Grain-size dependence of thermal properties of nanocrystalline elemental selenium studied by x-ray diffraction

Quantitative x-ray-diffraction measurements in a temperature range 88--325 K were performed on porosity-free nanocrystalline (nc) elemental Se samples with a hcp structure. The nc-Se samples with different grain sizes were synthesized by crystallizing a melt-quenched amorphous-Se solid. Thermal-expansion coefficients (TECs) for the nc-Se samples were determined according to the temperature dependence of the lattice parameters (a and c) and the unit-cell volume $(V).$ It was found that at higher temperatures the lattice expands along a axis but contracts along c axis. With a reduction of grain size, the linear TECs (both along a axis and c axis) increase significantly, resulting in an evident increase in the volume TEC that follows the D^-1 rule. The temperature dependence of the mean Debye-Waller parameter (DWP) was measured, from which the static and thermal components of the DWP, as well as the Debye characteristic temperature for the nc-Se samples were obtained. The observed enhancement in the mean DWP can be attributed mainly to the increase of static atomic displacement with a reduction of grain size that follows the D^-1 rule. The characteristic temperature for the nc-Se specimens was found to decrease significantly with a refinement of grains. These results suggest larger displacements of the atoms from their ideal lattice locations and more defects in the nc-Se samples with smaller grains.