close

Вход

Забыли?

вход по аккаунту

?

AN X-RAY STUDY OF THE STRUCTURE OF BENZENE, CYCLOHEXANE AND THEIR MIXTURES

код для вставкиСкачать
The Pennsylvania State College
The Graduate School
Department of Chemistry
AN X-RAY STUDY OF THE STRUCTURE OF BENZENE,
CYCLOHEXANE AND THEIR MIXTURES
A Thesis
by
Paul H. Bell
Submitted in partial fulfillment
of the requirements for the degree of
Doctor of Philosophy
June, 1940
Approved
£2
JHead of Department
Major Professor
l-q./fpo______Date of Approval
ACKNOWLEDGMENT
The author wishes to express his gratitude to
Dr. Wheeler P. Davey for his direction during the course
of the experimental work and assistance in preparation
of this manuscript.
220147
TABLE OF CONTENTS
Page
1
Introduction.........................
A p p a r a t u s ........ ................. .............
2
.....................
2
A.
X-Ray Radiation .
B.
Spectrometer and Slit S y s t e m ......
0.
Sample-holder and Temperature Control . . .
3
D.
Counting C i r c u i t ...........
5
2
.......................................
6
Experimental Procedure ...........................
7
Experimental Results . . . .............. . . . . .
9
Materials
Interpretation
ofExperimental Results ............
14
S u m m a r y ........................................... 29
Bibliography....................................... 30
Appendix I.
Apparatus....................... 32
A.
X-Ray Tube Circuit and Arrangement
....
B.
Counter Circuit..................... 33
32
(1) Geiger-Mueller Counter T u b e ...........33
(2) High Voltage Rectifier..............
33
(3) Power Supply for AmplifierCircuit . .
35
(4) Amplifier Oircuit
38
..................
Appendix II. Filter Transmission C u r v e ............ 40
Appendix III.
Additional D a t a ............... 42
A.
Shape of Entire Diffraction Curves
B.
Experimental and Theoretical Curves
....
for
Other M i x t u r e s ..................... 42
42
TABLE OF CONTENTS
Introduction.....................................
A p p a r a t u s ...........
Page
1
2
A.
X-Ray Radiation .........................
3
B.
Spectrometer and Slit System
. . . . . . .
3
0.
Sample-holder and Temperature Control . . .
3
D.
Counting C i r c u i t ...................
5
.......................................
Materials
6
Experimental Procedure...........
7
Experimental Results .............................
9
Interpretation of Experimental Results . . . . . . .
14
Summary
................................... 29
Bibliography....................................
30
Appendix I.
32
Apparatus ...........................
A.
X-Ray Tube Circuit and Arrangement
B.
Counter Circuit
....
......................... 33
(1) Gelger-Mueller Counter Tube . . . . .
(2) High Voltage Rectifier
(4) Amplifier Oircuit
. . 35
..................
Appendix II. Filter Transmission Curve
33
.............. 33
(3) Power Supply for AmplifierCircuit
Appendix III.
32
..........
38
40
Additional D a t a .................. 42
A.
Shape of Entire Diffraction Curves
....
B.
Experimental and Theoretical Curves for
Other M i x t u r e s ........................ 42
42
TABLES
I.
Page
Peak Positions..................................18
II. Relative Peak Intensities...................... 23
FIGURES
I.
Sample-holder
...............................
Page
4
II. X-Ray
Diffraction Curves; 100$ Benzene.......... 10
III. X-Ray
Diffraction Curves; 100$ Cyclohexane . . .
11
IV. X-Ray
Diffraction Curves; 51.4$ Benzene Solution
12
V.
Diffraction Curves; 74.5$ Benzene, 74.6$
X-Ray
Cyclohexane S o l u t i o n s .........
13
VI. Theoretical Curve due to Addition ofCurves for
Benzene and Cyclohexane
.....
...........
20
VII. Theoretical Curves; 51.4$ Benzene Solution . . .
25
VIII.Theoretical Curves; 74.5$ Benzene, 74.6$
Cyclohexane Solutions
.......................
26
IX. High Voltage Rectifier.............. ......... 34
X.
Power Supply.................................... 36
...........................
37
XII. Balanced Filter Transmission Curve............
39
XIII.Entire Diffraction Curves
...................
41
XIV. X-Ray Diffraction Curves .....................
43
XI. Amplifier Circuit
XV. Theoretical Curves; 62.4$ Benzene,62.8$
Cyclohexane Solutions
.......................
XVI. Temperature versus Angle Graphs
........ . . .
XVII.Temperature versus Intensity Graphs
..........
44
45
46
0.
Page
Peak Shift with Temperature............... 42
D.
Decrease in Peak Intensity with Temperature . 47
Bibliography for A p p e n d i c e s ....................... 48
Introduction
The structure of liquids has been studied by many
methods, including that of x-ray diffraction^ *^
their structure is not yet well understood.
, but
It is the purpose
of this paper to give the results of an x-ray study of the
mutual solutions of benzene and cyclohexane.
These results,
differing from those so far reported in the literature^ *
(4)»(5)» (6),(7),(8)^ ie£Uj
a better understanding of the
physical state of liquid structure.
All authors, with the
exception of H. K. Ward, seem to have obtained only one
peak in their diffraction curves from liquid solutions.
(8)
Ward' , working with benzene - cyclohexane solutions,
obtained two peaks corresponding to those given by pure
/g\
benzene and pure cyclohexane. Murray and Warren' ' repeated
Ward1s work and were unable to obtain two peaks.
Since the
experimental results conflicted with each other and with
the thermodynamic data of Scatchard, Wood and Mochel^,
new x-ray investigation was made on the same system with
an entirely different type of x-ray diffraction apparatus.
The new data showed not one or two peaks, but four.
Since
the data were definitely reproducible, they seemed to warrant
further study.
