
Shevyrnogov et al. [7] have shown that quasistationary areas can be a basis for the characteristic
of fundamental biological and hydrological processes in the ocean. It can be a basis for definition of
long-term trends of biological efficiency in the ocean. The continuous control of quasistationary areas
reveals abnormal conditions of oceanic ecosystems.
Nine years of SeaWiFS satellite data from 1997-2005 were used to produce seasonal means and
standard deviation estimates of chlorophyll-a concentrations for the global ocean. Seven years of
MODIS imagery for 2002-2008 and twenty one years of AVHRR imagery for 1981-2001 were used
to produce seasonal means and standard deviations of sea surface temperature for the global ocean.
These images were downloaded from NASA?s ocean color website.
Statistical techniques for data mining are designed to extract useful information from large
datasets and include methods such as moving mean, moving variance, smoothing of input and output
data. Special software was developed using IDL (interactive data language). As a result more than 100
images has been obtained and analyzed.
3. Results and discussion
The fi rst set of data we used was chlorophyll-a distribution imagery. The results are shown
in Fig. 1.
Dark areas correspond to the lowest values of variance, light areas it is areas with high variability
and instability of phytopigment concentrations during one year.
# 180 #
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Artem V. Khodyaev, Anatoliy P. Shevyrnogov? Using Moving Variance Method to Detect Ocean Currents from Space
Fig.1. Areas with the same type of seasonal dynamics (QSA) from 264th day of 1997 till 263rd day of 1998
Fig. 2. Areas with the same type of seasonal dynamics (QSA) from 264th day of 2006 till 263rd day of 2007
Fig.1 shows the end of summer and the beginning of autumn. Almost the same picture we can see
after nine years (Fig. 2).
These two images (Fig.1 and Fig.2) accurately allocate ocean structure. For instance, the map of
QSAs in the Atlantic and the Pacific Oceans clearly shows the boundaries of the shelf waters at the
western and the eastern coasts of the USA.
The next portion of data is satellite images of sea surface temperature. The results are shown in
Fig. 3.
Here we have another type of colouring. Dark pixels corresponds to the high instability areas and
light pixels belongs to areas with low variability of sea surface temperature.
Changing the size of a box it is possible to allocate structures of various scales. The smaller size
of a box gives more detailed picture however brings more noise in the image. Nevertheless, the big size
# 181 #
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Artem V. Khodyaev, Anatoliy P. Shevyrnogov? Using Moving Variance Method to Detect Ocean Currents from Space
Fig. 3. Areas with the same type of seasonal dynamics (QSA) from 172nd day of 2002 till 171st day of 2003
Fig. 4. Schematically image of Brazil Current
of a box smoothes border of oceanic structures, the smaller box accurately allocates it. The results are
shown in Fig. 4 and Fig. 5a, 5b.
4. Summary and conclusion
Method of ocean structure revealing was developed. This method is based on detecting of
quasistationary areas using ?moving variance? algorithm. We have improved this algorithm to detecting
areas with different spatial scales.
More than 1000 images have been processed. The ocean structure has been allocated using images
of chlorophyll concentration and sea surface temperature [8].
Seasonal dynamics of chlorophyll concentrations and sea surface temperature in the ocean is one
of the key factors indicating the types and intensity of hydrobiological exchange processes in the ocean
surface layer [9].
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Artem V. Khodyaev, Anatoliy P. Shevyrnogov? Using Moving Variance Method to Detect Ocean Currents from Space
Fig. 5a. Brazil Current after QSA treatment (2003,
21x21 pixel box)
Fig. 5b. Brazil Current after QSA treatment (2003,
11x11 pixel box)
By focusing on the seasonal dynamics, we developed a useful observational tool for characterizing
the type of dynamics.
Ocean structure revealed with the help of ?moving variance? algorithm may form the grounds to
characterize the fundamental processes of ocean biology and hydrology and helps to determine longterm trends of biological productivity in the global ocean. It also can help to check a hypothesis of
global thermohaline circulation by detecting a global path of heat-and-mass transfer in the ocean.
References
1. Legeckis, R., A survey of worldwide sea surface temperature fronts detected by environmental
satellites, Journal of Geophysical Research 83 (C9), 1978
2. Kartushinsky, A., The investigation on the dynamics of frontal zones in the ocean based
on the numerical modelling, using the AVHRR satellite data, Advances in Space Research 33 (7),
2004
3. Brown, C.A., Huot, Y., Werdell, P.J., Gentili, B., Claustre, H., The origin and global distribution of
second order variability in satellite ocean color and its potential applications to algorithm development,
Remote Sensing of Environment 112, 2008
4. Turiel, A., Sole, J., Nieves, V., Ballabrera-Poy, J., Garcia-Ladona, E., Tracking oceanic
currents by singularity analysis of Microwave Sea Surface Temperature images, Remote Sensing of
Environment 112, 2008
5. Radiarta, I.N., Saitoh, S.-I., Satellite-derived measurements of spatial and temporal chlorophyll-a
variability in Funka Bay, southwestern Hokkaido, Japan, Estuarine, Coastal and Shelf Science 79,
2008
6. Shevyrnogov, A., Vysotskaya, G., Gitelzon, J., Quasistationary areas of chlorophyll concentration
in the world ocean as observed satellite data, Advances in Space Research 18 (7), 1996
7. Shevyrnogov, A., Remote methods of biosphere studies at the Institute of biophysics of the
Siberian Branch of the Russian Academy of Sciences (Stages of Development), Solnechno-zemnaya
fizika 5, 2004
8. SeaWiFS Chlorophyll [??????????? ??????] / National Oceanic and Atmospheric
Administration. ? ????? ??????? : http://oceandata.sci.gsfc.nasa.gov/SeaWiFS/Mapped, ?????????. ? ????. ? ??????. ? ??. ????.
# 183 #
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Artem V. Khodyaev, Anatoliy P. Shevyrnogov? Using Moving Variance Method to Detect Ocean Currents from Space
9. MODIS Global Sea Surface Temperature [??????????? ??????] / National Oceanic and
Atmospheric Administration. ? ????? ??????? : ftp://oceans.gsfc.nasa.gov/MODISA, ?????????. ?
????. ? ??????. ? ??. ????.
??????????? ???????????? ???????
??????? ?????????? ????????? ?? ???????
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?.?. ?????????, ?.?. ?????????
?
???????? ????????? ?? ???,
?????? 660036, ??????????, ?????????????, 50/50
?
???????? ??????????????? ????????????? ?? ???,
?????? 660036, ??????????, ?????????????
?????? ?????? ???????????? ?????? ?????????? ????????????? ?????? ??????????
????????? ??? ??????????? ??????? ???????? ?????? ?? ??????, ?????????? ?? ????????
SeaWiFS ? MODIS. ?????? ????? ??????? ?? ?????????????? ????????? ???????? ??????????
??????????? ???????????? ????????????? ? ????????????? ???? ?????? ? ???????????
??????????? ???????????. ? ?????????? ???????????? ???? ????????? ???????? ?????
???????????? ??????? ? ??????????? ???. ??????????? ???????????, ???????????? ???
????????, ???? ??????????? ? ?????????????? ?????????????? ????? ?????? IDL.
???????? ?????: ???????????? ???????, ????????????? ???????????? ??????, ??????????
?????????.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 185-192
~~~
??? 621.3.029.6
???????????? ????????????
?????????????????????
????????????????????? ?????????????
?.?. ?????????, ?.?. ???????*
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
???????????? ? ???????????????? ??????????? ??????????? ???????????????? ????????????
???????????? ????????????????????? ????????????? ?? ?????? ????????? ?????????
?????????. ???????? ????????????? ?????????, ??????????? ???????? ?????????
??????????: ???????? ???????????? ?????? ????, ????????????? ?????? ?????? ???????????,
??????????? ??????????????? ????????????? ????????????? ??????? ????????? ? ??????????
???????????. ???????? ??????? ???????? ???????????? ????????????? ? ????????????
?????????? ??????? ??????????? ? ???????????????? ???????????. ????????? ??????
?????????????????? ???????????? ??????????????????? ????????????? ?? ????????????
??????????????? ?????????, ? ??????? ???????? ???? ????????????? ??????? ?????????
?????????? ????? ??????? ? ????????? ?? ??????. ???????? ??????????????? ?????????????
?????????????? ?????????? ? ????????????? ? ????????????? ?????????? ???? ????.
???????? ?????: ?????????????, ?????? ????????, ??????????????? ??????, ???????????
?????????, ???????? ????????.
????????
??????????????? ????????????? ???????? ?????????? ?????????? ???????????? ???????? ??????? ???????????????? ???????, ??? ???????????? ????? ? ??????????? ????????
?????, ? ????????? ????????????? ? ??????????? ???????????????. ????? ???? ?????????? [1]
? ????? ??????????? [2] ??????????? ??????????? ???????????????? ???????????? ???????????? ????????????????????? ?????????????. ?????????? ????? ????????????? ????????????
????? ??????????????? ??????, ? ??????? ? ???????? ???????? ???????????? ?????? ???????? (??). ????????? ??????? ??????????? ??????????????? ????????????? ? ?? ? ?????
??????????? ?????????? ??????????? ?????????? ????? ???????????????? ???-?????????
????? ????????? ??????????, ??????????????? ????? ???????????????? ???????????? ?
???????. ??? ???? ??????? ??????????? ??????????? ?????????? ??????????? ????????,
??? ? ????????????? ? ??? ?? ????????? ???????????? ???????? ??????, ?? ???????????? ?
???? ??????????????? ????? ????????, ??????????? ??. ????????????? ??????????? ???*
1
Corresponding author E-mail address: konstl@rambler.ru
© Siberian Federal University. All rights reserved
# 185 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
???. 1. ??????????? ? ????????? ??????????? ????????????????? ?????????????
???????? ????? ????? ??????????? ??????? ?????? ??????????? ?? ?????? ?? ???????? ? ???????????? ?? ????? ????????, ??? ??? ??????????? ?? ??????????? ? ? ?????????? ?????????
??????. ?? ???. 1 ???????? ??????????? ?????????????, ?????????? ?? ???? ???????????.
????????? ????????????? ?????? ?????? ????????, ??????? ???????????? ?????? ?????????????? ????????? ????? ??????? ???????????? ??????????? ? ?????? ? ???????.
????? ??????????? ???????? ???????????, ?????????, ????????, ???????????? ??????????
????????? ?? ???????? ?? ??????. ???? ? ????? ????????????? ???????????? ? ???????
?????? ???????? ? ???????? ?????????????? 50 ??.
?????????? ????????????? ????????????
??? ???????? ??????????? ????? ???????????? [2], ? ??????????? ??????????? ????????????? ???????? ???????????? ???????? ?????? ???????, ? ?????? ???????, ?? ????????? ??????????: ????????????? ?????? ?????? ??????????? ??????????, ?????????? ???????????
? ??? ? ??????????? ??????????????? ????????????? ??. ??????, ?????????? ??????????
?????? ???????????? ????????, ? ??????????????? ???????????? ??????????? ??????????? ??
???????????. ? ????? ? ???? ?????? ???????? ????????? ????????????? ??????????? ???????? ???????????? ???????? ?????? ???????????? ????????????? ?? ??? ???????? ?????????????? ? ????????????? ??????????.
?????? ????????? ???????????: ???????? ???????????? ???????? ?????? ? ??, ?????????? ??????????? ? ????????????? ? n, ?????? ?????? ??????? ?????? ????????????? ? ?f ,
?????? ?????? ??????????? ?????????? ? ?f , ???????? ?????????? ? ?????????? ?????????
?????????????? ????? ??????????????? ????????????? ?? ? ?|| ? ? ? , ??????????? ??????????????? ????????????? ? ??= ?|| ? ??, ??????? ???????? ??????????????? ????????????? ?? ?
?= (?|| ? ??)/2.
??????? ?????????, ??????????? ????????????? ?????? ?????? ??????????? ???????
?f f 0 ? ????????????? ??????? ?????? ??????? ?????? ?????????? ?f f 0 . ???????????, ???
??? ??????? ???????? ??????????????? ????????????? ?? ?????????? ????? ???????????
# 186 #
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?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
???. 2. ??????????-????????? ?????????????? ?????????? ??? ??????? ???????? ???????????????
????????????? ?? (?) ? ?????????? ????????? ? (?)
??????? ?????? ??????????? f0 ? ?????????? ?????? ?????? ??????????? ?f ?? ?????? -3 ??
(???. 2?). ????? ??? ????????? ??????????????? ????????????? ?? ??? ????????? ???????????? ????, ????? ??????????? ????? ?????? ??????????? ?? ??????????-????????? ?????????????? (???), ?????? ??? ???? ?????????? ??????? ??????? ?????? ?????????? ?f , ? ????????
??????? ?????? ?????? ?????????? ??????? ???????? ???????????? ? ????? ???????????,
? ?? ????? ??? ???? ????????? ??????? ??????????? ?????????? (???. 2?).
????? ??? ????????? ???????????? ???? ??????????????? ????????????? ?? ???????
??????????? ????????? ???????? ?|| = ? + ?? 2 , ????? ??????????? ??????? ?????? ???????????
?????? ?????? f 0? = f 0
?
, ? ??????? ? ?????? ??????? ?????? ??????????? f ?c ? f ?c , ??????||
??????????. ? ?????????? ???????????? ???? ??????????????? ????????????? ?? ??????????? ?? ? A = ? ?? . ??? ???? ??????????? ??????? ?????????? ?????? f 0cc
2
f0
H
, ? ???????
HA
? ?????? ????????? ??????? f ?cc ? f ?cc ?????????????? (???. 2?). ??????? ????????, ??? ???
??????????? ??-?? ????????? ????????????? ????? ????? ???????????? ???????? ? ??????
?????? ??????????? ??????????, ?????? ??? ????????? ???? (????????? ?????????), ? ?? ?
?????? ??????????? ????? ??????????.
??????? ????????? ??? ?????? ?????? ??????? ?????? ?????????????:
# 187 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
???. 3. ??????????-????????? ? ????-????????? ?????????????? ?????????? ???????
Gf
f ?c f ?cc
§ c 'f · § cc 'f ·
Ё f0 ё Ё f0 ё
2 № ©
2 №
©
f 0c f 0cc 'f
(1)
?????????? ????????? ??? f 0c ? f 0cc , ???????:
Gf
f0
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H
f0
'f .
H?||
HA
(2)
???????? ?? f0, ???????? ? ????????????? ?????????:
Gf f 0
H
H
'f f 0 .
?H||
HA
(3)
?????? ??????? ????????? ??? ????????? ??????????? ?? ? ???????? ????????????? ?????? ?????? ??????? ?????? ????????????? ?f f 0 ????? ??????????? ????????????? ?????? ?????? ??????????? ?????????? ??? ??????? ?f f 0 .
????? ???????, ??? ? ?????? ??????????? ?f ?????????? ???? ?????????? ??????? (???
????? ? ?????? ??????????? ??? ?????????? ??????????? ???????????) ?? ???????? ?
(???. 3).
????? ??????????? ?????? ???? ?? ??????? ????? ? ????? ?????? ??????????? ????????
?( f ) = k ( f ? f 0 ) + d ? , ??? f0 ? d? ? ?????????, ? ??????????? ?????????????????? k =
?
.
?f
??? ????????? ??????????? ??????? ?? f 0?? ?? f 0? ???????? ?????? ???? ? ??????? ??????
?????? ???????? ?? = k ( f 0?? ? f 0? ) . ?????????? ????????? ??? k, f 0?? ? f 0? , ???????:
?? =
? ? ?
? ?
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?.
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??|| ??
?f f 0 ? ? ?
?
# 188 #
(4)
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?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
??????? ?f f 0 ????? ?f f 0 ? ??????? ??????? (3) ? ?????????? ??? ???????? ? (4), ???????:
? ?
?
? ?
?
?.
?? =
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(5)
? ?
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??? ???? ??????? ?????????, ??? ? ? ?? ? ??? ??????? ???????? ? ??????????? ??????????? ??????????????? ????????????? ?? ????????. ???????? ????????? ???? ? ? ?????? ??????????? ?????????? ?f ??? ????? ??????????? n>1 ????? ??????????? ? ????
