Creator:John W. Stewart
Date Created:
Place Created:Charlottesville, Virginia
Keywords:phase transition,compressions,CH4,CD4,O2
Context:article from the University of Virginia Department of Physics
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DEPARTMENT OF PHYSICS UNIVERSITY OF VIRGINIA
McCORMICK ROAD CHARLOTTESVILLE, VIRGINIA
PHASE TRANSITION^ AND COMPRESSIONS -;—OT-OTEim^, CD^rAND 02*
John W. Stewart University of Virginia Charlotte s ville, Virginia
* Supported by the Department of Army, Office of Ordnance Research
ABSTRACT
The piston displacement technique previously described has been applied to a study of phase transitions and isothermal compressibilities of solid CH4, CD4, and 02 over the pressure range 0 - 19,000 kg/ cm2 and the temperature range - 120°K. Phase transitions appear as discontinuities in V (first order) or in (dV/dP)^ (second order).
Solid CH^ and CD^ each show three phases and one triple point. The transitions appear to be of the second order, with rather large "regions of indifference". There are isotopic differences between the two methanes. At atmospheric pressure CH^ shows only one of the transitions, at 20.5°K, while CD^ has both, 22.1° and 27-2°. There is at present disagreement between our results for CH^ and those obtained by Stevenson.
In the case of solid oxygen, the two well-known transitions have been traced to high pressure. The lower transition is evidently of the second order. The upper first order transition has a large volume discontinuity. Some difficulty was experienced from ignition of the steel pressure chambers by the solid oxygen under high pressure.
Pressure-volume relations for the three substances have been obtained at various temperatures.
PHASE TRANSITIONS AND COMPRESSIONS OF SOLID CH^, CD^, AND 02
I. Introduction
The specific heat anomaly in solid CH^ at 20.5°K at atmospheric pressure was first observed by Clusius1 in 1929. Since the
specific heat maximum appeared to be finite, it was assumed that
2
this transition was second order. Later work by Schallamach
employing X-ray diffraction showed that there was no change in the
o
fee structure of solid methane at 20 . The transition was assumed to involve a change in the rotational states of the CH^ molecules.
3
However, proton resonance measurements by Thomas, Alpert, and Torrey
showed that a state of free rotation of the molecules was not realized
at 20.5°, but only at much higher temperature.
If.
Kruis, Popp, and Clusius investigated the specific heat
o
of solid CD^ at low temperature and observed two anomalies, at 22.2 K and 27.1°K. These appeared also to be second order. Studies^ of mixtures of CH^ and CD^ showed that the upper transition in CD^ is analogous to the single transition in CH^, and that the lower transition in CD^ has no equivalent in CH^ at atmospheric pressure. The lowest temperature phase in CD^ is now known to be weakly doubly refracting so that its structure cannot be strictly fee. The lower transition must therefore be first order, with a very small latent heat of transition.
By means of specific heat measurements at atmospheric pressure, Giauque and Johanton^ observed two transitions in solid oxygen. Both were believed to be first order, with measured heats of
transition 22.k cal/mole at 23.7°K and 177-6 cal/mole at U3.8 . How-
7
ever, X-ray studies by Vegard indicate no change in crystal structure
at the lower transition, and subsequent thermal measurements by 8
Borovik-Romanov also lead to the identification of the lower transition as being of the second order.
The only previous high pressure work with solid CH^ appears
9
to be that of Trapeznikova and Miljutin . They measured the specific heat at pressures up to 2,000 atmospheres, and found a secend transition in CH^ at elevated pressures, evidently corresponding to the
lower transition in CD^. There appeared to be a triple point in
o	10
CH^ near 33 K and 2,600 atmospheres. The recent work of Stevenson
will be discussed below. The present results for CH^ represent an
extension of results previously presented^1 in a preliminary fashion.
There has apparently been no previous high pressure work with solid 12
CD^. Stevenson has also obtained high pressure data for solid 0^.