In the present work a Geiger-Mueller counter method
was used with compensating filters.
This method appears to
be much more sensitive than the photographic method and less
cumbersome than the ionization chamber method.
Apparatus
A.
X-Ray Radiation
A (G. E. X-ray Oorp.) molybdenum anode, Ooolidge type
tube was operated at 42 kilovolts (r.m.s.) and a tube current
of 30 milliamperes.
The voltage and tube current were
maintained to within ± 1 , 5 percent by use of voltage
regulators on the transformer primary circuits (Raytheon
Mfg. Go.).
To obtain a monochromatic beam of high intensity, the
method of balanced filters was u s e d ^ ^ * ^ ^ .
A filter of
filter paper saturated with Sr( 1103)2 was made such that its
x-ray transmission was equal to a Zr03 filter (Patterson
Screen Co.) for all wavelengths except the K«(
the tube.
doublet of
This was carefully balanced and ohecked over the
entire x-ray speotrum using the (100) plane of NaCl.
B.
Spectrometer and Slit System
A Spencer spectrometer (No. 818), on which angles could
be read to one minute of arc, was mounted in a rigid frame
in such a way that the moveable arm moved in a vertical
plane.
Soller slits^*^ were substituted for the slits and
telescope.
The slits for the collimator and Geiger-Mueller
counter consisted of 6 parallel slits 20 erne, long, 0.075 cm.
wide, by 1.0 cm. high.
The lead foil between slits was
0.0075 cm. in thickness, the spreaders 0.075 cm.
The geometry of the incident beam was such that only
three of the six collimating slits could be used.
The
thickness of liquid used in the specimen holder was such
that all six of the slits could be used on the swinging
spectrometer arm.
0.
Sample-holder and Temperature Oontrol
To eliminate the possibility of any contamination
the sample-holder was constructed entirely of glass. (See
Fig. I).
Fig. I
The cell windows were of Pyrex glass approximately 0.007 cm.
in thickness.
1.7 cm.
The thickness of the liquid in the cell was
This was large enough to insure a high intensity
of diffracted beam.
It was slightly less than the optimum
thickness given by
*
= ?
where t is the thickness and j-A is the linear coefficient
of absorption.
The liquid under investigation was brought up to
temperature, (io.5°C), in a glass coil immersed in a
thermostat.
The liquid was circulated through the coil and
the cell, by means of a pyrex paddle, at a linear speed of
approximately 3 cm. per second.
The temperature difference
between the cell and the thermostat was therefore negligible.
Temperatures between 5°0 and 10°C were obtained by circulating
ice water through a cooling coil immersed in the thermostat.
For a temperature of -21°0 a dry ice - acetone mixture was
X-RAYS
THERMOSTAT
LI QUI D
GO
Figure I
LEVEL
syphoned through the cooling coil, and a eutectic mixture
of NaCl and water was used in the bath.
D.
Oounting Circuit
The Geiger-Mueller counter was argon - oxygen filled.
The cathode had a sufficiently large opening to allow all
x-rays coming from the slits to enter the counter.
The
voltage supply was maintained at 850 volts by a voltage
regulator of the Street and Johnson t y p e ^ ^ .
The amplifier circuit consisted of three stages of
voltage amplification, using a 57 and finally two 56 tubes.
The amplified pulse was fed into a modified Pickering^4^
recording circuit, using a single 885 thyratron tube.
The
final counts were recorded by a Cenco counter in the plate
circuit of the thryatron tube.
With this oircuit it was
found necessary to shield the first stage of amplification.
The time constants for the circuit were sufficiently small
to allow the 60 cycle of the incident beam to be recorded.
A small loudspeaker was also built in the circuit, powered
by a 45 tube, so that the quality of sound from the speaker
gave an indication of the proper operation of the G.-M.
counter and of its circuit.
Materials
The benzene was Baker* s "O.P. Thiophene Free"
with the following physical constants:
B.P. 80°0; M.P.
+ 5.5°C; Index of refraction 1.5009 at 20°C.
The cyolohexane was obtained from Rohm and Haas
Co.
It was purified by a method somewhat similar to that
used by other workers^®^
.
The material as received
was shaken for 12 hrs. with fuming H3S04 (25$ S03), washed
with water, shaken with alkaline KMn04 and finally shaken
with water again.
It was then dried over metallic sodium
and finally distilled at a high reflux ratio in a 15 plate
column.
Further purifications were carried out by
fractional recrystallizations.
The physioal constants of
the final material were: B.P. 80.5°C; M.P.f-6.4°C; and
index of refraction of 1.4263 at 20°0.
The solutions, to be examined by diffraction
methods, were prepared on a weight basis.
They had
weight-compositions of (l) 74.5 percent benzene - 25.5
percent cyclohexane; (2) 51.4 percent benzene - 48.6 percent
cyclohexane; (3) 25.4 percent benzene - 74.6 percent
cyclohexane.
These corresponded to mol fraction compositions
of (l) 0.76 benzene - 0.24 cyclohexane; (2) 0.53 benzene 0.47 cyclohexane; (3) 0.27 benzene - 0.73 cyclohexane.
The exact percentages had no special significance, but were
those obtained after measuring the approximate amounts by
volume*
The index of refraction was measured before and
after each run and was found to be the same within 0*0001.
This indicated that the composition did not change during
the course of the experiments*
Experimental Procedure
To be certain that the apparatus was in a condition
to operate uniformly over a long period, it was in every
case allowed to warm up for one hour before making any
measurements.
The temperature of the G.-M* tube was always
kept within one or two degrees of 25°0 since these tubes
have a marked decrease in efficiency with rising temperature.
The data reported are for the K aC doublet lines
of Molybdenum, 0.710 $.
This was obtained by subtracting
the ”strontium filter” reading from the "zirconium filter”
reading, the difference being the K *
diffracted beam intensity.
contribution to the
The background correction due
to cosmic rays need not be subtracted because its average
intensity was eliminated by the two filter readings.
