Closing the gap between atomic-scale lattice deformations and continuum elasticity

TL;DR

This paper develops a method to derive continuum elastic fields from atomistic models, capturing microscopic details like dislocations and rotations, thus bridging atomic-scale and macroscopic descriptions of crystal deformations.

Contribution

It introduces analytic expressions for strain from Fourier amplitudes of lattice representations, linking microscopic atomistic data with continuum elasticity.

Findings

Provides formulas for strain from Fourier modes

Enables analysis of dislocations and rotations

Bridges microscopic and macroscopic scales

Abstract

Crystal lattice deformations can be described microscopically by explicitly accounting for the position of atoms or macroscopically by continuum elasticity. In this work, we report on the description of continuous elastic fields derived from an atomistic representation of crystalline structures that also include features typical of the microscopic scale. Analytic expressions for strain components are obtained from the complex amplitudes of the Fourier modes representing periodic lattice positions, which can be generally provided by atomistic modeling or experiments. The magnitude and phase of these amplitudes, together with the continuous description of strains, are able to characterize crystal rotations, lattice deformations, and dislocations. Moreover, combined with the so-called amplitude expansion of the phase-field crystal model, they provide a suitable tool for bridging microscopic to macroscopic scales. This study enables the in-depth analysis of elasticity effects for macro- and mesoscale systems taking microscopic details into account.