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 elast...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.展开更多
基金M.S.acknowledges the support of the Postdoctoral Research Fellowship awarded by the Alexander von Humboldt FoundationA.V.acknowledges support from the German Research Foundation under Grant no.Vo899/20 within SPP 1959K.R.E.acknowledges financial support from the National Science Foundation under Grant No.DMR1506634.
文摘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.
