THE DEBYE TEMPERATURE OF NANOCRYSTALLINE BETA-SN MEASURED BY X-RAY-DIFFRACTION

A nanocrystalline beta-Sn film of 7 nm average grain size was prepared by inert gas condensation followed by ballistic consolidation, and wa s investigated by x-ray diffractometry at temperatures of 77 and 293 K . Although Sn normally undergoes a beta --> alpha phase transformation at 286 K, this transformation was suppressed in the nanocrystalline f ilm. Compared with large-grained beta-Sn, a larger Debye-WaIler factor and a lower Debye temperature were measured for nanocrystalline beta- Sn; H-D = 133 K for nanocrystalline material while H-D = 161 K for lar ge-grained material. The lower Debye temperature of the nanocrystallin e beta-Sn indicates that its vibrational entropy is increased by 0.6 k (B)/atom with respect to large-grained material.