A blank run with the empty sample holder gave a
very small diffraction scattering with no peaks in the
region used in this work.
The counting rates were never
higher than 300 per min., so that it was possible to detect
failure of the mechanical counter by an audible method.
The loudspeaker volume was adjusted so that it was not
audible to the operator when the counter was operating.
Any skipping of the counter made it possible to hear the
loudspeaker pulse and thus to detect the failure of the
counter.
The ZrOg and Sr(N0g)2 filters were changed after
each minute interval, and all readings were thrown out for
which any counter failure was detected.
Statistics of Geiger-Mueller counters have been
developed by several authors^15^' (16)*
Hughes^17)
points out that
where n is the number of counts in a given time interval
and x the average number arriving in that time interval.
The mean deviation is therefore equal to the square root
of the counts recorded.
Sufficient counts were taken to
insure a valid graph over the range studied.
In the region
between 8°00* and 8o40' enough counts were made so that the
differences between counts of the peaks and of the adjacent
minima between the peaks were, in the most extreme cases,
greater than twice the mean deviation.
The shapes of the curves and peak positions were
determined for eaoh liquid sample at 40°C, 25°G, and in the
case of pure benzene, pure cyclohexane and the 51.4 percent
benzene mixture, additional curves were taken at 60°C, 10°0
and as close as possible to the melting points.
The melting
points are 5.5°0; 6.4°0; and -22°C^18^; respectively.
The shapes of the curves were reproducible but
the relative intensities varied from week to week.
This
was probably due to long time changes in the characteristics
of the counter circuit.
In order to put all curves on a
oommon intensity scale, the following method was used:
(1)
Data on all the peaks of all the liquid samples studied
were taken at each Of the constant temperatures mentioned
above, using a separate day for each temperature.
(2)
Measurements of the peaks of the 51.4 percent benzene mixture
(M.P. -23°C) at -21°C, 10°0, 25°0, 40°0 and 60°0, were made
on the same day.
(3)
The data from (2) were used to correct
the measurements of (1) so that the final results shown in
Figures II, III, IV and V, were what might have been
expected if all the data could have been obtained on a
single day.
Figures II, III, IV, V
Experimental Results
Diffraction curves for the pure liquids and mixtures
at various temperatures are shown in Figures II, III, IV and
V.
One unit on the intensity scale represents one hundred
counts per five minutes.
2 -O' is the angle of deviation from
the incident beam made by the diffracted x-rays.
INTENSITY
Q
Oo
Figure
Oo
II
$
m
Oo
INTENSITY
f0»
.>•
Oo
Figure
ro
III
4>
51.4 r?o b
N ZEN E
CD)0
COO
(A) I
(B)Q
Figure IV
13.
74.5 7. BE
74.6
% cyclohexane:
(C.D)0
(B)0
CA)0
2
■©■
Figure V
The range of 3 -©-studied, was from 2°00' to 11°00'.
This is not entirely reproduced in the curves shown, because
of the size of graphs necessary.
In all oases a small
intensity peak was observed at a low angle of diffraction.
The exact position of this peak was oarefully checked in
several cases.
In the case of pure benzene and cyclohexane
it was found, within the accuracy of measurement, to be at
one-half the angle of the high intensity peak (for small
angles sin©- =•©-).
For the mixtures no sharp peak was
obtainable but a diffuse peak was found between 2 © - = 4o00'
- 4°30'•
The intensities of these peaks were approximately
one eighth of the high intensity peaks.
The lowest temperature curves in the cases of
Figures II, III and IV were taken to determine whether the
liquid structure might change at a temperature just above
the melting point.
Interpretation of Experimental Results
Several theories have been proposed to explain
x-ray diffraction in liquids.
are those due to:
The more important of these
(19)
Raman and Ramanathan
, Zernike and
Prins^20) > ( 22), Debye^23) and Stewart^2).
The approach
of the first three is definitely mathematical in oharacter,
while that of Stewart is a non—mathematical picture of the
state of the liquid.
Raman and Ramanathan's function was
able to predict only one peak in the diffraction curve and
its exact position had to be obtained experimentally.
Zernike and Prins used a distribution function evaluated
in an empirical way.
Debye used the experimental data to
determine the distribution function.
These methods were applicable in the case of
molecules having spherical symmetry, and many liquids have
been worked out on the basis of the theories of Prins and
Debye,
The application of these theories to unsyrametrical
molecules such as benzene or cyclohexane has not been so
successful.
Several distribution functions have been used
^
for b e n z e n e > ( 25)>(26) »(S7).
these functions
gave fair checks at high diffraction angles, but not at
angles less than the principle peak.
It seems that one
must resort to the method of Stewart to explain the
experimental facts in the cases of solutions.
It is well accepted, that a liquid approximates
a crystalline powder in the sense that.the diffraction peak
positions must be close to those given by Bragg's formula
n A
-
3 d
sin-o-
(l)
Applying this formula (l) to the data of Figures II, III
we obtain,
for the x-ray radiation used ( A
= 0.710 $),
the following values of d at 25°C: for 100 percent cyclohexane,
2 0 = 8°00' and d = 5.09 ±.01 A; for 100 percent benzene,
2 0 s 8°40' and d >= 4.70 ±.01 $.
Such values of d have been
interpreted b y several authors as the effective thickness
of the molecules in the liquid
(28)
It remains to explain, if possible, the low peaks
at 2 ® = 4°00' - 4°20', and the three peaks shown by all
the mixtures at 2 ■©• = 8°00', 8°20« and 8°40’.
Let us
consider the solution to be made.up partly of randomly
distributed molecules of benzene and cyclohexane, and partly
of small groups, each existing temporarily, whose molecules
have an almost orderly arrangement.
This is consistant
with Stewart's explanation^^ of x-ray diffraction in
pure liquids.
