Effect of Cation Valence on Thermal Expansion of $MTi_2P_3O_{12}$ $(M=Na, Ca_{0.5}, and \hspace{2mm} La_{0.33})$ Compounds

The thermal expansion behavior of $MTi_2P_3O_{12}$ compounds with $M = Na^+, Cd_{0.5}^{2+}, and La_{0.33}^{3+}$ has been studied by high temperature X-ray diffraction. The difference in the anisotropic axial thermal expansion coefficients drastically varies for cations with varying charges but with similar sizes. The thermal expansion in this family of compounds seems to be essentially due to $M-O$ bond expansion. A new compound $La_{0.33}Ti_2P_3O_{12}$ with hexagonal structure $(a = 8.295$\AA and $c = 22.426$\AA) is reported