Measurement of surface tension by lattice parameter changes : theory for facetted microcrystals

A number of workers have estimated surface tensions of solids from measurements of the differences in the lattice parameters of bulk crystals and microcrystals. The data are then analysed by an expression valid only for spherical. isotropic microcrystals. Real microcrystals are usually facetted, resulting in a number of possible problems which are discussed here. The main results given are : (i) A general expression for the change in volume of a microcrystal for an arbitrarily anisotropic surface tension and arbitrary crystal habit; common special cases are also given; and (ii) a discussion of the relation between the volume change and the change in x-ray lattice parameter. This includes the effects of the dispersions in crystalline sizes and shapes. and the possible non-uniformity in internal strain produced. The main conclusion is that errors are likely to be modest, almost certainly less than a few tens of percent.