The thermal equilibrium shape and size of holes in solids

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Abstract
The generalized equations of state governing the attainment of equilibrium have been formulated for bubbles (holes containing gas under pressure) and for voids (holes containing no gas). The equilibrium shape of bubbles is shown to be that which produces the minimum surface energy (γ) for a specific volume, and is uniquely defined by the polar plot of surface energy with orientation (the γ plot). Examination of bubbles using the electron microscope has shown that their equilibrium shape is polyhedral, with faces formed from low index crystallographic planes. Measurements on such bubbles which should have relatively clean internal surfaces have provided information on the orientation dependence of surface energy: CU(600°c, γ100/γ110= 1·2, Al(550°c),γ100/γ110= 0·98;γ100/γ111= 1·13, MO(2000°c),γ100/γ110= 1·14. The equilibrium shape of bubbles in grain boundaries is discussed and shown to be dependent on the grain boundary energy. Holes not in complete equilibrium have been considered, and in this case their shape can range from polyhedral to spherical, depending on the nature of the elastic stress field which surrounds them, and some examples are shown.

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