II. Experimental Technique
Throughout the present investigation, the piston displacement
13
technique previously described in detail has been used. Volume
versus pressure data have been obtained over the pressure range
0 - 19,000 kg/cm and the temperature ranges - 120°K for CH^,
k° - 90° for CD, , and 30° - 65° for 0 . Pressure is applied by the 4	2
piston directly to the sample. Plasticity of the solidified gas is
relied upon for transmission of the applied uniaxial compressive stress
as an approximate hydrostatic pressure. A variable temperature cryostat
Ik
of the type designed by Swenson has been employed. Liquid helium
3
was the coolant for temperatures "between and 77 > and liquid
nitrogen was used for temperatures above 77°• The temperature of the
sample was determined by means of an indium resistance thermometer
of the type suggested by White and Woods1^. This thermometer will
16
be described in detail elsewhere
Four sizes of sample holder were used: 5/8 inch diameter
(stainless steel, Type 3(A) for pressures of 0 - 3,000 kg/cm (later
replaced by a l/2 inch stainless ste eL cylinder, pressure range 2
0 - 5,000 kg/cm ); 5/l6 inch diameter (AISI 4615 steel, heat treated),
/ 2	13
0 - 19,000 kg/cm . As before , the high pressure pistons were constructed from heat treated Ketos tool steel. The larger diameter cylinders give greater sensitivity at relatively low pressures than is afforded by the l/k inch cylinders. All the cylinders used were 3/4 to 1 inch in depth.
First order transitions in the sample produce volums discontinuities in the V vs P data, while, with a second order transition, the volume is continuous but there is a break in the slope, (dV/dP)^. Friction in the sample holders tends to "round the corners" of either type, and, unless the volume discontinuity is quite large, it is impossible to determine the order of a transition from the volume-pressure data alone. The friction was reduced by lining the pressure cylinder with 0.005-inch indium foil.
After initial compaction of the sample by one or two applications and releases of pressure, the pressure was decreased from its maximum value to zero in regular steps, and then was likewise increased back to the maximum value. This is the method originated
L
J
k
by Bridgman"^ for compressibility measurements on solids. At each
point, the position of the piston was observed after all drift has
stopped. A micrometer slide and telescope were used to follow the
motion of a scratch on the upper (room temperature) end of the stainless
steel compression member. Following completion of one or two such
"hysteresis loops", the sample was expelled by warming up the system
and applying pressure. The background stretch of the press was
then obtained by means of a pressure hysteresis loop with the piston
in contact with the bottom of the empty sample holder. For reasons
of economy of liquid helium, these "blank" runs were always carried
out at 77°. The elastic constants of the stainless steel tension
and compression members change very little with temperature in the
range of these measurements. The sample length at zero pressure was
13
determined from the blank run as previously described .
The temperature of the sample was controlled by adjustment of a needle valve in the helium discharge line from the cryostat. Liquid helium was forced through a vacuum jacketed transfer tube into the heat exchanger of the cryostat by pressurizing a 25-liter storage Dewar with gaseous helium. The flow rate of the evaporated helium could be monitored with a wet test meter. The temperature, as recorded by the indium resistance thermometer mounted on the bottom of the press in good thermal contact with the sample holder, was held constant within 0.5°K for periods up to three hours.
Data at temperatures above the melting points of the substances were obtained by initially applying pressure at a lower temperature and then allowing the sample to warm up at constant pressure. A hysteresis loop at pressures above the melting pressure was then run.
5
III. Results and Discussion
Methanes. Phillips Petroleum Company Research grade CH^ (99• or higher purity) was used. The CD^ was obtained from Tracerlab, Inc., and was stated to be at least 951° CD^. No additional purification was carried out in either case.
The behavior under pressure of the solid CD^ and CH^ was rather peculiar. The transitions were always much more conspicuous on the decreasing pressure side of the hysteresis loop than on the increasing pressure side. The break in slope on the decreasing side was accompanied by unusually large drift of the piston, which continued for 15 or 20 minutes after a change of pressure had been made. The drift first appeared several decrements of pressure above the apparent transition point, and increased in magnitude and duration at each point until the transition was complete. As the pressure was further reduced, there was no drift of the piston until very low pressures were reached. On account of friction, all the solidified gas samples studied so far have shown some drift of the piston at the extreme low pressure end of the decreasing pressure leg of the hysteresis loop.