It is inherent in the theory of x-ray
diffraction that sharp diffraction peaks require the diffract­
ing material to have a periodic structure, with enough
repetition of the fundamental structure to give a noticeable
contribution to the diffraction pattern.
For convenience
of reference we shall use the symbol (-B-B-B-) to represent
some definite grouping, composed entirely of pure benzene,
the symbol (-C-C-C-) to represent a similar grouping of
pure cyclohexane, and the symbols (-B-C-B-C-), (-B-0-C-B-C-C-)
(-B-C-B-C-C-B-), etc., to represent groups composed of both
benzene and cyclohexane.
Obviously the groupings (-B-B-B-)
and (-C-0-C-) show a repetitive structure with the single
molecule as the fundamental unit.
We should therefore expect
definite diffraction peaks corresponding to the grating
spaces given by adjacent molecules.
Such peaks were observed
experimentally in the present work.
Since we are dealing
with non-rigid liquids, instead of solid crystals, we must
expect the pure liquid to show an equilibrium state between
(“ ■®k” ^l
Bm“ Sn") anc* (“ ®k— ®r*®m— ®ri“) or between
(-0k-0i— Om-On-) and (-C^— C-^-Cra— Cn-).
This should give
a diffraction peak corresponding to the distance, B^-B^
(or 0]£“0ra)•
This spacing is obviously not far from twice
the mean spacing between adjacent molecules.
Such peaks
have been observed experimentally in every case.
They are
not shown in Figures II to 7 for lack of space.
The groupings (-Bd-Ge-B.f-0g-) show a slightly more
complicated periodic structure.
Such a grouping should show
a diffraction peak corresponding to the fundamental spacing
-B^-Bf- or -Cg-Gj?-, but since the diffracting power of B
and 0 are similar, this peak should be weak due to inter­
ference between B and 0.
Such peaks have been observed in
the case of all the mixtures studied.
The spacing -Bd-Ce-
obviously should be intermediate between the spacings
-B-B- and -0-0- appearing in the (-B-B-B-) and (-0-0-0-)
groupings, and this is found to be the actual case.
Because of the similarity in diffracting power of B and 0,
a definite diffraction peak should be found for all mixtures
of B and C at a distance corresponding to -Bd-Ce-, (i.e.
half the spacing Bd-Bf).
Experimentally such peaks were
found for all our mixtures.
They are shown in Figures IV
and V, and in detail in Table I; within experimental error,
these peaks fall half-way between the peaks of (-B-B-B-)
and (-C-0-C-).
Table I
Peak Positions.
Composition Temperature
100# 0 6 % 3
it
i!
6.7°C
Peak Positions
-0-C3-C2
d
10
°C
8°02« 5.07
ii
25
°C
8°00‘ 5.09
II
ii
40
°0
7°58' 5.11
II
ii
60
°0
7°55‘ 5.14
ii
10
°0
8°41» 4.69
II
ii
25
°C
8°40» 4.70
II
ii
40
°C
8 q 38« 4.72
II
ii
60
°C
8°35' 4.74
-31°0
8°04» 5.05? 8°43» 4.67
»
ii
ii
■B-0d
8°43' 4.682
5.7°C
II
51. 4# CgHg
3 -&•
8°03« 5.062
II
100# c 6h 6
-B-B-B3«d
i
?
01
Table I
8°24» 4.852
10°0
8°02» 5.07
8°42« 4.68
8°22» 4.87
it
25°C
8°00» 5.09
8°40» 4.70
8°20' 4.88
n
n
40 °0
7°58' 5.11
8°38' 4.72
8°18' 4.90
ii
ii
60 °C
7°56‘ 5.13
8°36' 4.73
8°15* 4.93
25°C
8°00* 5.09
8°40' 4.70
8°20« 4.88
40 °C
7°58‘ 5.11
8°39' 4.71
8°19» 4.89
25°C
8°00‘ 5.09
8°40' 4.70
8°20' 4.98
40 °0
7° 59' 5.10
8°38» 4.72
8°18» 4.90
62 .4$ CgHg
25°C
8°00» 5.09
8°40' 4.70
8°21' 4.88
63 .Sj, OgH12
25°C
8°00' 5.09
8°40' 4.70
8°19« 4.89
74 •5$ CgHg
it
II
74 .6% CgH^g
ii
H
The next most complicated grouping can be repre­
sented by (-Bg-Of-Cg-Bk-Cj-Cj-).
The basic repetitive
distance for this grouping is Be-Bh .
This distance would
have to be repeated several times to give a definite
diffraction peak.
The probability of many successive units
of (-B-0-C-) occurring in a single group is so small that
any diffraction peak would necessarily be weak.
Even if
such a definite peak were strong enough to be detected, it
would lie at too small a diffracting angle to be observed
on our apparatus with Mo Kflf rays.
A similar argument could
be used for still more complicated molecular groups.
It might be argued that the shapes of the experi­
mental curves are due to addition of two complete curves for
(-C-0-0-) and (-B-B-B-).
Fig. VI shows, by dotted lines, the
curves for (-B-B-B-) and for (-C-C-C-) obtained by multiplying
the experimental curves (at 25°C) of Figures II and III by
the mol fractions 0.534 and 0.466 respectively.
This composi­
tion corresponds to the weight-fractions 0.514 and 0.486 shown
in Fig. IV.
Fig. VI shows that the sum of the two dotted-line
curves does not even approximate the experimental curve.
■ I
■
— M |
......
—
...
■■
—
I
....
■—
... .
I .
1!
■■■
■■■ 1.1
* I ■■■
—
■
Fig. VI
Considering the diffraction effects of such groups
as (-Bg-Cf-Cg-Bh-Ci-C-j-) mentioned above, we see that
scattering over an angular range ought, however, to occur
due to spacings, Be-Cf, Cf-Cg, Cg-Bfc, etc., because of the
.11
\
>
g
o
o
Figure
ro
VI
A
IN T E N S I T Y
—
ro
u>
4^
c/i
o>
similarity of diffracting power of B and C, and the close
similarity of the distances, Be-Cf, 0f-0g, 0^-Bh, etc.