?(n)=0.7Ч(n-1)Ч180є [3].
?????????? (6) ? (5), ???????????? ????????:
?? =
?
.
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(7)
????? ???????, ??????? (7) ????????? ??????????? ???????? ???????????? ????????
?????? ? ??????? ?????? ?????? ?? ?????????? ??????????? ?????????????, ????????????? ?????? ?????? ??????? ?????? ? ???????? ??????????? ??????????????? ????????????? ??.
??? ???????? ??????????? ???? ????????? ??????????? ???????? ???????????? ???????? ?????? ?? ????????????? ?????? ?????? ??????? ?????? ???????????? ?????????????
(???. 4).
?????? ???? ?????????? ? ???????????????? ??????????? ? ????????? Microwave Office
? ?? ?????????? ??????? (7). ?????? ????????? ? ??????????? ??????????? n=5 ? n=9 ??? ??????????? ??????????????? ????????????? ?? ??=0,4 ? ??????? ???????? ???????????????
????????????? ?=3.
???????????, ???????????? ? ???????????????? ???????????, ??????? ?? ???? ????????.
??? ??????? ? ???, ??? ????????????? ?????? ?????? ?????? ??????????? ????????????? ??????? ?? ???????? ???????? ????????????? ??????????????? ?????, ?????????? ??? ???????????? ??????? (??? ??? ??????, ??? ?????? ?????? ??????), ? ??? ??????????? ?? ????????
??????????? ????? ?????????? ??????????? (100 ???) ?? ????? ???? ?????????? ????. ????????, ??? ?????????? ?????? ?????? ? ??????????? ????? ??????????? ???????? ?? ??????
????????? ????????? ????????? ?????????, ? ?? ??????????? ??????? ?????? ???????????
??????? ?????? ?????? ??????????? f0 [5]. ??????? ????????????? ?????? ????? ??????????? ?
??????????? ?? ?????? N ?????????? ?????? ? ?????????? ?f/(N f0). ? ????? ? ???? ????? ???????? ????????????? ?????? ?????? ??????? ?????? ???????????? ????????????? ???? ??????????? ?? ???????? ?????? ?????? ???????????. ??? ????? ?? ???. 4, ??????, ???????????? ??
?????????? ??????? (7) ? ? ???????????????? ???????????, ????????? ? ??????? ????????????
???? ? ??????, ??? ????????? ??????? ????? ?? ???????????? ?????????????? ???????????.
# 189 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
???. 4. ??????????? ???????? ???????????? ???????? ?????? ?? ????????????? ?????? ?????? ???????
?????? ???????????? ????????????? (???????? ????? ? ?????? ? ????????? Microwave Office, ?????????
????? ? ?????? ?? ?????????? ???????)
??????????? ???????????? ????????, ??? ??????????? ??????????? ????????????? ????????????? ???????????? ??? ????????????? ??????? ??????? ?????? ??????? ????? 20 %. ?
???? ?????? ?? ???????, ??? ?????? ?????? ????????, ?????????? ??????????? ????????,
??? ? ????????????? ?? ?????? ????????????? ????? ????????, ??????????? ??.
?????????? ????????????????? ????????????
??? ????????????????? ???????? ????????????????? ??????????? ??????????? ??? ???????????? ? ?????????? ????????????? ????????????? ??? ???????? ????????????????????
????? ? ???????? ???? 0,5 ??, ? ??????? ??????????????? ????????????? ??? ?????????????? ??????? ?????????? ? ???????? 2,7 ? 3. ?????????? ??????????? ?? ?????? ?????? ??????????? ? ???, ????? ????????? ??????????? ????? ????, ? ??? ?????????? ???????? ??????????? ? ?? ????????? ??????????? ?? ??????????? ????????? ???????? ???????? 0,3 ??
???????????? ?????????????? ?????? ??????. ??????? ?????? ?????? ?????????? ??????????
?f/f0 =10 % ? ????? ??????????? ??????? f0?26 ???. ????? ???????????? ?????? ????????????? ??????? ????????? ??? ??????????? ?????????? ?? ???????? ????????????? ??????????,
? ????? ?????? ??? ??????? ??????????? ? ????????? ??????? ??? ???????????? ?????????
??????????? ??????? ? ?????????????. ?? ???. 5? ???????????? ???????????? ? ??????????
??????????-????????? ?????????????? ?????????????? ??????, ? ?? ???. 5? ???????? ????????? ??????????? ???????????? ?????? ????. ??? ?????????????? ??????? ?? ????????????
??????? ????????? ???? ?????????????? 3 ??, ?????? ? ???? ?? ??????????? ????? ??????????? ? ????????????? ?????????? ????? ???????????????? ????, ???? ???????? ??????????
???????? ????? ???????????????? ???????????? ? ???????? ??????????. ?? ???. 5? ???????? ?????????? ?????????????? ?????? ?????????????.
?????????? ???????? ???????????? ???????? ?????? ? ?????? ??????? ?????? ?????? ????????? 225°, ??? ?????? ??????????? ? ?????????, ??????????? ?? ?????????? ??????? (7) ?
?????? ??????????????? ?????? ??. ????? ?? ?????? ?????????? ??????? ???????? ?????? ?
# 190 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
???. 5. ??????????-????????? ?????????????? (?), ??????????? ???????????? ???????? ????????????
???????? ?????? ?? ??????? (?) ? ?????????? (?) ?????????????? ????????????? (????? ? ??????, ????? ?
???????????)
????????????, ?? ? ???????????? ??????? ??????????? ????? ???? ? ?????????? ??? ???????
??????? ??? ?????????????. ?????? ???????? ??????????, ???????????? ??? ????????? ???????????? ???????? ???????????? ???????? ?????? ? ??????? ??????? [4] ? ????????????
??? ???????????? ????????? ????????? ??????????? ??????????????, ???????? 30 ????/??.
????? ????????, ??? ?????????????? ?????????? ? ??????? ?? ???????????? ???????? ?
??????????? ??????????????? ????????????? ??=0,3 ? ??????? ???? ??????????????? ??????
tg??0,02. ??? ????????????? ?? ? ??????? ???????????????? [6] ? ??????????? ???????????
????? ???????? ??????????? ??????? ??????????? ??????? ????? ??? ??????? ??????? ?
??????? ?????? ??????.
??????????
? ?????? ???????????? ? ???????????????? ??????????? ??????????? ????????????????
???????????? ???????????? ????????????????????? ?????????????. ???????? ?????????????
?????????, ??????????? ???????? ???????????? ???????? ?????? ? ????????? ??????????????? ? ?????????????? ??????????? ?????????????. ??????????? ???????????? ??????????? ??????????? ???????????? ????????????????????? ????????????? ???????? ?? ???????
????????????? ? ??????????? ????????????? ? ????????????? ? ????????????? ??????????
???? ????. ?????? ???????????? ????????????? ??????????? ???????? ??, ??? ??? ????? ????????? ??????? ???????-????????????? ???????. ? ????????? ??????? ??? ????? ??????????? ????????? ????? ????????? ????????, ??? ??? ??????????? ????????????? ????????????? ? ??? ?????????????? ????????-??????????? ?????????.
?????? ????????? ??? ????????? ??? «??????? ? ??????-?????????????? ????? ????????????? ??????» ?? 2009 ? 2013 ??.
# 191 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ???????. ???????????? ???????????? ????????????????????? ?????????????????????...
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
?????? ??????????
1. ??????, ?.?., ???????, ?.?., ????????, ?.?., ???????, ?.?. ??????????? ????????????? // ?????? ?????? ? 2257648. ?? ? 21. 2005.
2. ???????, ?.?., ?????????, ?.?. ???????????? ??????????? ??????????????? ???????????????????? ????????????? // ??????????? ???????? ????????????????: ??????? ??????? ??????. ??????????: ??? ???, 2009. ?. 111-114.
3. ???????, ?.?., ?????????, ?.?. ???????????? ???????? ???????????? ???????? ?????? ? ??????????? ???????????????? ????????????????????? ????????????? // ???????????
???????? ????????????????: ??????? ??????? ??????. ??????????: ??? ???, 2010. ?. 137141.
4. Vendik, O.G., Vendik I.B., Nikol'ski M.A. Comparison of MMIC phase shifters using figure
of merit as the main characteristic // Proceedings of the 15th International Conference on Microwaves,
Radar and Wireless Communications. 2004. Vol. 1. P. 333-335.
5. ??????, ?.?., ?????????, ?.?. ???????????? ????????????? ????? ??????????? ? ??????????????? ?????? ?????????? ???????????? // ???????????? ? ???????????. 2005. ?. 50.
? 8. ?. 910-917.
6. Muller, S., Goelden, F. Passive phase shifter for W-Band applications using liquid crystals //
Proceedings of the 36th European Microwave Conference. 2006. P. 306?309.
Investigation of the Microwave Controllable
Liquid Crystal Phase Shifter
Aleksey M. Serzhantov and Konstantin V. Lemberg
Siberial Federal University
79 Svobodny, Krasnoyarsk, 660041 Russia
The design of the controllable microstrip liquid crystal phase shifter based on the photonic crystal
structure is theoretically and experimentally investigated. An analytical expression relating the main
parameters of the device: the controlled phase shift, the fractional bandwidth, the anisotropy of the
used liquid crystal permittivity and the number of resonators is obtained. Good agreement between
the calculated characteristics and the results of the numerical analysis obtained in the quasistatic
approximation is shown. The results of the experimental investigation of the nine-resonator phase
shifter are presented. The phase shifter is based on an irregular microstrip structure in which the
nematic liquid crystal active layer is located between the screen and quartz suspended substrate. The
prospects of using the developed device in the centimeter and millimeter wavelengths are shown.
Keywords: phase shifter, liquid crystal, microstrip filter, resonant structure, photonic crystal.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 193-199
~~~
??? 630.377.4
?????????? ?????????????? ??????
????????????????? ????????
??????????? ??????????????
??????????? ???? ?????? 25 ??
?.?. ???????
????????? ??????????????? ??????????????? ??????????? ,
?????? 660049, ??????????, ??. ????, 82 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
?????? ????????? ???????? ???????? ?????????????? ??????????? ???? ?????? 25 ??
??? ?????????????? ?? ??????????? ???????? ? ???????????? ??????. ???????????????
? ?????????????? ?????????????? ??????, ??????????? ??????????? ?????
????????????????? ???????? ?????????????? ? ??????.
???????? ?????: ?????????????, ???????????? ????, ???????? ?????????, ??????? ??????,
???? ???????, ??????? ???????????, ?????????? ??????, ????????? ?????, ??????? ?????,
??????, ??????, ??????? ???????, ?????????????? ??????, ?????? ????, ??????? ???????,
????? ???????, ?????????, ?????????, ???????????? ???????, ????????????? ???????,
??????????? ???? ????.
????????
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??? ??????? ???????????? ? ??????? ?????? ???????????? ???????? ???????????? ????????, ???????????? ????????????? ?? ?????? ? ?????. ?????????????? ???????? ???????
??????? ??????????????? ??????????? ???? ?????????? ?.?. ???????, ?.?. ?????????,
?.?.??????????, ?.?. ?????????, ?.?. ?????, ?.?. ???????, ?.?. ?????????, ?.?. ????????, ?.?. ??????????, ?.?. ?????? ? ??. ??????????? ???????????? ??????? ?????????
????, ??????? ? ????????? ?????????????? ? ??????, ???????? ??????????? ????? ?? ????????? ?????? ? ????????? ??????? ? ????????????, ? ????? ??????? ?? ???????? ???????????
??? ???? ???????? ?????????????? ? ???????????????? ????????.
???????? ?? ???????????? ?????????? ????? ?? ???????????? ???????? ???????????????
??????????? ????, ?? ?????????? ??????? ??? ???????????? ??????? ???????? ??????????????
??????????? ???? ? ???????????? ??????.
*
1
Corresponding author E-mail address: guskov_gs@list.ru
© Siberian Federal University. All rights reserved
# 193 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????. ?????????? ?????????????? ?????? ????????????????? ???????? ??????????? ???????????????
???????, ?????????? ?????? ???????? ???????? ? ?????????? ?????, ??????????? ?
??????? ????????? ??????: ?.?. ????????? ? ?.?. ?????????, ?.?. ???????? ? ??., ?? ? ???
??????????? ?????? ?? ???????????? ?????? ???????? ????? ? ??????, ????????????? ????
??????? ?????? ? ??????????????? ? ?? ?????????? ??? ? ?????????????? ?????????.
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1. ??????????? ????????? ????? ???????????? ??????? «??????? ??????????? ? ???????
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?????? ??????????
1. ???????????, ?.?. ????????????? ??????????????? ????????? ?????? ?????. ?.: ????????, 1995. 257 ?.
2. ??????????, ?.?. ?????????????? ?????? ?????. ???????? ????????? ???????????
?????????? ???????????????: ????. ???????. ?????????? : ????, 1997. 248 ?.
3. ?????????, ?.?. ???????? ??????????. ?.: ??????????????, 1972. 329 ?.
Working out of Mathematical Model
of Unsteady Turn of a Caterpillar Tractor
Logger of a Class 25 kN
Sergey Yu. Gus?kov
Siberian State Technological University
82 Mira, Krasnoyarsk, 660049 Russia
Article is devoted turn of the tractor logger of a class 25 kN at maneuvering on a loading platform
with lengthy cargo. The mathematical model is developed and proved, allowing investigating a mode
of unsteady turn of a tractor logger with cargo.
Keywords: logger, lengthy cargo, wood loading, turn of the car, force of inertia, basic surface, track
laying vehicles, the settlement scheme, object of the labour, tree, arrow, running system, mathematical
model, flexible cargo, base tractor, the centre of gravity, rigidity, the equations, kinetic energy,
potential energy, tangent force of draught.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 200-212
~~~
??? 510.22
?????? ????? ? ?????? ?? ??????????
?? ?????? ???????? ????????
?.?. ??????a,
?.?. ??????? , ?.?. ??????????
?
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79
?
???????? ??????????????? ????????????? ?? ???,
?????? 660036, ??????????, ????????????? 1
?
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
?????????? ???????? ?????? ????????? ????????????????? ??????? ? ?????????,
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????????? ????????????? ?????? ??? ???????? ??????? ??????????????. ???????? ??????,
?????????????? ???????? ????????? ?????????????? ?????? ????????? ???????????
??????? ?? ???????? ??????. ???????????? ???????? ???????? ??????? ?????? ????????
??????? ? ??????? ???????? ??????? ????????? ?????????. ?????????? ?????? ?????????
????????????????? ??????? ???????? ???????????? ??? ????????????? ????? ? ????? ???????
?????? ??????????? ?????????? ??????????.
???????? ?????: ???????? ?????????, ????, ?????, ??????????, ????????? ???????????,
??????????????? ??????????, ???????? ??????????, ?????????? ????????????????????
?????????.
????????
?????? ?????????? ????? ???????????? ???????? (??) ?? ??????????? ?????????? ?? ?????????? ? ?????? ???????? ? ???? ?????? ??????????? ???????????????? ??????? ? ??????
??????. ? ???????? ????????? ? ???????????????? ??? ??? ???? ????????????? ??????????? ?
???????? ????????? ???????? ???????. ?????????? ???? ???, ?????????? ????????? ????????? ????????, ???? ?????????? ?????? ?????? ????????? ? ?????? ??????? ?? ???????????
????????, ?. ?. ????????? ?????????? ??????. ????????? ???? ?????????? ??? ????????????
????? ???? ?????????, ?????????? ?????? ?? [1-3].
??? ???????????? ??????????? ?? ?????????? ? ?????? ?????????? ????? ???? ?? ????????
??????? ????? ??????????? ? ?????????????? ???????? ??????????? ?????????? ??????????*
1
Corresponding author E-mail address: SVKirillova@rambler.ru
© Siberian Federal University. All rights reserved
# 200 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
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??????????? ??? ??????????????????, ??? ? ?????????????? ????????. ????????, ??? ????? ????? ????????? ??????? ??????????, ?????? ???????????????? ???????????, ???????? ???????
???????? ???????, ???????? ? ????? ?????????????? ???????????? ???????? ??? ? ????????????, ??????? ???????, ?? ???????? ?????????, ? ?? ?? ?????????????? ?????????? [4, 5].
