Determination of thermal-motion parameters using energy-dispersive powder diffraction

An intrinsic Ge detector is used to analyze the energy spectrum of a well collimated X-ray beam of white radiation diffracted from powder samples of Al, Mg and Ti. Two spectra on each sample are measured at scattering angles where reflections hkl and 2h_' 2k_' 2l occur at the same energies. The Bragg reflections are separated by fitting a model for the different components of scattering to the total spectrum. The thermal-motion parameter B is determined from the intensity ratio of several pairs of reflections. Most of the uncertainties due to a non-ideal sample or errors in the experimental parameters cancel out in the expression for B. The values of B are 0.86 (2) Å² for Al, B_a = 1.29 (8) Å² and B_c = 1.60 (9) Å² for Mg and B_a = 0.63 (4) Å² and B_c = 0.73 (7) Å² for Ti, where B_a is for directions perpendicular to the c axis and B_c for the direction of the c axis. The results are in agreement with published values of the thermal-motion parameters.