Measurement of the temperature dependence of Debye–Waller factors by energy-dispersive methods: application to NbC0.98

Abstract

A new method is reported for evaluating the temperature dependence of Debye-Waller factors, or equivalently the mean-square atomic displacements (MSD), from X-ray spectroscopic data. By irradiating a properly oriented single crystal with polychromatic radiation, several orders of a given Bragg reflection can be simultaneously excited at a fixed scattering angle. These multi-order peaks can then be recorded in a single measurement with an energy dispersive detector. For experiments requiring only relative intensity data, this method offers a number of improvements over conventional techniques, e.g., (i) a substantial reduction in data acquisition time, (ii) a possible reduction in angular flexibility requirements and (iii) access to regions of reciprocal space which might otherwise be inaccessible. This procedure has been employed to determine the temperature dependence of the mean-square displacements of NbC0.98 over the temperature range from 296 to 600 K. These results are compared with published values computed from a double-shell lattice-dynamical force model; the agreement is found to be satisfactory. The data have also been used to evaluate the thermal expansivity of NbC0.98 over the temperature range of measurement; excellent agreement is found upon comparison with published thermal expansion data.