Elastic constants from microscopic strain fluctuations

TL;DR

This paper introduces a method to accurately determine elastic constants of model solids from atomistic simulations by analyzing microscopic strain fluctuations and applying finite size scaling, applicable to various potentials.

Contribution

The paper presents a simple, efficient, and general method to extract elastic constants from microscopic strain fluctuations in atomistic simulations, including systems with singular potentials.

Findings

Successfully computed elastic constants for 2D soft and hard disk solids.

Validated the method by comparing with previous simulations and density functional theory.

Demonstrated the method's applicability to different potentials and system sizes.

Abstract

Fluctuations of the instantaneous local Lagrangian strain $\epsilon_{ij}(\bf{r},t)$, measured with respect to a static ``reference'' lattice, are used to obtain accurate estimates of the elastic constants of model solids from atomistic computer simulations. The measured strains are systematically coarse- grained by averaging them within subsystems (of size $L_b$) of a system (of total size $L$) in the canonical ensemble. Using a simple finite size scaling theory we predict the behaviour of the fluctuations $<\epsilon_{ij}\epsilon_{kl}>$ as a function of $L_b/L$ and extract elastic constants of the system {\em in the thermodynamic limit} at nonzero temperature. Our method is simple to implement, efficient and general enough to be able to handle a wide class of model systems including those with singular potentials without any essential modification. We illustrate the technique by computing isothermal elastic constants of the ``soft'' and the hard disk triangular solids in two dimensions from molecular dynamics and Monte Carlo simulations. We compare our results with those from earlier simulations and density functional theory.