On the increasing pressure side of the V vs P loop, it was difficult to distinguish breaks in slope from frictional irregularities in the piston motion. There was little or no drift as the transition was approached from the low pressure side. The size of feasible pressure increments could not be reduced below a minimum value. The piston motion became jerky if the increments were made too small, with a tendency for alternate points to lie on a smooth
6
curve. These effects are believed, to be caused by frictional
"hanging up" of the piston on the wall of the cylinder arising from
the finite shear strength of the solidified samples.
The transitions appear more clearly if the data are plotted
against pressure as differences between the observed piston position
and a straight line drawn between the maximum and zero pressure
points. This increases the scale of the irregularities in piston
motion over those appearing in a direct volume vs. pressure plot.
A typical plot of this kind is shown in Fig. 1. The transition
pressure is taken as the arithmetic mean of the pressures of the
breaks in the decreasing and increasing pressure curves.
The phase diagram for solid CH^ is shown in Fig. 2, and
that for CDj^ in Fig. 3. In the case of CH^, the present results
9
disagree in part with those of Trapeznikova and Miljutin , and Stevenson1^. Agreement is perfect with Trapeznikova and Miljutin for the I - II transition, but the present II - III curve lies at substantially higher pressure than those of either Trapeznikova and Miljutin or Stevenson. The reason for this discrepancy is not known. It is felt that our observed points for the II - III transition are more accurate than those at higher pressure.
In the present work, no evidence was found of the fourth
phase ($ )) stable at high pressure and low temperature, reported 10
by Stevenson . A careful search was made for this, but no irregularities in the piston motion consistent enough to be associated with a phase transition were observed. There is evidence that solid CH, becomes increasingly brittle in this region of the FT plane.
7
When the pressure was changed the piston moved in jerks accompanied by crunching sounds. Except for the lack of consistency between data at neighboring temperatures, it would be possible to mistake this behavior for a phase transition. Where the sample is brittle, the applied uniaxial compressive stress is not transmitted throughout as hydrostatic pressure, and the stress system in the sample is complicated. The compressibility and phase transition data then have doubtful validity.
Previous extrusion experiments in this laboratory have shown that solid CH^ is quite plastic near atmospheric pressure at 77°K. A pressure of 800 kg/cm2 applied to a solid sample in a l/U inch cylinder extruded the sample smoothly through a coaxial l/8 inch hole in the bottom of the cylinder. However, as the temperature is lowered, solid methane becomes increasingly brittle.
At higher temperatures, the present disagreement with Stevenson on the location of the I - III transition curve appears to arise from the fact that he was there working near the top of his available pressure range where the transition data are quite inaccurate.
All three sets of data lead to very nearly the same I - II -
o	. 2
III triple point parameters, namely 33 K and 2,700 kg/cm . In Fig. 2
the II - III and I - III transition is shewn as a continuous straight line through the triple point. From a consideration of thermodynamic potentials, it can be shown that at a triple point the transition line dividing the regions of stability of the ith phase and the jth phase must, when projected through the triple point, enter the region of stability of the kth phase. This theorem applies to transitions of all orders. Thus the I - III line cannot bend away from the temperature axis at the triple point (Fig. 2).
8
Presumably because of greater impurity content, the CD^
18
transitions appeared less distinctly than those for CH^. Bridgman has pointed out that the corners of transitions when plotted on a V-P diagram are rounded by the presence of impurity. In contrast to the situation in CH^, both transitions in CD^ occur at atmospheric pressure. Otherwise the two phase diagrams are qualitatively similar. At a given temperature, the transition pressure for CD^ is lower them the corresponding pressure for CH^. The triple point parameters
1 o	#2
for CD^ are 40 K and 3,000 kg/cm . These are less accurately known than is the case for CH^. There is no evidence in the present data for a fourth phase in CD^ analogous to Stevenson's £ in CH^.
