Study of phonons and normal mode analysis of perovskite-type superionic conductors

A de Launey angular force (DAF) model has been used to calculate the phonon frequency at zone centre (ZC) and normal modes in phase I of CsPbCl3 and the γ-phase of Ag3SI and Ag3SBr by assuming them to be ideal perovskite (P)-type structures. Three central force constants, α1, α2 and α3, and three angular force constants, α1′, α2′ and α3′, for Pb–Cl (S–Ag), Cs–Cl (I or Br–Ag) and Cs–Pb (S–I or Br) atoms are employed and determined from the experimental values of transverse infrared (IR) active phonon frequencies at ZC. The α3 value between Cs and Pb is the strongest among all of these compounds. This is reasonable since both kinds of ions compose the cage lattice in the superionic conduction phase. The normal coordinate of the highest frequency (ν1) mode is assigned to be different from that for other perovskites. It reasonably interprets the higher values of ν2 and ν3 for CsPbCl3 than those of Ag3SX (X=Br,I) and also the lower value of ν1 for CsPbCl3. Based on these results, the complete phonon dispersion curve is calculated.