close

Вход

Забыли?

вход по аккаунту

?

Thermodynamic properties and Sn-Sb phase diagram

код для вставкиСкачать
Thermodynamic properties and Sn-Sb phase diagram/
 20
Russian Journal of Physical Chemistry, Vol. 79, No. 1, 2005, pp. 20–28. Translated from Zhurnal Fizicheskoi Khimii, Vol. 79, No. 1, 2005, pp. 26–35.
Original Russian Text Copyright © 2005 by Vasil’ev.
English Translation Copyright © 2005 by Pleiades Publishing, Inc.
INTRODUCTION
Tin–antimony alloys and tin–antimony alloys doped
with, for instance, indium are of interest for optoelec-
tronics as an alternative to the CdTe–HgTe solid solu-
tion. Exact data on the phase diagram, crystal structure,
and thermodynamic properties of these alloys are nec-
essary for the technology of obtaining semiconducting
materials. The available data on the Sn–Sb system are
contradictory. There are more than ten variants of the
phase diagram of this system [1–14]. Each of these dif-
fers from the others in some respect. The reason for this
is the special properties of Sn–Sb alloys, namely, the
low rate of chemical and phase transformations and the
propensity to form metastable states. The question of
the phase composition of Sn–Sb alloys therefore
remains open in spite of the large number of works on
this system. This is especially true of the central part of
the diagram in which the β
phase exists.
We distinguish between three main points of view
on the nature of the β
phase. Some authors [10, 11, 13]
believe it to have a continuous region of solid solutions
of a complex configuration which extends from 40 to
65 at. % Sb and to melt incongruently at 698 K (
425°C
)
and 65 at. % Sb. According to other authors [2, 5], there
exist two different polymorphs of β
phase solid solu-
tions, low- and high-temperature. Lastly, it was shown
in [5, 8, 14] that the β
phase is a set of individual phases
separated by heterogeneous mixtures rather than one
solid solution, at least at room temperatures.
Among the works on the Sn–Sb phase diagrams, we
must mention that by Iwasé et al.
[5] (Fig. 1), where the
Sn–Sb system was studied by the differential thermal,
X-ray phase, and microstructural analysis methods and
by electrical resistance measurements using a large
number (more than 100) of alloys. The authors of [5]
suggested that there existed a broad region of β
solid
solutions in the system (43–56 at. % Sb) with a poly-
morphic transition at 593–598 K (
320–325°C
). The
compositions of the boundary β
phase solutions remain
virtually unchanged from room to transition tempera-
tures. According to [5], the Tammann triangles in the
left part of the Sn–Sb phase diagram provide convinc-
ing evidence of the absence of any intermediate phases
between the solid solution of antimony in tin (Sn) and
the left boundary of the β
phase (43% at. % Sb).
On the whole, the phase diagram reported in [11]
differs insignificantly from than obtained in [5]. The
authors of [11], however, abandoned the suggestion of
a polymorphic transition of the β
phase but claimed the
existence of an aerial Sn
3
Sb
2
phase, which had never
A Complex Study of the Phase Diagram of the Sn–Sb System
V. P. Vasil’ev
Faculty of Chemistry, Moscow State University, Vorob’evy gory, Moscow, 119899 Russia
E-mail: VVassiliev@veernet.ru
Received December 23, 2003
Abstract
—The Sn–Sb system was studied by the electromotive force method and the microstructural, X-ray
diffraction, differential thermal, and microprobe analysis methods. Phenomenological crystal chemical models
of the β
phase were suggested. The models were based on hexagonal polymorph transformation into a quasi-
cubic polymorph with a change in crystal symmetry corresponding to a second-order phase transition. The ther-
modynamic properties of the system were optimized.
CHEMICAL THERMODYNAMICS AND THERMOCHEMISTRY
t
°, C
600
500
400
300
200
100
Sn
20 40 60 80
Sb
(Sn) (Sb)
246°
325°
β
1
425°
320°
β
2
1
2
3
4
Fig. 1.
Phase diagram of the Sn–Sb system according to the
(
1
, 2
) differential thermal analysis data [5] [(
1
) cooling and
(
2
) heating], (
3
) electrical resistance measurements, and (
4
)
microstructural analysis data.
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY
Vol. 79
No. 1
2005
A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM
21
been mentioned previously. They based their sugges-
tion of the existence of Sn
3
Sb
2
solely on the differential
thermal analysis data. Alloys with 10–35 at. % Sb gave
a double thermal effect between 513 and 523 K. There
was, however, no well-defined boundary between
these effects. The existence of a Sn
3
Sb
2
phase has not
been substantiated by X-ray diffraction thus far.
