The effect of thermal vibrations on extended x-ray absorption fine structure. I

Abstract

The form of the Debye–Waller factor in EXAFS is discussed in detail, and an expression is obtained for this factor in a general three-atom system of Cs symmetry. The normal modes which contribute to the Debye–Waller factors for each scattering path are dependent on the symmetry of the system. A series of model three-atom systems with C2v symmetry are studied and the Debye–Waller factors as a function of the bridging angle are discussed for each of these systems. The temperature dependence of the Debye-Waller factor for each scattering path is also studied. In a system of C2v symmetry, approximating the double and triple scattering Debye–Waller factors by the second shell single scattering factor is shown to be strictly valid only for a system close to linearity. The error due to this approximation is dependent upon the amplitude of the individual scattering paths and is shown to increase with temperature. When the single scattering contribution is unimportant, there is shown to exist a temperature where the above approximation is exact.