Abstract
This theory shows that, as the ratio of the grain sizes increases, the boundary between the grains becomes more highly curved and the smaller grain becomes more deeply embedded in the larger one. At a ratio of only 1.57, the exposed portion of the small grain is too small to allow it to bond to a third, larger grain, and it cannot effectively connect to a chain of grains. For equal grains the theory reduces to the earlier theory but, as the size ratio increases, the stress gradient in the grain boundary decreases and the grain boundary becomes more tightly curved. These two factors decrease the rate of bonding, which decreases as either the ratio of the sizes, or their absolute sizes, increase.
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