In [4], the Sn–Sb system was studied by the elec-
trical conductivity and thermal and microstructural
analysis methods. The regions of primary solid solu-
tions of antimony in tin (0–9.8 at. % Sb) and tin in
antimony (89.9–100 at. % Sb) were determined. The
electrical conductivity curve maxima at 40.4, 49.4,
and 55.4 at. % Sb corresponded to ordered phases.
Two weak maxima at about 38.7 and 66.7 at. % Sb
were also reported.
The hypothesis of the discrete character of the β
phase with the alternation of narrow homogeneous and
heterogeneous regions was substantiated by the X-ray
study of the structural parameters of the β
phase in the
region 42–62 at. % Sb in the Sn–Sb binary system and
doped Sn–Sb (+2% In), Sn–Sb (+2% Cd), and Sn–Sb
(+1% Te) alloys [8]. For all these alloys, noticeable
deviations from the Vegard linear law were observed.
The composition dependences of the unit cell volume
V
cell
(
x
Sb
) contained regions where the unit cell volume
remained constant. Such deviations were especially
noticeable for the Sn–Sb and Sn–Sb (+2% In) sys-
tems in the interval 50–55 at. % Sb, which was evi-
dence of the possible existence of heterogeneous
regions in the β
phase. This experimental observation
was ignored in more recent studies of the phase dia-
gram of the Sn–Sb system and ternary systems deriv-
ative from it.
The Sn–Sb phase diagram in the concentration
range 0–25 at. % Sb was studied in [12] by the differ-
ential thermal and X-ray phase analysis methods. The
authors did not observe a doublet of thermal effects
between 515 and 523 K similar to that reported in [11].
Nevertheless, a comparison of the X-ray patterns of the
alloy containing 43.5 at. % Sb obtained at 293 and
573 K led them to suggest that the existence of an aerial
Sn
3
Sb
2
phase was possible. The phase with 43.5 at. %
Sb was identified as a face-centered cubic lattice of the
NaCl type with the parameter ‡
= 0.613 nm.
In [14], diffusion equilibrium between two pure
metals (tin and antimony) was studied at 493 K. Only
two intermediate phases of the compositions Sn
4
Sb
3
(42.86 at. % Sb) and Sn
3
Sb
4
(57.14 at. % Sb) were
observed; these compositions coincided with the data
obtained in [5] on boundary β
phase solutions to
within 1%.
The purpose of this work was to obtain consistent
data on the thermodynamic properties, structure, and
phase diagram of the tin–antimony system using our
own results obtained by the electromotive force method
and the microstructural, X-ray phase, differential ther-
mal, and microprobe analysis methods and the litera-
ture data.
THE X-RAY STRUCTURE AND MICROPROBE ANALYSIS DATA
It follows from [15] that tin crystallizes in at least
two modifications. The α
polymorph has a diamond-
like structure (space group Fd
3
m
), and the β
polymorph
has a distorted diamond-like structure (
I
4/
mmm
). The
α ⇔ β
transition occurs at 287 K [15]; β
-tin has a tet-
ragonal unit cell with the parameters a
= 0.370 nm and
c
= 0.370 nm at 299 K.
Antimony forms hexagonal arsenic-type crystals
with six atoms per unit cell under normal conditions;
the space group is P
6/
mmm
. The equivalent rhombohe-
dral cell (space group R m
) contains two antimony
atoms. The hexagonal structure of antimony consists of
corrugated layers linked with each other by covalent
interactions between atomic planes (Fig. 2).
The data on the crystal structure of Sn–Sb alloys
taken from various sources are listed in Table 1. The
structure of the β
phase with various compositions can
3
0.133
c
0.200
c
0.133
c
0.200
c
0.133
c
0.200
c
Fig. 2.
Shubert projection of the hexagonal antimony cell
[16]; Ò
is the hexagonal cell parameter.
22
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY
Vol. 79
No. 1
2005
VASIL’EV
be described as either hexagonal or rhombohedral
packing. Changes in the hexagonal unit cell parameters
from Sb
hex
to β
-SnSb
hex
occur as a decrease in the
Ò
parameter from 1.127 (100 at. % Sb) to 1.06 nm
(44 at. % Sb), the ‡
parameter remaining virtually con-
stant (
‡
= 0.431 ± 0.001
nm).
Without taking into account superstructural reflec-
tions from the β
phase, it can conventionally be
described in terms of a NaCl-type face-centered cubic
lattice. Ignoring lattice distortions, the a
parameter of
such a lattice is 0.613 nm.
An alloy of the composition 43.5 at. % Sb was stud-
ied in [12] at 300 and 573 K to find out whether or not
the Sn
3
Sb
2
phase (40 at. % Sb) existed above 523 K.
