Experimental determination of the equation of state of solid hydrogen and deuterium at high pressures

Isochores of solid hydrogen and deuterium have been measured for melting line pressures up to 2000 bar. These are corrected to correspond to para-H₂ and ortho-D₂. The 4.2 K isotherm of H₂ has been determined and compared to the extrapolated low-pressure isochore of Anderson and Swenson (AS). Deviations have led us to reanalyze the AS data. The 4.2 K isotherm and the isochores are used, with the aid of a Mie-Grüneisen analysis, to determine P-V-T data for these solids up to 25 kbar. An analysis is presented which enables a determination of P-V-T-C ₁ for all values of C ₁, the ortho-para concentration. Results, including the Debye temperature, Grüneisen constant, and bulk modulus, are presented both in tabulated and graphical form. We also present what we feel to be the best of the 4.2 K, zero-pressure molar volumes of disordered H₂ and D₂ as a function of C ₁. Our measurements show no indication of the premelting phase transition reported in recent Russian literature and a possible explanation is presented.Supported in part by the Stichting FOM.     

Specific heats of solid hydrogen,solid deuterium,and solid mixtures of hydrogen and deuterium

Measurements have been made in the temperature range 0.5–5 K of the specific heats of pure solid H₂, pure solid D₂, and four solid mixtures of H₂ and D₂ with D₂ fractions between 15 and 95%, all of which systems had low concentrationc of molecules in the rotational stateJ=1. For the H₂,c=0.0023, and for the D₂,c=0.030. It was found that the observed specific heats could be described as the sum of three terms as follows. (1) A lattice specific heat. This was found to follow aT ³ function with _D =122 K for solid H₂ and _D=113.8 K for solid D₂. For the solid mixtures the lattice specifi heats have in first approximation values given by a weighted mean of the lattice specific heats of the pure components. (2) A Schottky term with a maximum at about 1.3 K for solid H₂ and 1.4 K for solid D₂, which can quantitatively be described in terms of electric quadrupole-quadrupole (EQQ) interactions in nearest-neighbor pairs and triples of molecules in the rotational stateJ=1. This term led to evaluation of , the EQQ interaction energy, giving /k=0.9 ± 0.1 K for solid H₂ and 0.93 ± 0.05 K for solid D₂. It was found, moreover, that in solid H₂ there was an appreciable enhancement with time of the number of clusters of molecules in the rotational stateJ=1 at the expense of the number of isolated singles of similar molecules, due to rotation diffusion. On the other hand no rotation diffusion was observed in solid D₂ or in the solid mixtures of H₂ and D₂, except possibly in those mixtures containing 85% H₂. (3) A second anomalous term occurring at temperatures below about 0.8 K and, by extrapolation, having its maximum below 0.5 K (the lowest temperature of our measurements). This anomaly was observed only in those samples containing D₂ and is, as yet, unexplained in detail. A further major conclusion from our results in the temperature range 0.5–5 K is that there was no evidence in the form of a sharp anomalous jump in the specific heat of any of the mixtures which could be interpreted as indicating the occurrence of isotopic phase separation. This absence of phase separation is noted, in spite of the fact that thermodynamically it is energetically favorable in the temperature range of observation.Work partially supported by a grant from the National Science Foundation and by contracts with the Office of Naval Research and DOD (Themis Program).     

Elastic constants of solid hexagonal close-packed hydrogen and deuterium

Zero-pressure elastic constants for hcpp-H₂ ando-D₂ atT=0 K are calculated within the framework of the self-consistent phonon approximation with cubic anharmonicities. A pairwise additive model potential of the Barker-Pompe form, which reproduces the equation of state in the solid over a wide range of pressures, is used for the calculations. Debye temperatures and Grüneisen constants are also presented and the results are compared with recent experiments on the velocity of sound, inelastic neutron scattering, and specific heat.     

