Self -organization of three-dimensional nano-void superlattice in electron irradiated calcium fluoride.

Abstract

To improve the scientific understanding of a spectacular phenomenon observed in electron irradiated calcium fluoride (CaF₂), the formation of ordered arrays of nano-voids, three-dimensional nano-void superlattice has been fabricated with high energy electrons and studied with <italic>in-situ </italic> TEM. Energy transferred from electrons to the atoms in the sample by radiolysis and ballistic processes have been calculated respectively. Unlike the commonly observed randomly distributed defect clusters or precipitates, the voids in these superlattices are extremely uniform in size, about 5 nm in radius, and the lattice parameter of the simple cubic superlattice lies in the range of 15-20 nm. Three void lattice growth/ordering modes have been identified by the <italic>in-situ</italic> TEM observation. A series of experiments indicates that higher total electron fluence is required at the low temperature for superlattice formation, and the faceted voids forms at the higher temperature with the periodicity starting to disappear at 100&deg;C or higher. Advanced analytical TEM techniques provide solid evidences that these defects are real voids, instead of previously considered Ca colloids. A self-organized ripple pattern is also created on the surface of CaF₂ by ion irradiation and characterized using AFM and TEM. The wavelength of the ripple pattern is found to be much larger than the lattice parameter of the void superlattice. The mechanisms responsible for the formation of void superlattice have been discussed. Anisotropic defects diffusion and elastic interactions between voids may explain the self-ordering process. <italic>ab initio</italic> total energy calculations has been used to determine that the absorption at octahedral sites of displaced F or Ca atoms gives the lowest energy in the irradiated material. The octahedral sites in the crystal are stable sites for Ca interstitial atoms and the interaction between Ca interstitial and CaF₂ molecule is strong. Molecular dynamics simulations have been performed to evaluate the Frenkel pair formation energy. Displacement energy and vacancy migration energy along various directions are calculated for both Ca and F, respectively. The anion vacancies have been found to move easily along <100> directions while the cation vacancy has the lowest migration energy along the <110> directions.