The authors determined the lattice cell parameter of this
alloy at 573 K (
‡
= 0.6130 nm) on the assumption that
it was the high-temperature Sn
3
Sb
2
phase with a
NaCl-type structure. The unit cell parameters obtained
in [18] for the alloy with 45 at. % Sb at room tempera-
ture and the unit cell parameter for the alloy with
43.5 at. % Sb at 573 K [12] virtually coincided on the
assumption that the angle of the cubic unit cell was
α = 90°
in both structures. Our data on the β
phase
recalculated in the simplified approximation of the
NaCl and CsCl structures yield parameters that exactly
coincide with those reported in [12, 18, 20]. It becomes
clear why the authors of [12] were unable to obtain the
high-temperature diffractogram of the alloy containing
40.0 at. % Sb. The appearance of a substantial amount
of melt at 573 K interferes with the recording of reliable
X-ray patterns of this alloy.
As X-ray analysis does not allow us to unambigu-
ously distinguish between phases close in structure, we
performed a phase analysis of a series of unannealed
and annealed Sn–Sb alloys (a total of 25 samples) by
the microprobe method. The results are listed in
Tables 2 and 3. The measurements were performed for
5–10 points on a polished surface of each sample along
its length. The diffusion layer between tin and anti-
mony was measured separately. Tin and antimony pol-
ished surfaces were brought into contact for two
weeks at room temperature. The intermediate layer
between pure metals was found to contain phases with
5.59
± 1, 10.33 ± 1,
and 43.92
± 0.3
at. % Sb. All these
data correspond to averaged compositions.
MODEL DESCRIPTIONS OF THE β
PHASE
We suggested structural models of the β
phase on
the basis of the microprobe and X-ray data. Pure anti-
mony and the β
phase are structurally similar in many
respects. Both crystallographic cells are rhombohedral
of the R m
type, and both structures can be described
as hexagonal packings of periodically arranged six
planes along the Ò
direction. On the other hand, the β
phase can be described as a face-centered quasi-cubic
lattice of the NaCl type. Such a face-centered unit cell
can also be represented as a rhombohedron with the α
angle close to 60
°.
3
Table 1. Structure of tin–antimony alloys
Structure typeSb, at. %Systema, nmc, nmα, degRefs.
β-Sn (I4/mmm)0.020.3700.337– [17]
(Fm3m)
(distorted
NaCl type)
43.51(0.613)– – [12]
44.030.4311.06– [16]
45.040.61389.7[18]
(Fm3m)
(distorted
NaCl type)
50.030.43261.0693– *
40.4352– 59.87
30.86291.0656– [19]
40.61389.7
(Pm3m)50.01(0.4315)– – [20]
(Fm3m)55.040.6150– 89.18[18]
P6/mmm60.030.4311.09– [16]
Sb P6/mmm (Rm)
10030.43081.1274– *
30.43071.1273– [21]
30.43261.1274– [16]
40.45067– 57.11
Note:1, Cubic; 2, tetragonal; 3, hexagonal; and 4, rhombohedral system.
* This work.
3
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM
23
Table 2. Microprobe analysis of unannealed Sn–Sb alloys
c
2
Possible phasesc
3
c
1
= 47.44, from 670 K
9.36 ± 0.5(Sn
max
)9.5
45.0 ± 1.4Sn
9
Sb
7
or Sn
17
Sb
15
43.75 or 46.87
53.73 ± 0.5Sn
15
Sb
17
53.12
56.49 ± 0.5Sn
7
Sb
9
56.25
c
1
= 49.96, from 670 K 8.7 ± 1.0(Sn
max
)9.5
44.98 ± 1.0Sn
9
Sb
7
or Sn
17
Sb
15
43.75 or 46.87
c
1
= 50.19, from 640 K
8.46 ± 1.0(Sn
max
)9.5
48.33 ± 1.0Sn
17
Sb
15
46.88
56.85 ± 0.6Sn
7
Sb
9
56.25
62.54 ± 0.6Sn
3
Sb
5
62.5 c
1
= 52.03, from 670 K
8.02 ± 1.0(Sn
max
)9.5
47.5 ± 0.7Sn
17
Sb
15
46.88
52.24 ± 0.9Sn
15
Sb
17
53.12
56.55 ± 0.5Sn
7
Sb
9
56.25
58.0 ± 1.4Sn
13
Sb
19
59.38
53.86 ± 0.9Sn
15
Sb
17
53.12
57.37 ± 1Sn
7
Sb
9
56.25
88.02 ± 0.5(Sb
max
)88.89
c
1
= 64.95, from 640 K
57.61 ± 1.0Sn
7
Sb
9
56.2
60.88 ± 0.3Sn
7
Sb
11
61.11
89.72 ± 0.8(Sb
max
)88.89
c
1
= 69.59, from 640 K
63.16 ± 1.0Sn
3
Sb
5
62.5
89.65 ± 1.0(Sb
max
)88.89
c
1
= 74.40, from 670 K
60.88 ± 0.5Sn
7
Sb
11
61.11
61.92 ± 0.8Sn
7
Sb
11
or Sn
3
Sb
5
61.11 or 62.5
88.42 ± 1.0(Sb
max
)88.89
Note:All the alloys were cooled from the specified temperatures in
air; antimony contents (at. %): c
1
, in initial alloys; c
2
, analytic
data; and c
3
, in possible phases; Sn
max
is the maximum sol-
ubility of tin in antimony and Sb
max
is the maximum solu-
bility of antimony in tin.