The same argument applies also to more disordered groups,
such as (-B-C-B-C-C-B-), and to molecules which may be in
such a chaotic configuration as not to show even a definite
molecular orientation.
The contribution to the diffraction
curve due to all such groupings should be a diffuse peak,
with its maximum between 2-©-= 8°00' and 8°40'.
To summarize the above, we may consider that the
total x-ray diffraction curve is made up of the following:(1) sharp peaks due to the order states (-B-B-B-), (-0-C-0-)
and (-B-G-B-B-) and (2) a diffuse peak, due to more compli­
cated groupings and randomly distributed molecules.
It remains to determine the relative magnitude
of the order and disorder contributions to the diffraction
curve, both in the case of the pure liquids and in the case
of the solutions.
This may be done as follows:- (1)
A
smooth curve was drawn on the curves of Figures II, III,
IV, V connecting the points on both sides of the main peak,
where the slope seemed to change most rapidly.
This was
4
entirely arbitrary but is apparently justified by the end
results.
It is similar to the method of Stewart in obtaining
half-peak width^28^.
The area under this curve was considered
to represent the contribution due to all the disorder states.
(2)
The area above the smooth curve of (1) was considered
to be due to the x-ray diffraction of the order states
(-B-B-B-), (-C-0-C-) for pure benzene and pure cyclohexane
respectively, and of the order states (-B-B-B-), (-0-0-0-)
and (— B-G—B-G— ) of the mixtures.
If we assume that the
(-B-B-B-) and (-C-C-C-) groupings in the mixtures are in
every way the same as in the pure liquids, then the amounts
of (-B-B-B-) and (-C-C-G-) present in a given mixture should
be proportional to the mol fraction of each in that mixture.
In other words, the intensity of (-C-C-C-) in the pure
cyclohexane times the mol fraction of 0 in the solution
should equal the intensity of (-0-C-C-) in the solution.
A similar argument should hold for benzene.
Using the
(-B-B-B-) and (-0-C-C-) values of Figures II and III placed
on an arbitrary base line, as shown, the theoretical curves
of Figures VII and VIII were obtained.
The (-B-0-B-C-)
peak intensity was made such that the addition of all
curves would give the experimental peaks of Figures IV and V.
Using the method of (1) and (2) the peak intensi­
ties were determined and tabulated in Table II.
Table II
The
Relative Peak Intensities
intensities are expressed in terms of counts per 5 minutes,
as before.
Those given in parenthesis are the theoretical
values from Figures VII and VIII.
Figures II, III, IV and V.
The others are from
The half-peak widths are for
the order state curves for the pure liquids, and over the
entire three-order peaks for the solutions.
Table II
Relative Peak Intensities
Composition
Tempera­
ture
100# OsH 12
6.7°C
290
30*
Relative Peak Intensity
Half Peak
-0-0-C—B-B-B- -C-B-C-BWidth
II
II
10 °0
240
35'
II
II
35°0
200
35'
II
II
40 °C
170
35*
II
II
60 °0
150
25*
100# 06H6
5.7°0
340
20*
tl
II
10 °0
200
30*
II
II
25°0
150
30*
II
II
40 °C
130
30*
II
II
60 °C
110
30*
51.4# 06H 6
-21 °C
160 (135) 150 (130)
(140)
55'
(no)
1°05*
ii
ii
10 °0
120 (110) 110 (110)
it
ii
35°0
110 (100)
ii
ii
40 °C
85
ii
ii
60°C
74.5# 06H6
ii
ii
74.6# 06H12
ii
ii
90
(85)
(90)
1°00»
(80)
80
(70)
(80)
1°05*
80
(70)
70
(60)
(60)
1°05*
25°0
60
(50) 110 (110)
(100 )
55*
40 °0
80
(40)
90 (100)
(90)
1°05*
25°C
140 (145) 100
(40)
(130)
1°00*
40 °C
110 (130)
40
(35)
(100 )
1°00*
(70) 130
(90)
(130)
55*
90
(60)
(no)
1°00'
62.4# C6H6
25°C
62.8# C6H12
25°0
70
180 (120)
The complete theoretical curves are shown in
Figures VII and VIII,
The top dotted line is the addition
Figures VII and VIII
of all the curves contributing to the x-ray diffraction.
Curves of Figures VII and VIII and those of Figures IV and
V are in good agreement.
The data for absolute intensities
in the case of the 51.4 percent benzene mixture was better
than the other mixtures since they were very carefully
checked.
The other mixtures were studied more to prove
whether all the peaks could be detected than to ascertain
their absolute heights.
The theory did not give very good
agreement in the case of the -21°C curve of the 51.4 percent
benzene mixture, since it was necessary to use the data
for the pure liquids, approximately 15 degrees higher.
A few possible objections to this present work
must be met and, if possible, satisfied.
The matter of peak
(29)
resolution, which was first considered by Meyer
, and
later by Murray and Warren^
seems to be adequately
answered, if the interpretation given in Figures VII and VIII
is correct.
It is true that these separate peaks have not
been observed by other workers, but most of them except
Wara^®^, used a photographic method.
It seems questionable
that a photographic method would ever resolve peaks of such
intensities as those obtained, because of the high background
density of the film, and the small distance on the film
between peaks.
The experimental peaks, it is true, as
51.4 7o
benzene
- T H E O R E T CAL
oO
z 3
/
-/
: \/
V
v
\ / \ '
\/
t)s_ A
-7 \ 7 '
(E)0
(D)0
COO
(B)0
CA) I
Figure VII
\
V
\
26.
