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

Abstract

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 CsPbCl 3 and the γ-phase of Ag 3SI and Ag 3SBr by assuming them to be ideal perovskite (P)-type structures. Three central force constants, α 1, α 2 and α 3, and three angular force constants, α 1′, α 2′ and α 3′, 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 α 3 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 ( ν 1) mode is assigned to be different from that for other perovskites. It reasonably interprets the higher values of ν 2 and ν 3 for CsPbCl 3 than those of Ag 3SX (X=Br,I) and also the lower value of ν 1 for CsPbCl 3. Based on these results, the complete phonon dispersion curve is calculated.