Table 3. Microprobe analysis of annealed Sn–Sb alloys
No.c
1
T
anneal
, Kc
2
c
3
198.0*67397.8 ± 0.8(Sb)
296.0*67395.5 ± 0.8(Sb)
394.0*67393.8 ± 0.8(Sb)
492.0*67391.3 ± 0.8(Sb)
590.00*67388.75 ± 0.8(Sb
max
)
61.44 ± 0.5Sn
7
Sb
11
(61.11)
689.0067388.71 ± 0.5(Sb)
762.4250356.36 ± 0.5Sn
7
Sb
9
(56.25)
57.42 ± 0.5Sn
3
Sb
4
(57.14)
87 ± 3
(traces)
(Sb
max
)
861.1663361.17 ± 0.5Sn
7
Sb
11
(61.11) 959.3950354.46 ± 0.5β phase
55.76 ± 0.5Sn
4
Sb
5
(55.56)
57.66 ± 0.5Sn
3
Sb
4
(57.14)
1056.3050355.47 ± 0.5Sn
4
Sb
5
(55.56)
1153.1263352.68 ± 0.5Sn
17
Sb
19
(52.78)
1250.0850350.00 ± 0.5SnSb (50.00)
1346.8750346.94 ± 0.5Sn
17
Sb
15
(46.88)
1440.6050343.42 ± 0.5Sn
9
Sb
7
(43.75)
1540.00 5438.7 ± 1.0(Sn
max
)
43.92 ± 0.5Sn
9
Sb
7
(43.75)
1637.5150343.15 ± 0.5Sn
9
Sb
7
(43.75)
41.9 (traces)Sn
19
Sb
13
(40.62)?
Note:For each alloy, analyses were performed at nine points along
ingot length (20 mm, ingot diameter was 5 mm). All the
annealed alloys except 1–5 were quenched in water; alloys
1–5 were cooled in air; (Sb) denotes solid solutions of tin in
antimony of various concentrations; for the denotations
c
1
−c
3
, Sn
max
, and Sb
max
, see Table 2.
24
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
VASIL’EV
Consider the model of a hexagonal lattice of the β
phase (Fig. 3). The initial formation of the primary
solid solution of tin in antimony occurs as statistical
distribution of tin in the hexagonal lattice. Upon the
attainment of the limiting saturation concentration
(11.11 at. % Sn), ordering of the distribution of tin
atoms occurs in the second and sixth layers (counting
from the upper plane of the unit cell), but statistically,
they only occupy one third of the sites in each layer
(Fig. 3a). According to numerous differential thermal
and microprobe analysis data, the limiting concentra-
tion of the saturated solid solution of tin in antimony is
also 11 ± 1.5 at. % Sn. The complete replacement of
antimony atoms in the second and sixth layers results in
the formation of the SnSb
2
structure.
The replacement of antimony with tin in the mid-
dle layer of the β phase unit cell can occur statistically
continuously at elevated temperatures from 66.67 to
50 at. % Sb with the formation of the intermediate
phases Sn
7
Sb
11
and Sn
4
Sb
5
(Figs. 3b, 3c). This homol-
ogous series of phases based on hexagonal antimony
manifests itself when solid solutions experience
ordering. At a 1 : 1 ratio between Sn and Sb atoms, the
hexagonal structure acquires features of a distorted
NaCl-type structure. The distance between the (001)
planes then becomes equal to 0.166Ò.
Tin–antimony alloys with a NaCl-type structure can
be formed in two ways. First, the atoms of both metals
may be distributed statistically, and rock salt symmetry
may remain unchanged on average. On the other hand,
atoms of the two metals may alternate, that is, occupy
different layers (ABCABC…) of the face-centered
metal sublattice alternating along the body cell diago-
nal. The crystal then acquires a rhombohedral shape
and stretches or shrinks along the (111) axis.