??? ??????? ????? ????? ?????? ??????? ?????? ?????????? ??????????? ?????????????? ????????, ????? ??? ???????????? ????????????? ?????????? ??????, ??? «?????», «???????» ? ?. ?. ??????? ??????, ??????????? ?? ???????? ??????? ??????? ??????, ???????? ?????????. ??????? ?????? ????? ??????? ?? ???????????? ?????? ????????? ? ???????? ? ????
???????????????? ? ???????????????, ??????? ????? ????????? ? ???????? ???????? ???????.
? ????????? ????? ????????, ??? ?????? ???????? ???????? ??????? ??? ??????? ??????? ? ??????, ????? ?????? ???????????? ? ????? ??????????????? ????????? (????????) ?
??????? ?? ???????????? ?????? ????????? [6]. ???????????? ????????? ???????, ????? ?????????? ???? ??????? ??????????? ??? ?????? ????????? ?????????. ???????????, ??? ??????? ??
?????? ?????????? (??????? ??????), ????? ??? ????????, ?????????????? ??????????, ????????? ???????????? ????????? ?????????, ??????? ?????????? ?????? ? ???????? ? ???
?????. ? ?????? [7] ???? ?????? ???????? ??? ???????? ????????? ???????? ? ?????????? ????????????? ???????????.
? ????? ???????????????, ?????????? ?????? ???????, ?????? ????????? ??????? ?????????????, ???????????? ??????????? ???????????? ????????? ? ???????????? ????? ?????????. ????? ????, ????????? ?? ?????????? ?????? ?????????????? ??????? ??????????
????????? ???????????, ??????? ?????????? ???????????? ??????, ??????? ????? ???????????? ??????? ????????. ??????? ??????????? ?????? ? ?????????? ?????????????? ??????
?????????? ?? ?????? ?????????? ???????????, ??????? ????????? ?????????? ??????? [8].
?????? ???????? ?????? ????????? ??????????? ??????? ?????? ? ?????????????? ??????
??????. ????? ? ??? ????????? ??????????? ????????? ?????????? ?????-???? ???????, ???????, ???????????? ? ????????? ??????????? ???????? ??? ????????? ?? ???????. ????? ??
?????????? ???????? ??? ?????? ????? ???????? ?? ?????????????? ?????????, ??????????????? ?? ?? ???????????. ??????? ??? ?????????? ????????????, ??? ??????????????? ??????? ??? ?????? ????????????? ?????? [9-14], ? ????? ??????? ????????? ????????????? ?????
?? ?????? ?????????? ???????? ???????? [15,16] ? ???????????? ?????????? [17-23].
? ?????? ???? ???????? ???????? ?????? ????????? ????????????????? ???????, ????????????? ??????????? ?????????? ????????? ??????? (??????? ?????????? ??? ??????????
?? ???????? ????????), ? ?????????????? ?????? ???????? ????????. ???????????? ????????
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??????????????? ??? ?????? ?????????? ?????? ?? ?????????? ?, ?????????????, ??????????
????? [24,25].
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??????????? ????????????? ???? ?????????? ??? ?????????????? ??????? R(x) ??? ???? ?? ????????? ??????????? [26]:
# 201 #
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???????????) ????????????????? ??????? ?? ????????? ? ????? ???????????????? ???????.
????????? ?????? ?????????? ???????????? ?????????? ????????? ??????:
? ????????????? ???????? ????? ?? ?? ?????????, ????????? ? ?????????, ???????????? ? ???????????? ???????? ??????? ?? ??????????? ??????????????? ????????;
? ????????????? ????????????? ???????? ????? ?? ???????? ????????? ??????????, ?.?.
????????? ??????? ??????? ? ???? ??? ????? ??????, ?????? ????????? ??????? ? ?.?.;
? ??????????? ??????? ?????????? ??? ??????? ?????? ????????, ?.?. ?????? ???????????
????? ???????????? ???????? ??????? ? ???????? ??????.
??? ???? ???????? ????, ??? ??????? ?????? ?????? ??????????? ??????? ?????? ??????? ?????? ?????????? ??????????? ?????????????? ????????, ????? ??? ???????????? ????????????? ??????????. ??????? ?????? ???????? ? ???? ???????????????? ? ???????????????,
????????????? ??????????????? ?????? ?????????. ????????, ????????, ??? ?????????? ??????? ??????? ?? ????????????? ??????? ???????, ??? ?? ???????????, ?? ????????? ???????????
?????????? ?? ???????????? ?????????? ?? ????????????? ??????????????? ???? ????? ?????????? ?????? ???????. ??? ???? ????????? ????????? ??????????? ??????? ????? ?????
?????????? ??? ??????? ???????? ????????.
???????? ????????? ???????????? ????? ???????????? ????????? ????????? ???????,
???????????? ??????? ?????? ? ?????? ??????????????? ??????????, ??????????? ??? ????
???? ??????? ??????????????? ???????????? ??????? ????????? ??? ??? [27].
???????? ?????????? ?????????? ???????????? ????????????? ??? ??? ????????
? { x | P A ( x ) !} , ??? x ? ??????? ?????????? ?????????????? ????????? ??? ?????????? X, ?
? A(x) ? ??????? ??????????????, ??????? ?????? ? ???????????? ??????? x ? X ????????? ?????????????? ????? ?? ?????????? ????????? [0, 1], ?.?. ?????? ??????? ???????????? ? ?????
???????????:
P A ( x ) : X o [0, 1] .
???????? ?????????? ???????????? ??? ??????: <?, X, A>, ??? ? ? ???????????? ????????
??????????; X ? ??????? ?? ??????????? (?????????); ? { x | P A ( x ) !} ? ???????? ?????????
?? X, ??????????? ????????? ????????, ??????? ????? ????????? ???????? ?????????? ?.
??????????????? ?????????? ???????????? ??? ??????: <?, T, X, G, M >, ??? ? ? ???????????? ??????????????? ??????????; T ? ??????? ????-????????? ??????????????? ??????????
??? ????????? ?? ???????? (??????), ?????? ?? ??????? ???????????? ????? ???????????? ????????? ???????? ?????????? ?; X ? ??????? ??????????? (?????????) ???????? ??????????,
??????? ?????? ? ??????????? ??????????????? ?????????? ?; G ? ????????? ??????????????
?????????, ??????? ????????? ??????? ??????????? ?? ????????? T ?????, ??????????? ?
??????????????? ????????? ???????? ??? ?????? ??????????????? ?????????? (????????, ?
# 202 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
??????
???????????? ???? ?????? ??????
????????? ??????
???????????? ??????? ??????????
????????????? ?????????? ? ????????
???????? ?????????
??????????? ?????????????
? ???????? ???????? ?????????
??????????????? ??????????
???????? ?????? ?????????
??????????????
?????
???. 1. ???????? ????? ????????? ????????? ??????
??????? ?????????? ?????? «?», «???» ? ????????????? ???? «?????», «??????» ? ??.);
M ? ????????????? ?????????, ??????? ????????? ????????? ? ???????????? ??????? ??????
???????? ?????? ??????????????? ??????????, ??????????? ? ??????? ????????? G, ????????? ??????????? ?????????? ??????????? ???????????? ???????????????? ?????????
?????????.
?? ?????? ???? ??????? ???????? ????????? ????????? ??????????? ??????, ??????? ??????????? ? ?????????? ???????? ? ???????????? ??? ???????? ??????? ? ??????????????????
???????, ????? ?????????? ?????? ? ???? ???????? ?????? [28]. ???????? ????????? ??????
??????? ?? ???. 1.
? ????? ????????? (????????? ??????????????) ???????????? ?????????????? ????????
???????? ?????????? ?? ?????? ?? ????????? ???????.
????? ?????? ???????. ????? ??????? ??? ???????? ??????? ?????????????? ?? ???????
Max
і x � P ( x) dx
y
Min
Max
,
і P ( x) dx
Min
# 203 #
(2)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
??? y ? ????????? ??????????????; x ? X (X ? ??????? ??????????? ???????? ??????????,
??????? ?????? ? ??????????? ??????????????? ?????????? ?); ?(x) ? ??????? ??????????????
????????? ?????????, ???????????????? ???????? ?????????? ? ????? ????? ???????????;
Min ? Max ? ????? ? ?????? ????? ????????? ???????? ????????? ????????? ???????????????
???????? ?????????? ?.
????? ?????? ??????? ??? ???????????? ????????. ????? ??????? ??? ????????????
???????? ?????????????? ?? ???????
n
¦x
y
i
� P ( xi )
i 1
n
¦ P(x )
,
(3)
i
i 1
??? n ? ????? ???????????? (??????????????) ???????? ????????, ?????? ?? ??????? ????????????? ???????????? ???????? ??????????????? ???????? ??????????????? ??????????.
????? ?????? ???????. ????? ??????? ????? y = u, ??? ???????? u ???????????? ?? ?????????
u
Max
Min
u
і P ( x) dx і P ( x) dx ..
(4)
????? ???????, ???????????? ?????? ????????? ???????? ?????????????? ?????? ?????????????? ???????, ???? ???????? ?????????? ?????? ???????.
2. ?????? ????????? ??????????? ???????
2.1. ???????????? ???? ?????? ?????? ????????? ??????
?????????? ?????? ?????????????? ?????? ????????? ??????????? ??????? ?? ????????
??????. ????????, ???????????? ????????? ??????? ? ?????????? ??????????, ????? ????????? ?? ????????? ??????.
????????? ????????? ?? ?????? ??????????? ??????? ??????? ??????????: A1 ? ???????
?????????? ? ?????? ? ??????, ??????????? ?????, ????????, ??????? ? ?????????? ????,
??????, ????, ???????, ??????? ???????????.
????????? ?????????, ?????????? ?? ?????? ?????????? ? ???????????: A2 ? ????????? ????????????? ??????? ??????? ??? ??????????? ?? ??????; A3 ? ????????? ?????????????
?????? ??? ??????????? ??????????; A4 ? ????? ?????????? ? ????????? ??????? ?????? ??
????? ??????????.
????????? ????????? ?? ?????????? ?????????? ?? ???????: A5 ? ???????????? ????????; A6 ? ?????? ? ????? ??????; A7 ? ?????????????? ?????????? ? ??????; A8 ? ???????
??????????.
????????? ?? ????????? ????? ???? ?????????? ????????, ?????? ???????? ?????????????? (????????). ?????? ??? ????????????? ? ?????????? ? (???) ??????????????
???????? ?????? ????? ???????, ??? ??????? ???????? ????????????? ???????????????
??????????.
?????????????? ????? ?????????? ???? ????? ????????? ???????????:
«???» ? ?????????? ??????????? ??? ?????????????? ????????????? ???????????;
# 204 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
«??????» ? ????????? ?????????????? ????????????? ??????????? (???????, ??????,
???????? ???????????, ??????????? ???? ? ??????);
«?????????» ? ????????????, ???????????? ????????????? ???????????, ????? ??????????? ??????????? ??????????? (?????? ? ??????? ??????, ???????? ??????????? ?????????);
«???????» ? ??????? ??????????? ???????????, ???????? ?????? ????????????? ??????????? (??????, ?????????? ? ??????????? ??????????);
«??????????????» ? ?????? ?????????? ?????? ? ??????? ?????.
???????????? ?????? ? ??????????????? ?????????? ??????? ????? ???? ????????????
? ????? ????????????? ??????, ??????? ??????????? ? ?????? ?????? ????????? ???????????
???????. ????????:
? ???? ??????????? ??????? ?????????? ?????????? ? ?????? ? ??????, ???????????
?????, ????????, ??????? ? ?????????? ????, ??????, ????, ???????, ??????? ??????????? ? ?????? ??????, ?? ????????? ??????????? ????? ??????????????;
? ???? ??????????? ??????? ?????????? ?????????? ? ?????? ? ??????, ??????????? ?????, ????????, ??????? ? ?????????? ????, ??????, ????, ???????, ??????? ??????????? ? ?????? ??????, ?? ????????? ??????????? ????? ???????;
? ???? ??????????? ??????? ?????????? ?????????? ? ?????? ? ??????, ???????????
?????, ????????, ??????? ? ?????????? ????, ??????, ????, ???????, ??????? ??????????? ? ?????? ?????, ?? ????????? ??????????? ????? ???????, ? ?.?.
??? ?????????? ????? ?????????????? ??? ?????????? ???? ?????? ??????? ?????????
??????, ??????? ????????? ??????? ????????? ???????????. ?? ???????? ???? ?????? ???? ??????????? ???????? ?????????????? ?????? ????????? ??????????? ????? ??????????, ???,
? ?????, ?? ????????? ??? ?????? ? ??????? ?????, ?? ??????????? ?????????? ??? ??????
??????????????.
????? ???????????? ??????? ????????? ?????????? ??? ????????????? ??????? ???????????? ? ????????, ????? ?????????? ?????????? ?????? ??????????? ?, ?????????????, ?????????? ? ????? ????????, ???, ????????, «??????? ??????????», ???? ?? ?????. ? ???? ??????
??? ?????? ????????? ??????????? ???????? ????????????? ?????????, ???????????????:
? ???????? (????????????) ?????????;
? ????????????? ??????? ?????????? ???????;
? ??????? ??????????.
??? ???????????? ???? ?????? ?????? ????????? ?????? ?????????????? ?????????
??????? ? ???????? ??????????????? ?????????? ? ??????????????? ?? ?????-?????????,
? ????? ??????? ??????????? (??????????) ???????? ??????????, ??????? ?????? ? ??????????? ??????????????? ??????????????? ??????????.
???????? ???????????????? ??????????? ????????: ?1 ? «??????? ??????????» ? ?2 ?
«??????? ??????????».
????????? ????? T1 ????????? ???????? ??????????????? ?????????? ?1: T1 = {«???»,
«????», «???????», «?????»}. ??????? ??????????? (?????????) ???????? ??????????, ???????
?????? ? ??????????? ??????????????? ?????????? ?1, ?????????: X 1
x1 Џ R 0 d x1 d 100
(x1 ? X1 ???????????? ??? ??????? ???????????? ??????? ??????????? ???????).
^
# 205 #
`
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
T2 ? ????????? ???????? ??????????????? ?????????? ?2: T2 = {«?????», «???????? 25 ???»,
x 2 Џ R x 2 t 0 ,, ???
«???????? 50 ???», «???????? 75 ???», «??????»}. ????????? ??? ?2: X 2
x2 ? X2 ???????????? ??? ??????? ?????????? ? ?????.
???????? ??????????????? ?????????? ???????? ? ? «????????? ???????????». ????????? ???????? ?: T = {«???», «??????», «?????????», «???????», «??????????????»}. ?????????
??? ?: X ^ x Џ R 0 d x d 16 ` (x ? X ???????????? ??? ????? ??????????? ??????? ? ????????
??????????????????? ?????).
??????? ?????????????? ??? ???????? ?????????? ?? T1 ????? ????????? ???:
1
1
P ( x; a, b, c)
? ???????????????? ???????, ??? a, b, c ? ?????????, ????????????
2b
xc
1
a
^
???????? ??????????.
???????
??????????????
P 2 ( x; a, b, c)
0,
­
°x a
,
°° b a
®c x
°
,
°cb
0,
Ї°
???
????????
??????????
`
??
T2
??????:
xda
ad xdb
bdxdc
? ??????????? ???????, ??? a, b, c ? ?????????, ?????????-
cdx
??? ???????? ??????????.
???????, ??? ??????? ?????????????? ???????? ?????????? ????? ???? ?????? ???????????? ???? ???????? (???? ???????? ???????? ??????? ?????????????? ?????? ??? ????????? ????????????? ????????? ?????????????? ?????????). ? ????? ??????? ???????
?????????????? ??? ???????? ??????????????? ?????????? ?1 ? ?2 ?????? ???????????? (???.
3, 4), ? ??? ???????? ? ? ????????? ???????? (???. 2).
????? ???????? ???? ???????? ??????????????? ??????. ? ????? ??????? ??????? ????????? ??????, ??????????????? ????????????? ????????, ???????????? ????, ????? ????????? ??? ??????? ???????? ????????? ?????????? ????:
??????? 1. ???? ?1 ???? «?????» ? ?2 ???? «??????», ?? ? ???? «??????????????».
