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

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Abstract
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. The author discusses problems arising from the fact that real microcrystals are generally faceted. A general expression is given for the change in volume of a microcrystal for an arbitrarily anisotropic surface tension and arbitrary crystal habit; common special cases are also given. The discussion of the relation between the volume change and the change in X-ray lattice parameter includes the effects of the dispersions in crystalline sizes and shapes, and the possible non-uniformity in internal strain produced. It is concluded that any errors will be small.

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