Determination of bond lengths from extended x-ray absorption fine structure using the linear phase functions

The extended x-ray absorption fine-structure (EXAFS) spectra of many elements and compounds have been analyzed to determine their phase functions as a function of the zero of kinetic energy, $E_0$, of the excited electron and the weighting power of the wave vector used in the Fourier transforms. It is found that a linear phase function exists for any material at some particular value of $E_0=E_c$. The procedure for determining this $E_c$ value is described. A linear-phase-function method of determining bond lengths is proposed and compared to other existing methods of EXAFS bond-length determinations. The many advantages of using these linear phase functions in EXAFS analysis are discussed. With the use of the linear phase functions with a linear extrapolation of their parameters, it is demonstrated that it is possible to verify the existence of a more general form of phase transferability which relates the phase functions of different atom pairs. Such relations allow the number of phase functions needed to characterize a system of $N$ atoms to be reduced from $N^2$ to $2N-1$. This type of comparison is not feasible with the usual nonlinear phase functions.