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 macroscale and mesoscale systems taking microscopic details into account.
Highlights
Strains and defect-induced deformations have tremendous effects on the macroscopic properties of single and poly-crystalline materials.[1]. These effects have fostered a huge variety of studies for more than a century, starting with the first theories describing the elastic field generated by dislocations in solids.[2,3]
Real amplitudes, which may be regarded as a special case of the amplitude expansion of the PFC model (APFC) model, have been considered,[26,27] delivering long-range order parameters as in the classical phase-field approaches based on atomistic descriptions
They can be used to account for bridging-scale descriptions of elasticity effects by means of additional contributions as, e.g., in the presence of precipitates, alloys, or point defects.[28–32]
Summary
Strains and defect-induced deformations have tremendous effects on the macroscopic properties of single and poly-crystalline materials.[1]. Associated continuous elastic fields, are very useful for describing elastic effects on the mesoscopic and/or macroscopic scales In this approach, a continuous representation of the displacement of atoms in a lattice with respect to a reference crystal is employed.[5]. Real amplitudes, which may be regarded as a special case of the APFC model, have been considered,[26,27] delivering long-range order parameters as in the classical phase-field approaches based on atomistic descriptions They can be used to account for bridging-scale descriptions of elasticity effects by means of additional contributions as, e.g., in the presence of precipitates, alloys, or point defects.[28–32]. We consider numerical simulations for some generic systems involving strained/tilted crystals and apply the new framework in order to depict and analyze the resulting deformations To this purpose, we numerically solve the equations of the APFC model directly delivering the amplitudes function.
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