??????? 2. ???? ?1 ???? «???????» ? ?2 ???? «??????», ?? ? ???? «???????».
??????? 3. ???? ?1 ???? «?????» ? ?2 ???? «?????», ?? ? ???? «???????».
2.2. ?????????? ????????????? ??????? ??? ??????? ??????????????
?????????? ????????? ?????????? ????????????? ??????? ??? ??????? ??????????????, ???????? ????????, ? ??????? ???????????? ????????? «??????», ? ?????? ????????
????? ????????????? ????????????? ?????? [29]. ????????? ??????? ?? ????????? ??????.
1. ???????????? ??????????????? ?????????????? ??????:
yi
ln(P i ) ,
(5)
??? ?i ? ???????? ??????? ?????????????? ? ????? xi.
2. ???????? ? ??????? ???????????? ????????? ????????????? ?????? ? ????:
M
y ( xi )
b c ¦ sin(M j Z j xi ) ,
j 1
# 206 #
(6)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
?
?
"?????????????? ???????????"
"??? ???????????"
1,2
1,2
1
1
0,8
0,8
???????
??????????????
0,6
???????
??????????????
0,6
??????
0,4
0,4
0,2
0,2
0
??????
0
1
3
5
7
9
11
13
15
1
3
5
7
9
11
13
15
???. 2. ???????? ??????????????? ?????????? ? ? «????????? ???????????»: ? ? ???????? ????????? ????????
«???» P exp{7,94 13,6 � [sin(1,77 0,13x) sin(2,92 0,17 x) sin(0,17 0,14 x)]} ; ? ? ???????? ?????????
???????? «??????????????» P exp{9,69 16,63[sin( 0,03 0,12 x ) sin( 1,42 0,16 x ) sin( 0,86 0,17 x )]}
??? y ? ?????; x ? ????; b, c, ?j, ?j ? ?????????????? ????????? ( j 1, M ); M ? ??????????
???????? ???????????????? ???????.
????????????? ?????? ???????? ?? ??????? ??????????? ???????????:
n
¦ §Ё© y( xi , p) yi ·ё№
H
&
2
,
(7)
i 1
r
??? n ? ?????????? ?????; p ? ?????? ?????????????? ??????????.
3. ???????????? ???????? ??????????????. ? ?????????? ??????? ?????????????? ?????
???
P
M
exp(b c ¦ sin(M j Z j x)) .
(8)
j 1
??????? ??????????? ?????????????? ????????????? ??????? ?????????????? ??? ?????? ??????????????? ?????????? «????????? ???????????» ???????????? ?? ???. 2 ?, ?.
2.3. ???????? ????????? ??????
???????????? ??????? ??????????. ?? ???. 3?5 ????????? ??????? ?????????? ??????? ?????????????? ??? ????????? ??????????????? ?????? (????????) ???????????????
??????????????? ?????????? ?1 ? «??????? ??????????» (???. 3), ? 2 ? «??????? ??????????» (???. 4) ? ? ? «????????? ???????????» (???. 5). ??? ???? ??????? ?????????? ???????????? ??? ??????? ???????????? ??????? ??????????? ???????, ??????? ??????????
?????????? ? ?????, ? ????????? ??????????? ??????????? ? ???????? ??????????????????? ?????.
????????? ? ???????? ????????? ?????? ???????? ??????? [28], ?????????? ?????? ???
?????????? ??? ??????, ????? ??????? ?????????? 70 %, ? ??????? ?????????? ?????????? 92
????. ? ???? ?????? ???????????? (????????? ?????????? ???????? ??????? ??????????????
# 207 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
???. 3. ??????? ??????? ?????????????? ??? ?????? ??????? ??????????????? ?????????? ?1 ?
«??????? ??????????»
???. 4. ??????? ??????? ?????????????? ??? ?????? ??????? ??????????????? ?????????? ?2 ? «???????
??????????»
???. 5. ?????? ??????? ?????????????? ??? ?????? ???????? ??????????????? ?????????? ? ?
«????????? ???????????»
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
?????? ?? ?????? ???????, ?? ????????, ???????? ??????) ?????? ??????? ???????????????
?????????? ???????? ? ???????? ??????? ?????????? 0,96 ??? ????? «???????» ? 0,5 ??? ?????
«?????» (???. 3), ? ???????????? ?????? ??????????????? ?????????? ???????? ? ????????
?????????? 0,6 ??? ????? «??????» (???. 4). ??????????????? ?????????? ???????????? ? ???????? ???????? ????????? ? ???????? 1 ? 2. ??? ??????? ????????? ????????? ? ???????????? ? ??????? ???????? ????????? ??????.
????????? ???? ????????? ??????: ????????????? ? ????????? ??????????? ??????? ?????????? ??????? ?? ??????? ?? ?????? ??????? ????????? ??????. ??????? ?????? 1 ? 2 ??????? ?? ??????????, ????????? ?????????? «?», ?????????????, ??? ????????????? ???????????? ???????? min-??????????. ????????????? ?????????? ??????? 1 ???? ? ?????????? ?????
0,5, ? ????????????? ?????????? ??????? 2 ? ????? 0,6.
????? ?????????? ????????? ?????????? ??????? ?????????? ??????? ?? ?????????????
?????? ???????? ????????? ? ???????????. ????????? ??? ?????????? ?????? ?????? ? ?????
???????? ??????????????? ???????????? ????: «? ???? ?», ??? ?? ???????????? ??????????????? ??????????, ? ? ?? ????????, ? ??????? ???????????? ?????? ?? ????????? ????? 1,
?? ??????????? ?????? 1 ? 2 ???????? ? ???? ???????? ??????????, ?????????????? ?? ???. 5
(??????? 1 ? ??? 6, ??????? 2 ? ??? 7).
????????? ????: ??????????????? (???????????) ? ????????? ?????????? ??????? ?????????????? ??? ?????? ?? ???????? ??????????????? ??????????. ??????????????? ?????????? ???????? ?????? ????????? ? ?????????????? ???????? max-?????????? ??? ?????? 1 ? 2 ???????? ? ?????????? ? ????????? ?????????, ??????? ?????????????? ????????
?????????? ?? ???. 5 (??? 7).
?????????????? ?????? ???????? ?????????????? ? ????????? ?????????? ???????? (??
?????????) ???????? ??? ?????? ?? ???????? ??????????????? ??????????. ??????????????
???????? ??????????????? ?????????? «????? ???????????» ??????? ?????? ??????? ???
???????????? ???????? (3) ???????? ? ???????? ???????? ??????????, ?????? 11,61 ??????
??????? ??????????. ???? ???????????? ??????????? ????????????? ??????? ?????????????? ??? ?????? ??????????????? ?????????? «????????? ???????????», ?? ??? ?????????????? ???????? ??????????????? ?????????? ????? ??????????????? ??????? ?????? ???????
(2) ? ??????? ?????? ??????? (4). ? ???? ?????? ???????? ????????, ?????? 11,33 ? 11,72 ?????
??????????????.
? ?????????? ????? ?????????????? ?????? ????????? ??????????? ????????????????? ??????? ??? ??????????. ???????????? ???????? ????? ????????????? ??? ??????? ?????????? ???????, ??????????????? ??? ?????????? ??????????? ?????????? ?????????? ?
?????? ?????. ????? ???????, ???????, ????????? ???????????? ???????? ?????? ?????????
????????????????? ??????? ? ???????? ????????? ??????? ? ??????????? ????????????? ??????????, ?????????? ???? ??? ?????????????? ???????? (???? ??? ??? ????????? ????????) ??
????????? ??????? ????????? ?? ???????????? ????? ?t:
R x ('t ) Px ( H ) � S ( x, k ) � v( x, k , H ) ,
(9)
??? x ? ???????? ?????????? ????? ??????? ????????? ??????????; Px(H) ? ??????????? ????????? ?????????? ??? ???? x; S(x, k) ? ????????????? ????????? ???????, ????????? ?? ?????# 209 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
?? ????????????? x ? ?????????? ?????? ????????????? ??????? k; ?(x, k, H) ? ?????????????
?????? ????????? ??????????? ??????? ??? ?????????? ?????????.
????????? ????????????? ????? ? ????? ???????? ??????? ? ?????? ??????? ??? ????????????? ??????? ????? ???? ?????????:
? ???????? ?????? ???????? ?t (????????, 100 ???);
? ???????????? ???????????? ????????? ?????????? (???????????? ?????? ?????) ???
??????? ??????? x ?? ?t;
? ??????????? ????????? ??????????? ??????? ??? ?????????? ????????? (?? ???????
??????? x);
? ??????????? ???? ??? ?????????????? ??????? ?? ?????? ?????????????? ???????.
? ???????????? ????? ???????.
???? ??????? ?????? ????? ? ???, ??? ???? ??????????? ?????, ?? ??? ???????????????
??????????? ????????????? ????????? ????????: ????????, ???????? ????????? ??????????? ??? ?????????? ????? ????????? ?????????? ?????????????, ?????????? ? ?.?., ? ?????
?????????? ????? ????? ? ??????? ???????.
??????????
????? ???????, ?????????? ???????? ?????? ????????? ????????????????? ??????? ??
?????? ?????? ???????? ???????? ? ?????????? ???????????????????? ?????????.
???????? ??????? ?? ????????? ??????:
? ????????? ?????????, ???????????? ????????? ??????? ? ?????????? ??????????, ?
??????????? ??????????????? ?? ??????????????? ??????????;
? ??????????? ??????????????? ?????????? «????????? ???????????»;
? ?????????? ????????????? ??????? ??? ??????? ??????????????, ???????? ????????,
???????? ?????????? ???????????????????? ?????????;
? ?????????? ???? ???????? ??????????????? ??????;
? ????????????? ? ???????? ????????? ?????? ???????? ???????.
??????????? ???????? ?????????????? ?????? ?????? ??????????? ?????????????????
???????.
???????? ????? ????????? ?????? ?????? ???????? ??????? ? ??????? ???????? ???????
????????? ?????????.
?????????? ?????? ????????? ????????????????? ??????? ????? ???????????? ??? ????????????? ????? ??? ??????? ?????? ??????????? ?????????? ??????????.
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
?????? ??????????
1. ??????, ?.?., ???????, ?.?., ??????, ?.?. ????????? ? ??????????? ????????????
????????: ?????????, ??????, ?????. ?.: ??? ??? «??????? ????????», 2001. 343 ?.
2. ??????, ?.?., ??????, ?.?., ??????, ?.?. ?????? ??????? ? ?????????? ?????? ? ????????? ? ??????????? ??????. ?.: ??? ??? «??????? ????????», 2004. 352 ?.
# 210 #
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?.?. ??????, ?.?. ???????? ?????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ????????
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24. ?????????, ?.?., ??????, ?.?., ???????, ?.?. ????????????? ????? ? ?????? ?? ?????????? ?? ?????? ???????? ???????? // ?????????????? ??????????. 2006. ?. 11. ?. 51-58.
25. ??????, ?.?., ??????????, ?.?., ???????, ?.?. ?????? ?????? ????????? ???????? ??
???????????????????? ????????????? ????// ?????? ?????????? ???????????? ????????????.
????? «??????? ? ??????????». 2008. ?. 1. ?2. ?. 207-218.
26. ?????? ????? ?????? ? ????????????? ????? ????????? ??? ??????????? ??????? / ?.?.
????, ?.?. ?????, ?.?. ???????, ?.?. ?????????. ?. ? ???? ? ?????????, 2005. 61 ?.
27. ??????, ?. ???????? ? ?????? ???????? ????????: ???. ? ?????. ?.: ????? ? ?????,
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???. 7. ?. 103?120.
Risk and Damage Estimation
from Floods Based on Fuzzy Sets Theory
Michael V. Noskova,
Konstantin V. Simonovb and Svetlana V. Kirillovaa
a
Siberian Federal University,
79 Svobodny, Krasnoyarsk 660041 Russia
b
Institute of Computational Modeling SB RAS, ICM SB RAS,
Akademgorodok, Krasnoyarsk, 660036, Russia
An estimation method for the status of the hydrotechnical object and coast prone to floods of different
origin is proposed using the fuzzy sets theory and nonlinear multiparameter regression. The basic
signs defining a status of the object as a result of flooding are allocated. The linguistic variable ?status
of damage? is defined. On a basis of regression data simulations analytical models for the prescribed
membership functions are constructed. The example illustrating the method of reception a quantitative
estimation of a status of damage for object using the fuzzy data is offered. The proposed methodology
is the basis for decision-making systems in control services of dangerous natural processes. Received
estimations of a status of hydrotechnical object may be use for risk simulation in the problem of zoning
the coastal territory.
Keywords: Fuzzy set, risk, damage, flood, status of damage, linguistic variable, fuzzy variable,
nonlinear multiparameter regression.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 213-224
~~~
??? 681.3.06
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????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
? ?????? ???????????? ?????? ??????? ?????????????-????????? ???????????? ????????,
?????????????? ?????? ?????? ???????????? ????????? ? ?? ?????????? ?????????? ? ?????????
???????. ?????????? ?????? ? ?? ?????????? ???????????, ???????????? ?? ????????,
??????????? ? ??????????? ?????? ??????, ????????????? ?????? ???????? ???????. ???
????????? ???????????????? ???????????? ??????????????? ???????? ??? ??????????
?????????????????? ????????????? ???????.
???????? ?????: ???????, ???????????, ???????????? ??????????, ?????????????-?????????
???????????? ????????????????.
????????
??????? ? ??????????? ???????? ??????? ??????? ???????? ?????????? ????????????
???????????. ?????? ???????, ????????? ? ??????????? ? ??????????? ??????, ??????????
??????? ???????? ??? ????????????????? ????????????????. ???????????? ????????? ????????? ???????????? ????????????? ?????? ? ???????????, ???????? ??????? ??? ?????????? ?????????? ????????, ??????? ?????? ????????? ??????? ??? ????????, ??????? ???????? ??? ??????????? ????, ????????? ??????? ? ?.?. ????????? ?????????????? ????????
????? ????????????? ???????? ??????????????, ??????????? ???????? ? ??????????? ???
???????, ????????????? ??????????? ?????, ????????? ??????? ???????? ????????????? ????????. ??? ???????? ? ???????????? ??????????? ??????? ??????? ?????????????? ??????????????? ??????????? [1,2], ???????????????? ?????????? ?????????????? ?????????. ?
?????????, ?????????? ????????????? ??????????? ? ????????? ????????, ??????????? ???
?????????????? ????????? ? ???????, ??? ????? ????? ??????, ??? ? ????? ?????? ????????
?????????. ? ????????? ????? ?????? ??????? ???????????? ???????? ????????? ????????????????. ?????????? ???????????? ?????? ? ?????????? ???????????? ??? ??????, ???????????? ??? ??????, ??? ? ???????? [3-6].
*
1
Corresponding author E-mail address: uuuu82@inbox.ru
© Siberian Federal University. All rights reserved
# 213 #
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?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
??????????? ? ???????, ???????????? ?? ??????????? ??????? ?????? ? ??????? ??
?????????????. ??????????? ?????? ?????????? ??????????? ???????????? ????????, ?????????????? ?????????????? ?????? ???????????? ?????????????? ?????????. ??????????? ???????????? ?????? ?????????? ???????????, ???????????? ?? ???????? ??????? [1,7].
???? ??????? ????????? ?????????? ?? ?????????? ??????????? ?????? ? ?? ??????????
???????????? ?????????, ?? ??????????? ????????? ????????????? ???????? ???????????????? ????????? ?? ?? ?????? [8-11] ??? ???????????? ??????? ???? ????????? ????? ?????????? ???????????? ????????? [1,7,12,13]; ???????? ?????? ?????????? ??????????? ???????????? ???????? [14].
???????????? ? ????????? ????? ??????? ???????? ??????????? ????????????? ???????????? ??????????? ????????? ??? ???????, ????????? ? ????????????????? ? ?????????????? ????????, ?????????????? ??? ?????? ???????????? ???????????, ??? ? ????????