Far-infrared absorption in solid hydrogen and deuterium in the ordered state as a function of density

We present an experimental study of the infrared absorption spectra of solid enriched ortho-hydrogen and para-deuterium in the ordered state for pressures up to 6 kbar. From our observations we can conclude that the structure of the ordered state remains the Pa3 space group for all pressures studied. We find that the low-frequency optical phonon remains sharp at increased density and we have determined the mode Grüneisen constants as H ₂=1.95±0.03 and D ₂=1.87±0.03. The high-frequency optical phonon remains broad, and develops a double-peaked structure with increasing density, which is explained by anharmonicity and two-phonon decay. Comparison is made to theoretical expressions and numerical results for the absorption due to various microscopic processes involving phonons and combinations of librons and phonons. The integrated absorption intensity is also obtained, and compared with calculations based upon the quadrupole-induced dipole mechanism.Financially supported in part by the Stichting FOM, Utrecht.     

Calculation of theJ=3 roton spectrum of solid hydrogen and deuterium

A model for collective rotational excitations (rotons) with angular momentumJ=3 in solid ortho-hydrogen and para-deuterium at low temperatures is proposed. The theory is an extension of previous Bloch-type models of librons in orthohydrogen and rotons in para-hydrogen. The present model gives fairly good agreement with the positions and relative intensities of the observed Raman lines. As is the case for the libron spectrum, a discrepancy between theory and experiment is found. Improvements of the theory, which may give better agreement with the observed Raman spectra, are discussed.Supported by NSF Grant GP-9042.     

Semiempirical multiphase equation of state for hydrogen

A semiempirical multiphase equation of state for liquid hydrogen is given in view of the metal-dielectric transition. The position of the curve of “dielectric” fluid-conducting fluid equilibrium is determined. The experimental data of Nellis et al. [1] on abnormal compressibility of hydrogen are described within the constructed model. Predictions by the present model are compared with the experimental data of [1–4].     

The high-pressure equation of state of solid molecular tritium

We have calculated the equation of state for solid molecular tritium using a semiempirical approach, closely guided by experimental results for H₂ and D₂. TheT=0 K isotherm is calculated from a self-consistent phonon model of the free energy. Temperature effects are treated by the Mie-Grüneisen model. A tabulation of pressure, bulk modulus, and thermal expansion is given for a dense set of molar volumes, as a function of temperature up toP=22 kbar.     

A universal hydrogen and deuterium liquefier

The design is given of an economical H₂ and D₂ liquefier which works by the boiling off of liquid He vapour. The decisive role played by the gas condenser in the operation of the liquefier is demonstrated. The relationships between the flow rates of He and of the liquefied gas are calculated and measured. The helium consumption is 2.85 l for liquefying 1 l of H₂ and 3.8 1 l of D₂, which agrees with the calculations.     

An equation of state of high-temperature superconductor

In the present paper the expression of cohesive energy and the bulk modulus as a function of volume are formulated for high-T _c copper oxide superconductors. The model employed consists of long-range electrostatic Coulomb interaction and short-range overlap repulsion. The short-range overlap potential is considered in the Born-Landé inverse power form. The model, parameters of the Born-Landé model are calculated from the equilibrium condition and data of bulk modulus at room temperature. The computed values of pressure derivatives of bulk modulus atP=0 and the values of bulk modulus are found to be in very close agreement with experimental values for high-T _c copper oxide and their nonsuperconducting parent compounds. It is also found that the quantity ΔU/U(V _o) of these compounds increases with increasing hydrostistic pressure.     

An analytical equation of state for mercury

This paper presents a procedure for predicting the equation of state of mercury, by including mercury in the scope of a new statistical mechanical equation of state that is known for normal fluids. The scaling constants are the latent heat of vaporization and the density at the melting temperature, which are related to the cohesive energy density. Since experimental data for the second virial coefficient of mercury are scarce, a corresponding-states correlation of normal fluids is used to calculate theB(T) of mercury. The free parameter of the ISM equation, λ, compensates for the uncertainties inB(T). Also, we can predict the values of two temperature-dependent parameters, α(T) andb(T), with satisfactory accuracy from a knowledge of ΔH _vap andp _m, without knowing any details of the intermolecular potentials. While the values ofB(T) are scarce for mercury and the vapor pressure of this metal at low temperatures is very small, an equation of state for mercury from two scaling parameters (ΔH _vap,p _m) predicts the density of Hg from the melting point up to 100° above the boiling temperature to within 5%.     

