The Mean-Square Relative Displacement and Displacement Correlation Functions in Tetrahedrally and Octahedrally Coordinated ANB8-N Crystals

Abstract

The Debye-Waller factors of atoms in Ge, GaN, ZnO, CdS, CdSe, CuBr, CuCl, AgI, CdO, AgBr, KBr and RbCl in order of Phillips ionicity (f i) are studied by both EXAFS and the diffraction method. The displacement correlation functions (DCF) are derived from the mean-square relative displacement (MSRD) and the mean-square displacement (MSD) at room temperature. The magnitudes of the MSRD and MSD correlate well with the coordination number and ionicity. The MSRDs of tetrahedrally coordinated compounds show a gradual approach to those of octahedrally coordinated ones as the ionicity increases. A divergent-like curve toward f i=0.785 is observed for the MSD in the tetrahedrally coordinated compounds, which indicates the behavior of lattice instability. In the tetrahedrally coordinated covalent materials, the MSRD is nearly half the MSD cation or MSD anion and the ratio of the DCF to MSD given by 2DCF/(MSD cation+MSD anion) is about 80%. In the octahedrally coordinated ionic materials, the MSRD is comparable to the MSD and 2DCF/(MSD cation+MSD anion)=50%. An anharmonic contribution to the Debye-Waller factor determined by EXAFS appears pronouncedly when the magnitude of σ(2) is greater than 0.01 Å2. The MSRD for the tetrahedrally coordinated compounds of silver and copper halides obeys the systematic ionicity dependence and pronounced specificity of anharmonicity was not observed: AgI, CuBr and CuCl of which the high-temperature forms are typical superionic conductors have a broad interatomic potential which is similar to that of the octahedrally coordinated compounds and strongly correlated displacement in thermal vibration between cation and anion.