Exchange Charge Model for $Fe^{3+}:LiAl_{5}O_{8}$

The aim of this paper is the theoretical investigation of $Fe^{3+}$ doped in the ordered phase of $LiAl_{5}O_8$. We used the shell model and pair potential approximation to optimize the geometric structure of $LiAl_{5}O_{8}$. This approach enables the modeling of the crystal field parameters of $LiAl_{5}O_8$ and then calculates the energy levels scheme of $Fe^{3+}$ ions doped in tetrahedral sites in the title crystal. Consistent crystal field analysis and the energy level splittings for $LiAl_{5}O_{8}$ doped with $Fe^{3+}$ ions was performed in the frame of the exchange charge model of crystal field. The comparison of the theoretically obtained results for energy levels with the experimental data, yields satisfactory agreement and confirms the validity of the exchange charge model.