The experimental uncertainties in the transition pressures are of the order of the smallest pressure increment that could be applied without irregular piston motion. The transitions observed in the larger holders have a smaller absolute error than those observed in the smaller, higher pressure, holders. The relative uncertainties are nearly the same. The large spread in transition pressures observed at 77° is not understood. Some of the earlier values11 are now believed to be too high and have been assigned smaller weight in the location of the transition curves.
The spread between the transition points observed with increasing and decreasing pressure is considerably greater than the friction. With a closely fitting piston and indium liner the half-width of the friction hysteresis loop was of the order of of the maximum pressure. The width of the "region of indifference" was at least as large as the friction, but showed no obvious dependence upon temperature, pressure, sample length, or sample holder diameter.
9
In general, the friction tends to be less with samll length-to-
diameter ratio for the sample. On the other hand, the magnitude of
the piston displacement then becomes inconveniently small, so that
one does not gain in accuracy by reducing the sample length below
a certain value. The samples used in this investigation had length-
to-diameter ratios of between 1.0 and 2.0.
A total of 36 runs were made with CH. and l8 with CD. .
4	4
One to four separate runs were made with each samplef the most common
number being two.
Table I. Compression Data for Solid CHj,, CD^ and 0,
	CH^		CD4		°2	
	77°KjO =0.507 gm/cm3		77°K	32 °K	51 °K f =1.36 gm/cm3	
1 Pressure ,	Mol. Vol.)	-AV/V0	-AV/Vq	-AV/Vo	Mol.Vol. Q	-AV/Vo
kg/cn2	3 cnr				cm	
0	31.6	0	0	0	23.5	0
1,000	29.9	.054	.049	.032	--	—
1,100	--	--	—	--	22.2	.054*
1,100	—	—	—	—	21.2	.096*
2,000	28.8	.090	.083	.058	20.6	.122
2,500	--	—		.067*	--	
4,000	27.1	.141	• 133	.097-	19.6	.167
6,000	25.9	.179	.169	.128	18.8	.198
7,400	__	_ _	.187*	m _	mm —	m»mm
7,900	—	—	-- .		18.4	.219*
8,000	25.0	.208	.196	■151	—	— .
10,000	24.3	.230*	.221	.170	17.8	.241
12,000	23-7	.251	.242	.187	17.4	.258
14,000	23.I	.268	.260	—	17-1	.272
16,000	22.7	.281	.274	—	16.8	.283
19,000	22.2	.299	.292	—-	16.5	.298
* Phase Transition
10
The pressure-volume relations for CH^ and CD^ at 77°K are
shown in Table I. The method of calculation is the same as described
previously.13 The observed difference between AV/Vq for CH^ and CD^
is less than the estimated 5$ precision of measurement. One might
expect CDi, to be slightly less compressible than CH , particularly * k
at low pressure, because of the smaller zero point energy of CD^. Owing to the width of the regions of indifference, the difference in compressibility at the transitions cannot be. determined accurately. One must extrapolate the experimental curves from each side of the transition so that they meet without a discontinuity in volume. In all cases it is observed that the compressibility of the high pressure phase is greater than that of the low pressure phase at the transition point.
The molar volume data for solid CH^ given in Table I are
+ i / 3	°
based upon the value of 0.507 - 0.004 gm/cm for the density at 77 ,
19
obtained in this laboratory by LaRock . Since no accurate measurement of the density of solid CD^ seems to have been made, no molar volumes are given.
In the previous determinations of FV isotherms for solidi-13,20
fied gases	the Murnaghan theory of finite strain was found to
be quite useful for empirical fitting of the experimental data. However, because of the phase transitions, no attempt has been made to apply this theory to the present compressibility data. At a given temperature, different values of the two adjustable constants weuld be needed for each phase. It was not felt that this representation would be particularly useful.
11
Oxygen. Linde Company oxygen (U.S.P.) was used without additional purification. Judging by the charpness of the transitions, the purity must have been quite high. Both transitions were evident on both the decreasing and increasing pressure legs of the
hysteresis loop. Fig. k shows the phase diagram for solid oxygen.
12
The present results agree closely with those of Stevenson.
A previous extrusion experiment similar to that described above for CH^ showed that solid oxygen is brittle at 4°K. However, it appears to transmit hydrostatic pressure satisfactorily at temperatures above 30°.
