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

We use a self-consistent statistical method to study formation of vacancies in rare-gas crystals at high temperature. The vacancy formation energy is calculated by minimization of the relaxation energy of the vacancy surrounding with respect to distribution parameters of atomic displacements for four coordination spheres of the vacancy. An emphasis is placed on the analysis of the role the vibrational anharmonicity plays in formation of defects in a crystal at high temperature. It is shown that the vacancy formation energy rapidly falls as temperature approaches the melting point of the crystal. Assuming that the crystal melts as temperature reaches the region of instability of the solid state, we compute the melting curve of Ar.

Figure 1

The free energy of the vacancy formation in solid Ar at zero pressure calculated up to the instability point. Curve 1 was obtained in the quasi-harmonic approximation taking into account the relaxation of atoms of four coordination spheres of the vacancy. Curves 2 and 3 were computed within the model with the cubic anharmonicity taken into account, including the relaxation of atoms of two and four coordination spheres of the vacancy, respectively.

Figure 2

Average potential energy per atom of solid Ar calculated within the quasiharmonic model (dotted line) and taking the cubic anharmonicity into account (solid line).

Figure 3

Melting curve of Ar. Experimental values are from Refs. 12, 13.