Porosity-free nanocrystalline (nc) element Se samples with mean grain sizes ranging from 13 to 70 nm were synthesized by crystallizing a melt-quenched amorphous Se solid. Microstructures of the nc-Se (with a hcp structure) samples were characterized by means of quantitative x-ray-diffraction measurements. The Bragg reflection and the background intensities, as well as the reflection shape of the x-ray-diffraction patterns for the nc Se were analyzed according to data fitting of the measurement results. The grain-size dependencies of the microstrain, lattice parameters, unit-cell volume, and the mean Debye-Waller parameter were determined. With a reduction of grain size, the microstrain increases significantly along 〈100〉 direction but decreases along 〈104〉 direction, and exhibits an increasing anisotropic microstrain behavior. The lattice parameter $a$ was found to increase evidently while $c$ decreased slightly with a decreasing grain size, resulting in a significant lattice distortion with a dilated unit-cell volume. It agrees with the observation that the mean Debye-Waller parameter increases with a reduction of grain size, suggesting larger displacements of atoms from their ideal lattice sites in the nc-Se samples with smaller grains. The similarity of the grain-size dependencies of these structural parameters as that of the grain-boundary volume fraction implies that the intrinsic microstructure feature of nc materials is closely related to the crystallite dimension and the amount of grain boundaries.

• Received 4 February 1997

DOI:https://doi.org/10.1103/PhysRevB.56.14322