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Lecture

WEB Closing the gap between atomic-scale lattice deformations and continuum elasticity within the phase-field crystal framework

Friday (25.09.2020)
11:50 - 12:05 M: Modelling and Simulation 2
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The Phase-Field Crystal (PFC) model allows for describing atoms in a lattice through a continuous probability density and investigating diffusive time scales. In the amplitude expansion of the PFC model (APFC), a coarse-grained description of the atomic probability density is obtained by focusing on its complex amplitudes and, in turn, on their dynamics. These amplitudes vary on length scales larger than the atomic spacing but still retain details of the crystal lattice. Numerical simulations based on the APFC model and exploiting the Finite Element Method are shown to reproduce defects structures in two and three dimensions for different crystal symmetries as well as their dynamics [1]. The derivation of continuous deformation fields from the complex amplitudes, their connections with the elasticity theory, and the characterization of dislocations by the Burgers vector density [2,3] are also discussed. These findings assess the APFC model as a reliable coarse-graining of the PFC model. More importantly, the description of crystal structures through amplitudes is shown to provide a natural framework connecting atomic-scale lattice deformations and continuum elasticity.


[1] M. Salvalaglio et al, Phys. Rev. Materials 2, 053804 (2018)

[2] M. Salvalaglio et al, npj Comput. Materials 5, 48 (2019)

[3] M. Salvalaglio et al, JMPS 137, 103856 (2020)

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