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

• Published in: npj computational materials Vol. 5; no. 1
• Main Authors: Salvalaglio, Marco, Voigt, Axel, Elder, Ken R.
• Format: Journal Article
• Language: English
• Published: London Nature Publishing Group UK 11.04.2019; Nature Publishing Group
• Subjects: 639/301/1034/1036; 639/301/1034/1037; Amplitudes; Characterization and Evaluation of Materials; Chemistry and Materials Science; Computational Intelligence; Crystal lattices; Deformation; Dislocations; Elasticity; Lattice vibration; Materials Science; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Strain analysis; Theoretical
• ISSN: 2057-3960; 2057-3960
• DOI: 10.1038/s41524-019-0185-0

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.