Phase equilibria in gas mixtures at high pressures: Implications for planetary structures

1972, Phys. Earth Planet. Interiors 5, 357-366. North-Holland Publishing Company, Amsterdam

P H A S E E Q U I L I B R I A I N GAS M I X T U R E S A T H I G H

PRESSURES:

IMPLICATIONS FOR PLANETARY STRUCTURES

W. B. STREETT and A. L. ER1CKSON

Science Research Laboratory, U.S. Military Academy, West Point, N. Y. 10996, U.S.A.

Received 28 September 1971 Revised 18 January 1972 An understanding of phase equilibria in gas mixtures under pressure is essential to the study of the deep-atmosphere and interior structures of the outer planets. The results of experiments on phase equilibria in mixtures of He with Ar and N2, at pressures up to 10000 atm, are presented, and serve as the basis for a

discussion of the characteristics of phase diagrams for two-component gas mixtures at high pressures. The application of these results to problems of planetary interiors is briefly discussed. A brief description of the experimental method is included.

1. Introduction

posed behave essentially as single-component systems (RAMSEY, 1951 ; DEMARcUS, 1958; PEEBLES, 1964; HUBBARD, 1969; etc.). In recent years, a wealth of new information about phase equilibria in binary gas mixtures at high pressures has been obtained from laboratory experiments. This work has been reviewed by SCHNEIDER (1972). The phase diagrams derived from these experiments are characterized by a remarkably varied and complex geometry, even for simple molecules, which defies easy description, either graphical or mathematical. Consequently, their full meaning is only slowly being assimilated into current physics and chemistry, and their relevance to planetary atmospheres and interiors has gone almost completely unnoticed. We have called attention to this matter in several recent papers (STREETT 1969, 1971; STREETT and HILL, 1971a; STREETT et aL, 1971) and at the same time we have undertaken a series of laboratory experiments designed to provide a better understanding of high-pressure phase behavior in gas mixtures of planetary interest. In this paper we report the results of phase equilibria experiments on the binary systems H e - N 2 and H e - A r at pressures to 10000 atm. Other mixtures studied in this program include N e - A r (STREETTand HILL, 197 l b), Ne-CH4 (STREETT and H1LL, 1971c), and H e - C H 4 (STREETTet al., 1972). These results, together with those for other systems, such as CO2-H20 (TAKENOUCHIand KENNEDY,1964) and various hydrocarbon systems (see

Knowledge of interior structures in the terrestrial planets is derived, in part, from high-pressure experiments on phase equilibria in rocks and minerals. Because of technological limitations, these experiments have generally been limited to simple mixtures and to pressures below about 300000 atm - the pressure estimated to exist within the Earth at a depth of about 10% of its radius. Hence knowledge of the interior structures of the terrestrial planets is far from complete (KAULA, 1968; WILDT, 1961). Even less is known about the interior structures of the outer planets. These bodies are composed mainly of gases (H2, He, CH4, NH3, HEO, etc.), for which relatively little high-pressure data are available. Apart from scattered measurements of density and melting behavior, few properties of gases have been measured at pressures above about 15000 atm. In this pressure range, the experimental work has until recently been limited largely to pure gases, and relatively little is known about the high-pressure behavior of mixtures of two or more components. As a result, scant attention has been given to the possible influences of multi-component phase behavior on the interior structures of the outer planets. With the exception of the work of SMOLUCHOWSKI (1967, 1970), models for the interior structures of these bodies have been based on the tacit assumption that the gas mixtures of which they are c o m 357

358

W. B. STREETT AND A. L. E R I C K S O N

SCHNEIDER, 1972, for references), provide an insight into patterns of phase behavior in fluid mixtures at high pressures. Earlier experiments on phase equilibria in gas mixtures under pressure have been limited largely to the equilibria between fluid phases; however, our work includes measurements in the three-phase region solidfluid-fluid, in which the solid phase of the less volatile component is in equilibrium with two fluid phases. For a binary system, this three-phase region is an analogue of the melting curve for a single component system; hence the experiments in this series form the beginning of a systematic study of melting under pressure in two component gas mixtures. BR1DGMAN(1958) and STEWART 0965) have pointed out that no such systematic studies have been reported.