??? ??????????. ??????? ??????????????? ?????????????? ???????, ?????????? ????????????? ????????????? ????????????????. ? ?????????, ???????????? ???????? ?????????????????????? ????????? ???????????????? ???????????? ???????? ????????-???????????? ???????????? [15,16]. ?? ?????? ???? ????????? ?????????? ???? ???????????????? ??????? [17],
??????????? ?????? ????????????-??????????? ???????????? ?????????. ?????? ???????
? ??????????? ?????????????-????????? ???????????? ???????? [18,19] ???? ???????????
???????????? ??? ????????????? ???????, ???????????? ???????????? ?????? ??????????,
? ??????? ??????????? ??????? ??????????, ??????????? ??????? ??????? ????????, ? ?????? ????? ???????????? ?????????.
????? ?????? ???????? ?????????? ????? ??????? ??????? ? ?????????? ???????????,
??????????? ???????????????? ????????? ?????????????-?????????? ????????????? ????????????????. ????????? ????????????? ???????? ??????????? ?????? ? ????????? ??
???? ????? ?????????? ? ?????????? ????????????? ??????, ????????????? ??????? ?????????? ??????????? ????????? ???????? ?????????? ?????????????-????????? ????????????
????????.
?????? ??????? ?????????????-?????????
???????????? ????????
?????? ?????????? ?????????? ?????????????-????????? ???????????? ????????? ???
?????????????? ????, ? ??????? ??????? ?????? ???????????, ? ???? ? ????? ????? ????.
???????????? ?????????? ???????? ?? ???, ??? ???????????? ??????????? ????? ?????? ??
?????????, ????? ???????? ??? ?????????????? ??????. ????? ???????? ??? ???? ????????, ?????????? ?????????? ???? ??? ????????????????, ??????? ??????? ? ???. ???????
?????????????-????????? ???????????? ????????? ????? ????????? ? ????? ?? ??????? ???????: ????????? ???????, ??????? ?????, ??????? ?????? ? ???????? ??????.
????? ????????? ??????? ?????????????-????????? ???????????? ????????? ??????? ????????????????? ?????? ???????. ??????????? ??? ????????????? ??????????? ?????????? ????? ????????????????. ???? ??? ?????????? ????????? ????? ???? ??????????
?????? ???? ?????? ?????, ??? ??? ????????? ???????, ??? ???????? ?? ???????? ? ????????????? ?????????? ?????, ??? ????????? ????????????? ??????, ??????????? ????????
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???. 1. ?????? ?????????? ?????????? ?????????? ?????????????-????????? ????????????
?????????
?????????? ??????????? ??????????, ????????????? ???????????? ??????. ????????, ????
??????????? ????????? ??????????? ??????????, ?? ???????, ? ????? ??????? ??? ???? ?????????. ??????? ??????? ??? ????? ?????????? ?????? ????????? ??? ??????? ????????? ?
????????? ??????? ??????. ???? ?????????????????? ?????????? ?????????? ???? ? ???????
?????, ?????? ????????? ????? ????? ???? ????????? ?????????? ?????? ? ???????????? ??????? ? ????????? ?????, ?? ?????????? ????? ?????, ?? ????? ????????? ???????????????
?????????. ????????? ????? ??????? ?????????? ????????? ?? ?????????? ????? ????? ? ?????? ?? ???????? ? ????????????? ? ???????????????? ??????????? ?????????, ?? ????? ??
?????? ??????????? ??????? ?? ?? ?????????.
????? ??????? ????? (??????) ????????????, ??? ?? ?????? ???? ??????? ???????????
?????? ????, ?.?. ??? ?? ?????????, ??????? ????????? ?????? ??????? ????????? ? ?????????
(???. 1). ????? ????, ??? ??? ????????? ???????? ????????????, ? ????? ????????? ??????????????? ?? ??????? ?????????? ??? ???????????, ? ?? ????????? ???? ??? ??????????
?????????? ??? ?? ?????????-???????, ??????? ????? ?? ????? ????? ??????????? ??????;
????? ??????? ??????????? ????????? ????.
? ?????? ??????? ????? ?? ???? ??? ??????????? ????????? ??????????, ? ????? ????????? ?????? ? ????????? ??????? ??? ????????????? ?????? ?? ????? ??? ?????????? ??????????. ????? ???????? ?? ???????? ??????????? ?????????? ????, ??? ????????? ?????? ???? ??
???????? ????? ?????. ?? ?????? ?????????? ? ????????? ???? ???????? ?????? ??? ???????
????????. ???? ? ?????????????-????????? ????????? ????????? ??????????? ???????? ???????? ?? ????? ??????, ?? ?? ??? ????? ?????????? ??? ??? ??????????? ????????. ???? ?????
? ???? ?????? ??????????? ???????? ??????, ????? ?????????? ??????, ? ????? ????????
?????? ?????????????? ???????????? ???????????. ??? ??????? ????? ?????????? ??????????? ?????????, ???????????? ????????? ????? ????????, ??? ??????? ?? ????, ????? ?? ??????? ??????, ?????????????? ???????? ??? ?????? ? ???????? ? ?.?. ? ???????? ??????? ????? ??????????? ??? ??????????? ??????????????? ????????? ?????? ?? ????? ?????????.
??????? ?? ????? ????????????? ???????????? ??????????? ???????? ??????? ??????????
????? ????????? ? ?????????? ?????????? ? ?????? ????, ?? ???? ?????????? ??????? ???????
???????????? ?????????? ?????????. ????? ????? ?????????? ???????? ????? ??????????
?????? ?????????????-????????? ?????? ??????????.
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???. 2. ????????????? ?????? ??? ??????? ?????????? ?????????????-????????? ????????????
?????????
???. 3. ???????? ?????? ??? ??????? ? ?????? ???????? ??????
????????? ????? ??????? ???????? ????????? ??????????. ???? ????? ????????????
?????????? ?????????? ?????? ???????, ?? ????? ?????? ?????????? ????? ? ?????? ??????,
? ???? ?? ?????????? ?????????? ????? ???? ????? ??????????? ??????? ????????? ???????.
??? ?? ????????? ??????????? ?????????? ?????, ?? ?????????? ????? ?????? ??? ???????
???????????? ???????????? ?????? ???????.
????? ??????? ?????? (???. 2) ????????????, ??? ?? ?????? ???? ??????? ??? ?????????? ?????????? ??? ????????? ??????????? ????? ??????????????? ?????. ????? ?????????
?????? ??????????? ? ??????? ??????????????????, ???????? ?????? ?????????. ??? ????????? ???????? ? ???????????? ????????? ?????????, ??????? ????? ???? ????????? ??????
???? ?? ??????, ?? ??? ???? ?? ????????? ? ????????? ?????-???? ?????? ??????? ????????
?? ?????? ??????.
????? ??????? ?????? ????????? ??????????? ?????????????????? ?????? ?? ???? ???,
??? ? ???????????? ??????? ????? ????????? ????? ???????? ?????????.
????? ???????? ?????? (???. 3) ????????? ???????????? ????????? ?? ?????????????
??????-??????????? ??????????? ??????????? (?????????? ??????????? ?? ????? ???????????????? ???????), ???????????? ? ???????? ???????? ???????? ??????? ??? ????????,
# 216 #
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?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
???. 4. ?????? ??? ???????
??????????? ????? ?????-?????????? ?????. ???? ???????????? ??????? ?? ???????????,
??????? ??????????? ?? ???? ???, ??????????? ??? ???? ????? ? ??? ?????????????? ???????????.
??????? ?????, ?????????? ???????????, ?????????? ??? ????????, ???? ?????????,
????????? ?????????????, ?????????? ??????, ??? ??? ??????, ???? ???? ?? ???? ?? ????????? ?? ????? ??????. ??? ?????? ????? ??????? ?????? ?? ????????? ????????????????
????????? ????????? ????? ??????? ??????????? ???????? ???????????. ????????????????
??????? ????? ????? ?? ?????? ?????????? ????????, ?? ? ????? ??????: ?????????????, ????????????, ?????????, ?? ? ???? ?????? ???? ????? ????? ??????? ??? ??????. ???? ???????????? ??????? ???????? ???????????, ????? ????? ??????? ????????? ? ?????? ????????
??????????? ???????, ?? ???? ???????????????? ??????? ???????? ??????????? ?? ??????
????????.
?????????, ?????????? ?????????????, ?????? ?????????? ? ????????? ?????? ?????????. ????? ???????? ?????? ????????? ??????????, ????????????? ?? ?????????? ?????????
??????????? ???????????? ??? ?????????? ????????? ??????, ??? ????????? ??????????
??? ???????????? ?????????, ?? ????? ????????? ? ???? ?????????.
?????? ????????? ??????? ???????, ??????????? ????? ????????? ???? ?????:
summa << funcdef ?
{ ( (x:1,x:1):*, (x:2,x:2):* ):+ >> return; }
????? ? ???????? ????????? ??????? ???????????? ?????? x = (4, -2).
????? ??? ?????????? ?????????? ???????? ???? ?????????? ????????? ?????, ???????
???????? ??????????? ???? ???????? ????????? (???. 4).
?? ???? ?????????? ???????? ? ???? 0:
1-? ???????? x:1 ????????????? ? ??????????? (4,-2):1 ? ???? 4;
2-? ???????? x:1 ????????????? ? ??????????? (4,-2):1 ? ???? 4;
3-? ???????? x:2 ????????????? ? ??????????? (4,-2):2 ? ???? -2;
# 217 #
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?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
???. 5. ?????? ??? ???????
???. 6. ?????? ??? ???????
4-? ???????? x:2 ????????????? ? ??????????? (4,-2):2 ? ???? -2.
? ???? ????????? ???????? ??????? «?????????» ?? ?????????? ????:
summa << funcdef (4,-2) { ( (4 ,4):*, (-2 ,-2):* ):+ >> return;}
?????????? ?????????? ??????? ???? ?? ?????? ???? ??????? (???. 5) ????? ??????? ??
?????????? ??????????:
???????? (x:1,x:1) ????????????? ? (4 ,4 );
???????? (x:2,x:2) ????????????? ? (-2 ,-2 ).
????? ????? ???? ? ???????????? ??????? ?????????? ????????? ?????? ?????????????? ??????? (??? ?????????? ???? ???????? ? ??????????????):
# 218 #
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???. 7. ????????? ??? ???????
summa << funcdef (4,-2) { ( (4 ,4):*, (-2 ,-2):* ):+ >> return;}
????????? ???? ?????? ? ??????????? ???? ???????? ????????? (???. 6):
???????? (x:1,x:1):* ????????? (4, 4):* ? ???? 16;
???????? (x:2,x:2):* ????????? (-2, -2):* ? ???? 4.
?? ??????? ???? (???. 6) ? ???????????? ??????? ?????????? ????????? ?????? ?????????????? ??????? (??? ?????????? ???? ???????? ? ??????????????):
summa << funcdef (4,-2) { (16, 4):+ >> return;}
? ???? ??????????? ????? ??????????????: ???????????? ?????? ??? ???????????? ???????? ?????????, ???????? ????? ?????? ? ??????? ?????????? ?????????? ???????. ???? 5,
???????????? ?????????? ?????????, ?????? 20, ????? ? ???? ???????, ????????????? ??
???. 7.
???????, ????? ?????????? ???????, ???????? ????????? ???????:
summa << funcdef (4,-2) { 20 >> return ;}
?????? ????????????? ????????? ? ?????? ???????? ??????. ?????????? ???????
???? ?? ??????? ? ?????? ???????? ??????. ??????? ?????????? ? ???? ????? ????? (???. 8),
??? (NODE,0):> ????????, ??? ???????? ???????-????????? ?????? ????, ? (NODE,0):= ????????, ??? ???????? ???????-????????? ????? ????.
??????? ???????? ?? ???? ??? (???. 9), ?? ??????? ??????????? ???????? ?????????? ?
?????????, ??????????? ? ?????. ? ??????????? ?? ???????? ????????? ??????????????
???? ?????, ?? ??????? ?? ??????? ? ???????????? ????????? ????? ??????? ??????? ? ??
????????; ???, ??? ??????????????? ???? ????? (NODE,0):> ? (20,0):> ? true.
? ??????? ???? ????? ????? ???? ????????? ????????? ?????????, ??? ???? ?????? ????????? ??????????? ? ??????? ?????????? ????? ???????????????? ? ????? ??????????
????????? ??????????; ????????, ??????? ((NODE,(0, NODE:|):dup):#:[]:>):+ ??????, ???
????????? ????????? ???????? ???????, ? ??????? ?????????? ???? ?? ???? ??????? ??????
????.
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???.8. ??????? ???????????? ? ?????? ???????? ??????
???. 9. ?????????? ??????? ? ?????? ???????? ??????
????? ??????????? ?????????????-????????? ???????????? ????????,
???????????? ??????????? ??????
????????? ??????????? ???????????? ???????? ??????????? ? ???????? ??????????
????????? ?????????????????? ?????????? ??????????, ? ??????? ?????????? ?? ?????? ?????????? ??????, ?? ? ??????, ????????? ? ???????????? ??????????? ?????????? ????????:
?????? ?????????????? ? ?????????????; ?????????, ??????????? ??? ????????????? ????????? ?????????? ????????? ? ????? ? ??? ?? ????? ???????? ? ?. ?.
?????? ?????????????-????????? ???????????? ?????????? [15-17] ????????? ??????
?????????????? ? ?????????????, ? ????? ??????????? ??????????? ?? ??????? ??????????
??????????, ??????? ? ??????????. ?????????? ?????????? ????????, ??????????? ??? ????????????? ??????????? ??????? [20]. ??????? ?????? ??????? ???????????? ???? ??? ?????????, ????? ??? ??????????? ?????? ?????? ?????? ?????????????? ??????? (????????
«1») ? ??????, ????????? ?? ???? ?????????? ????????? (???????? «-1»), ????? ??????? ?????
???? ??? ?? ?????????. ????? ???????, ???? ????? ?????????? ????????? ???????????? ???# 220 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
??? ??????????? ????, ?? ??? ?????? ???????? ????????? ??????? ????????? ?????? ?? ?????? ????? ??????????, ? ????? ? ??? ????????? ?????? ? ????????? ????????? ??? ?????????
??????? ????????? ????????? ?? ???????????? ??????.
??????????? ????? ????????? ??????? ? ???????? ???? ????????? ?????????? ????????? ???????????? ?????? ??? ?????? ???????? ?????? ????????. ??? ???? ????????? ??????????? ??? ?????????? ?????????? ???????. ???????? ?????????????? ????????????
?????????? ?????? ? ????????? ?????????, ???????????? ?? ???????????? ?? ?????????.
??? ???????????? ???????????? ?????? ? ?????? ??????????? ??????? ????????? ??? ???
????????, ????? ?????????? ?????????? ???? ????????? ?????????? ???????. ?? ????? ??????? ??????????? ?????? ??????????????? ??? ??????? ??????. ??? ?????? ???????????
???????????? ?????? ? ??? ???? ??????????? ???????? ??????? ?? ????, ??? ??????? ?????
????????? ?????????? ????????? ??????????.
????? ??????????? ????????? ??????????? ??? ????????? ???????? ????????? ???????????? ?????? ? ???????? ????, ?????????? ????????????. ???? ??????????? ? ??????????,
???????? ?? ??? ????????? ???? ?????????? ??????????? ????????? ? ??????????? ??????????, ??? ?????????? ????, ??????????? ?????? ????????. ??? ???? ????, ?????????? ?
?????? ???????????, ????? ???? ???????? ???????????? ????????????.
?????????? ??????????? ???????, ?????????? ??????????? ?????? ? ???????? ????
??? ?????. ? ?????? ?????? ??????? ????????? ????????? ?1+?2-?3+?4-?5+?, ?? ?????? ?
?1-?2+?3-?4+?5-?
F << funcdef A {
// ?????? ?????????: A=(asynch(x1, x2, ... , xn),op)
// ??? x1, x2, ... , xn ? ?????, n>=2, ? op ? ???? ??? ?????
x << A:1; // ????????? ???????????? ?????? ? ?
op << A:2; // ????????? ???????? ? op
x1 << x:1; // ????????? ??????? ???????? ????? ?? ???????????? ?????? ? ? ?1
tail_1<< x:-1; // ????????? ?????????? ???????? ???????????? ?????? ? tail_1
// ????????? ???? ?? ???????? ? ? tail_1
[((tail_1:|, 0):[=, !=]):?]^
( x1:op, //???? ????????? ? tail_1 ???, ?? ?1 ???????????? ????????
