Computer simulation study of defect formation and migration energy in calcium fluoride

A theoretical study of the defect formation (vacancy, interstitial and Frenkel defects) energy, and vacancy migration energy in calcium fluoride is presented in this paper. Calculations were conducted using the ab initio method with the plane-wave pseudopotential and molecular-dynamics simulation to determine the energetic and defect properties of the CaF2 crystal. For cation and anion vacancies, the relaxed vacancy formation energies were calculated to be 13.75 and 8.34 eV, respectively. It was also found that only the octahedral positions are stable sites for Ca and F interstitial atoms. For cation the second nearest neighbor Frenkel defects were found to be stable within the simulation time (5ps) and the defect formation energy was estimated to be 9.3 eV, while the third nearest neighbor Frenkel defects for anion were stable and the formation energy was only 2.49 eV. The results are in agreement with Ure’s experimental results. The migration energy of cation vacancy in the direction of 〈1 1 0〉 is lower than that of 〈1 0 0〉 (3.93 eV versus 4.62 eV), suggesting 〈1 1 0〉 is the most likely path for Ca vacancies to migrate, while most anion vacancies may diffuse in the 〈1 0 0〉 directions due to a very low (0.33 eV) anion migration energy in the direction. The data are useful for better understanding the formation of nano-scale void superlattice in calcium fluoride under electron beam irradiation.