2. Experimental method and apparatus In these experiments we have used a vapor-recirculating equilibrium system, shown schematically in fig. 1.

J

---]

Fig. 1. Schematic diagram of the apparatus. Legend: A and B, gas cylinders; C, two-stage diaphragm compressor; D, pressure intensifier; E, hydraulic p u m p ; F, manganin pressure gauge; G, Wheatstone bridge; H, high-pressure cell; I, magnetic pump (see fig. 2) ; J and K, sampling lines ; L, thermal conductivity gas analyzer; M, cryostat; T, thermocouple; P and Q, sampling valves.

The method of operation is as follows. The mixture under study is pumped into the high-pressure system, containing the cell H and magnetic pump I, under conditions of pressure, temperature and total composition which produce a two-phase fluid mixture in H. These

conditions are determined partly by trial and error and partly by the trend of previous data. Through the action of the pump I (described below), the light phase is withdrawn from the top of cell H, pumped around a closed loop (as indicated by the small arrows), and bubbled through the dense phase. This mixing action promotes a rapid approach to equilibrium. After 10 to 15 min of recirculation, samples of the two phases are withdrawn through sampling lines J and K by opening the valves P and Q. These samples enter the gas analyzer L at atmospheric pressure and room temperature, where their compositions are determined by the method of thermal conductivity. The gas analysis equipment has been described elsewhere (STREETT and JONES, 1965). Successive points are run by varying the pressure while maintaining a constant temperature in the cryostat M. A complete experiment consists of pressure-composition measurements for about ten isotherms. The upper pressure limit for each isotherm is determined either by the appearance of a solid phase or by the design pressure of the apparatus (10000 atm), whichever is lower. When a solid phase forms, it plugs the circulation line and its presence is detected by noting the pressure at which circulation stops. The pressure-temperature trace of the three-phase region is located in this way, but it is not possible to withdraw samples of the solid phase for analysis. The "flowmeter" used to detect circulation in the loop consists of a thermocouple T (fig. 1) attached to the exit line from the cryostat. If gas is flowing, it cools the tubing at T and the output of the thermocouple is detected by a potentiometer. Pressures in the system are generated in three stages: the two-stage diaphragm compressor C (fig. 1) boosts the gas pressure from cylinders A and B to 1350 atm, and the intensifier D, driven by hydraulic pump E, boosts the pressure to 10000 atm. Pressures are measured by a calibrated manganin gage F and Wheatstone bridge G, with an estimated accuracy of +_5 atm. Temperatures in M are controlled to within ±0.02 K and measured with an accuracy of _+0.01 K by a platinum resistance thermometer and Mueller bridge. The sampling lines J and K are hypodermic needle tubing, 0.229 mm O.D. x0.076 mm I.D., inserted into the 0.625 mm I.D. tubing in the high-pressure system. The construction and operation of the magnetic pump are illustrated in fig. 2. The pump always con-

GAS MIXTURES AT HIGH PRESSURES

359

Fig. 2. Magnetically operated vapor recirculating pump. Legend: A, beryllium copper cylinder; B, beryllium copper plug; C, steel cap; D, stainless steel piston; E, teflon piston rings; F, iron armature; G, electromagnet; H, piston return spring.

tains gas at the system pressure, and it serves only to recirculate this gas around a closed loop at constant pressure. Cylinder A (inside diameter ~6.3 ram) and plug B are non-magnetic beryllium copper, and piston D is non-magnetic stainless steel. The piston has a small hole drilled through its center and is fitted with teflon piston rings E. During operation, the electromagnet G is pulsed several times per second, and with each pulse the iron armature F is pulled to the right, against D, producing a net flow of fluid to the right. On the return stroke, provided by spring H, gas flows around F and through the hole in D, and there is no net flow in or out of the pump. A check valve in the recirculation loop prevents backflow during the return stroke. The pump produces a net flow of about l0 cma/min. It has performed satisfactorily at pressures up to 10000 atm in pumping fluids through approximately 3 m of 0.625 mm I.D. tubing.