{ // ???? ???????? ? tail_1 ????
block {
x2 << tail_1:1; // ????????? ??????? ???????? ????? ?? tail_1 ? ?1
s << (x1,x2):op; // ???????? ??? ????? ???????? ??????????
tail_2<< tail_1:-1; // ?????????? ???????? ???????????? ??????
//??????? ???? ?? ????? ? ????????
[((op,+):[=, !=]):?]^( { op << ? ; }, { op << + ; } ) ;
// ??????????? ????????? ?????????? ????????? ???????????? ??????
[((tail_2:|, 0):[=, !=]):?]^
( s, { (asynch( s, tail_2:[]),op):F } ):. >>break }
}
):. >>return; }
# 221 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????????? ????? ??? ( asynch(S,??????? ??????), + )
??? ??? ???????? + ???????? ??????? ??????????
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
???. 10. ??????????? ???? ?????????? ??????????? ?????????
? ???????? ????????? ?????? ?????? ?????? ???? (asynch(1,2,3), -). ?????????? ??? ????????? ???? ?????????? ??????????? ????????? (???. 10).
????? ??????????? ???????? ??????????, ??? ????????? ?????????????????? ??????????
????????? ? ?????? ???????? ? ?????? ??????????? ??????????? ??????? (0 ??? 2 ??? 4), ?
????? ????????? ??? ????????? ???????? ????????? ???????????? ?????? ? ????????? ????.
???? ??????????? ??????? ???????? ??????????? ????????, ???????????
?1+?2+?3+?4+?5+?, ??????? ???????? ???????????? ?????? ???????, ??? ????????? ?????????? ?????? ???????? ? ????????????? ?? ???????? ?????? ??????????.
??????????
????????????? ?????????????-????????? ????????? ???????????????? ?????? ????????????? ????????????? ??????? ????????? ?????????? ??? ?????????? ???????????? ???????? ?? ???? ??????, ??????????????? ?????????? ???????????, ???????????? ?????
?????????????????? ??????????. ?????? ? ???, ??? ?? ????? ? ???????????? ??????????
?????? ? ???? ??????, ??????????? ??? ????? ??????? ?????????????? ???????????? ?????????. ???????????? ? ?????? ?????? ??????? ? ??????????? ???????????? ????? ?????????,
?? ????????? ? ??? ????????????? ???????????, ????????????? ?????????? ?????? ? ????????? ??????? ???????????? ? ?????????? ????????? ??????.
?????????? ??????????? ?????????????-????????? ???????????? ????????, ???????????? ?? ???????? ?????????? ??????, ??????????? ? ??????????? ??????, ????????? ????????? ??????????? ?????????? ?? ?????????????????? ?????? ? ??? ????? ??????? ??? ??????????? ??????, ????????? ? ???? ???????????? ????? ????????????????.
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
# 222 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
?????? ??????????
1. ??????, ?.?. MODEL CHECKING. ??????????? ???????????? ? ??????????????
??????????? ??????. ???.: ???-?????????, 2010. 560 ?.
2. Information Flow and Usage in an E-shop Operating within an Agent-based E-commerce
System / Drozdowicz M., Ganzha M. Paprzycki M., Gawinecki M., Legalov A. // ?????? ??????????
???????????? ????????????. 2009. ?1. ?. 3-22.
3. ???????, ?.?., ????????, ?.?., ???????, ?.?. ??????? «???» ? ???????????? ??????????// ????? ????????? ?????????? ???????????????? ??? ??? 5 ? 2004. ? ?. 89-101.
4. ???????? Panorama. [??????????? ??????] ? ????? ???????: http://www.cs.ucsd.edu/
users/berman/panorama ? ????. ? ??????.
5. ???????? TotalView. [??????????? ??????] ? ????? ???????: http://www.totalviewtech.
com/products/totalview.htm ? ????. ? ??????.
6. ???????? Ozcar. [??????????? ??????] ? ????? ???????: http://www.mozart-oz.org/
documentation/ozcar/index.html ? ????. ? ??????.
7. ?????, ?.?., ????????, ?., ?????, ?. ??????????? ??????? ????????. ?.: ?????,
2002. 416 ?.
8. ????, ?. ????? ????????????????. ?.: ???, 1984. 416 ?.
9. ??????, ?., ?????, ??. ????????????? ?????????? ? ???????????? ??? ?????????? ????????. ?.: ???, 1989. 424 ?.
10. ??????????? PVS. [??????????? ??????] ? ????? ???????: http://pvs.csl.sri.com ? ????.
? ??????.
11. ??????????? Isabelle. [??????????? ??????] ? ????? ???????: http://www.cl.cam.ac.uk/
research/hvg/Isabelle ? ????. ? ??????.
12. ??????????? Spin. [??????????? ??????] ? ????? ???????: http://www.netlib.bell-labs.
com/netlib/spin ? ????. ? ??????.
13. ??????????? Bogor. [??????????? ??????] ? ????? ???????: http://bogor.projects.cis.
ksu.edu ? ????. ? ??????.
14. ??????????, ?.?., ?????, ?.?. ?????????? ?????? ??????????? ????????. ?: ????? ? ?????, 1988. 255 ?.
15. ?????? ???????????? ?????????? ??????????????? ?????// ???????? ????. ???????
??????? ??????. ???. 500. ????????? ? ?????????????? ??????????? ??????????????????
???????. ???., 1996. ?. 56-63.
16. ???????, ?.?. ?? ?????????? ???????????? ? ???????????? ???????? ? ?????? ????????????????// ??????? ??????? ????. 2004. ? 3 (18)?. 63-72.
17. ???????, ?.?. ?????????????? ???? ??? ???????? ????????????-??????????? ???????????? ????????// ?????????????? ??????????. 2005. ? 1 (10). ?. 71-89.
18. ??????? ?.?., ???????, ?.?., ??????????, ?.?. ???????? ???????
?????????????-????????? ???????????? ???????? / ??????? ?? ?? ??. 2008. ? 1
(10). ?. 96-105.
19. ???????, ?.?. ?? ??????? ? ??????????? ?????????????-????????? ????????????
????????. [??????????? ??????] / ?.?. ???????, ?.?. ???????, ?.?. ??????????, ?.?. ????????? // ???????????? ?????????????? ?????????? (????'2009): ????? ????????????? ??# 223 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
????? ??????????? (?????? ????????, 30 ????? ? 3 ?????? 2009 ?.). ??????????: ???. ?????,
2009. ? ?. 757-764. ? 1 ????????. ???. ???? (CD?ROM).
20. ???????, ?.?. ????????????? ??????????? ?????????? ? ?????????????? ??????
????????????? ???????????????? // ?????????????? ? ?????????? ??????????: ?????????
????????? ????????? ?????-????????. ??????????, 2005. ?. 172-183.
Debug and Verification
of Function-Stream Parallel Programs
Julia V. Udalova,
Alexander I. Legalov and Natalie U. Sirotinina
Siberian Federal University,
79 Svobodny, Krasnoyarsk 660041 Russia
Debug function-stream parallel program can pass in one of the four realized modes: mode of
incremental debug, mode of layer debug, mode of branch debug and mode of formula?s checking.
Verification of function-stream parallel programs with asynchronous lists is described in article.
Keywords: debug, verification, function-stream parallel programs.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 225-234
~~~
??? 621.791.763.1
?????????????? ?????????????
????????????? ? ???????? ?????
??? ????????????? ??????????
???????? ??????
?.?. ?????????, ?.?. ????????,
?.?. ???????????, ?.?. ???????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
??????????? ? ??????????? ?????????????? ?????? ????????????? ? ???????? ????????? ???
????????????? ?????????? ???????? ??????. ???????? ??????? ????????????? ?????????
???? ??? ?????? ? ??????? ? ??????????, ? ????? ? ?????????? ????????. ??????????? ???????
????????? ???????? ?? ????????????? ????????? ????, ? ????? ?? ???????? ????????????
?????? ?????? ??? ??????.
???????? ?????: ?????????? ??????, ?????????????? ?????????????, ??????????????
???????????, ????????????? ????, ???????? ????.
????????
????????????? ?????????? ???????? ?????? (????) ??????? ???? ?????????? ?????????
????????? ????? ???????????? ?? ????????? ? ?????????????: ?????????? ??????????????????; ??????? ????????????? ???????? ???????????? ??-?? ????????? ???????? ??????????
???????, ??? ????????????? ???????? ??? ???????????? ?????????????; ? ????? ? ????????????? ???????? ???? ?????????? ??????????? ? ????????????? ???????? ??????; ???????????
?????? ??????? ????? ???????? ??????; ????????????? ???????????, ??? ????????? ????????????? ?????? ?????????? ? ????? ?????????? [1-3].
????? ???????????? ?????????? ????? ??????? ???????????, ????????? ? ???????? ????
????????????, ???????? ?? ??????? ?????? ? ?? ???????????? ? ??????????? ??????? ?????. ?????????? ????? ???????? ????? ???????, ??? ???????? ????????, ????????, ???????,
??????? ?? ??????????, ???????????? ? ???????? ???????? ? ??????, ????? ??????????, ???????????????????? ??????? ??? ???????. ??? ??? ????? ???????? ? ????????????? ?????????
????????????? ???????? ???????????. ????????? ????? ??????????? ??????? ?? ?????????? ????? ??????? ? ??????? ????????? ????? ?????? ??????????, ??? ????? ??????? ? ?????????????
??????????? ????????. ?????? ??????, ? ????????, ????????? ???????????????? [1, 4-6].
*
1
Corresponding author E-mail address: dealig@rambler.ru
© Siberian Federal University. All rights reserved
# 225 #
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??????????????? ????????????? ????????? ?????????.
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???? [?]; x, y, z ? ?? ?????????? [?].
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??? ?????????? ????????? ?????? ??? ?????? ??? ?????????. ??????? ??????? ?????????? ????????? ???????? ???????? ??????. ???????? ???????? ??? ?????? ??????? ??, ?????? ?????????? ?? ??????????? ???????? ???????? ? ?????? ?? ??? ???????????????? ??????
(???. 1). ?? ????????? ??????? ???????? ???????????? ? ????????? ???????? ? ?????? ? ?????? ? ??????, ??????? ??????? ?????????? ??????????? ????????. ???? ?? ???????? ???????
????????????? ????????????? ???????? ??????, ????????, ?????????? ? ??????????? ???????
? ??????????, ????????????.
?????? ?? ???????? ????????? ??????? ??????? ????????? ???????????? ?? ???. 1. ??????? ?????? ???????????? ? ?????????????? ?????????? ????????? D?, ??????? h? ? ?????
??????? ??????? ????? ??. ?????? ????????? ???????? ? ?????? ? ?????? ? ?????? ?????????
? ???? ????????? ??????????? ????????? l?, ? ?4. ???????? ????????? ????? d?. ???????
?????? ?????? ???????????; ???????? l? ????? ???????? ?????????? ????? ???????????. ???????? ????? ?????? ???????????? ?????? ??????????? ????????? ?3. ????????? Z0Y ????????
?????????? ????????? ?????????????? ? ?????????????? ?????. ?????? ?????? ???????? ?????? ??????????????????????? ??????????, ????????????? ??? ??????????? ? ???????????
?? ???????????.
??????? ? ????????? ??????? ???????? ? ???????????? ? ???????? ???????????????
?????????. ?? ????????? ???????? ? ?????? ????????????? ???????? ?????? ??????? ????????????? ??????????????? ? ?????????? ????????????? ???????????. ?? ??????? ???????
????????? ??????????? ????????? ? ????? ??????????? ??????????? ????, ? ????????? ?????
???????? ???????? ?????????? ?? ?????????? ??????. ?? ??? ????????? ??????: ??? ????????? ???? ?????????? ????????? ??????, ? ??? ?????????????? ? ??????? ?????????.
???????????? ?????? ????????????? ?????? ??????? ???????? ?????????. ??? ?????????? ?????? ???????? ???????? ??????? ????????? ???????? ? ??????????? ?? ?? ?????????# 226 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
???. 1. ??????? ??????? ????????? ??????
?????: ? ???? ??? ?????????? ??????? ????????? ?????????? ? ?????????, ? ??? ???? ????
??? ????????????? ? ?????????????? ?????????? ?? ???? ???????? ?? ????. ????????? ?????? ????????? (1) ?????? ?? ????? ??????????? ????? ? ??????????? ??????????? ???????
????????. ??? ??????? ??????? ????????? (2) ???????????? ??????? ????????-??????????
????? ??? ??????????? ???????????? ??????? [11, 12].
????????? ?????????????????????? ???????, ? ????? ???? ??????? ??????? ?????????
??????????? ?? ????????????? ????????.
???????? ??????? ???????? ???????????? ????????????? ?????????????? ??????????,
????????? ???? ? ???????????, ? ????? ??????????? ????????? ??????? ????????? ?? ??????
????????? ????.
??? ?????? ???????????? ?????????????? ?????? ????????? ??????, ????????? ??
?????? ?????????? ?????????? ???????, ? ??????, ????????? ????????? ??????????? [13].
?????? ?????????? ??????????? ????? 410, ??? ? ????????? ?? ???????? ????????? ?????? ?
??????????? ??????? ???? d? ???, ???????????? ?????? ?? ??????? h?1 ? h?2 ? ???? ??????????? ?????????????? 0,33, 0,1 ? 0,16 ??. ??????, ????????? ? ?????????? ??????, ? ?????
??????????? ?????? ?????? ?????????? ?????????????? ????????????? ??????????? ? ??????? ????????? ????????????. ????????? ?????? ??? ????????? ???????? ?? ??3 ???????
30 ??, ???????? 1+3 ?? ??? ?????????? ????? ??????????? 40 ??. ??????????? ?????????
??? ???? ??? ?????????? ?????????? ?????? ??????. ???????? ????????? ?????? ?????????
?? ??????????? ??????????, ??????????? ? ?????????, ?????????? ????? ??? ?????????
??????????. ??????? ??????????? ??? d? ???, h?1 ? h?2 ????????? ?????????????? 13,6, 8,4 ? 34 %.
?????????? ??????????? ????????? ?????????????? ????????? ???????????? ??????????????
???????? ?????? ? ???????? ????????????. ?????????? ???????? ???????? ?????? ????????????? ??????????? ? ? 0,95 ????, ??? ??????????? ??????????? ????????????? ? ?????????????????? ??????? ?? ??????? (???. 2).
# 227 #
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?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
???. 2. ????????? ??????????? ????????????? ? ?????????????????? ???????: ???????? ????? ? ?????
????? ?? ??????????; ????????? ? ????? ????? ?? ??????????? ?????????????
?????????? ????????????
? ??????? ????????????? ?????? ????????? ????? ?????????????? ?????????????. ?
?????????, ?????????? ????????? ???? ? ??????????? ??????? ? ????????? ? ?????? ?????????
???? ? ? ???????? ??????. ????????? ????????? ????????? ???? ? ????????? ???????? ??????? ? ??????????, ? ????? ??????? ??????????????? ????????? ???? ? ???????? ???????? ? ?????? ?? ?????????? ???? ????????? ? ??????????? ?? ???? ???????? ???????? ????????: ????
??????? ??????? ???? ????????? ? ?????????? ????? ???????? ??????????. ??? ??????????
?????? ? ???????? ????????? ????????? ??????? ???????????? ? ??????????? ???????? ????????? ???? ?? ?????, ??????????? ? ??????????? ??????? ???????????? ???????:
Jmax = f (??, l?),
Jmax / Jmin = f (??, l? ).
(3)
????????????? ????????? ??? ????????? ??????????: ??????? ??????? 1+3 ??, ??????
??????? 30 ??, ?????????? ?? ?????? ???????, ?????????? ?? ?????????? 1,4 ?, ??????? ?????????? 8 ??. ??????????? ???????? ?? ??????? ?????????????? ?????????????? ????? ???
?????????? ?????? ??????? ???????. ????????? ?? ?????????? ??????????? ?????????????
?????????? ???????????? ?? ???. 3 ? 5.