At elevated temperatures, the NaCl-type β phase
forms a continuous series of solid solutions. Solid solu-
tions experience ordering as the temperature decreases
with the formation of intermediate phases that only dif-
fer from each other by superstructural peculiarities. The
crystal chemical models of such phases can be con-
structed on the basis of the model of the unit cell of the
SnSb (1 : 1) phase.
The unit cell of the SnSb (1 : 1) superstructure with
the parameter 2‡ consists of eight face-centered unit
cells of the NaCl type (Fig. 4). Such a superstructural
cell contains (8 × 8) 64 atoms, 32 tin and 32 antimony
atoms. At a 1 : 1 ratio between the components, anti-
mony and tin atoms alternate. The replacement of
antimony with tin and tin with antimony only occurs
along the central axes (I–IV) in each quarter of the
superstructure unit cell. The replacement of antimony
with tin occurs in the central plane (001) of the super-
structure cell with the formation of the phases Sn
9
Sb
7
(43.75 at. % Sb) and Sn
17
Sb
15
(46.88 at. % Sb).
(a)
Sb Sn
(b) (c)
Fig. 3. Structural models of antimony and its alloys with tin: (a) saturated solid solution of tin in antimony (88.89 at. % Sb), (b)
Sn
17
Sb
11
(61.11 at. % Sb), and (c) Sn
4
Sb
5
(55.56 at. % Sb).
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
I
II
III
IV
Sb Sn
Fig. 4. Model of a superstructural phase of the NaCl type.
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM
25
The replacement of tin with antimony occurs only in
the center of the cube of each of the eight simple unit
cells with the formation of the phases Sn
15
Sb
17
(53.12 at. % Sb) and Sn
7
Sb
9
(56.25 at. % Sb). Such a
replacement is only possible if the symmetry of trans-
lation axes (I–IV) remains unchanged. The severe lim-
itations specified above allow only a limited number
of superstructural phases of the homologous series
Sn
16 – n
Sb
16 + n
, where n = –2, –1, 0, 1, and 2, to be
formed. The compositions of these phases were sub-
stantiated by our microprobe data. The Sn
7
Sb
9
super-
structural phase probably has a narrow homogeneity
region from 56.25 to 57.14 at. % Sb (Sn
3
Sb
4
).
We do not exclude the possibility of the existence at
room temperatures of the metastable phases Sn
3
Sb
2
(37.5 at. % Sb), Sn
19
Sb
13
(40.62 at. % Sb), and Sn
2
Sb
3
(62.5 at. % Sb).
Table 4. Coefficients of the E(T) dependences for the liquid single-phase region and solid-phase heterogeneous regions of
the Sn–Sb system
Nox
Sb
a, mV
b × 10
3
,
mV/K
l, K, mV
× 10
2
,
(mV)
2
Σ(T
i
–)
2
,
K
2
T
min
–T
max
,
K
10.1024–0.2274.6239710.533.050.04121572638–811
20.21070.04410.8640711.627.770.04123413638–811
30.30130.52717.8638709.1013.190.06118528638–811
40.31963.16124.0034723.2620.520.1492595655–811
50.43042.71628.8915747.3324.310.1026805678–811
60.45097.32125.2029725.225.600.1136331638–811
70.45968.65024.2876744.0426.710.26108513673–818
80.48038.70926.9326731.228.400.1827268681–787
90.499610.53626.5162752.2430.480.30 49961700–821
100.501910.38927.4922739.230.710.04 17968697–787
110.52038.28232.9658777.8033.920.0670247702–827
120.529212.72828.2117749.833.880.139475710–787
130.539911.23731.1061762.5134.950.2746807712–825
140.580812.90835.48 50 770.7 40.260.50 29053726–821
150.599211.90639.0443790.7342.780.1327154739–830
160.620316.02037.6331780.7145.390.8016932745–822
170.649512.48547.8236799.2850.700.1611527763–830
180.696211.92756.8726830.3959.15140262 798–913
190.800623.3066.016904.8383.035443893–919
200.88088.33 109.2 10891.50105.68211583872–913
210.919921.87112.311896.64122.58182985872–923
220.960546.21116.914898.14151.20193322872–923
S10.744– 59.58–46.3868637.4430.02643673592–682
0.696
S20.650– 61.63–52.6857637.3928.05832848592–682
0.599
S3'0.529269.972–70.1761613.3425.93411200589–638
S3''0.520371.455–76.2923624.2223.83410120592–659
S40.50194.21211.72108606.611.323211356589–627
S50.4803–11.72334.7358605.19.29179450589–623
T
ε
S
0
2
T
Table 5. Coefficients of the E = a + bT + cT
2
+ dT
3
dependences for heterogeneous regions l
1
+ (β) and l
2
+ (β)
Regionx
Sb
abc × 10
3
d × 10
6
l
, (mV)
2
T, K
l
1
+ (β)0.54–0.74–1337.525.71678–8.241184.088311830.01699–827
l
2
+ (β)0.38–0.6279.58620.139822–1.21431.30095210.2589–697
S
0
2
26
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
VASIL’EV
THE THERMODYNAMIC PROPERTIES AND PHASE DIAGRAM OF THE Sn–Sb SYSTEM
The electromotive force method was our main tool
for studying the Sn–Sb alloys.
