Anomaly melting transition of silicon using free energy analysis from pseudo-supercritical thermodynamic path: a molecular dynamics study

Abstract

Silicon shows a very different trend while melting. Melting has remained a challenging subject from a long time. Especially, predicting the melting temperature of any solid substance still exists as a problem in many cases. Recently, various studies and new rules and set of parameters have simplified things, but its mechanism is yet to be studied properly and there still does not exist any generalized concept regarding this. Also, there are certain anomalies in silicon, which makes it’s melting and phase transition mechanism more difficult to understand and predict. In order to understand the phenomenon, it is important to know the interaction potential governing the silicon system. Stillinger-Weber potential is a good model for Si atoms which takes into account two and three particle interactions. Melting of Silicon atoms is studied using Molecular Dynamics Simulation with the help of LAMMPS software. The only extensive property that remains constant during phase transformation is the Gibbs free energy. Using this beautiful property one can estimate true thermodynamics melting temperature. Estimation of Gibbs free energy is performed with the help of pseudo-supercritical reversible thermodynamic cycle along the help of multiple histogram reweighting diagrams. Heating and quenching processes is implemented on a system of Si atoms. An estimated melting temperature is determined from density hysteresis plot. The pseudo-supercritical reversible thermodynamic cycle is conducted at estimated temperature to determine free energy difference between solid-liquid phases. Supercritical path is constructed with the help of more than one reversible thermodynamic path. The sufficient and necessary condition is that there should not be presence of any first order phase transition and pressure remains unaltered at the beginning and at the end of the path. It is consisting of three steps, for each I performed NVT simulation varying coupling parameter. The value of coupling parameter varies from zero to one. The potential energy and density appear to be steady, indicating pre-melting. Melting temperature can be predicted using Gibbs free energy. Gibbs free energy calculation involve with thermodynamics integration and multiple histogram reweighting(MHR) method.