5 7* i i E N Z E N
I . O H i X AN E
EOF!
CAL
i \.lLA
Figure VIII
pointed out by Murray and Warren, should not be sharp but
slightly rounded.
The data of the present work, taken at
small angular intervals show a definite rounding, although
the scale of Figures II, III, IV and V does not bring this
out clearly.
Also one might ask whether the (-B-B-B-) and
(-C-G-C-) groupings found in the mixtures were due to
insufficient mixing of the components.
Experimentally,
the x-ray diffraction results were independent of the
amount of stirring.
The effects observed could not have
been caused by a streaming effect in the liquid, for curves
run at room temperature, with and without stirring, were
identical.
The results reported here may be discussed with
relation to other data from the literature.
The data for
the unit diffraoting distance in a given group, (d = nV2sin^),
read off a graph of d versus T, over a temperature range
from 10°G to 60°0, (see Table I) show that the increase in
d is more than 6 percent and less than 18 percent, with a
probable value of 12 percent.
results now in the literature
diffraction of liquids.
This is consistant with the
' (30), (31), (32) Qn 3C_ray
The faot that the I.O.T. tables
show, for both benzene and cyclohexane, a volume expansion
of only 6 percent, indicates strongly that only a small
fraction of the liquid can be in an order state at any one
time.
This conclusion is consistant with thermodynamic data
on liquids in general^*^ *
hexane systen/^.
, and on the benzene - cyclo­
The positions of the (-B-B-B-) and
(.0-0-0-) peaks at the freezing points of the pure liquids
strongly indicate that the order state is nearly that of
the solid, in one dimension at least.
The two strong lines
of the solid benzene arising from the (ill) and (020) planes
give an average d of 4.65 X^35), the experimental value
from the liquid peak at 5.7°0 gives d = 4.68 X.
Two very
strong lines for solid cyclohexane gave an average d of
5.04 X
compared to a value at 6.7°0 of 5.06 X for the
liquid cyclohexane.
The positive deviation of the benzene - cyclohexane
system from Raoult' s L a w ^
on mixing^®) *
and the increase in molal volume
would lead to the conclusion that the
intermolecular forces between benzene and cyclohexane
molecules were less than those between benzenejbenzene or
cyclohexane-^cyclohexane molecules.
Therefore the probability
of the (-B-0-B-C-) array appearing in the liquid should be
less than that predicted on the basis of mol fractions.
If
the forces had been all equal, the (-B-C-B-C-) peak intensity
should have been between the (-B-B-B-) and (-C-0-0-) inten­
sities.
In the case of the carefully studied 51.4 percent
benzene mixture, Table II shows that not only is the
(-B-C-B-C-) peak intensity lower than the average intensity
of the benzene and cyclohexane peaks, but also that it is
almost always lower than the benzene peak itself.
This is
consistant with the above prediction based on Raoult* s Law.
Summary
(1)
A low intensity peak at half the diffraction angle of
the main peaks has been detected and a plausable explana­
tion has been given for its existance.
(2)
The main peak from x-ray diffraction measurements of
benzene - cyclohexane solutions has been resolved experi­
mentally into three peaks.
(3)
The observed diffraction peaks in the liquid mixtures
are explained on an order - disorder basis, which is
consistant with existing thermodynamic data.
(4)
Theoretical curves are shown to give intensities
comparable to measured values, for the most probable order
states in the solutions.
(5)
The usefulness of Geiger-Mueller counters for liquid
x-ray diffraction studies has been demonstrated.
Bibliogranhv
(1) G. W. Stewart, Ohem. Rev. 6, 483 (1929).
(2)
3
G. W. Stewart, Rev. Mod. Phys. 2, 116 (1930).
For reviews of papers and theories see:
(a) The Diffraction of X-rays and Electrons by
Amorphous Solids, Liquids and Gases.
J. T. Randall, John Wiley & Sons, Inc.
New York (1934)
(b) 0. Drucker, Phys. Zeits. 29, 273 (1928).
(3
P. Krishnamurti,
(1929).
Ind. J. Phys. 3, 331 (1929); 3, 507
“
“
(4
A. W. Meyer, Phys. Rev. 38, 1083 (1931).
(5
R. W. 0. Wyokoff, Am. J. Sci. 5, 455 (1923).
(6
G. E. Murray and B. E. Warren, J. of Ohem. Physics 7,
141 (1939).
(7
S. Parthasarathy, Phil. Mag.' 18, 90-7 (1934).
(8
H. K. Ward, J. Ohem. Physics 2, 153 (1934).
(9
G. Scatchard, S. E. Wood and
Chem. 43, 1119-130 (1939).
10
P. A. Ross, Phys. Rev. 28. 425A (1926).
11
W. C. Pierce, ibid. 38, 1409 (1931).
12
W. Soller, ibid. 24, 159 (1924).
13
J. C. Street and T. H. Johnson, J. of Franklin Institute,
214. 155 (1932).
14
W. H. Pickering, Rev. Sci. Inst. .9, 180 (1938).
15
Ruark and Brammer, Phys. Rev. 52. 322 (1937).
16
Alaoglu and Smith, ibid. 53. 832 (1938).
17
A. L. Hughes, Am. Phys. Teacher _7, 271-292 (1939).
18
International Critical Tables IV p. 133.
J. M. Mochel, J.
of
Ph.
0. V. Raman and K. R. Ramanathan, Proc. Indian Assn.
for Cultr. Sc. p. 127 (1923).
Zernike and J. A. Prins, Z. ftlr Phys. 41, 184 (1927).
J. A. Prins, ibid. 56, 617 (1929).
J. A. Prins, Naturwiss. 19. 435 (1931).
P. Debye, Phys. Zeits. 31, 348 (1930).
S. Katzoff, J. Ohem. Phys. 12, 841 (1934).
von L. Bewilogua, Ph. Zeits. 33, 688-92 (1932).
von Gustav Thomer, ibid. 38, 48-58 (1937).
