  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.
