Melting as a first‐order phase transition in a system of defects

Abstract

The self-consistent quasiharmonic modol is used to describe the equilibrium atomic structure of a crystal and the thermodynamical properties of vacancies at high temperature. It is shown that an increase in the amplitude of the thermal atomic vibrations with temperature leads to a considerable reduction of the vacancy formation energy in the high-temperature region, which results in the generation of a large number of defects near the melting point and, as a consequence, in the significant softening of the acoustic vibration modes of the crystal. The effective attraction between the vacancies through the phonon subsystem of the crystal is found to lead to the first-order phase transition with a discontinuous change in the defect conceritration at the transition point. The melting lines are calculated for the rare gas crystals. The effects of the solid-vapour interface on t,he kinetics of the solid-liquid transition are studied.

Schottky Defects in Nanoparticles

“…Indeed, the presence of vacancies in the crystal lattice will modify the lattice structure around the vacancies and then result in a decrease of the lattice parameter. ,− The size effect on the lattice parameter is attributed to the lattice strain induced by the formation of vacancies . The creation of vacancies also reduces the force constants seen by the atoms neighboring the vacant site and thereby decreases the local vibration frequencies , in agreement with our eq . Furthermore, the hardness and the yield strength of the material typically increase with decreasing size, a phenomenon known as the Hall−Petch effect. , The size-dependent hardness enhancement at a temperature well below the melting temperature is due to the bond length contraction and the associated bond strength gain .…”

High Temperature Specific Heat of BSO Crystals

“…Also, the temperature range and the value of Einstein temperature Q E b Q D , are far from the melting temperature of the BSO crystal, T m 1274 K, so that some possible modifications of the vibrational frequencies can be neglected [15].…”

Thermodynamics and microstructure of vacancies in rare gas crystals at high temperature

“…Particularly, we checked the assumption that the vacancy concentration is constant along the melting line [31]. We successfully tested the present high-temperature approximation to the self-consistent statistical model by calculation of the equation of state for perfect Ar crystal at 293 K up to 80 GPa.…”