Fig. 7. Nonhydrostatic stress effect on vacancy migration: anisotropic migration volumes. Suppose you are concerned about diffusion in the [001] direction in a coherently strained thin film on a thick substrate. The change in the dimensions of the sample when a vacancy reaches its saddle point in migration could be very different in the [001] and [100] directions (as drawn, the migration volume in the [001] direction is large and negative; the migration volume in the [100] direction is small). Hence different components of the stress tensor couple differently to the different components of the migration volume. It turns out that the migration volume is actually a tensor, called the "migration strain tensor". Because a vacancy in the diamond cubic lattice jumps along body diagonals (unlike in this cartoon), crystal symmetry dictates that the migration strain tensor have only one independent component and therefore no anisotropy; however, the migration strain tensor for an interstitialcy mechanism has two independent components and therefore can have a significant anisotropy.

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