3. Experimental results The experimental results consist of isotherms at which equilibrium fluid phase compositions have been measured at fixed pressures up to a maximum of 10000 atm. For the H e - N 2 system, ten isotherms in the temperature range ll2.10 to 162.00 K have been studied, and for the H e - A r system, nine isotherms in the range 150.02 to 199.00 K. The results are recorded in tables l and 2. These results are extensions of earlier work on the same systems (STREETT and HILL, 1970, 1971a). In the earlier papers we pointed out that these systems exhibit fluid-fluid phase separations - that is, the

mixtures separate into two distinct fluid phases at high pressures and at temperatures above the critical temperatures of both components. Indeed, most of the new results are in the fluid-fluid region. In the following discussion we have not used the terms liquid and gas to distinguish between phases, because this distinction loses meaning at high pressures and supercritical temperatures. The term fluid is used instead, and for each system we distinguish between the He-rich phase, F2, and the N 2 or Ar-rich phase, F t. The N 2- and At-rich solid phases are designated S1. The complete results for each system extend upward from the triple point of the less volatile component (N 2 or Ar) to a temperature above its critical temperature. Within the expzrimental ranges of pressure and temperature, N 2 and Ar can exist either as fluid or solid, in the pure state, while He is always a supercritical fluid. The regions covered by the experiment are: (1) the region of equilibria between two fluid phases (F~ and F2) ; and (2) the three-phase region solid-fluidfluid (S1-Fx-F2) in which a N2-rich or an Ar-rich solid phase is in equilibrium with the two fluid phases. The Gibbs phase rule forms the basis for the interpretation and discussion of the phase diagrams. The application of phase rule principles to diagrams of the type at hand has been discussed in one of our earlier papers (STREETT and HILL, 1971b). It is sufficient to remark here that in a three-dimensional pressure-temperature-composition (P-T-X) diagram for a two-component system, equilibrium between two phases is represented by two surfaces, and equilibrium between three phases by three lines, in P-T-X space.

360

W. B. STREETT AND A. L. E R I C K S O N TABLE 1 Experimental result~ tor He-Ar P (atm)

T = 150.02K 3810 4218 4459 4622 b) T = 159.90 K 3469 3949 4422 4898 5316 5571 5592 b) T = 170.0~ K 4014 ~) 404~ 4088 4150 4224 4361 4565 4898 5381 5857 6116 6551 6728 b) T = 183.00 K 5728") 5796 5857 5918 5993 6211 6469 6939 7418 7864 7905 ~) T = 193.03K 7728 ~) 7833 7898 7973 8037 8248

F1 (mol % He)

Fz (tool % He)

29.41 28.25 27.44 27.0

93.53 94.35 94.72 94.9

42.40 39.04 36.40 34.29 32.72 31.91 31.7

87.21 89.72 91.35 92.56 93.42 93.84 93.9

68.2 61.14 58.93 56.72 55.41 53.01 50.20 46.95 43.24 40.5l 39.47 37.60 36.8

68.2 77.37 79.58 80.86 82.62 84.70 86.89 89.27 90.79 91.71 92.61 93.0

70.2 62.17 60.02 58.77 57.31 54.19 51.43 47.72 44.83 42.65 42.4

70.2 78.35 79.91 81.04 82.07 84.19 86.03 88.18 89.83 90.79 91.0

71.5 63.46 61.93 60.42 59.49 56.97

71.5 79.89 80.86 82.10 82.80 84.33

P (atm)

T=

T=

T=

T=

8565 8884 9143 9190 b) 193.00 K 8403") 8544 8571 8612 8653 8850 9129 9442 9544 b) 195.00 K 8857 ~) 9031 9061 9095 9139 9224 938l 9755 9810 b) 197.00K 9238") 9395 9429 9466 9510 9656 9850 10020 10071 b) 199.00K 9633") 9714 9741 9765 9803 9891 9912 10927 10272 10344 b)

F1 (mol % He)

F2 (mol H He)

