Role of anharmonicity of atomic vibrations in formation of vacancies in rare-gas crystals

Melting and thermodynamic properties of rare gas nanocrystals

“…If the melting temperature T m is assumed to be identical to the temperature of anharmonic instability of the crystal [33,34], then it can be shown in the framework of the present statistical model that T m is related to the factor n( ) t as…”

“…The method has been applied to description of thermal characteristics of the rare gas crystals (RGC) [36][37][38] and some simple fcc metals [39]. In the framework of this method we also computed the formation energy of a vacancy in the RGC as a function of temperature and demonstrated that approaching the melting point (which is assumed to be directly related to the point of anharmonic instability) is accompanied by dramatic reduction of the energy required to create structure defects of the lattice [33,34,40]. As in our previous studies, we assume the interatomic interaction to be pairwise and approximated by the Morse potential…”

“…33 so that calculated values of interatomic distance, bulk modulus, and sublimation energy at zero temperature fitted the corresponding experimental data. In this work we restrict ourselves to the high-temperature limit when the distribution function of atomic displacements in a simple crystal may be presented as a product of one-particle Gaussian functions [33] given by…”

“…The third term determines a contribution to the free energy of the crystal due to the cubic anharmonicity of collective atomic vibrations, evaluated in the second order of the perturbation theory ( . a 3 2 31 » for the RGC [33,34]). The next term takes into account the long-range attraction between atoms of the crystal, with e and s being the parameters of the Lennard-Jones potential and k l = 4 91…”

“…For a bulk fcc crystal, n 0 2 = , n 1 5 6 = / . Equations (5) and (6) In the high-temperature approximation the Gibbs free energy F of a simple fcc crystal consisting of N atoms can be written as [33,36] …”