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The Astrophysical Journal, 186:1107-1125, 1973 December 15 .186.1107S . © 1973. The American Astronomical Society. All rights reserved. Printed in U.S.A. 3ApJ. 197 PHASE EQUILIBRIA IN MOLECULAR HYDROGEN-HELIUM MIXTURES AT HIGH PRESSURES* W. B. Streett Science Research Laboratory, U.S. Military Academy, West Point, New York Received 1973 June 11 ABSTRACT Experiments on phase behavior in hydrogen-helium mixtures have been carried out at pressures up to 9.3 kilobars, at temperatures from 26° to 100° K. Two distinct fluid phases are shown to exist at supercritical temperatures and high pressures. Both the trend of the experimental results and an analysis based on the van der Waals theory of mixtures suggest that this fluid-fluid phase separation persists at temperatures and pressures beyond the range of these experiments, perhaps even to the limits of stability of the molecular phases. The results confirm earlier predictions concerning the form of the hydrogen-helium phase diagram in the region of pressure-induced solidification of the molecular phases at supercritical temperatures. The implications of this phase diagram for planetary interiors are discussed. Subject headings: gas dynamics — interiors, planetary — molecules I. INTRODUCTION The properties of hydrogen-helium mixtures are of interest for several reasons. From a theoretical standpoint, they are of interest because they are composed of the two elements with the simplest atomic and molecular structures, and would seem to be among the mixtures most amenable to a theoretical treatment based on first principles. However, it is fair to say that a satisfactory theory of dense mixtures of molecular hydrogen and helium has yet to be developed. This is due in part to their quantum nature, and in part to the lack of understanding of interactions between unlike molecules. On the other hand, significant progress has been made in developing satisfactory theories of the two pure substances—especially hydrogen—and a better understanding of mixtures can be expected to follow. It goes without saying that hydrogen-helium mixtures are of enormous cosmological importance. Among the cold cosmic bodies composed largely of hydrogen and helium are the giant planets Jupiter and Saturn (DeMarcus 1958; Wildt 1961; Peebles 1964; Hubbard 1968, 1969, 1970). The development of accurate models for the interior structures of these bodies poses formidable theoretical and experimental problems, because of the requirement for knowledge of the equilibrium and transport properties of dense mixtures of several light substances over wide ranges of temperature and pressure. Current estimates of the central temperature and pressure of Jupiter, for example, are ~104°K and ~35 megabars (Smoluchowski and Hubbard 1973). Models developed during the last few decades have relied on tenuous extrapolation of meager experimental data, supplemented by the gradual accumulation of theoretical studies of dense fluids and solids. Much remains to be done. Smoluchowski and Hubbard have emphasized that one of the principal unsolved problems is the lack of knowledge of the properties of molecular hydrogen and helium, and their mixtures, at pressures between a few kilobars and 1 or 2 megabars. * Supported in part by NASA (NASA-Defense Purchase Request No. W13, 142), and in part by the U.S. Army Research Office (Intra-Army Order for Reimbursable Services #AROD-3-73). 1107 © American Astronomical Society • Provided by the NASA Astrophysics Data System .186.1107S 1108 W. B. STREETT Vol. 186 . In the search for knowledge of the interiors of the giant planets, progress on the 3ApJ. theoretical side has, for obvious reasons, far surpassed that on the experimental side. The theoretician, using his equations as a vehicle and the laws of physics and thermo- 197 dynamics as his guide (and with an assist in recent years, from his computer), descends with relative ease to what he perceives to be the very centers of these bodies. On this point the experimentalist is tempted to quote Samuel Johnson: “And bid him go to Hell, to Hell he goes.” However, this only reveals the latter’s frustration with the practical problems which have severely limited his access to states of matter presumed to exist in planetary interiors. The atomic and molecular simplicity of hydrogen and helium—the very properties which to some extent facilitate theoretical studies—cause them to rank among the least tractable of all substances for high-pressure experiments. Part of the problem is the result of their high volatility and small molecular size, which enable them to escape past high-pressure seals that eifectively contain other fluids. In addition, there are the problems of hydrogen embrittlement—the deleterious effects of hydrogen on the mechanical properties of metals—and the explosive nature of hydrogen-air mixtures. (The flammable limits of hydrogen in air, by volume, are 4-75%, and the explosive limits, limits within which detonation waves can be propa- gated, are approximately 20-50%.) In view of these problems it is perhaps not surprising that experimental