42.65 51.67 59.33 50.0

86.05 87.62 88.21 88.3

71.9 62.59 61.24 59.27 57.12 54.32 52.08 52.0

71.9 80.73 81.82 82.64 83.10 84.61 86.27 87.50 87.8

72.2 60.26 60.10 59.75 59.51 58.00 56.22 53.47 55.0

72.2 82.50 82.52 83.17 83.44 84.42 85.48 87.06 87.2

72.3 62.04 61.60 60.98 60.34 58.60 56.67 55.33 56.0

72.3 81.60 82.10 82.55 82.89 84.16 85.22 86.05 86.2

72.4 64.97 64.32 63.68 62.89 61.19 60.56 59.41 56.81 56.0

72.4 79.89 80.20 80.77 81.20 82.03 82.44 83.35 85.12 86.0

") Critical pressures ( ± 2 0 atm). b) Three-phase pressures ( ± 10 atm).

4. The helium-argon phase diagram

c o n t o u r lines c u t in t h e P - T - X s u r f a c e s w h i c h d e s c r i b e the F1-Fz equilibria. These two surfaces have a comsystem have

m o n b o u n d a r y in t h e critical line a n d t h e A r v a p o r

been studied in this w o r k a n d earlier work. T e n o f these

Twenty-five isotherms of the He-Ar

p r e s s u r e c u r v e . ( T h e l a t t e r c u r v e lies in t h e left e d g e o f

a r e p l o t t e d in fig. 3. T h e s e i s o t h e r m s c a n b e v i e w e d as

fig. 3.) T h e left b r a n c h o f e a c h i s o t h e r m lies in t h e F1

361

GAS M I X T U R E S AT H I G H P R E S S U R E S TABLE 2 Experimental results for H e - N 2 P (atm)

F1 (mol%He)

T -- l 1 2 . 1 0 K 2431 3061 3408 3748 4116 4446 4456 4648 4765 4776 4857 b) T-- I17.13K 1091 1350 1943 2766 3401 3748 4095 4449 5045 5501 5578 5646 b) T = 124.05K 2388 2705 2746 3082 3110 3551 4122 4611 4993 5450 5993 6517 6752 6871 b) T = 130.00K 4030 4503 4854 5527 6186

F2 (mol%He)

30.35 28.66 27.80 26.94 26.03 25.17 25.1 24.74 24.57 24.56 24.4

95.44 96.44 96.80 97.16 97.5 97.69 97.63 97.78 97.75 97.84 97.9

42.24 41.06 38.35 35.0 32.48 31.26 30.51 30.03 27.57 26.60 26.2

85.68 87.54 91.35 94.41 95.65 96.02 96.38 96.65 97.25 97.60 97.65 97.7

47.73 45.37 44.94 42.94 40.17 37.68 33.90 32.63 31.22 30.06 29.48 29.0

88.50 89.50 90.48 92.06 92.17 92.89 94.63 95.39 95.92 96.42 96.91 96.95 97.33 97.4

45.21 42.47 40.73 38.11 35.78

91.57 92.90 94.06 95.25 96.02

P (atm)

F1 (molto He)

6648 7110 7581 7761 7810 7879 7946 8005 8068 b) T = 134.00K 4091 4788 5313 5815 6302 6863 7333 7814 8102 8336 8709 8857 8939 b) T = 138.00K 4109 a) 4194 4226 4294 4370 4435 4503 4590 4918 5327 5800 6272 6279 6823 7330 7844 8297 3707 9256 9432 9796 b)

F2 ( m o l ~ He)

34.34 33.44 32.47 32.19 31.64 31.50 31.43 31.33 31.2

97.83 97.81 96.49 96.93 96.89 96.80 97.1

52.31 47.37 44.75 41.24 39.49 37.56 36.11 34.83 33.54 33.24 32.52 32.18 32.1

87.73 91.41 92.55 93.99 94.73 95.34 95.64 95.81 96.0 96.66 96.93 97.0

73.4 64.68 63.07 61.81 60.51 59.26 58.55 57.33 54.29 50.93 48.17 45.77 45.40 43.15 41.05 39.70 38.02 37.16 35.97 35.66 34.7

73.4 92.92 81.59 84.47 85.78 86.51 87.06 87.74 89.38 90.89 92.34 93.45 93.49 93.91 94.30 95.05 95.62 95.74 96.28 96.3

P (atm)

F1 (molto He)