????? ??? ?????????? ??????:
? = ?? + ?1?1 + ?2?2 + ?11?12 + ?12?1?2 + ?22?22.
(4)
???????????? ??? Jmax: a0 = 16,42; a1 = -1,09; a2 = -1,72; b11 = 0,24; b12 = 0,11; b22 = 1,07; ??? Jmax
/ Jmin: a0 = 4,53; a1 = -0,42; a2 = -0,33; b11 = 0,19; b12 = 0,03; b22 = 0,2.
?????????? ??????????, ????? ????????, ??? ???????? ??????? ????????? ???? ??????????? ? ???????? ???????? ? ??????. ?? ????????????? ???????? ????? ?????????
???? ? ?????????? ???????? ????????? ??????? ???? ??????? ??????? ????? ????????? ?
?????????? ????? ???????? ??????????: ? ?? ??????????? ??????? ?????????? ???????????. ? ???????? ?????? ??-?? ?????????? ????????????? ????? ???????? ???????? ????????? ???? ? ???????? ??????????? ?????????????. ?????????????, ??? ???????? ?????????? ???????????? ??????? ????? ??????? ?????????? ????????? ? ?????????? ?????
??????? ??????? ?????.
# 228 #
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?
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???. 3. ????????????? ????????? ???? J, ?/?2, ? ??????? ? ????????? ? ?????? ????????? ????: ? ? ? ? = 150,
l? = 30 ??, ? = 1+3 ??, d ? = 8 ??, ?????? ??????? 30 ??, U?/2 = 0,7 ?; ? ? ? ? = 600, l? = 100 ??, ?= 1+3 ??, d ?=
8 ??, ?????? ??????? 30 ??, U?/2= 0,7 ?
?
?
???. 4. ????? ????????? ???? ? ???????? ???????? ? ?????? ? ?????? ????????? ???? ?=1+3??, d ?=8 ??,
?????? ??????? 30 ??, U?/2=0,7 ?; ? ? ? ? = 150, l? = 30 ??; ? ? ? ? = 600, l? = 100 ??
?
?
???. 5. ??????????? ????????? ?max ? ?max/?min ?? ? ? ? l? (?) ? ????????????????? ????????? ???? ? ??????????
???????? ? ???????? ?????? (?)
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8
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??? ???? ????????? ??????????????? ??????????? ??????????, ????????????????
??? ????????, ????? ???????? ???????? ???????????? ?????? ?????? h?2, ? ????? ?? ???????????, ? ??????????? ??????? ???? d? ????, ?. ?. ??????? ? ????????? ???????? ????? ????????.
??? ???? d? ???? ? ????????, ??????????? ?? h?2. ??? ??????????? ???, ??? ?? ??????????? ?????
??????????????? ?????????????, ? ????? ?? ???????????, ?????????? ??????? ??????????????? [1, 4-6], ???????? ???????????? ??????? ?????? h?1 ? ????? ?????? ?????????? 70 ? 90 %
?? ??????? ??????, ?. ?. ?????????? ??? ??????????? ?????????.
??????? ??? ?????????? ??????????????? ???????????? ?? ????????? ???????????? ???????? ????? ??? ???? ??? ????? ?????? ???????????? ????????? ????????? h?2 ? ??????????? ?? ??????? ??????????: ??????? ??????? ? ?????? ?????? ?1 ? ?2, ???????? ??????????
????? ??????????? l?, ???????? ????????? d?, ?????? ?????? ?????? ?2, ????? ???????????
???????????? ?????? ??????? ?4, ?????????? ?? ?????????? U?? ? ??????? ??? ?????????? t??.
?????? ??????? ?????? ?1, ???? ??????? ??????? ???? ????????? ?? ? ?????????? ?? ????????
???????? ? ?????? ?? ??? ???????????????? ?????? ????????? ?? ???????? ??????????? ?????????? ? ?????????? 30 ??, 300 ? 5 ?? ?????????????? (??. ???. 1).
????? ???????, ? ???????????? ???????????? ???????????:
h?2 = f (?1, ?2, ?2, ?4, d?, l?, U??, t??).
(5)
??????? ??????? ? ????????? ?? ???????????? ????????? ? ????. 1.
??????????????? ?????? ?????? ??????? ?????????? ??????? ?????????? ???????? ??
h?2, ??????? ???? ??????? ?????????? ?????? ??????? ???????. ?????? ??? ????? ???????
????? ??????? ?????????? ?????????? ?????? ?????? ??????? ????????? ????? (38) ?????????????, ??????? ???? ?????? ???????????? ???????? ?????????. ??? ???? ??????? ??????
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# 230 #
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(6)
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
?
?
???. 6. ???????? ?????????????? ???? ??? ????; U?? = 1,6 ?; t?? = 0,3 ?; l? = 50 ??; d ? = 7,5 ??; ? = 1+3 ??;
? ? = 37,50
?????? (6) ???????? 16 ?????????????, ??????? ??? ?? ?????????? ????????? ???? ?
?????? ????????????? N ? 16. ? ???????? ??????, ??????????? ? [14], ??? ?????? ??????????
????, ??????????? ???????? 2..37 //18.
? ?????????? ???????? ????????? ??????:
? = 0,893 ? 1,017?1 + 0,791?2 + 0,116?3 ? 0,097?4 +
+0,075?5 + 0,088?6 + 0,093?7 + +0,683?8 + 0,123z1 +
+ 0,031z2 ? 0,024z3 ? 0,095z5 ? 0,067z6 + 0,028z7 ?0,078z8.
(7)
?? ???. 6 ???????? ????????????? ???? ?? ?????????? ??????? ??????? ? ????????? (???. 6 ?)
? ? ??????? ?????? (???. 6 ?).
?? ???. 7 ???????????? ??????????? h?2 ?? ??????? ???????, ?????????? ????? ???????????, ?????????? ?? ?????????? ? ??????? ??????, ?????????? ?????????????? ????????? (7).
??? ?????????? ???????? ??????? ???????, ?? ????????? ? ???, ????????? ??????? ???????? ???????? (?? ????. 1).
????????? ???????? ????????????? ai ? aii ?????????????, ??? ?? ??????? ??????????
???????? ???????? ?????????? ??? ???? ? ???????? ???????????? ?????? ?????? ? ????????
??????? ?????? ??????? ??????? ? ?????? ???????, ??? ????????? ??????? ??????????????
? ????? ??? ??????????, ?????????? ????? ???????????. ??????? ??????? ??????? ??????? ??
?? ?????????????? ?????????????, ???????? ???????? ?? ??????? ????, ??????? ??????????
????. ??????? ?????? ??????????? ??????? ? ????????????, ??? ??????. ??? ?????????? ??????? ?????? ???????????? ?????? ?????? ????? ?????????????; ?????????? ?????????? ??
# 231 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
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???. 7. ??????????? ??????? ???????????? (h ?) ?? ??????????????? ?????????? ??????, ??????????
?????????????? ??????????????: ? ? ?? ?????????? ????? ??????????? ??? ??????? ??????? ??????
?1: 0,5 ??; 2-1,0 ??; 3-1,5 ??; ? ? ?? ??, ??? ??????? ?????? ?????? ?2: 1-2 ??; 2-3,0 ??; 3-4 ??; ? ? ??
???????? ?????????? U?/2 ??? ???????????? ?????? t??: 1-0,1 ?; 2-0,3 ?; 3-0,5 ?
?????????? (?????????? ????) ?? ???????????? ??????????? ????? ???????. ???????? ? ???????? ?????????????? ???? ?????????? ????????????, ??? ? ???????? ?????? ? ??????????? ????????????? ??????? ?????? ?????????? ????????????????? ???? ? ???????: ?????????? ????
???????????? ? ?????????? ???? ??????. ??????? ????? ??????? ?????, ??? ?????????????
?????? ??????? ??? ???? ????????????????. ??? ???? ??-?? ???????????? ??????? ????????
?????????????? ?????? ??????? ??????? ????????? ?????? ?? ????????????????? ???? ?, ???
?????????, ?? ???????????? ?????? ?????? ??????? ????????????????? ????????. ????????
??????? ?????????????? ???????? ?? ???????? h?2, ????? ????????, ??? ???????? ????????? h?2
??????? ?????????????? ??????????? ???? ???????????? ?? ???? ?? ????????: ? ???????????
???? ???????????? ???????????? ?????? ?????? ???????????.
??????
1. ??????????? ? ?????? ??????? ???????? ????????? ???????????????????? ?????? ???????? ????, ?????????? ?? ?????????? ??????? ????????? ?????????????? ?????????? ? ????????????????. ????????? ? ????????? ??????? ????????????? ????????? ???????????????? ????????. ?????? ????????? ?????? ????????? ?????????????????????? ??????? ?????????
??????? ? ?????????? ? ??????????? ?? ???????????, ? ????? ??????? ??????? ??????? ???????.
# 232 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
2. ???????????, ??? ???????? ??????? ????????? ???? ??? ?????? ??????????? ? ????????
???????? ? ??????. ?? ????????????? ???????? ????? ????????? ???? ? ?????????? ???????? ????????? ??????? ???? ??????? ??????? ????? ????????? ? ?????????? ????? ????????
??????????: ? ?? ??????????? ??????? ?????????? ???????????. ? ???????? ?????? ??-?? ?????????? ????????????? ????? ???????? ???????? ????????? ???? ? ???????? ??????????? ?????????????.
3. ?? ???????? ???????????? ?????? ?????? ??? ???? ???????? ???????? ??????? ????????? ??????? ??????? ? ?????? ???????, ??? ????????? ??????? ?????????????? ? ?????
??? ??????????, ?????????? ????? ???????????. ??????? ??????? ??????? ??????? ?? ?? ?????????????? ?????????????, ???????? ????, ???????? ?? ???????, ? ??????? ??? ??????????.
??????? ?????? ??????????? ??????? ? ????????????, ??? ??????. ??? ?????????? ???????
?????? ???????????? ?????? ?????? ????? ??????????.
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
?????? ??????????
1. ??????????, ?.?. ???????? ? ????????? ????????????? ???????????? ?????? ? ???????. ?.: ??????????????, 1974. 232 ?.
2. ??????, ?.?. ?????????? ???????? ? ????????? ?????? ??????. ?.: ??????????????,
1978. 246 ?.
3. ????????, ?.?. ?????????? ??????: ????. ??????? / ????. ???. ???. ??-?. ? ?????, 2006. 83 ?.
4. ??????, ?.?. ???????????? ???????????????? ????? ??? ?????? ?????????????? ??????? ?? ???????????????? ?????: ????. ? ????. ????. ????. ?., 1961. 156 ?.
5. ??????????, ?.?., ?????????, ?.?. ???????????? ???????? ????????????? ???????????? ??????// ?????????????? ??????. 1965. ? 6. C. 3-6.
6. ????????, ?.?. ???????????? ?????????? ???? ??? ????????, ???????? ? ??????
??????// ?????????? ??????. ?.: ??????, 1951.
7. ????????, ?.?. ????????????? ? ????????? ????. ?.: ???????, 1968. 368 ?.
8. ????????, ?.?., ???????, ?.?., ???????, ?.?. ?????????????. ?.: ???????, 1975. 488 ?.
9. ???????, ?.?., ?????????, ?.?. ????????? ?????????????? ??????. ?.: ?????, 1999. 799 ?.
10. ??????, ?.?., ???????, ?.?., ?????, ?.?. ?????????????? ????????????? ????????
????????? ???????????????? ????????? ??????????-???????? ?????????? ?????????? ??????????// ?????? ?????????? ???????????? ????????????. ??????? ? ??????????. 2008. ?1. ?.
68-75.
11. ???????, ?. ?., ?????????, ?.?. ?????????? ?????. ?.: ?????, 1977. 440 ?.
12. ?????????, ?.?., ?????, ?.?. ???????????? ?????????? ????. ???. 2-?, ????, ???. ?.:
?????, 2005. 384 ?.
13. ??????, ?.?., ???????, ?.?. ?????? ????????? ????????? ?? ???. ????: ???, 1986.
100?.
14. ?????, ?.?., ?????, ?.?. ??????????? ????????? ?????????? ?????????????? ???????? ???????????? ?????????????. ?.: ??????????????, 1980. 304 ?.
# 233 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ?????????, ?.?. ????????? ?????????????? ????????????? ????????????? ? ???????? ??????
Mathematical Modeling of Electric
and Thermal Fields
at Indirect Resistance Welding
Ksenya V Solov?eva, Alexandr I Demchenko,
Yuri G. Novoseltsev and Alexandr N. Shmarlovsky
Siberian Federal University,
79 Svobodny, Krasnoyarsk 660041 Russia
A mathematical model of electric and thermal processes at indirect resistance welding has been
developed and realized. The picture of current density during welding is shown in the parts and also
in transitive contact. The influence of some factors on density current distribution and also the value
of bottom part profusion during welding was established.
Keywords: resistance welding; mathematical modeling; electric field; thermal field.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
? ??????
?????????? ?????????? ??????????
17 ??????? 2010 ?. ????????? ????????? ?????????, ?????????, ?????? ???. ????, ?????????? ???????? «?????????????? ????????? ? ???????????
???????????????? ?????????», ??????? ???? 60-??????
??????.
?.?. ????????? ????? ???? ???????? ???????????? ? ???????????? ????????? ??????? ????????
??. ???????? ? 1972 ?. ? ????????? ??????????. ?
1999 ?. ??? ?????????? ?????? ??????? ??????? ?????????? ????, ? 2001 ?. ????????? ?????? ??????
??????????.
? ????????? ????? ?.?. ????????? ??????????? ??????? «?????????????? ????????? ? ??????????? ???????????????? ?????????» ?????????
??????? ???????? ? ???????????????? ??????????
???????????? ????????????. ????????? ?????????????? ? ??????-????????????????? ??????? ??????????, ??????????? 5 ???????? ? 16 ?????????? ????. ??? ??? ????????????
?????????? ??? ????????? ????, ? ????????? ????? ?????????? ?????? ???? ??????????
? ??????? ????? ????????? ? ????????????. ??????? ?????? ?.?. ?????????? ????????? ??????? ??????????? ?????????????????? ?????, ??????? ? ???????? ????? ???????,
?????????? ?????????????? ? ??????????????? ???????????? ?????????? ? ?????????
??????????.
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?????????????? ??????? ????? ? ???????? ?????????? ????? ???????? ???? ? ????????????????, ???????????? ????? ??? ? 100 ??????? ? ??????-???????????? ??????.
????????? ?.?. ????????? ??????? ???????????? ? ?????????????, ????????????????
? ??????-?????????????????? ????????????? ?. ??????????? ? ??????, ?????? ??? ??? ??
???, ??????? ??????????????? ???????????, ???? ?? ???, ?????-?????????? ????????,
???? «????????», ??? «? ? ?».
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? ?????????? ?????????? ?? ??? ? ????????? ??????????????? ??????????????? ????????????.
????????? ????????? ???????????? ??????????? ????????? ??????????? ?????????????
???? ? ????? ??????. ? ??????? 2003 ?. ?????? ?????? ??????????? ????????? ???????? ???????? ?? ??????????? ???????????? ??????-?????????????? ???????????? ? ????????????
????? ? ?????????? ??????????????????????? ????????????. ? 2004 ?. ?.?. ????????? ????
????????? ????????????? ?????? ????? ?????? ???????????. ? 2006 ?. ????????? ????????
???????????? ??????????? ? ????? ?????????? ?????????.
# 235 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
? ?????? ?????????? ?????????? ??????????
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????? ?? ???? ????? ?????????????? ?????? ? ????????.
? ????????? ????????? ????????? ??????? «?????????????? ????????? ? ??????????? ????????????????
?????????» ????????? ??????? ???????? ? ???????????????? ?????????? ???????????? ????????????
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
? 85-?????
????? ???????????? ????????
??????? ????? ??????????? ??????? 20 ??????
1925 ?. ? ??????? ??????? ??????????? ?????? ????????. ????????, ? ????? ? ??????? ?? ?????, 10 ??????? 1943 ?. ??????? ? ???????? ?????????? ???????
?????. ?????? ????????????-???????????, ?????????? ? ??????? ?????, ???????????? ??????. 27 ???????? 1943 ?. ??? ?????? ?????.