The lower temperature transition ( - y, Fig, 4) is assumed to be of the second order. The discontinuity in piston motion for this transition was very small, and because of friction it is not possible.to distinguish between a small volume change and a jump in (dV/dP)^. The compressibility of phase y is greater than
that of phase (g at the transition pressures observed (7,900
o	, 2	Ov
at 51 j 2,500 kg/cm at 32 ). The differences between the compressi
bilities appear to be smaller than is the case with the second order
transitions of the solid methanes.
The a - fi transition shows a large volume change, and is
7
certainly first order. The X-ray data show that, in the a phase, pairs of 02 molecules are arranged with their centers in a fee array In the f phase the structure is either trigonal or rhombohedral. The y phase was found to have the same structure as the fz phase.
The volume changes observed for the as * fi transition were 1.09 - 0.05 cm3/mole at 47° and O.98 - 0.05 cm3/mole at 51°. Less
o
accurate values, which appear to be smaller, were obtained at 59 and 66°. The latter two were not converted to cm3/mole because the pressure hysteresis loop could not be carried to zero pressure at temperatures above the melting point of oxygen. A linear extrapolation of the results at 47° and 51° leads to AV - 1.18 - 0.C6 cm3/mole at 43.8 , the temperature of the transition at atmospheric pressure.
6
Using Gianque's value of the latent heat of the transition (177.6 - 0.5 cal/mole) and the slope, dP/dT, of the a - p transition line (determined from Fig. 4) in Clapeyron's equation, we
calculate AV = 1.16 - 0.14 cm3/mole. The agreement is excellent.
o
The density of solid oxygen at 51 was calculated from
an extrapolation to the melting point of values of the density of
21
the liquid as a function of temperature given by van Itterbeck and from the volume change at fusion (54.3°) determined from Clapeyron's
equation. Giauque's^ value of the latent heat of fusion (106 cal/mole)
22
and Lisman's determination of dP/dT based upon melting curve measurements to 170 kg/cm2 were used. The value adopted for the density at 51° is I.36 - 0.01 gm/cm3. From this the molar volumes in Table I were determined.
In some of the oxygen runs trouble was experienced from chemical reaction at high pressure of the solid oxygen samples with the steel pressure cylinder. Once such a reaction started, it proceeded explosively, and pressure was quickly lost as the sample
vaporized and leaked past the piston. This happened on three
o	2
separate occasions, as follows: 4l , 12,000 kg/cm , on initial
13
increase of pressure; 51°, 16,000 kg/cm2, as pressure was being
increased for the third time on that particular sample (after a
o	2
successful run had been completed); 70 , 19,000 kg/cm , sample warming up at constant pressure. In each case as the oxygen escaped, a channel was melted in the piston and cylinder. This combustion could usually be prevented by the indium liner. On the first occasion no liner was used; on the latter two it presumably was torn. One might suppose that it would be impossible to initiate this spontaneous reaction at reproducible temperatures and pressures, since it presumably requires sufficient activation energy to be supplied by the compression at one spot on the wall of the pressure chamber. This would vary with friction.
IV. Conclusion
The exact nature of the methane phase transitions is not yet understood theoretically. They are believed to involve changes in rotational states of the molecules in the solid crystal, although there must also be a slight change in the crystal structure in the lower temperature transition of solid CD^ to account for the aniso-tropy of phase III. The same might well be true for the II - III
transition of CH^. No studies of the refractive properties of phase III
23
of CH. have been made. James has carried out a classical statisti-cal mechanical calculation for CD^ at atmospheric pressure, based upon quadrupole-quadrupole interaction between the molecules. This accounts reasonably well for the observed two transition temperatures. His theory is not yet applicable to CH. , for which quantum effects
14
are more important. Neither does it apply to CD^ under pressure because lattice compressibility is neglected. It is the author's understanding that further calculations to take account of these effects are in progress at the present time.
