Molecular Dynamics Studies of the Melting of Copper with Vacancies amd Dislocations at High Pressures
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Molecular Dynamics Studies of the Melting of Copper with Vacancies amd Dislocations at High Pressures Clarence C Matthai and Jessica Rainbow School of Physics and Astronomy, Cardiff University Cardiff, UK. ABSTRACT Molecular dynamics simulations of the melting process of bulk copper were performed using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) with the interatomic potentials being described by the embedded atom method. The aim of the study was to understand the effects of high pressures and defects on the melting temperature. The simulations were visualised using Visual Molecular Dynamics (VMD). The melting temperature of a perfect copper crystal, was found to be slightly higher than the experimentally observed value. The melting temperature as a function of pressure was determined and compared with experiment. Point and line defects, in the form of dislocations, were then introduced into crystal and the new melting temperature of the crystal determined. We find that the melting temperature decreases as the defect density is increased. Additionally, the slope of the melting temperature curve was found to decrease as the pressure was increased while the vacancy formation energy increases with pressure. INTRODUCTION The melting transition has been studied extensively over many decades and over the years many theories of this transition have been expounded. It had been suggested that melting occurs when the atom vibrations, as the crystal is heated, become large enough at the melting temperature such that the long range order is lost. Lindemann postulated that at the melting temperature could be approximately defined as the point at which the mean interatomic spacing exceeds its equilibrium spacing by 10%. This is the so-called Lindemann criteria [1] for melting. It is now generally agreed that defects, and in particular line defects, play an important role in the melting transition. In dislocation theories of melting, the number of dislocations increases according to some power law at the transition temperature. More recently, it has been suggested [2] that a wide variety of phase transitions may be formulated in terms of the formation of quasi-particles at the transition. In this phenomenological theory it was proposed that the transition temperature T t could be written in the form k B T t =Echar e −γ where Echar is some characteristic energy associated with the transition and k B is the usual Boltzman constant. The quantity γ is related to the energy required to create the quasi-particle appropriate to the transition. It was further proposed that for melting the characteristic energy is related to the bulk modulus, B, through the relation Echar =Ω B where Ω is the atomic volume. The quasi-particles in this formulation are the phonons associated with the shear modulus. Point and line defects allow for the annihilation of these quasi-particles. In this study we have investigated the dependence of the melting temperature on the defect (point and line) density. In addition, we have also in
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