Experiments show that vacancies in a solid may coalesce into voids and self-organize into a super-lattice. The voids have diameters around 10 nm and spacing of tens of nanometers. This paper develops a thermodynamic model to explain and simulate the remarkable phenomena. We incorporate free energy of mixing, interface energy and elasticity into a continuous phase field model. It is well known that the total interface energy reduces when the voids grow larger. Simulations show that elastic anisotropy may limit the coarsening. Starting from randomly distributed vacancies, the process of coalescence and void lattice formation demonstrates rich dynamics. Long-range elastic interaction and elastic anisotropy are found to play a significant role that determines the self-assembled super-lattice.

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