The electromotive force of electrochemical cells of
the type
(–)Sn Sn
2+
in salt melt Sn
x Sb
1 – x
(+) was measured in the concentration and temperature
ranges 0.1 ≤ x
Sb
≤ 0.96 and 589 ≤ T ≤ 830 K, respec-
tively. Part of the experimental results were reported in
[22, 23]. In this work, additional electromotive force
measurements were performed for five alloys with x
Sb
=
0.3832, 0.4509, 0.4803, 0.5019, and 0.5292 in the tem-
perature range 589–678 K. For these alloys, 716 mea-
surement results were obtained for heterogeneous
regions in the solid and liquid-solid states. The set of
the coefficients in the E(T) equations for the Sn–Sb sys-
tem is given in Tables 4 and 5. The E(T) dependences
are also shown in Fig. 5. The intersection points between
straight lines 3–18 and curves L1 and L2 yield liquidus
temperatures directly. Straight line 4–18 regions to the
left of curves L1 and L2 describe supercooled alloys.
Straight lines S1–S5 correspond to solid alloys, S1, S2,
S4, and S5, to heterogeneous regions, and S3' and S3",
to the homogeneous region of the β phase. The intersec-
tion points between straight lines S1, S2, S3'', S4, and
S5 and curves L1 and L2 give the peritectic reaction
temperatures, and S3" gives the solidus temperature of
the β phase for the alloy with 52.92 at. % Sb. Table 6
contains the temperatures found directly from these
intersection points.
It can be assumed that the change in the sign of the
partial entropy of formation of solid β phase alloys of
the series (S1–S3) and (S4, S5) [∆ = nF(∂E/∂T)] is
related to a change in crystal symmetry.
The β phase at elevated temperatures (starting
with 643 K) has a homogeneity region from 50 to
55.56 at. % Sb. Close to 600 K [5], the hexagonal struc-
ture transforms into quasi-cubic. We obtained the
microstructure of this alloy annealed at 633 K and
quenched in water. It contained well-discernible con-
cretions of hexagonal crystals. The existence of the
β phase with a composition close to 53 at. % Sb, which
melts incongruently at 680 K, was substantiated by dif-
ferential thermal analysis in studying ternary In–Sn–Sb
alloys [24, 25].
The phase diagram shown in Fig. 6 was constructed
on the basis of electromotive force and electrical resis-
tance measurements and the differential thermal, X-ray
phase, microstructural, and microprobe analysis data.
In our view, the variant of the phase diagram
reported in [11] with a broad region of β solid solutions
from 47.7 to 65.2 at. % Sb is a metastable form of the
crystallization of alloys of these compositions, which,
when annealed for a long time, form a series of inter-
mediate stoichiometric phases. The peritectic tempera-
ture 597 K attributed to the Sn
3
Sb
2
phase (40 at. % Sb)
in [11] in reality corresponds to the peritectic formation
of the Sn
9
Sb
7
phase (43.75 at. % Sb). The existence of
the Sn
3
Sb
2
aerial phase (40 at. % Sb) suggested in [11]
has not been substantiated by any other researchers.
We stress that the microprobe method is used to
determine the local chemical composition of an alloy at
a certain point. The quenched metastable phases
present in a sample are then easily detected at room
temperatures. The alloy with 40 at. % Sb annealed at
540 K and quenched in water did not contain even
traces of the Sn
3
Sb
2
compound. The differential ther-
S
i
0
600
E, mV
T, K
2
900
800
700
40
60
13
11
10
14
12
9
8
7
6
5
4
3
2
1
L1
S1
S2
S4
S5
L2
S3'
S3''
15
16
17
18
Fig. 5. Dependences E(T) for Sn–Sb alloys: (1–18) liquid
alloys; L1 and L2, heterogeneous systems (liq + sol); and
S1–S5, solid alloys.
