Mean square amplitudes of vibration and associated Debye temperatures of rhenium, osmium and thallium

The directional mean square amplitudes of vibration, Debye–Waller factors and associated Debye temperatures of hexagonal rhenium, osmium and thallium have been obtained from X-ray integrated intensities. The integrated intensities have been measured with a Philips 3020 powder diffractometer fitted with a proportional counter using filtered CuKα radiation at room temperature and have been corrected for thermal diffuse scattering. Within the limits of experimental errors, the anisotropy observed in these parameters is negligible. The experimental values of directional Debye temperature have been compared with corresponding values obtained from theoretical calculations. Vacancy formation energies of Re, Os and Tl have been estimated using a relation connecting it with the X-ray Debye temperature.