T = 144.00K 5286 a) 5361 5456 5537 5619 5707 5807 5918 6173 T = 154.00K 7517 a) 7633 7823 7959 8184 8347 8578 8850 9191 9517 9680 T = 158.0K 8456 a) 8469 8510 8551 8585 8605 8687 8871 9129 9381 9599 9796 I0000 T = 162.00K 9449 ~) 9531 9599 9653 9782 9932 10068

F2 (molto He)

74.9 66.53 63.11 63.12 61.21 60.19 59.29 58.26 55.32

74.9 86.63 85.29 86.34 86.94 87.35 87.89 88.52 89.87

75.5 67.23 63.88 62.10 60.25 58.51 56.79 54.80 52.95 51.36 50.42

75.5 85.05 86.43 87.54 91.92 88.78 91.47 91.18 91.88 92.43 93.29

76.0 69.38 68.80 67.80 67.44 66.99 65.12 63.16 60.71 58.71 56.82 55.9 54.61

76.0 86.26 86.65 86.22 85.80 84.73 85.76 87.16 90.41 89.71 90.00 90.96 91.38

76.7 68.87 67.19 66.39 64.42 62.89 61.52

76.7 84.45 85.2 85.85 86.99 87.89 88.61

a) Critical pressures ( ± 2 0 atm) b) Three-phase pressures ( ± 10 atm)

(Ar-rich) surface and the right branch in the F 2 (Herich) surface. These surfaces are continuous, in a mathematical sense, across the critical line, and the critical point on each isotherm is a maximum or minimum. The horizontal dashed lines mark the pressures at

which an Ar-rich solid phase, $1, is in equilibrium with F1 and F 2. These lines lie in the imaginary ruled surface containing the three lines which represent the S I - F 1 - F 2 equilibria. To avoid overcrowding, the threephase lines have not been shown in fig. 3. If they were

362

W. B. S T R E E T T

A N D A. L. E R I C K S O N

shown, the F 1 and F 2 lines would pass through the left and right ends, respectively, of the horizontal dashed lines, and the S1 line would lie to the left of the F1 line. All three would terminate at low pressure in the triple point of Ar, on the left edge of the diagram. These lines are shown in the three-dimensional sketch in fig. 5, described below. The principal P - T boundaries of the two-phase regions are shown in fig. 4. These are: the vapor-pressure curve EA, melting curve E G and sublimation curve E K for pure Ar; the mixture critical line AB; and the three-phase line EB. The F~-F2 region is bounded by the lines AEBA, the S1-F 1 region by EG and EB, and the S1-F 2 region is bounded on the low pressure side by EB. The intersection, B, between the critical and threephase lines has not been confirmed in the experiment; however, the rapid convergence of these lines at the experimental limits of pressure and temperature suggests that the intersection lies at about 11000 arm and

F-B

,4 / I

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--

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X

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8

170,00

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----k--

It

t \

8,02 0

50 I

i00

Mole % He Fig. 3. P r e s s u r e - c o m p o s i t i o n d i a g r a m s h o w i n g ten isotherms in the fluid-fluid region o f the H e - A r system. L e g e n d : - - O - - experimental results; - - E 3 - - critical line; three-phase pressures.

/ /

80

I01188.0193'00°K0~ 1800.0

/

!

120

160

I

t

200

T.l( Fig. 4. P r e s s u r e - t e m p e r a t u r e d i a g r a m for H e - A r , s h o w i n g the principal P - T b o u n d a r i e s o f the two p h a s e regions. L e g e n d : - - t w o - p h a s e b o u n d a r y lines for pure A r ; - - E 2 - - critical line; - - A - - t h r e e - p h a s e line. (See text for further discussion.)