measurements of the high-pressure properties of hydrogen and helium have, until recently, been limited to the density measurements of Bridgman (1924) at 30° and 65° C and pressures to ~ 13 kilobars, and those of Stewart (1956) at 4.2° K and pressures to 20 kilobars, and to a few measurements of melting pressure as a function of temperature. No significant experiments on mixtures of hydrogen and helium under pressure have been reported. An intense interest in the properties of hydrogen at high pressures has developed in recent years, partly as a result of growing interest in the outer planets, and partly as a result of the suggestion (Ashcroft 1968) that metallic hydrogen might be a high-temperature superconductor. Modern dynamic methods for research at very high pressures, including shock-wave and explosive compression techniques (Grigoriev et al. 1972; Hawke et al. 1971), have made possible equation-of-state experiments at pressures in the megabar range. (Grigoriev and his colleagues have reported the first experimental evidence of the metallic transition in hydrogen.) The interpretation of the results of these experiments is not entirely unambiguous, however, especially where pressure-induced phase transitions are con- cerned. Notwithstanding the successes of these dynamic high-pressure experiments, there remains an important role for laboratory experiments on hydrogen and. helium by static high-pressure methods. With present techniques, a variety of static experi- ments can be carried out at pressures up to about 20 kilobars and at temperatures to several hundred degrees C. These limits will of course be extended in the future, perhaps quite rapidly if the present level of interest in high-pressure hydrogen is sustained. The results of static experiments can be used to develop detailed tables of physical and thermodynamic properties and to test molecular theories. Although a pressure of 20 kilobars barely “scratches the surface” of the giant planets, static experiments in this range will ultimately help to bridge the gap between low pressures and the very high pressures that are becoming increasingly accessible through shock- wave and explosive compression experiments. In order to carry out systematic experiments on hydrogen-helium mixtures under pressure, it is essential to know something about the phase diagram of the system. That is, it is essential to know the locations, in P-T-X (pressure-temperature-composi- tion) space, of the lines and surfaces which define the regions of existence and co- existence of different phases. We have recently reported the results of experiments on the phase behavior of several binary mixtures of light gases at pressures up to 10 kilo- bars, including neon-argon, neon-methane, helium-nitrogen, helium-argon, and helium-methane (Streett and Hill 1970, 1971<z, b, c\ Streett, Erickson, and Hill 1972; © American Astronomical Society • Provided by the NASA Astrophysics Data System No. 3, 1973 PHASE EQUILIBRIA IN H2-He MIXTURES 1109 .186.1107S . Street! and Erickson 1972). An important feature of our experiments, which has been 3ApJ. absent from most of the other work in this field, is the study of pressure-induced solidification in two-component gas mixtures. Virtually all of the other published work 197 in this field has been confined to studies of coexisting fluid phases (Krichevskii 1940; Tsiklis 1946, 1952; Schneider 1972). Hence the results of our experiments provide, inter alia, information about how the melting behavior of gas mixtures differs from that of pure gases. The most significant general conclusion drawn from these results is that the presence of a second component leads to phase diagrams considerably more complex than those of single-component systems. We have suggested (Streett 1969, 1971 ; Streett, Ringermacher, and Veronis 1971) that in an analogous way the pressure- induced solidification of a mixture of gases in a planetary body can result in a physical structure more complex than that of a pure hydrogen body—the framework around which models for the interior structures of the giant planets have often been con- structed. More specifically, we have pointed out that pressure-induced phase separa- tions in hydrogen-helium mixtures might result in unusual types of layered structures, and could provide a mechanism for the partial separation of these gases in the outer layers. It has therefore seemed worthwhile to carry out phase-equilibrium experiments on these mixtures. In this paper, the results of these experiments are reported for temperatures from 26° to 100° K and pressures to 9.3 kilobars. These results consist of equilibrium phase compositions for the region of coexistence of two fluid phases, as well as for the regions in which a hydrogen-rich solid phase is in equilibrium with one or both of these phases. Two distinct fluid phases have been found to exist at supercritical temperatures and high pressures. These findings, and those of similar experiments on other mixtures, have been used to develop a proposed form for the hydrogen-helium phase diagram over the region of pressure-induced solidification of the molecular phases.