Self-Consistent Theory of Elastic Properties of Strongly Anharmonic Crystals I: General Treatment and Comparison With Computer Simulations and Experiment for FCC Crystals

Abstract

Based on the correlative method of an unsymmetrized self-consistent field,16–23 we have derived expressions for elastic constant tensors of strongly anharmonic crystals of cubic symmetry. Each isothermal elastic constant consists of four terms. The first one is the zeroth approximation containing the main anharmonicity (up to the fourth order). The second term is the quantum correction. It is important at temperatures below the De-bye characteristic temperature. Finally, the third and fourth terms are the perturbation theory corrections which take into account the influence of the correlations in atomic displacements from the lattice points and that of the high-order anharmonicity respectively. These corrections appear to be small up to the melting temperatures. It is sufficient for a personal computer to perform all our calculations with just a little computer time. A comparison with certain Monte Carlo simulations and with experimental data for Ar and Kr is made. For the most part, our results are between. The quasi-harmonic approximation fails at high temperatures, confirming once again the crucial role of strong anharmonicity.

On the thermal vacancy effects on thermodynamic properties and stability of Van der Waals crystals

“…The defects reduce the spinodal tem- Fig. 4 Thermal expansion coefficient 10 5 α in K -1 and the Grüneisen parameter γ for the hypothetical perfect crystal (the lower lines) and with vacancies (the upper lines): α in the equilibrium with the saturated vapor (1), at 500 (2) and 1000 (3) bar and γ in the equilibrium with the saturated vapor (4) and at 1000 bar (5). Experimental data are from [25] perature by about 4%.…”

“…Based on the correlative method of the unsymmetrized self-consistent field (CUSF), we study the thermodynamic properties of crystals with various types of the chemical bonds, see e.g. [1][2][3][4][5][6][7][8][9]. The CUSF enables one, taking into account the strong anharmonicity of the lattice vibrations [1][2][3] that takes place at temperatures more than about one half of the melting point [10], to calculate a complete set of thermodynamic properties of crystals [5][6][7], their stability and loss mechanisms [4,9].…”

Intermolecular Correlations and Mean Square Relative Displacements in C60 Fullerite

“…In both cases, we take into consideration their terms up to the fourth order since the higher ones are generally small [7,8]. As usual, the potential energies (1) and (5) are represented as power series of the molecular displacements.…”

On the Limit of the Thermodynamic Stability of Superheated Crystals and Mechanisms of Its Loss

“…In this case, the Helmholtz free energy of a cubic one-component crystal with pairwise central interactions F(r) and its equation of state at the hydrostatic pres-sure P are of the form, e.g. [11,19],…”

“…The CUSF enables one to take into account the many-body interactions, e.g. [11,19], and the intramolecular degrees of freedom in molecular crystals [20]. It also has been generalized to crystals with compound lattices [21].…”