Three dimensional structures predicted by the modified phase field crystal equation

Abstract We present the first numerical results on three dimensional structures predicted by the modified phase field crystal equation. The computations are performed using parallel algorithms based on isogeometric analysis, a generalization of the finite element method. The evolution of crystal structures to their steady equilibrium state is predicted for various atomic densities and temperatures. These steady structures are consistent with the phase diagram predicted earlier using one-mode approximations of analytical solutions to the classical parabolic phase-field crystal equation.

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