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Monte Carlo methods for the determination of phase diagrams

By: João Sousa
From: Universidade de Aveiro
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2014-05-15] 14:00

Monte Carlo (MC) and Molecular Dynamics (MD) methods are extraordinarily useful techniques which allow one to extract important equilibrium properties of arbitrary fluid and solid systems given a microscopic model of interactions. They are not, however, necessarily fit to study problems of phase stability, i.e., they do not immediately answer the question of which macroscopic phase is more stable for the system at a given thermodynamic state.

In principle, one would only require the knowledge of the free energy or, equivalently, the chemical potential, as a function of temperature, density or composition to draw the phase diagram for a model system with the desired precision. Unfortunately, standard MC and MD are not designed to sample free energies, which are a function of the whole volume of phase space and can not be expressed as a simple ensemble average over a finite number of samples. Likewise, an analytical or numerical solution is impossible for any but the simplest and smallest systems. The standard solution is to integrate the free energy starting from some reference states, where its absolute value is known, but this technique is not without its problems and limitations.

In this seminar I will present some of the most common approaches used to solve the problem of phase determination in the context of MC simulations, with special emphasis on the liquid-solid transition, which is a more challenging and interesting issue. Techniques based on free energy calculations will be explained in detail and an overview given of specialized methods which present unique solutions to this problem.