205 K. This suggestion is supported by the trend, with increasing temperature, of the F1-F 2 isotherms in fig. 3. We believe this to be the first experimental evidence of an intersection of critical and three-phase lines in a binary gas mixture at a temperature above the critical temperature of both components; however, the possibility that such intersections occur has been suggested (STREETT and HILL, 1970). The discovery of this intersection sheds new light on the phenomenon of fluidfluid equilibria. Until now it has been assumed that, barring a reversal in the slope of the critical line at higher temperatures, the fluid-fluid phase separations observed in many binary systems would persist up to the limits of stability of the molecular phase. However, our results for H e - A r show that, in some cases at least, the P - T extent of the fluid-fluid region is limited by the pressure-induced solidification of the less volatile component. A three-dimensional sketch of the P - T - X diagram is shown in fig, 5. The dark portions of the isotherms T3

GAS M I X T U R E S AT H I G H PRESSURES I

f~

/

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r4

\

X Fig. 5.

Three-dimensional sketch of P - T - X diagram for He-Ar. (See text for discussion.)

and T4 lie in the F I - F 2 region covered by the experiment. The remaining portions of these isotherms, as well as the entire isotherms T1, T 2 and T 5, show the assumed forms of the remaining two-phase regions. T3 and T4 correspond, approximately, to the 170.00 and 120.01 K isotherms in fig. 3. The dash-dot line at the top of the diagram, IMHLJ, is an isobar, shown here to aid in describing the phase surfaces. The lettering of phase boundary lines in fig. 5 is consistent with that in fig. 4. The two-phase boundary lines for pure Ar, EA, E G H and EK, lie in the left P - T face of the diagram, while the critical line AB and the three-phase lines EF, ECB and EDB extend into P - T - X space. EF represents the S~ phase in the three-phase region, ECB the F1 phase and EDB the F 2 phase. As noted above, these lines lie in an imaginary ruled surface, and they have a

363

common P - T projection, EDCFB, in fig. 4. If all these boundary lines can be visualized in P - T - X space, the shapes of the surfaces which define the various twophase equilibria are readily apparent. Although there are only three distinct phases in the system in the range of interest here ($1, F1 and F2), each phase takes part in two separate, two-phase equilibria, so there are six phase surfaces in fig. 5. In the F~-F2 region, the F~ surface is bounded by ABCEA, and the F2 surface by ABDEA. In the S1-F~ region, the F~ surface is bounded by EG and ECB and the $I surface by E G and EF. The small wedge-shaped portions of the isotherms T2, T 3 and T 4 lie in this region. In the $1-F2 region, the S~ surface extends upward from EK and EF and is cut along MI by the isobar at the top of the diagram. At temperatures between E and B, the F 2 surface is bounded on the low pressure side by EDB and is cut along LJ by the isobar at the top of the diagram. The isotherms T2, T 3 and T4 lie in this range. At temperatures below E, such as Ts, the F2 surface terminates at low pressures in the argon sublimation curve EK. B is the upper critical end point of the fluid-fluid region - the highest temperature and pressure at which two distinct fluid phases exist. The isotherm T 2 passes through this point. At temperatures above T2 the distinction between F~ and F2 disappears, and the F~ and F2 surfaces merge into a single surface, as at T~. Point F, at the same temperature and pressure as B, is the upper end of the three-phase line EF. This line is a discontinuity between the two S~ surfaces in the S~-F~ and S1-F 2 regions. It is interesting to compare the He-Ar phase diagram to that of N e - A r (STREETT and HILL, 1971b). In the latter system the upper critical end point, B, lies at 93.1 K (below the critical temperature of argon) and at a pressure of about 1030 atm, and the system does not exhibit fluid-fluid equilibria. Nevertheless, there are many similarities in the P - T - X diagrams of the two systems (see fig. 4 of STREETTand HILL, 1971b). 5. The He--N 2 phase diagram

The H e - N 2 phase diagram is shown in figs. 6, 7 and 8. It is similar to that of He-Ar, the principal difference being the absence of an upper critical end point for H e - N 2 within the range of the experiment. Fig. 7 shows that the P - T projections of the critical and three-phase

364

W. B. S T R E E T T

A N D A. L. E R I C K S O N

lines are approximately parallel at a pressure of 10000 atm, and it is clear that the flluid-fluid phase Separation persists to pressures and temperatures beyond the range of this experiment. The isobar I L M O P Q J at the top of fig. 8, is an inverted form of the isotherms T 1 and T 2 - inverted in the sens~ that the critical point P on the isobar is a temperature maximum, while the critical points on T t and T 2 are pressure minima. If an isobar at a pressure below that of B were drawn in fig. 5, it would be similar in form to the isobar in fig. 8. The He-N2 diagram is similar in some respects to that of H c - C H 4 (STREETT et al., 1972). In the latter system the P - T projection of the critical line leaves the CH4 critical point with a positive slope, and moves directly to higher temperatures and pressures. It does not pass through a temperature minimum as in fig. 7.

