Quantum rotors in Pca2₁ lattice

Analytical calculations of the potential barrier hindering rotation of the hydrogen molecules in the molecular field of neighboring molecules are performed for molecular solid hydrogen. The calculations are made for the four-sublattice Pca2₁ lattice which minimizes the electrostatic energy of classical quadrupoles on an hcp lattice

Many-body interactions and high-pressure equations of state in rare-gas solids

The T 0K equations of state (EOS) of rare-gas solids (RGS) (He, Ne, Ar, Kr, and Xe) are calculated in the experimentally studied ranges of pressures accounting for two- and three-body interatomic forces. Solid-state corrections to the pure two-body Aziz et al. potentials included the long-range Axilrod–Teller three-body interaction and short-range three-body exchange interaction. The energy-scale and length-scale parameters of the latter were taken as adjustable parameters of theory. The calculated T 0K EOS for all RGS are in excellent agreement with experiment in the whole range of pressures. The calculated EOS for Ar, Kr, and Xe exhibit inflection points where the isothermal bulk moduli have non-physical maxima indicating that account of only three-body forces becomes insufficient. These points lie at pressures 250, 200, and 175 GPa (volume compressions of approximately 4.8, 4.1, and 3.6) for Ar, Kr, and Xe, respectively. No such points were found in the calculated EOS of He and Ne. The relative magnitude of the three-body contribution to the ground-state energy with respect to the two-body one as a function of the volume compression was found to be non-monotonic in the sequence Ne–Ar–Kr–Xe. In a large range of compressions, Kr has the highest value of this ratio. This anomally high three-body exchange forces contributes to the EOS so large negative pressure that the EOS for Kr and Ar as a function of compression nearly coincide. At compressions higher approximately 3.5, the curves intersect and further on the EOS of Kr lies lower than that of Ar

Lattice distortion of quantum cryocrystals under pressure

The hcp lattice distortion parameter δ, the deviation of c/a ratio from the ideal hcp value √ 8/3 , have been calculated for solid He under pressure taking into account two- and three-body interatomic forces. The resulting lattice distortion parameter is small and negative, that is the lattice is slightly flattened compared with the ideal hcp lattice. It monotonically increases in absolute value with pressure and reaches 10⁻³ for molar volume of ~ 2.5 cm³/mol. Such small distrotions are most likely outside of possibilities of x-ray or neutron experiments but can be detected by optical methods based on measurements of the birefringence. The data on δ can be used as a probe of the many-body forces

Lattice distortion in hcp rare gas solids

The lattice distortion parameter δ≡c/a – √8/3 has been calculated as a function of molar volume for the hcp phases of He, Ar, Kr, and Xe. Results from both semi-empirical potentials and density functional theory are presented. Our study shows that δ is negative for helium in the entire pressure range. For Ar, Kr, and Xe, however, δ changes sign from negative to positive as the pressure increases, growing rapidly in magnitude at higher pressures

Molecular rotation in p-H₂ and o-D₂ in phase I under pressure

The orientational order parameter, rotational ground-state energy, and lattice distortion parameter (the deviation of the c/a ratio from the ideal hcp value 1.633) in hcp lattice of phase I of p-H₂ and o-D₂ are calculated using a semi-empirical approach. It is shown that the lattice distortion in these J-even species is small compared with that found in n-H₂, and n-D₂. The difference presumably is caused by the J-odd species

Poisson’s ratio in cryocrystals under pressure

We present results of lattice dynamics calculations of Poisson’s ratio (PR) for solid hydrogen and rare gas solids (He, Ne, Ar, Kr and Xe) under pressure. Using two complementary approaches — the semi-empirical many-body calculations and the first-principle density-functional theory calculations we found three different types of pressure dependencies of PR. While for solid helium PR monotonically decreases with rising pressure, for Ar, Kr, and Xe it monotonically increases with pressure. For solid hydrogen and Ne the pressure dependencies of PR are nonmonotonic displaying rather deep minimums. The role of the intermolecular potentials in this diversity of patterns is discussed

Sound velocities in solid hydrogen under pressure

We present results of semi-empirical lattice dynamics calculations of the sound velocities in solid hydrogen under pressure based on the many-body intermolecular potential and first-principle density-functional theory (DFT). Both the sound velocities and elastic moduli are in excellent agreement with data from Brillouin scattering measurements while Silvera–Goldman and Hemley–Silvera–Goldman potentials tend to overestimate the sound velocity. It is shown that the stiffer is the potential the greater is overestimated the sound velocity. As was the case for equation of state and Raman-active lattice phonon calculations, the employed many-body potential works well for phases I and II (up to ~ 140 GPa while for higher pressures the use of the DFT is preferable

A non trivial extension of the two-dimensional Ising model: the d-dimensional "molecular" model

A recently proposed molecular model is discussed as a non-trivial extension of the Ising model. For d=2 the two models are shown to be equivalent, while for d>2 the molecular model describes a peculiar second order transition from an isotropic high temperature phase to a low-dimensional anisotropic low temperature state. The general mean field analysis is compared with the results achieved by a variational Migdal-Kadanoff real space renormalization group method and by standard Monte Carlo sampling for d=3. By finite size scaling the critical exponent has been found to be 0.44\pm 0.02 thus establishing that the molecular model does not belong to the universality class of the Ising model for d>2.Comment: 25 pages, 5 figure

Low-temperature anomalies in the magnetic and thermal properties of molecular cryocrystals doped with oxygen impurity

The magnetic properties of oxygen pair clusters are investigated theoretically for different cluster geometries which can be realized by doping molecular cryomatrices with oxygen. Anomalous temperature and pressure behavior of the magnetic susceptibility, heat capacity, and entropy is predicted. It is proposed to use these anomalies for studying the parameters characterizing the oxygen clusters and the parameters of the host matrix: the effective spin-figure interaction constant D for the molecule in the matrix, the exchange parameter J, and the number of pair clusters Np, which can deviate markedly from the purely random value Np=6Nc² (N is Avogadro’s number, and c is the molar concentration of the impurity). The data on the magnetic susceptibility may be used to analyze the character of the positional and orientational short-range order in the solid solution. The value of D contains information about the orientational order parameter; the distance and angular dependence of the exchange interaction parameter are still subject to discussion in the literature. The temperature dependence of Np contains information about diffusion and clusterization processes in the system

Broken symmetry phase transition in solid HD: a manifestation of quantum orientational melting

Theoretical study of the broken symmetry phase (BSP) transition line in solid HD reveals that its anomalous features provide evidence for quantum orientational melting. The observations of unusual reentrant behavior is a consequence of the symmetry properties of the system, namely, the fact that in HD all rotational states and transitions between them are allowed, in contrast to the behavior of the homonuclear isotopes H₂ and D₂. The systematic underestimation of the transition pressure characteristic of all theories of the BSP transition can be removed if crystal-field effects are taken into account. Remove selecte