An analytical equation of state for refrigerants

The liquid density of halogenated hydrocarbons has been calculated using an analytical equation of state. The temperature-dependent parameters of the equation of state have been calculated using our previous corresponding-states correlation based on the normal boiling point constants. In this work, it is shown that the equation of state for halogenated paraffins could be expressed in terms of the minimum input information, namely the normal boiling point temperature and the liquid density at the normal boiling point. The equation of state has been employed to calculate the liquid density of a great number of refrigerants both at saturation and compressed states, over a wide range of temperatures and pressures. A comparison of the predicted results with experimental data shows that the agreement is quite good.     

Dynamic equation of state of a gas mixture containing solid particles

A dynamic equation of state is derived, describing the relationship between the pressure and volume of a thermal-nonequilibrium gas mixture. The methods of nonequilibrium thermodynamics are used to calculate the relaxation time.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 34, No. 5, pp. 833–838, May, 1978.     

Correlations and effective potential in the ground state of a one-dimensional model for solid helium and deuterium

The ground-state energyE can be calculated exactly by the transfer-integral method if the total wave function is assumed to be a product of single-particle functions and nearest-neighbor correlation functionsf. The variation ofE with respect tof for fixed leads to a Schrödinger equation for the relative motion of two particles which is coupled to the transfer integral equation by an effective potential V. For the case of a Gaussian the optimalf, the one- and two-particle probability amplitudes, and other quantities are computed by iteration of the Schrödinger equation with the transfer integral equation until self-consistency is achieved. The minimum ofE as a function of the Gaussian width is obtained for different values of the lattice parameter. The shape of V andf is discussed. The self-consistentf describes both short- and long-range correlations.     

Negative charges in liquid hydrogen and deuterium

The temperature and pressure dependence of the mobilities of negative charges injected into liquid hydrogen and deuterium have been measured. We propose the existence of two types of charge carriers in liquid parahydrogen. One is a bubble with an electron inside while the other has higher mobility. Relaxation of the current through liquid hydrogen was observed. It is suggested that in liquid and solid hydrogen under -irradiation neutral complexes are created which can trap the negative charges and have a lifetime of about 10 hours.     

聚酯材料状态方程的实验研究

在单级轻气炮上对聚酯材料的激波状态方程进行了实验研究.最高掩击速度为526 m/s,相应在靶中得到的最高撞击压力为2.14 GPa.压力测试采用锰铜计,PVDF产生的压电信号用于判读激波速度.由实验结果拟合得到了聚酯材料的Hugoniot线性关系和多项式状态方程以及Gruneisen状态方程.     

An analytical equation of state for refrigerant mixtures

We have extended our previous work on the equation of state for refrigerants to their mixtures successfully. The temperature-dependent parameters of the equation of state have been calculated using our previous corresponding-states correlation based on the normal boiling point temperature and the liquid density at the normal boiling point. We have applied a simple combining rule for the normal boiling point constants to extend our previously proposed equation of state to mixtures of refrigerants. In this work the liquid densities of a large number of refrigerant mixtures have been calculated and the results are compared both with experimental data and a recent correlation by Nasrifar et al. (1999). The agreement is good.     

An improved hydrostatic method of measuring solid volumes and densities

Translated from Izmeritel'naya Tekhnika, No. 3, pp. 28–30, March, 1988.     

An interim analytic equation of state for sulfurhexafluoride

An interim analytic equation of state for Sulfurhexafluoride is given in the form of a reduced Helmholtz energy function. It represents the thermodynamic properties over the temperature range 222.38 to 525 K for pressures up to 55 MPa. The data selected for determining the linear coefficients of the equation are given, which includes some values predicted using the principle of corresponding states. The method used for the multiproperty fitting is given and, in particular, the functions used for fitting isobaric heat capacities as primary data. Comparisons with values predicted by the equation of state are given for saturation properties, second virial coefficients, densities, and isobaric and isochoric heat capacities. The accuracy of the representation of the equation of state is discussed and, also, the problems arising from inconsistencies between the different data sets. The interim status of this equation of state is due to these inconsistencies.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.