Scaling of superionic transition temperature in M3D(XO4)2

In order to clarify the role of superionic phase transition temperature in M3D(XO4)2, we have investigated the relation between a phase transition temperature TcD and a lattice strain a0. It was found that the square of a0 is proportional to TcD. This result indicates that the lattice strain is significantly important to determine the appearance of superionic conductivity. Furthermore, it was also found that the minimum kinetic energy ΔK in deuterated materials is smaller than that in hydrated materials. Considering that ΔK means the breaking energy of hydrogen bond, it is deduced that the lowering of the phase transition temperature in deuterated materials is caused by the decrease of ΔK which corresponds to the breaking energy of hydrogen bond.