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Crystal lattice deformations can be described microscopically by explicitlyaccounting for the position of atoms or macroscopically by continuumelasticity. In this work, we report on the description of continuous elasticfields derived from an atomistic representation of crystalline structures thatalso include features typical of the microscopic scale. Analytic expressionsfor strain components are obtained from the complex amplitudes of the Fouriermodes representing periodic lattice positions, which can be generally providedby atomistic modeling or experiments. The magnitude and phase of theseamplitudes, together with the continuous description of strains, are able tocharacterize crystal rotations, lattice deformations, and dislocations.Moreover, combined with the so-called amplitude expansion of the phase-fieldcrystal model, they provide a suitable tool for bridging microscopic tomacroscopic scales. This study enables the in-depth analysis of elasticityeffects for macro- and mesoscale systems taking microscopic details intoaccount.

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