Non-monotonic lattice parameter variation with crystallite size in nanocrystalline solids

An anomalous dependence of the lattice parameter on the crystallite size of nanocrystalline ball-milled powders of metals was observed: lattice contraction followed by lattice expansion with decreasing crystallite size. These data were determined by application of detailed X-ray diffraction measurements. To this end the lattice parameters of the metals investigated – nickel, copper, iron and tungsten – were precisely determined by correcting for influences of stacking faults, in the face-centred cubic metals, as well as by correcting for instrument-related aberrations. The non-monotonic variation of the lattice constant was interpreted as the result of two competing mechanisms: interface-stress-induced contraction vs. expansion as a result of the stress field generated at the crystallite boundary due to the increased excess free volume in the crystallite boundary upon decreasing crystallite size