relax_box calculation style

Lucas M. Hale, lucas.hale@nist.gov, Materials Science and Engineering Division, NIST.

Introduction

The free_energy calculation style uses thermodynamic integration to evaluate the absolute Helmholtz and Gibbs free energies of a solid phase by comparing it to a reference Einstein solid.

Version notes

  • 2022-09-20: Calculation first added to iprPy

Additional dependencies

Disclaimers

  • NIST disclaimers

  • The simulations used by this method are all fixed volume and therefore will not relax the system to a given pressure. Instead, it is expected that the given system is already relaxed to the target pressure of interest.

Method and Theory

The calculation performs two different simulations: an nvt simulation to estimate Einstein solid spring constants for each atom type, and thermodynamic integrations from the selected interatomic potential to the Einstein solid model and back. The method follows what is described in Freitas, Asta, de Koning, Computational Materials Science 112 (2016) 333–341.

The Einstein solid spring constants, \(k_i\), are evaluated using an nvt simulation run and measuring the mean squared displacements, \(\left<\left( \Delta r_i \right)^2\right>\), averaged for each atom type \(i\) and over time

\[k_i = \frac{3 k_B T}{\left<\left( \Delta r_i \right)^2\right>}\]

For the integration, TBD…