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

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 macro-and mesoscale systems taking microscopic details into account.

Modeling buckling and topological defects in stacked two-dimensional layers of graphene and hexagonal boron nitride

“…Free-energy density difference between strained and unstrained states as a function of system size. The slope of the best fit line (dashed line) is 1.96. prior work [62,63]. The comparison is given in Fig.…”

Phase field crystal based prediction of temperature and density dependence of elastic constants through a structural phase transition

“…Likewise, one could generalize the approach to two-mode expansions. While the current work focuses on obtaining expressions for the elastic constants based on expressions for the state variable, one could follow [18] and attempt to derive analytic expressions for strain components across phase transitions. .…”

“…Thus, by using the above equation and (A.2), and equations (A.6)-(A.8), we can obtain the pre-existed pressures for stripes, and hexagons and Bcc, i.e., equations (24), (27) and (30). For the elastic constants C 11 , we have from (18), (20), (A.1) and (A.4) that…”

An efficient numerical framework for the amplitude expansion of the phase-field crystal model

“…The evaluation of rotations considered here is well posed in the solid phase and also at defects [19]. However, it is not well posed for the liquid, disordered phase as η j 's vanish.…”

“…Although not addressed here, this criterion can be extended in order to account for amplitude oscillations due to strain fields, exploiting continuous strain-field components, as derived in Ref. [19], instead of ω.…”