FIRST PRINCIPLES ELECTRONIC STRUCTURE CALCULATIONS OF BaF2 AND GENERATION OF PARAMETRIZED POTENTIAL FOR MOLECULAR DYNAMICS STUDY OF THE SUPERIONIC PROPERTIES OF c-BaF2
The electronic structure and defects of barium ﬂuoride, BaF2, have been studied using the denstiy functional theory, DFT and density functional perturbation theory, DFPT. Lattice parameter of 6.10 Å was calculated comparable to experimental value of 6.20 Å for the cubic phase. Orthorhombic and hexagonal phases also give values close to experimental. Band gap of 7.20 eV in this work appears closer to experimental value of 10 eV in comparison to other theoretical results. Phonons and phononic properties have also been investigated and are discussed in this work. Elastic contants of cubic, orthorhombic and hexagonal phases of BaF2 are calculated and discussed and do show good comparison with both experiment and other calculations. Stability parameters are also presented for all the three phases. Calculations using ab initio methods to ﬁnd the defect formation energy and vacancy migration energies in barium ﬂouride have been done for both anion and cation. Interstitial and Frenkel defects have also been studied and their eﬀect on the band gap width analyzed. Migration of an anion and cation was found to show good agreement with experimental data and migration paths were also considered. Anion migration energy is easiest in the VFh100i at 0.53 eV comparable to experimental value of 0.59 eV. Migration energies for anion in the other low index directions VFh110i and VFh111i were calculated as 1.17 eV and 1.15 eV, respectively. The migration energy was highest at 2.22 eV for the cation in the VBah100i direction, while the other paths were found to be unfavourable for the cation. It was found that the interstitial formation energies for cation and anion were 3.14 eV and -0.62 eV, respectively. Vacancy formation energies were 15.64 eV and 8.73 eV for the anion and cation, respectively. This is slightly higher than 8.34 eV for anion and 13.75 eV for cation in CaF2. Frenkel defect energies were also determined at near and inﬁnite distances and were found to be 8.11 eV and 18.78 eV for the anion and cation, respectively. Potential parametrization was also considered in this study and it was found to improve the previously used pair potentials in the molecular dynamics study of BaF2. Molecular dynamics and thermodynamics properties were investigated using a classical inter-atomic force ﬁeld parametrized using the forces, stresses and energies obtained from the ab initio calculations. Using the parametrized potentials developed in this study, the superionic properties of cubic BaF2 were studied through the phase transition diagram (energy versus temperature), where it was found out that the superionic transition of BaF2 occured at about 1000 K, while melting temperature was established at about 1700 K. This shows a great improvement which this new potential brings into the understanding of the superionic properties of BaF2 over previous works. Radial distribution functions and mean square displacements of cations with BaF2 have also been studied where it was established that at around 800 K, both cation and anion are still at their mean positions, whereas at 1000 K, the anion (F−) starts diﬀusing. The anion on the other hand was found to move from its mean position at about 1700 K conﬁrming this as the melting temperature of c-BaF2. Diﬀusion constant was found to be in the range of 4.55× 10−5 cm2/s at around 500 K to 1.52× 10−4 cm2/s at 1000 K which is typical of superionic conductivity.