0. M. Sogani, Indian J. Phys. 1, 357 (1927).
G. W. Stewart, Phys. Rev. 33, 889 (1929).
A. W. Meyer, ibid. 38, 1083-93 (1931).
E.
W. Skinner, ibid. 36, 1625-30 (1930).
S.
S. Ramasubramanyan,
Indian J. Phys. 3, 137-4-9 (1928).
V. I. Vaidynathan, ibid. 5, 501-24 (1930).
J.
G. Kirkwood, J. Ph.
Ohem. 43,97 (1939).
G. Scatchard and W. J. Hamer, J. Am. Ohem. Soc. 57,
„ 1805 (1935).
E. G. Cox, Proc. Roy. Soc. A. 135, 491 (1932).
K. Lonsdale and H. Smith, Phil. Mag. 28, 614 (1939).
H. Poltz, Z. fur Ph. Chemie B32 243-73 (1936).
appendix
I
Apparatus
A.
X-Ray Tube Circuit and. Arrangement
The wiring of the x-ray tube was very similar to that
used previously in this laboratory^38).
To insure steady
x-ray tube currents, a Raytheon voltage regulator was used
to supply the 110 v. A.O. used for the filament transformer.
Voltage regulator data:
Raytheon Manufacturing Oo., Waltham, Mass.
Type VR-3
Model 1
Watts 120
A.O. voltage 95-130, 60 cycle
Output 115 ll
The x-ray tube was mounted in a vertical position with
the high-potential anode projecting through the table top
to the transformer.
The table was tall enough to allow
for 10 inches of clearance between the transformer high
potential and the table-top.
The transformer was completely
protected with wire netting fastened to the table legs.
The
x-ray tube shield, consisting of an iron pipe with flange,
was fastened to the table-top at an angle of 4° from the
vertical.
Inside the iron pipe a lead oxide packed glass
shield protected the iron shield from high potential.
One-
quarter of an inch of lead gave x-ray protection around the
iron shield.
The x-ray tube was supported by an adjustable
damp on the cathode, fastened securely to the iron shield.
The transformer cage, x-ray tube cathode and metal shielding
were all grounded to a water pipe.
This arrangement allowed the most intense beam produced
by the x-ray tube, to be collimated by slits parallel to the
table-top, and passed through the spectrometer and counter
system previously described.
B.
Counter Circuit
(1)
Qeiger-Mueller Counter Tube
The counter tube used was constructed by Mr. A. G.
Nestor of Bartol Research Foundation, Swarthmore, Pennsylvania,
and was very similar to those used previously in this
(39)
laboratory' ', the essential difference being in the size
of the slit in the cathode.
The cathode had the following
dimensions:- 3.0 cm. long; 1.3 om. in diameter and a slit
3.0 cm. by 0.9 cm. through which the x-rays entered.
Geiger-Mueller tube characteristics:
Starting Potential 830 volts
Tested to 950 volts
Operating Potential 840-860 volts
Resistance 500 meg. ohms.
(2)
High Voltage Rectifier
The constant D.C. voltage for the G.-M. tube was
supplied by the circuit shown in Fig. IX.
This circuit is
essentially that of Street and Johnson^^, except that a
57 R.C.A. tube was used rather than the 24A which they
HIGH V O LT A G E RECTIFIER
j | IIOV.A.G.
mnmm fttrvn
KI 5 I 2
c
a>
;o
I^
I^
4 5V
K2538
X
CM
IIOV.A.C.
F IG U R E
M
IX
reoommended.
The rectified D. C. high voltage was supplied
through a 866 half-wave mercury vapor rectifier tube.
voltage delivered was measured by the ammeter
the current through the bleeder resistances.
positive or negative side may be grounded.
The
measuring
Either the
In this case
the positive was connected to the chassis and grounded.
All part numbers as given in Fig. IX refer tojWholesale Radio Co. catalog numbers, Catalog No. 69 (1938).
(3)
Power Supply for Amplifier Circuit
Use was made of two 83 full-wave mercury vapor
rectifier tubes to supply D.C. voltages for the plate
circuits of the amplifier (See Figure X).
Voltages for the
grid biases were supplied by potentiometers connected in
parallel between the center tap and ground on one of the
transformers.
The voltages given by these potentiometers
could be varied from 0 to -37 volts.
Condensers were
connected between the grid bias leads and ground to smooth
out the voltages (not shown in Fig. X).
R 5 and R 6 were 5000 ohms.
These resistors should
be 100,000 ohms to reduce continuous drain on the transfor­
mers.
Difficulty was experienced with the fine wire of
these high resistances burning out, hence the smaller
resistances were used.
These power supplies were each
capable of producing 235 milliamperes at a maximum of 400
volts.
POWER SUPPLY
K42S
r\
^IwOtwuiK
«4*-<■>
nrmn (Tsvnr
8&S"
• •
fil.Supply GRID BIAS
Rr 2SOOJX
All p^Kt Numbers
Rx R ^ R ^ - S O O O H
Wholesale Radio C ata lo g No.'s
No. G9 (1938)
R s R fc- SOOOSi
C, Ca C3 C4 -
.dufF IG U R E
X
jUUtUMlUiU/
83
ivnvrnrsi
83
R,~-— >v.
COUNTER CIRCUIT
45V
+220 V
4
57
56
865
56
r\
r\
050V
4SV—
Rx- / o v i o ‘ i i
R2> ^ By —SoooIL
stHrlxidfl
(3)- M A GNETIC
SPEAKER
@
F IG U R E V!
- CENCO COUNTER
37.
Rll-5'06fl0il
^
C„- .25C^oCB )C^jC/0
(4)
Amplifier Circuit
The circuit finally adopted is shown in Fig. XI.
