Dislocation Lines as the Precursor of the Melting of Crystalline Solids Observed in Monte Carlo Simulations

Abstract

The microscopic mechanism of the melting of a crystal is analyzed by the constant pressure Monte Carlo simulation of a Lennard-Jones fcc system. Beyond a temperature of the order of 0.8 of the melting temperature, we found that the relevant excitations are lines of defects. Each of these lines has the structure of a random walk of various lengths on an fcc defect lattice. We identify these lines with the dislocation ones proposed in recent phenomenological theories of melting. Near melting we find the appearance of long lines that cross the whole system. We suggest that these long lines are the precursor of the melting process. : 64.70.Dv, 61.72.Bd, Melting is one of the rare phase transitions that can be observed in real life, outside of laboratories. Being a common-life process, the melting mechanism has been of interest for centuries. However there is yet no complete understanding of the atomistic dynamics involved in the melting transition. This is due to several difficulties found both in the experimental and theoretical studies of this problem. Let us discuss some of these difficulties. PACSUpon a phase transition long-range order found in the low temperature phase (LTP) disappears at the transition temperature. In the simplest cases, such as a structural phase transition, order is associated with a geometrical quantity which distinguishes LTP from the high temperature phase (HTP). The dynamical collective structural deformation, namely phonons, converting LTP into HTP is already present in the higher-symmetry phase. It is therefore natural to assume that the softening of this phonon excitation is the essential mechanism of the phase transition capturing the most important dynamics of the particles near the transition point.However, at the melting temperature T m , both translational and rotational symmetries of a crystal are destroyed, and it is much more complicated to construct simple models including the relevant excitations on both sides of the transition temperature. Hence, one-phase models have been developed. Starting in the solid phase, the question is what kind of excitation could destroy crystalline order. It is easy to see [1] that phonons alone cannot convert a solid into a liquid, some kind of crystalline defects should be invoked. Kosterlitz and Thouless [2] proposed a fundamental theory of the thermal breakdown of long-range order in two dimensions (2D) by topological defects, and related it to transitions in 2D crystals, superfluids and magnets, the relevant topological defects in the case of melting being crystalline dislocations (which are point defects in 2D). Their theory was greatly extended and detailed by Halperin and Nelson [3] and Yound [4] who predicted that the complete transition from solid to liquid takes place in two steps: the dissociation of dislocation pairs drives a crystal into a liquid-crystal phase that retains finite-range orientational order, then a second transition at higher temperature completes the conversion to an isotropic liquid. This complete theory gave det...

Equation of state from the Potts-percolation model of a solid

“…The influence of interatomic distance fluctuations on the nature of the phase transitions in this model will be addressed in a future study. Finally, let us note that while it is known that the solid phase cannot survive at finite T in two dimensions with continuous degrees of freedom of atom motions, our present study with discrete degrees of freedom shows some interesting behaviors which would serve as a starting point to study three-dimensional solids where melting mechanisms are not well understood [1,2]. ACKNOWLEDGMENT M.K.…”

“…The mechanical properties of solids, such as melting [1,2] and mechanical failure [3][4][5][6], are topics of considerable interest. In this paper we continue the analysis of an equilibrium statistical mechanics model [7,8] of a solid.…”

Numerical simulations of atomic-scale disordering processes at impact between two rough crystalline surfaces

“…Such loops, with lifetimes on the order of 20 ps, roughly correspond to Shockley partial dislocations surrounding stacking faults. 37 The loops on the Ni side of the Ni-Zr interface are seen to glide mainly along the ͓101͔ and ͓110͔ crystallographic directions. On the Zr side of the interface, the loops glide instead mainly along the ͓110͔ and ͓210͔ crystallographic directions.…”

Synergic Role of Self-Interstitials and Vacancies in Indium Melting

“…More recently, melting has been investigated by Monte Carlo computer simulations [10][11][12]. Gomez et al [11,12] evaluated the percentage of defects near TM and showed that defects form clusters, which are not isolated, but rather linked over long distances near the phase transition.…”

“…Gomez et al [11,12] evaluated the percentage of defects near TM and showed that defects form clusters, which are not isolated, but rather linked over long distances near the phase transition. In fact, their calculations indicate that the linked clusters are dislocations and melting is consistent with the saturation of the crystal by dislocation loops.…”