Temperature Diffuse Scattering of X-Rays in Cubic Powders. I. Comparison of Theory with Experiment

Abstract

Temperature diffuse scattering of x-rays (TDS) has been examined in cubic powders to test the reliability of current TDS theory. Measurements are reported of the diffuse scattering of copper and lead along with the Bragg reflections of these metals at room and liquid nitrogen temperatures. These measurements were made using a scintillation counter diffractometer and crystal monochromated CuKα radiation. The TDS so otained is compared with TDS calculations based on the one- and two-phonon calculation as well as on the Warren (modified one-phonon) calculation. Both formulas are found to fit the magnitude of TDS by choosing appropriate Debye characteristic temperatures. The Debye Θ's which fit the copper and lead TDS data at room temperature are: 324° and 96° (one- and two-phonon) and 269° and 64° (Warren formula) as compared to values of 307° and 79° taken from the temperature dependence of the Bragg reflections and 315° and 88° from specific heat values for copper and lead, respectively. Evidence is also found for extra diffuse scattering in the low-angle region. This extra scattering is tentatively ascribed to a multiple scattering process.