SIZE CHANGES OF LATTICE-PARAMETERS IN SMALL PARTICLES OF HEXAGONAL CRYSTALS

The role of particle size in the change of lattice parameters is theoretically and experimentally studied. A monotonous increase of the lattice parameters a and c with decreasing particle size is established by means of X-ray analysis for a series of fine-dispersed powder samples of quartz obtained by fractionation. It is shown that the effect cannot be explained by impurity or intrinsic defects in the small quartz particles. Analytical expressions are obtained to calculate the size changes of the lattice parameters in crystals with hexagonal syngony and external shape of a hexagonal prism. The expressions derived are based on the size dependence of the internal stress - the intracrystalline pressure stipulated by the interaction of the elements of the crystal charge lattice. Calculations made for the ion charge lattice of quartz evidence the monotonous increase of the lattice parameters with decreasing particle size and agree with the results of the X-ray experiment.