One advantage of this circuit is that it is only necessary
to shield the first amplifier tube (57 tube), condenser 0^
and the resistances
Rg and Rg.
The quality of the
pulse could be checked in each stage of the amplification
by use of phones in the jacks in the plate circuits.
The
volume of the speaker could be varied by R^g, without
changing the tube current in the 45 power tube.
The
filament for the 885 thryatron must be supplied by a separate
filament transformer which is not grounded.
This is essential
for operation of this circuit, since the cathode potential
goes from+*20 v to+-230 v when a pulse causes the tube to
lose control and discharge condenser Cg.
The amplifier, power and high voltage supplier
were
all mounted in a cabinet so that adjustments might be
made
from the bottom of each chassis without removing.
If
necessary each chassis could be removed independently.
The bias voltages used for most efficient
operation were approximately:
No.
1
57
tube bias
- 3v.
No.
3 56 tube bias
-lOv.
No.
3 56
-4.5v.
tube bias
885 thryatron bias
-llv.
885 thryatron cathode potential + 20v above ground.
40
BALANCED
38
F IL T E R
T R A N S M IS S IO
1V0.
30
Sr
34
32
30
,30
.40
.5 0
X -K A Y
.60
WAVELENGTH
Figure XII
80
IN A
90
APPENDIX II
Filter Transmission Qurve
The transmission of the ZrOg and Sr(NC>3)3 filters
measured for the x-ray spectrum of molybdenum is shown in
Fig# XII#
The wavelengths were determined using a NaCl
crystal, aligned so that the (100) plane was diffracting.
Using the value of d],qq = 2.8135 2 and
measured on the
spectrometer, the wavelengths were determined by Bragg's
law#
The x-ray tube was operated at 42 kilovolts
(r.m.s.), the value used in all the experimental measurements,
with a tube current of 10 railliamperes to reduce the counting
rate.
The cross hatohed area, of Fig. XII, represents the
wavelengths transmitted by the Zr02 filter and not by the
Sr(N03)2*
It was therefore these wavelengths which contri­
buted to the diffraction curves.
The intensity of the
doublet was very much greater than indicated, since the
counter would only record 3600 pulses per minute (60 cycle
of the x-ray tube).
IN TEN SITY
FIGURE
XIII
'If'
APPENDIX III
Additional Data
A.
Shape of Entire Diffraction Curves
Since it was not possible to reproduce the entire
range of angle of diffraction studied in Figs. II - V,
three representative curves are shown in Fig. XIII.
All of the curves taken exhibited the small peak at angles
between 3^-= 4°00' to 4o20' depending on the mixture taken.
B.
Experimental and Theoretical Curves for Other Mixtures
Curves were obtained for mixtures other than those
given in the main body of this thesis.
The shape of the
curves and peak intensities were in agreement with the
others taken.
These are reproduced in Figures XIV and XV.
As pointed out previously, these curves were not checked
so carefully for absolute peak intensities as for existance
of peaks, hence the check between theory and experiment was
not as good as the 51.4 percent benzene
C.
case.
Peak.Shift with Temperature
The values of d corresponding to each peak increases
with rising temperature, as can be seen from Table I.
This
increase in d is given by a decrease in the angle of diffrac­
tion for the peaks.
In Fig. XVI the peak positions (2-©*) are plotted against
temperature, for each peak of the 51.4 percent benzene
mixture and the two pure liquids.
43.
CA) - 3 7 . 2 7.
B\iN Z fIN
E
CB) -B 2 .4 7. B H N Z I1 N E
(B)0
Figure XIV
44.
( A ) - 3 7 . 2 7, B E N Z E N E
<B) 4 - 6 2 . 4 7 . BE N Z E N
- THEORETICAL
oG
(B)0
CA) 0
Figure X V
45
•
----- —
-----i----
-
CB) — 8°2 0'
11
CO
—
8°4 o'
ri
(D)
—
e?oo'p EA K
CE)
&°o4► \ U
8°0 y p EA K
—
8°4 0'
\
*•
-----
ii
5 14 7.
io
!**
CVI
CA)
1 p ° Vo
o 1
®
* !
<t> ---- j-----
100 7.
Hb
JIV
c * H*
/
'
.
* vL /
i. r \ \
w /
&N
f) trfc.7
fC.\
-
/n\
) VI37
r
8 4 0J \\-»7
CA')
WV/
•>—
4i
* / r»\
) "VO/
t
i
%
(C)
8 0 0) rAv
9
>Tttr
|---
.10
0
10
20
TEMPERATURE
30
C° C)
r> r*\
o c?rn
V / WS-S
TEM
PER
C°C)
&VII.
ATURE
Figure
m
D.
Decrease in Intensity with Temperature
The intensity data tabulated in Table II may be found
reproduced graphically in Figure XVII for the liquids
studied over the range of temperatures.
If the diffraotion peaks are due to the so called
"cybotactic1* order groups existing in the liquid, then the
- intensity of the peak should be proportional to the number
of such groups present at any given instant.
Then the
intensity I should be some function of the form of a
Maxwell-Boltzman distribution.
where
is some function of the energy.
- In I =
4>
T°K
+
constant
If this was true then a plot of In I against l/T°K
should give a straight line.
These plots were made for
the pure benzene and cyclohexane and the peaks of the 51.4
percent benzene solution.
Nearly straight lines were
obtained except in the region near the freezing points.
The data however do- , not seem accurate enough to justify
saying anything further about the distribution function.
48.
Appendices Bibliography
(38)
0. W. Mclenathen, M.S. Thesis (1939).
(39)
H. M. Sullivan, Ph. D. Thesis (1938).
(40)
Duffendack, Lifschutz, and Slawsky, Ph. Rev. 51.
1331 (1937).
Документ
Категория
Без категории
Просмотров
0
Размер файла
2 062 Кб
Теги
sdewsdweddes
1/--страниц
Пожаловаться на содержимое документа