Investigation of the Thermodynamic Properties of Anharmonic Crystals with Defects and Influence of Anharmonicity in Exafs by the Moment Method

Abstract

By the moment method established previously on the basis of the statistical mechanics, the thermodynamic properties of a strongly anharmonic face-centered and body-centered cubic crystal with point defect are considered. The thermal expansion coefficient, the specific heat C v and C p , the isothermal and adiabatic compressibility, etc. are calculated. Our calculated results of the thermal expansion coefficient, the specific heat C v and C p ... of W, Nb, Au and Ag metals at various temperatures agrees well with the measured values. The anharmonic effects in extended X-ray absorption fine structure (EXAFS) in the single-shell model are considered. We have obtained a new formula for anharmonic contribution to the mean square relative displacement. The anharmonicity is proportional to the temperature and enters the phase change of EXAFS. Our calculated results of Debye-Waller factor and phase change in EXAFS of Cu at various temperatures agrees well with the measured values.

Thermodynamic Properties of Free Standing Thin Metal films Investigated Using Statistical Moment Method: Temperature and Pressure Dependence

“…In principle, Eqs. (14), (16) and (17) permit to find the nearest neighbour distance a ng @P; HA, a ng1 @P; HAand a tr @P; HA for surface layers, next surface layers and internal layers atoms at zero temperature and pressure P , respectively.…”

Atomistic Study of Fracture of Crystalline Materials by Lattice Green's Function Method: Effects of Anharmonicity of Lattice Vibration

“…We expand the potential energy ' i0 ðjr i þ u i jÞ in terms of the atomic displacement up to the fourth-order terms. [32][33][34][35] Here, we note that the formulation can be done in a similar manner when the nonpair wise energetics such as the electronic many body potentials 4) are used. The atomic force acting on a central 0-th atom can be evaluated by taking derivatives of the interatomic potentials.…”

“…[32][33][34][35] The sum of the harmonic and anharmonic contributions to the free energy É ¼ É 0 þ É 1 in the above eq. (20) can be calculated by the following integration procedure…”

“…To derive the temperature dependent lattice spacings, force constant matrix and non-linear cohesive forces near the crack tip region, we use the moment method in the quantum statistical mechanics. [31][32][33] This method allows us to take into account explicitly the anharmonicity effects of thermal lattice vibrations on the thermodynamic quantities of materials, and it is applicable to a wide temperature range from absolute zero to the melting temperatures.…”

Thermodynamic Properties of Free Standing Thin Metal films Investigated Using Statistical Moment Method: Temperature and Pressure Dependence

“…In this article, we present an analysis which can be used to extract the thermodynamic properties of the free-standing metal thin films, as a function of the pressure, using the moment method in the statistical dynamics [12][13][14] and derive the explicit expressions of the free energies of the system. In particular, the thermodynamic properties of the free-standing metal thin films with face-centered cubic (fcc) structure are investigated within the fourth order moment approximation of the atomic displacements.…”