Further experimental studies of the solid methanes under pressure would be highly desirable. In particular, specific heat measurements, nuclear magnetic resonance measurements, and perhaps neutron diffraction measurements should be carried out at as high a pressure as possible. In order to improve materially upon the present accuracy of the piston displacement technique, it will be necessary to embed the solid methane in a medium which transmits hydrostatic pressure. Solid hydrogen could be used at the lower temperatures. Gaseous helium would be suitable over the entire range if only relatively low pressures were desired.
The author wishes to express his appreciation to Major Ralph I. LaRock and Major Robert F. Patterson for their invaluable assistance in designing some of the equipment and especially in the taking of the data. He would also like to acknowledge the contribution of Mr. Fhilipp Sommer, who constructed much of the apparatus.
15
References
1.	K. Clusius, Zeit. Physik. Chimie (B) 3, 4l, (1929); K. Clusius and A. Perlick, Zeit. Physik. Chimie IB) 24, 313, (1934).
2.	A. Scfcallamacb, Proc. Royal Soc.'(A) 171, 569 (1939)-
3.	J. Thomas, N. Alpert, and H. Torrey, J. Chem. Phys. 18, 1511 (1950).
4.	A. Kruis, L. Popp, K. Clusius, Zeit. Electrochem. 66b (1937); K. Clusius and L. Popp, Zeit. Physik. Chimie (B) 467 63 (1940).
5.	E. Bartholome, G. Drikos, and A. Eucken, Zeit. Physik. Chimie (B) 39, 371 (1938).
W. F. Giauque, and H. L. Johnston, J. Amer. Chem. Soc. 51, 2300 (1929).
7.	L. Vegard, Nature 136, 720 (1935).
8.	A. S. Borovik-Romanov, M. P. Orlova and P. G. Strelkov, Doklady Akad. Nauk SSR 99, 699 (1954).
9.	0. Trapeznikova and G. Miljutin, Nature 144, 632 (1939).
10.	R. Stevenson, J. Chem. Phys. 27, 656 (1957).
11.	J. W. Stewart, Proceedings of the Fifth International Conference on Low Temperature Physics and Chemistry, University of Wisconsin Press, Madison, 1958. Page 522.
12.	R. Stevenson, J. Chem. Phys. 27, 673 (1957).
13.	J. W. Stewart, J. Phys. Chem. Solids 1, 146 (1956).
14.	C. A. Swenson, Rev. Sci. Instr. 25, 608 (1954).
15.	G. K. White and S. B. Woods, Rev. Sci. Instr. 28, 638 (1957).
16.	J. W. Stewart, To be published.
17.	P. W. Bridgman, Proc. Amer. Acad. Arts and Sciences 74, 425 (1942).
18.	P. W. Bridgman, "The Physics of High Pressure", G. Bell and Sons, London, 1949. Page 191
19.	R. I. LaRock, Thesis, University of Virginia, 1958. For details of the method, see reference 20.
20.	J. W. Stewart, R. I. LaRock, J. Chem. Phys. 28, 425 (1958).
16
21.	A. van Itterbeck in C. J. Gorter (Ed) "Progress in Low Temperature Physics", International Publishers, Inc., New York, 1955* Vol. 1, page 366.
22.	J. Lisman and W. Keesom, Physica 2, 901 (1935).
23.	H. James, J. Chem. Phys. (To be published).
Phase Transitions and Compressions of Solid CH^, CDj^, and 0^
John W. Stewart Figure Captions
Fig. 1 "Hysteresis" loop for locating phase transitions in solid CH^.
A straight line was drawn connecting the maximum and zero
pressure points on a plot of piston position vs. weight on
dead weight gauge pan. The ordinate on the graph shown here
is the difference between the piston position corresponding
to the actual point and that corresponding to the linear
relation. The abscissae are essentially pressure; 1 kg on
dead weight gauge pan is equivalent to 15k kg/cm sample
pressure for the l/k inch sample holders. The run shown is
o
for solid CH^ at 57 K.
Fig. 2 Phase diagram for solid CH^. The results of earlier investigators are shown.
Fig. 3 Phase diagram for solid CD^. The inset shows the lower portion of the diagram at twice the scale of the main plot.
Fig. k Phase diagram for solid 0^.
L
i
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