Table 6. Peritectic reaction temperatures
Phase
region
Phasex
Sb
T, K
S1SnSb
2
0.6667696.0
S2Sn
6
Sb
11
0.6111690.1
S3'β(Sn
15
Sb
17
)0.5312680.1
S3''β(Sn
17
Sb
19
) (solidus)0.5278672.6
S4SnSb0.5000633.9 S5Sn
9
Sb
7
0.4375622.6
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
A COMPLEX STUDY OF THE PHASE DIAGRAM OF THE Sn–Sb SYSTEM
27
mal analysis of alloys with 10–50 at. % Sb performed
in this work did not reveal the presence of a double ther-
mal effect between 240 and 250°C similar to that
described in [11]. The phase with 61.11 at. % Sb was
shown to exist by the electromotive force and micro-
probe methods. It had a homogeneity region of ~1–
1.5% on the side of tin. The phase richer in antimony
(66.67 at. % Sb) was only observed by the electromo-
tive force method. When alloys containing 62 at. % Sb
or more were slowly cooled, the SnSb
2
phase underwent
peritectic decomposition with the formation of the phase
with 61.11 at. % Sb, which was more stable under
quenching conditions, and the solid solution of tin in
antimony (Sb).
THE OPTIMIZATION OF THE THERMODYNAMIC PROPERTIES
OF THE Sn–Sb SYSTEM
The optimization was performed with the inclusion
of the calorimetric data on the heats of mixing [26–29],
the results of electromotive force measurements [30],
and our experimental E(T) dependences. The following
description was obtained:
∆G(T, x)/R, K = x(1 – x)[–681.4821 – 108.3456(1 – 2x) + 146.9628(1 – 2x)
2
+ 105.2240 (1 – 2x)
3
+ 78.3754(1 – 2x)
4
] + T[xlnx + (1 – x)ln(1 – x)]
for liquid solutions, where x = x
Sb
and R =
8.31451 J/(mol K), and ∆G(T, x)/R, K = x(1 – x)(795.2333 – 1.015436T) + T[xlnx + (1 – x)ln(1 – x)]
for antimony-based solid solutions.
400
0.20
0.4
0.6
0.8 1.0
600
800
1
2
3
4
5
6
7
590
515
519
600
597
623
634
680
697
x
Sb
T, K
(Sb)(Sn)
β
2
β
1
[1]
[2]
[3]
[5]
[6]
[10]
[11]
[12]
[13]
[22]
9
8
Fig. 6. Phase diagram of the Sn–Sb system constructed on the basis of the electromotive force (this work), differential thermal anal-
ysis [1–3, 5, 6, 10–13], microstructural analysis [9, 11], and microprobe (this work and [13]) data; ∼ 600 K is the supposed tem-
perature of the β
1
β
2
structural transition and (Sn) is the solidus line according to [9]. Intermediate phases: (1) saturated
solid solution of tin in antimony (88.89), (2) SnSb
2
(66.67), (3) Sn
7
Sb
11
(61.11), (4) Sn
3
Sb
4
(57.14), (5) Sn
4
Sb
5
(55.56),
(6) Sn
15
Sb
17
(53.12), (7) SnSb (50.00), (8) Sn
17
Sb
15
(46.88), and (9) Sn
9
Sb
7
(43.75) (given in parentheses are antimony contents
in at. %).
0.2
∆
f
G/R, K
x
Sb
400
1.0
0.8
0.4
0.6
0
0
–400
1
2
3
Fig. 7. Dependences of ∆
f
G/R on the mole fraction of anti-
mony for tin–antimony alloys at 605 K: (1) melts, (2) solid
solution, and (3) compounds; standard states: liquid tin and
solid antimony. 28
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY Vol. 79 No. 1 2005
VASIL’EV
The Gibbs energies of intermediate solid phases
were calculated on the assumption that these phases
were stoichiometric. The standard states of the ele-
ments were liquid tin and solid antimony. Recalculation
to the standard state was performed using the data from
[31]. The results were:
∆G(T, 0.666667)/R, K = –311.5340 + 0.025562T,
∆G(T, 0.6111)/R, K = –391.8849 + 0.104464T,
∆G(T, 0.53125)/R, K = –570.1572 + 0.33836T,
∆G(T, 0.5)/R, K = –540.2636 + 0.29897T,
∆G(T, 0.46875)/R, K = –483.8746 + 0.22056T.
The phase stablest thermodynamically was Sn
15
Sb
17
(53.12 at. % Sb) (Fig. 7).
According to the optimization results, liquid solu-
tions of tin in antimony have ideal entropies of forma-
tion; that is, these solutions are regular. In our view, the
optimization of the Sn–Sb phase diagram performed in
[13, 32] corresponds to a variant of its metastable state.
