The Debye temperature of nanocrystalline β–Sn measured by x-ray diffraction

A nanocrystalline β–Sn film of 7 nm average grain size was prepared by inert gas condensation followed by ballistic consolidation, and was investigated by x-ray diffractometry at temperatures of 77 and 293 K. Although Sn normally undergoes a βα phase transformation at 286 K, this transformation was suppressed in the nanocrystalline film. Compared with large-grained β-Sn, a larger Debye–Waller factor and a lower Debye temperature were measured for nanocrystalline β-Sn; Θ_D = 133 K for nanocrystalline material while Θ_D = 161 K for large-grained material. The lower Debye temperature of the nanocrystalline β-Sn indicates that its vibrational entropy is increased by 0.6 k_B/atom with respect to large-grained material.