Relationship between microstrain and lattice parameter change in nanocrystalline materials

A lattice distortion, represented by microstrain and lattice parameter change, is frequently observed in nanocrystalline (NC) materials. In this letter, we develop a quantitative model to account for this phenomenon. The internal stress induced by the excess volume at grain boundaries is suggested to be the main reason for the lattice distortion. NC materials, prepared by the milling and crystallization method, were used for analysis and comparison. Theoretical calculation shows a reasonable agreement with experimental observations in the grain-size range from 5 to 100 nm. Our results indicate that there is an inherent relationship between microstrain and lattice parameter change in NC materials.