?????? 1944 ?. ???????? ? ?????????? ???????? ??????? ????????, ??????? ? ???????? ???????
? 1950 ?., ??????? ???????????? ??????? ????????.
?? ???????????????? ?????????, ?????????? ?????????? ??????????? ? ?????? ???????? ?? ??????????, ?????????? ? ?????????? ????????, ????????
???????? ? ??????? ? ??????? ????????? ???????,
? 2005 ?. ??? ????????? ?????? «?????????? ?????
III ???????».
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????? ?? ?????? ????????????? ????, ??????, ??? ????????? ??????, ??? ????? ??? ??????.
???????????? ???????? ? ??????????? ? ? 1955 ?. ??????? ??????? ???? ?? ?????? ? ??????
??????????? ?? ?????????? ???????? ????????????? ? ????????? ???????????? ?????????? ????? ?????????? ?? ???????????.
?? ?????????????? ??????? ??? ?????? ?? ?????????? ?? ??????????? ??????? ? ??????? ?????? ? ????????? ?? ???? ? ??? ?.?. ????????, ?????? ? ???? ????????????, ??????????? ? ????????????, ???????? ????????? ? ??? «??????? ???????? ? ?????? » (?? ????????? 1983 ?.). ??????? ?????????????? ?.?. ???????? ??? ????????? ?????????? ???????????
«??????????? ???????????????? ??????? ??? ? ????????? ??????», ??????? ?????????? ?
??? ?? ???? 19 ?????? 1970 ?., ? ???? ??????????? ???? ??????? ????????? ???????? ???????, ? ?.?. ??????? ???? ?????? ???????? ???? ? ???? ????.
??? ???????? ??????? ???? ????????? ?? ?????? ? ????? ??????????? ??????????? ??????? ????? ?????? (???, ???, ????, ???, ???, ????, ?????); ????? ???????,
?????????? ??????, ????????? ?? ????? ??? ???? ?????????. ? ?????????? ?? ??????? ??????? ??????? ?????????????? ?????? ?????? ??? ? ???, ???? ????? ?? ?????? ? ??????.
?????????????, ??? ??? ???????????????? ????? ?.?. ??????? ??????? ?????? ???. ?? ?????? ????????? ??? ?????????? ?????? ???????? ? ????, ? ?????? ?????????? ?????? ?????
«??????-??????????? ?????????????» ?? ????????? ???????? ???????????? ???????? ???????
(2004 ?.).
? ?????????? ????????????? ?????????????? ????? ?????????? 16 ?????????? ? ??????
??????? ????. ??? ??? ??????? ? ??????????????? ???????: ????????????? (???????) ? ???# 237 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
? 85-????? ????? ???????????? ????????
??? (??? ?? ???, ??? ??? ???). ? 60 ? 80-? ??. ?????? ? ?????? ?????? ? ?????????????
?????? ??????????, ? ? 1996 ?. ?? ????????? ????? ? ???? ??? ???????.
??????? ???????? ?.?. ???????? ? ??? ????? ? ?????? ???????????? ??? ?????????????
? ???? ???????? ????????? ??????????? ?????????? ????????????? ? ???????????? ???????????? ?? ???? ???????? ????????????: ????????????????? ?????? ??????????, ?????????
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????? 150 ?????????????? ????? ?.?. ???????? ???????????? ? ????????? ??????, ???????? ? 2000 ?. (16 ?.?.). ? ????????? ???? ????????? ??? ????????????? ??????-????????????
???????????, ??????????? ?.?. ????????, ? ?????????, ?? ????: «??????????? ????????? ?
?????????????», ????????? ??????? (20 ?.?.) ?????? ? 2005 ?.
?????????? ??????-??????????????? ?????????? ?.?. ???????? ?????:
? ??????? ?? ?????????? ????????? ?????????? ??????? ??????????? ? ??????
(1962 ?.);
? ????????? ? ?????? ????????? ???? ?? V ????????????? ?????? ????????? (1967 ?.);
? ?????????? ????????? ?????? «??????????? ??????? ????? ? ??????? ?????» (1982 ?.),
??????? ??????? ???? ? ????????????? ?? ??????????? 20 ???;
? ???????? ??????-??????????????? (1995 ?.), ????? ?????????????? ?????? (1998 ?.)
????????????? ???????? ???? ?????? ?????;
? ???????? ???????? ?????? ???????? ?????? ???? (2005 ?.);
? ????????? ? ???????????? «??????? ? ?????? ???????? ??????» (2000 ?.).
??????? ??? ????? ???????? ???????? ???????????? ????????????. ? ????????? ? ?????????? ? ???? ??????? ????????? ????? ? ???????? «??????» ?????????? ??????, ?????? ? ????.
? 1961-1965 ??. ? ??????? ?????????, ? 1971-1975 ??. ? ??????? ?????????? ? ???????????? ???
?????????? ???????? ?? ????????? ???????????.
?????? ??????? ?????? ???? ???? ??? ????????? ? ???????? ??????????? ?? ??? ???? (?
?????????? ??????????). ????? 30 ??? ? ???????????? ?????????????? ???????? ??????? ??????, ?? ??? ??????????? 79 ?????????????? ???????? ?????? ?????? ??????????. ? 1971-1992
??. ? ???? ??????????? ??????? «???????? ?????» ? ???????????? ????????? ??????? ??????.
? 70-? ??. ??????? ????????????? ?????? ?????? ???????? ???????? ??????.
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??????? ?? ?????? ? ???, ??? ?? ??????? ?????? ? ????, ??? ???-???? ?? ?????????? ??????
????, ?? ? ? ???, ??? ??? 66 ??? ???????? ? ????? ? ??? ?? ??????????? ?????????, ????????
?????? ???? ??????????? ??????.
???????? ?????? ?????? ?????????? ??????? ????????? ????????, ? ????? ?????. ? 1951 ?.
45 ?????????? ??? ??? ???????????? ?????????? ??????? ? ???? ????? ??????????????, ???.,
# 238 #
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?.?.?., ?????????????? ??????? ???, ?????? ????? ????????? ? ???????? ???????????, ???????????? ??????? ???? ??????. ?????? ??? ? 1995 ?. ? ?????????? ?? ????? ????? ???????? «???????». ??????? ???????? ????????? ????? ?????, ??????? ?? ???????, ??????? ???????,
???., ?.?.?., ???? ???????? ?????? ???????? ???, ??? ???????? 4 ??????? ????.
?.?. ??????? ? ????????? ????? ?????????? ???????? ? ???????????? ?????????
??????????-????????????.
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???? ?????? ??? ??????? ????????.
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block {
x2 << tail_1:1; // ????????? ??????? ???????? ????? ?? tail_1 ? ?1
s << (x1,x2):op; // ???????? ??? ????? ???????? ??????????
tail_2<< tail_1:-1; // ?????????? ???????? ???????????? ??????
//??????? ???? ?? ????? ? ????????
[((op,+):[=, !=]):?]^( { op << ? ; }, { op << + ; } ) ;
// ??????????? ????????? ?????????? ????????? ???????????? ??????
[((tail_2:|, 0):[=, !=]):?]^
( s, { (asynch( s, tail_2:[]),op):F } ):. >>break }
}
):. >>return; }
# 221 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
??????????? ????? ??? ( asynch(S,??????? ??????), + )
??? ??? ???????? + ???????? ??????? ??????????
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
???. 10. ??????????? ???? ?????????? ??????????? ?????????
? ???????? ????????? ?????? ?????? ?????? ???? (asynch(1,2,3), -). ?????????? ??? ????????? ???? ?????????? ??????????? ????????? (???. 10).
????? ??????????? ???????? ??????????, ??? ????????? ?????????????????? ??????????
????????? ? ?????? ???????? ? ?????? ??????????? ??????????? ??????? (0 ??? 2 ??? 4), ?
????? ????????? ??? ????????? ???????? ????????? ???????????? ?????? ? ????????? ????.
???? ??????????? ??????? ???????? ??????????? ????????, ???????????
?1+?2+?3+?4+?5+?, ??????? ???????? ???????????? ?????? ???????, ??? ????????? ?????????? ?????? ???????? ? ????????????? ?? ???????? ?????? ??????????.
??????????
????????????? ?????????????-????????? ????????? ???????????????? ?????? ????????????? ????????????? ??????? ????????? ?????????? ??? ?????????? ???????????? ???????? ?? ???? ??????, ??????????????? ?????????? ???????????, ???????????? ?????
?????????????????? ??????????. ?????? ? ???, ??? ?? ????? ? ???????????? ??????????
?????? ? ???? ??????, ??????????? ??? ????? ??????? ?????????????? ???????????? ?????????. ???????????? ? ?????? ?????? ??????? ? ??????????? ???????????? ????? ?????????,
?? ????????? ? ??? ????????????? ???????????, ????????????? ?????????? ?????? ? ????????? ??????? ???????????? ? ?????????? ????????? ??????.
?????????? ??????????? ?????????????-????????? ???????????? ????????, ???????????? ?? ???????? ?????????? ??????, ??????????? ? ??????????? ??????, ????????? ????????? ??????????? ?????????? ?? ?????????????????? ?????? ? ??? ????? ??????? ??? ??????????? ??????, ????????? ? ???? ???????????? ????? ????????????????.
?????? ???????????? ? ??????????? ??? ????????? ????????? ???????? ??????????
???????????? ????????????.
# 222 #
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?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
?????? ??????????
1. ??????, ?.?. MODEL CHECKING. ??????????? ???????????? ? ??????????????
??????????? ??????. ???.: ???-?????????, 2010. 560 ?.
2. Information Flow and Usage in an E-shop Operating within an Agent-based E-commerce
System / Drozdowicz M., Ganzha M. Paprzycki M., Gawinecki M., Legalov A. // ?????? ??????????
???????????? ????????????. 2009. ?1. ?. 3-22.
3. ???????, ?.?., ????????, ?.?., ???????, ?.?. ??????? «???» ? ???????????? ??????????// ????? ????????? ?????????? ???????????????? ??? ??? 5 ? 2004. ? ?. 89-101.
4. ???????? Panorama. [??????????? ??????] ? ????? ???????: http://www.cs.ucsd.edu/
users/berman/panorama ? ????. ? ??????.
5. ???????? TotalView. [??????????? ??????] ? ????? ???????: http://www.totalviewtech.
com/products/totalview.htm ? ????. ? ??????.
6. ???????? Ozcar. [??????????? ??????] ? ????? ???????: http://www.mozart-oz.org/
documentation/ozcar/index.html ? ????. ? ??????.
7. ?????, ?.?., ????????, ?., ?????, ?. ??????????? ??????? ????????. ?.: ?????,
2002. 416 ?.
8. ????, ?. ????? ????????????????. ?.: ???, 1984. 416 ?.
9. ??????, ?., ?????, ??. ????????????? ?????????? ? ???????????? ??? ?????????? ????????. ?.: ???, 1989. 424 ?.
10. ??????????? PVS. [??????????? ??????] ? ????? ???????: http://pvs.csl.sri.com ? ????.
? ??????.
11. ??????????? Isabelle. [??????????? ??????] ? ????? ???????: http://www.cl.cam.ac.uk/
research/hvg/Isabelle ? ????. ? ??????.
12. ??????????? Spin. [??????????? ??????] ? ????? ???????: http://www.netlib.bell-labs.
com/netlib/spin ? ????. ? ??????.
13. ??????????? Bogor. [??????????? ??????] ? ????? ???????: http://bogor.projects.cis.
ksu.edu ? ????. ? ??????.
14. ??????????, ?.?., ?????, ?.?. ?????????? ?????? ??????????? ????????. ?: ????? ? ?????, 1988. 255 ?.
15. ?????? ???????????? ?????????? ??????????????? ?????// ???????? ????. ???????
??????? ??????. ???. 500. ????????? ? ?????????????? ??????????? ??????????????????
???????. ???., 1996. ?. 56-63.
16. ???????, ?.?. ?? ?????????? ???????????? ? ???????????? ???????? ? ?????? ????????????????// ??????? ??????? ????. 2004. ? 3 (18)?. 63-72.
17. ???????, ?.?. ?????????????? ???? ??? ???????? ????????????-??????????? ???????????? ????????// ?????????????? ??????????. 2005. ? 1 (10). ?. 71-89.
18. ??????? ?.?., ???????, ?.?., ??????????, ?.?. ???????? ???????
?????????????-????????? ???????????? ???????? / ??????? ?? ?? ??. 2008. ? 1
(10). ?. 96-105.
19. ???????, ?.?. ?? ??????? ? ??????????? ?????????????-????????? ????????????
????????. [??????????? ??????] / ?.?. ???????, ?.?. ???????, ?.?. ??????????, ?.?. ????????? // ???????????? ?????????????? ?????????? (????'2009): ????? ????????????? ??# 223 #
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
?.?. ???????, ?.?. ???????... ?????? ??????? ? ??????????? ?????????????-????????? ???????????? ????????
????? ??????????? (?????? ????????, 30 ????? ? 3 ?????? 2009 ?.). ??????????: ???. ?????,
2009. ? ?. 757-764. ? 1 ????????. ???. ???? (CD?ROM).
20. ???????, ?.?. ????????????? ??????????? ?????????? ? ?????????????? ??????
????????????? ???????????????? // ?????????????? ? ?????????? ??????????: ?????????
????????? ????????? ?????-????????. ??????????, 2005. ?. 172-183.
Debug and Verification
of Function-Stream Parallel Programs
Julia V. Udalova,
Alexander I. Legalov and Natalie U. Sirotinina
Siberian Federal University,
79 Svobodny, Krasnoyarsk 660041 Russia
Debug function-stream parallel program can pass in one of the four realized modes: mode of
incremental debug, mode of layer debug, mode of branch debug and mode of formula?s checking.
Verification of function-stream parallel programs with asynchronous lists is described in article.
Keywords: debug, verification, function-stream parallel programs.
Copyright ??? «??? «??????» & ??? «A???????? K????-C?????»
Journal of Siberian Federal University. Engineering & Technologies 2 (2011 4) 225-234
~~~
??? 621.791.763.1
?????????????? ?????????????
????????????? ? ???????? ?????
??? ????????????? ??????????
???????? ??????
?.?. ?????????, ?.?. ????????,
?.?. ???????????, ?.?. ???????????
????????? ??????????? ???????????,
?????? 660041, ??????????, ??. ?????????, 79 1
Received 5.04.2011, received in revised form 12.04.2011, accepted 19.04.2011
??????????? ? ??????????? ?????????????? ?????? ????????????? ? ???????? ????????? ???
????????????? ?????????? ???????? ??????. ???????? ??????? ????????????? ?????????
???? ??? ?????? ? ??????? ? ??????????, ? ????? ? ?????????? ????????. ??????????? ???????
????????? ???????? ?? ????????????? ????????? ????, ? ????? ?? ???????? ????????????
?????? ?????? ??? ??????.
???????? ?????: ?????????? ??????, ?????????????? ?????????????, ??????????????
???????????, ????????????? ????, ???????? ????.
????????
????????????? ?????????? ???????? ?????? (????) ??????? ???? ?????????? ?????????
????????? ????? ???????????? ?? ????????? ? ?????????????: ?????????? ??????????????????; ??????? ????????????? ???????? ???????????? ??-?? ????????? ???????? ??????????
???????, ??? ????????????? ???????? ??? ???????????? ?????????????; ? ????? ? ????????????? ???????? ???? ?????????? ??????????? ? ????????????? ???????? ??????; ???????????
?????? ??????? ????? ???????? ??????; ????????????? ???????????, ??? ????????? ????????????? ?????? ?????????? ? ????? ?????????? [1-3].
????? ???????????? ?????????? ????? ??????? ???????????, ????????? ? ???????? ????
????????????, ???????? ?? ??????? ?????? ? ?? ???????????? ? ??????????? ??????? ?????. ?????????? ????? ???????? ????? ???????, ??? ???????? ????????, ????????, ???????,
??????? ?? ??????????, ???????????? ? ???????? ???????? ? ??????, ????? ??????????, ???????????????????? ??????? ??? ???????. ??? ??? ????? ???????? ? ????????????? ?????????
????????????? ???????? ??
1/--страниц
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