To summarize, we performed complete analysis of
the literature data on the phase diagram of the Sn–Sb
system. We showed the possibility of the existence of
metastable and stable β phase forms. For the first time,
crystal chemical models of the hexagonal and super-
structural quasi-cubic β phase forms, whose intercon-
version involved changes in crystal symmetry, was sug-
gested. β-Phase solid solutions were shown to undergo
ordering with the formation of homologous series of
two symmetry types, hexagonal and quasi-cubic. The
thermodynamic properties of the Sn–Sb system were
optimized. A thermodynamically stable β phase close
in its composition to Sn
15
Sb
17
(53.12 at. % Sb) was
observed; this phase had a homogeneity region from
50 to 55.56 at. % Sb at elevated temperatures.
ACKNOWLEDGMENTS
The author thanks Prof. G.F. Voronin (Faculty
of Chemistry, Moscow State University) and Prof.
J.-K. Gachon (University Nancy-1, France) for their
help with this work.
REFERENCES
1.W. Reinders, Z. Anorg. Chem. 25, 113 (1900).
2.F. E. Gallagher, J. Phys. Chem. 10, 93 (1906).
3.R. S. Williams, Z. Anorg. Chem. 55, 12 (1907).
4.N. Konstantinov and W. A. Smirnov, Int. Z. Metal-
lografie 2, 154 (1912).
5.K. Iwasé, N. Aoki, and A. Osawa, Scientific Reports of
Tohoku Imperial University 20, 353 (1931).
6.R. Blondel, Thése du Docteur (1936) (cited from [11]).
7.D. Hanson and W. T. Pelle-Walpolle, J. Inst. Met. 58 (1),
299 (1936).
8.K. Schubert, Z. Metallkd. 44, 457 (1953).
9.B. L. Eyer, J. Inst. Met. 88 (5), 223 (1960).
10.A. Stegher, Doctor–Ingenieurs Genehmigte Dissertation
(Technischen Hochschule, Aachen, 1969).
11.B. Predel and W. Schwermann, J. Inst. Met. 99, 169
(1971).
12.W. P. Allen and J. H. Peperezko, Scr. Metall. Mater. 24
(11), 2215 (1990).
13.H. Ohtani, K. Okuda, and K. Ishida, J. Phase Equilib. 16
(5), 416 (1995).
14.P. J. T. L. Oberndorff, A. A. Kodentsov, V. Vuorinen,
et al., Ber. Bunsen-Ges. Phys. Chem. 102 (9), 1321
(1998).
15.Termal Constants of Substances: A Handbook, Ed. by
V. P. Glushko (VINITI, Moscow, 1971), Vol. 4 [in Rus-
sian].
16.K. Schubert, Kristallstrukturen Zweikomponentiger
Phasen (Springer, Heidelberg, 1964; Metallurgiya, Mos-
cow, 1971).
17.C. Barnett, J. Appl. Phys. 37, 1041 (1966).
18.G. Hägg and Hybinette, Philos. Mag. 12, 441 (1931).
19.G. Hägg and Hybinette, Philos. Mag. 20, 913 (1935).
20.E. G. Bowen and W. Morris, Philos. Mag. 12, 441
(1931).
21.H. Swanson and H. Fuyat, Natl. Bur. Stand. (U.S.), Circ.
539 3, 14 (1954).
22.V. Vassiliev, Y. Feutelais, M. Sghaier, and B. Legendre,
J. Alloys Compd. 314, 197 (2001).
23.V. Vassiliev, M. Lelaurain, and J. Hertz, J. Alloys
Compd. 247, 223 (1997).
24.B. Legendre, E. Dichi, and V. Vassiliev, Z. Metallkd. 92
(4), 328 (2001).
25.K. Lönberg, Metall. (Berlin) 22, 777 (1968).
26.F. E. Wittig and E. Gehring, Ber. Bunsen-Ges. Phys.
Chem. 71 (4), 372 (1967).
27.A. Yazawa, T. Kawashima, and K. Itagaki, Nippon Kin-
zoku Gakkaishi 32 (12), 1288 (1968).
28.F. Sommer, R. Luck, N. Rupf-Bolz, and B. Predel,
Mater. Res. Bull. 18, 621 (1983).
29.M. Azzaoui, Thése du Docteur (Université Henri
Poincaré, Nancy, 1995).
30.J. A. Yanko, A. E. Drake, and F. Hovorka, Trans. Electro-
chem. Soc. 89, 357 (1946).
31.A. T. Dinsdale, CALPHAD: Comput. Coupling Phase
Diagrams Thermochem. 15, 317 (1991).
32.B. Jonsson and J. Agren, Mater. Sci. Technol. 2, 913
(1986).
Автор
valeryvassiliev
Документ
Категория
Исследования
Просмотров
544
Размер файла
104 Кб
Теги
Vassiliev V.P.
1/--страниц
Пожаловаться на содержимое документа