Absolute Intensities of X Rays Diffracted in Anomalous Transmission through Nearly Perfect Copper Crystals: A Comparison between Theory and Experiment

Abstract

The absolute integrated intensities diffracted in anomalous transmission through nearly perfect crystals of copper were measured for various wavelengths and reflections by means of a double-crystal spectrometer. Great care was taken to mount and support the crystal in such a way as to minimize the effect of elastic strains. The experimental data are compared with those calculated by using: (1) the formulas of the dynamical theory of diffraction, (2) the semiclassical theory of photoelectric absorption to determine the ratio between the dynamical and the average absorption coefficient, and (3) the experimental value of the average absorption coefficient. The agreement between experiment and theory is satisfactory provided that the Debye temperature of Cu is taken equal to about 300\ifmmode^\circ\else\textdegree\fi{}K. This value is in good agreement with that reported from the dependence of anomalous transmission intensities on temperature, but it is somewhat lower than the Debye temperature (315-317\ifmmode^\circ\else\textdegree\fi{}K) deduced from data obtained by neutron inelastic scattering, Bragg x-ray measurements on powders and single crystals, and calculations from specific-heat data. An analysis is made of the various factors which can influence the experimental or calculated intensities, such as lattice defects, thickness measurements, ratio between dynamical and average absorption coefficients, contribution of the thermal diffuse and Compton scatterings to the absorption coefficient of x rays, and the choice of the Debye temperature.