Extended x-ray-absorption fine-structure study of copper under high pressure

Abstract

We examine copper as a pressure calibrant for extended x-ray-absorption fine-structure (EXAFS) measurements of solids under pressures ranging from 0 to 10 GPa. Great care must be exercised both in the theoretical formulation of EXAFS and in the data analysis in order to achieve the high precision required to make copper a useful pressure marker. From the first-shell k-space data, phase and amplitude information is extracted both with the ratio method and from fitting parameters with the help of theoretically calculated central-atom phase shifts [B.-K. Teo and P. A. Lee, J. Am. Chem. Soc. 101, 2815 (1979)] and curved-wave backscattering phase shifts and amplitudes [A. G. McKale et al., J. Am. Chem. Soc. 110, 3763 (1988)]. Both techniques yield practically identical results confirming the reliability of the phase and amplitude tabulations. But both techniques suffer from the ambiguity that the results depend on how many EXAFS parameters are kept variable. It is shown that, for copper, only nearest-neighbor distances and second cumulants (EXAFS Debye-Waller factors) have to be taken into account. Then pressures can be determined with an accuracy of about 0.5 GPa. We also present two models for the pressure dependence of the second cumulant: (1) a correlated Debye model along with simple parametrizations of the isothermal equation of state and the Gr\"uneisen parameter, and (2) a model for the calculation of the moments of the nearest-neighbor distance distribution from an expansion to third order of the potential energy. Both models confirm our data analysis.