Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions

Abstract

The problem of predicting polymorphism in atomic and molecular crystals constitutes a significant challenge both experimentally and theoretically. From the theoretical viewpoint, polymorphism prediction falls into the general class of problems characterized by an underlying rough energy landscape, and consequently, free energy based enhanced sampling approaches can be brought to bear on the problem. In this paper, we build on a scheme previously introduced by two of the authors in which the lengths and angles of the supercell are targeted for enhanced sampling via temperature accelerated adiabatic free energy dynamics [T. Q. Yu and M. E. Tuckerman, Phys. Rev. Lett. 107, 015701 (2011)]. Here, that framework is expanded to include general order parameters that distinguish different crystalline arrangements as target collective variables for enhanced sampling. The resulting free energy surface, being of quite high dimension, is nontrivial to reconstruct, and we discuss one particular strategy for performing the free energy analysis. The method is applied to the study of polymorphism in xenon crystals at high pressure and temperature using the Steinhardt order parameters without and with the supercell included in the set of collective variables. The expected fcc and bcc structures are obtained, and when the supercell parameters are included as collective variables, we also find several new structures, including fcc states with hcp stacking faults. We also apply the new method to the solid-liquid phase transition in copper at 1300 K using the same Steinhardt order parameters. Our method is able to melt and refreeze the system repeatedly, and the free energy profile can be obtained with high efficiency. © 2014 AIP Publishing LLC.

A metadynamics study of the fcc–bcc phase transition in Xenon at high pressure and temperature

“…In this paper, we apply metadynamics to explore a solid-solid phase transition in Xe modelled with the Buckingham potential for which the T-induced phase is known to exist [11], and confirmed by a recent study using the adiabatic free energy dynamics (AFED) approach [21]. The aim of this study is to determine the range of applicability of the metadynamics approach.…”

Recent developments in computational modelling of nucleation in phase transformations

“…5,[74][75][76][77][78] As a model system, copper is used to study the melting of a solid. The interatomic interactions were modelled using the embedded atom method potential for Cu developed by Mishin et al 79 To efficiently explore the relevant parts of the configuration space and study the microscopic mechanisms of melting, the AFED, [80][81][82] a recently developed exploration technique, was used. Techniques like the AFED and the TAMD 82,83 exploit the adiabatic time scale separation between the evolution of the atomic DOF and the collective variables (CVs) by assigning fictitious masses to the CVs that are much larger than the atomic masses, and at the same time, maintaining the CVs at a temperature much higher than the physical temperature.…”

Interfacial diffusion aided deformation during nanoindentation

“…The high temperature assigned to the macroscopic variables ensures that the system can overcome all barriers and explore processes with long waiting times. [19][20][21] Because the dynamics of the macroscopic variables in d-AFED are fictitious, important information about the kinetics of the diffusive processes are essentially lost. 19,20 Consequently, we used high temperature MD simulations to gain quantitative insights into these processes.…”

“…[19][20][21] Because the dynamics of the macroscopic variables in d-AFED are fictitious, important information about the kinetics of the diffusive processes are essentially lost. 19,20 Consequently, we used high temperature MD simulations to gain quantitative insights into these processes. High temperatures provide enough kinetic energy to the system so that it can easily hop from one local minimum to another that allows us to analyze the defect kinetics and determine the parameters that control the transition between the different deformation modes.…”

“…First, we used an order parameter aided temperature accelerated free energy 18 sampling technique called driven adiabatic free energy dynamics (d-AFED). [19][20][21] Next, we used high temperatures to accelerate the kinetics of thermally activated processes in MD simulations. Using d-AFED, we were able to investigate the free energy landscape of the system and relevant parts of the configuration space and using high temperature MD, we were able to gain a quantitative understanding of the diffusive processes.…”