10

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6. Discussion K E

The experimental results reported here provide significant new information about the form of phase diagrams for two-component gas mixtures at high pres-

E

.,..,

7O w..X

144.0( 134.00

124.01"

11,, i 100.61

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50

i00

Mole % He Fig. 6.

6

P r e s s u r e - c o m p o s i t i o n d i a g r a m s h o w i n g ten i s o t h e r m s for the H e - N 2 system. Legend s a m e as in fig. 3.

x, A

l

I

100

I

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140

I

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160

T,K Fig. 7.

158.00 10

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P r e s s u r e - t e m p e r a t u r e d i a g r a m for H e - N 2 . Legend same as in fig. 4.

sures. The phase diagrams of these mixtures are far more complex than those of one-component systems, largely because of the added degree of freedom introduced by the second component. The phase diagrams of systems of three or more components are even more complex. Each additional component introduces another degree of freedom into the system, and it becomes increasingly difficult to visualize the phase diagrams, because, in general, the complete graphical representation of the diagram of an n-component system requires a space of n + 1 dimensions. At pressures beyond the range of these experiments, complete solidification of H e - A r and H e - N 2 mixtures presumably occurs. Extrapolation of the known melting curve of He to high temperatures and pressures leads to an estimate of 30000 to 100000 atm for its solidification pressure in the temperature range of interest here. No experiments on the complete solidification of binary mixtures at high pressures have been reported, so one must resort to empirical evidence to suggest possible forms these diagrams may take at very

GAS M I X T U R E S AT H I G H PRESSURES ,I

.J j .J

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IT3

"4

I Fig. 8.

Three-dimensional sketch o f P - T - X diagram for He-NE.

high pressures. This matter has been discussed elsewhere (STREETT, 1969; STREETTand HILL, 1971a). The limited understanding of high-pressure phase behavior in gases, and of the chemical and thermal properties of the outer planets, rules out any quantitative calculations of the effects of high pressure phase equilibria on their interior structures. It is possible, however, to draw certain general conclusions regarding qualitative aspects of the problem. The first one concerns the existence of multiple fluid phases (fluid-fluid equilibria) in mixtures at high pressures. The available evidence suggests that these phase separations are the rule, rather than the exception, in mixtures of unlike molecules at high pressures and densities, All He binary systems which have been studied at high pressures have been found to exhibit fluid-fluid phase separations. If these separations occur deep within the atmospheres of the major planets, they must exert a strong influence

365

on both physical structure and hydrodynamic behavior in the dense fluid regions. They would also provide a mechanism for the partial separation or fractionation of the component gases. The second general conclusion concerns the structure of a planetary body in the region of fluid-solid transition at high pressures. The tendency to think in terms of one-component systems oversimplifies the problem. In a single component system the melting pressure is a unique function of temperature; hence a planet composed of, say, pure H z would solidify abruptly at a depth at which the equation of path crosses the H2 melting curve. Considering a more realistic model, consisting of a HE-He mixture, one concludes that the added degree of freedom (in a phase rule sense) results in a far more complicated structure (STREETT, 1969, 1971). Solid and fluid phases can coexist over finite ranges of pressure and temperature, corresponding to a range of depths within the atmosphere. Within this range, density inversions can occur, resulting in masses of Hz-rich solid floating within a fluid HE-He layer of equal density. This suggestion has been used as the basis of a new hypothesis for Jupiter's Great Red Spot (STREETT e t al., 1971). The principal mixture of interest in connection with the outer planets is HE-He. Future experiments in this laboratory will include a study of the HE-He phase diagram at pressures up to 10000 atm.

Acknowledgments Financial support for this work was provided by the U.S. Army Research Office, Durham, North Carolina, and is gratefully acknowledged.

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