Self-consistent phonon calculations and equations of state of solid hydrogen and deuterium

1976 ◽  
Vol 14 (2) ◽  
pp. 814-822 ◽  
Author(s):  
A. B. Anderson ◽  
J. C. Raich ◽  
R. D. Etters
Keyword(s):  
Equations Of State ◽  
Solid Hydrogen ◽  
Self Consistent

ON THE THERMODYNAMICS OF AN ANHARMONIC CRYSTAL WITH HIGH ANISOTROPY

1995 ◽  
Vol 09 (04n05) ◽  
pp. 585-597 ◽  
Author(s):  
V.I. ZUBOV ◽  
M.P. LOBO ◽  
J.N.T. RABELO
Keyword(s):  
Equations Of State ◽  
Quantum Corrections ◽  
Anharmonic Crystal ◽  
Cubic Crystal ◽  
Specific Heats ◽  
Atomic Displacements ◽  
High Anisotropy ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Strong Anharmonicity

The correlative method of the unsymmetrized self-consistent field is used to study the atomic properties of a simple model of an anharmonic crystal with strong anisotropy, namely, a crystal with primitive hexagonal (PH) lattice. The self-consistent potential, Helmholtz free energy and mean-square atomic displacements are obtained in the case of weak anharmonicity. Equations of state are derived and solved. The internal energy and specific heats are calculated. The first quantum corrections are expressed in terms of the de Boer parameter included. An influence of anharmonicity is analyzed. The thermal expansion of the model considered is very anisotropic but the quantum corrections to the lattice parameters are isotropic. The results of calculations are compared with those for one- and two-dimensional models and for the isotropic crystal with the same coordination number as in the PH lattice, i.e. a body-centered cubic crystal. Other things being equal, the coefficient of volume expansion and specific heats of anisotropic crystals are greater than those of isotropic ones. A possibility of studying the strong anharmonicity in anisotropic crystals is discussed.

scholarly journals An Improved Equation of State for Hydrogen

1993 ◽  
Vol 137 ◽  
pp. 307-309 ◽  
Author(s):  
D. Saumon ◽  
G. Chabrier
Keyword(s):  
Phase Transition ◽  
Equation Of State ◽  
Order Phase Transition ◽  
Equations Of State ◽  
First Order ◽  
First Order Phase Transition ◽  
Self Consistent ◽  
Plasma Phase ◽  
Consistent Treatment ◽  
First Order Phase

An improved theory of fluid hydrogen at high density, based on a detailed treatment of inter-particle correlations and a self-consistent treatment of pressure ionization, has become available recently (Chabrier 1990, Saumon and Chabrier 1991, 1992). We present a preliminary comparison between this new EOS (hereatfer SC) and equations of state frequently used in astrophysical contexts, namely: Fontaine, Graboske and Van Horn 1977 (FGVH), Däppen et al. 1988 (MHD) and Magni and Mazzitelli 1979 (MM).The SC theory predicts a first-order phase transition in the region of pressure-ionization (the so-called Plasma Phase Transition, or PPT), between an essentially neutral mixture of atoms and molecules (xe– < 10−2), and a partially ionized plasma (xe– ≈ 50 %), with a critical point located at Pc = 0.614 Mbar, Tc = 15300K and pc = 0.35 g/cm3.

The use of the self-consistent field method to take into account the anisotropy caused by the orientation and shape of the grains of metals

2003 ◽  
Vol 3 ◽  
pp. 82-95
Author(s):  
V.N. Nikonov
Keyword(s):  
Mechanical Properties ◽  
Bauschinger Effect ◽  
Equations Of State ◽  
Field Method ◽  
The Self ◽  
Metallic Material ◽  
Consistent Field ◽  
Self Consistent ◽  
Speed Range ◽  
Self Consistent Field

In the process of manufacturing parts by plastic deformation, the shape and orientation of the grains of the metallic material changes. The emerging mechanical texture causes anisotropy of the mechanical properties of the material. On the basis of the analysis of the interaction of grains at the microlevel, equations of state are obtained that describe the mechanical properties of the material in a wide temperature-speed range under the action of alternating loads, the superplasticity state, and the Bauschinger effect. The knowledge of the anisotropy introduced by the technology of manufacturing the part is necessary for a numerical analysis of the residual mechanical properties of the parts.

Theory of the interaction of the lattice vibrations with the vibrational excitations in solid hydrogen

1970 ◽  
Vol 48 (5) ◽  
pp. 489-501 ◽  
Author(s):  
J. Noolandi ◽  
J. Van Kranendonk
Keyword(s):  
Solid Hydrogen ◽  
The Self ◽  
Order Perturbation ◽  
Lattice Vibrations ◽  
Phonon Coupling ◽  
Phonon Interaction ◽  
Self Consistent ◽  
Vibrational Excitations ◽  
Intramolecular Vibrations ◽  
Quantum Crystals

The theory of the interaction of the vibrational excitations (vibrons) with the lattice vibrations in solid hydrogen is developed. The phonons are treated in the self-consistent harmonic (SCH) approximation appropriate to quantum crystals. The vibron–phonon interaction is expanded in terms of the SCH phonon operators rather than in powers of the displacements of the molecules from their equilibrium positions. First- and second-order perturbation corrections to the vibron energies arising from the vibron–phonon coupling are calculated. The effect of the anharmonicity of the intramolecular vibrations in conjunction with the vibron–phonon coupling is also discussed.

scholarly journals A self-consistent approach to describe unit-cell-parameter and volume variations with pressure and temperature

2021 ◽  
Vol 54 (6) ◽  
Author(s):  
Ross Angel ◽  
Mattia Mazzucchelli ◽  
Javier Gonzalez-Platas ◽  
Matteo Alvaro
Keyword(s):  
Cell Parameter ◽  
Equations Of State ◽  
Unit Cell ◽  
The Self ◽  
Polynomial Functions ◽  
Unit Cell Parameters ◽  
Cell Parameters ◽  
Self Consistent ◽  
Consistent Manner ◽  
Consistent Approach

A method for the self-consistent description of the large variations of unit-cell parameters of crystals with pressure and temperature is presented. It employs linearized versions of equations of state (EoSs) together with constraints to ensure internal consistency. The use of polynomial functions to describe the variation of the unit-cell angles in monoclinic and triclinic crystals is compared with the method of deriving them from linearized EoSs for d spacings. The methods have been implemented in the CrysFML Fortran subroutine library. The unit-cell parameters and the compressibility and thermal expansion tensors of crystals can be calculated from the linearized EoSs in an internally consistent manner in a new utility in the EosFit7c program, which is available as freeware at http://www.rossangel.net.

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