= Solution
The nickel-rich $\gamma$ matrix is a disordered substitutional <solid solution> on a <face-centered cubic lattice>. The ordered $\gamma^{\prime}$ phase has the <L12 structure>, approximately $\mathrm{Ni_3Al}$: <aluminium> occupies <cube> corners and <nickel> occupies face centres. Its occupied-site geometry is often called ordered FCC, but \b[its chemically labelled <Bravais lattice> is primitive cubic], with a four-atom basis. A face-centre <translation> exchanges chemical sublattices and is not a symmetry of the ordered crystal.
Each Al atom has twelve nearest-neighbour Ni atoms at <Euclidean distance> $a/\sqrt2$. Each Ni atom has twelve nearest neighbours too, but these are \b[four Al and eight Ni]. The chemical distinction matters for slip. In disordered $\gamma$, the shortest perfect <Burgers vector> is
$$
\boxed{\mathbf b_\gamma=\frac a2\langle110\rangle,\qquad |\mathbf b_\gamma|=a/\sqrt2.}
$$
For the ordered primitive cubic <translation> lattice, the shortest order-preserving perfect vector is
$$
\boxed{\mathbf b_{\gamma^{\prime},\min}=a\langle100\rangle,\qquad |\mathbf b|=a.}
$$
This does not imply that $\langle100\rangle$ slip must dominate. A vector must lie in a favourable glide plane and have an accessible core structure and activation <stress>. Matrix <dislocations> commonly glide on $\{111\}\langle110\rangle$ systems. A single $a\langle110\rangle/2$ passage through $\gamma^{\prime}$ leaves an <antiphase boundary>; a second matching passage restores order, giving total vector $a\langle110\rangle$. Such a <superdislocation> has a longer total vector than $a\langle100\rangle$, yet its constituent <dislocations> can move on the favourable close-packed planes and interact with the matrix. Paired motion balances line and antiphase-boundary energies, so the shortest abstract lattice <translation> alone does not select the active <slip system>.<Nickel based superalloy: dislocation structure by H. K. D. H. Bhadeshia>[explanation of matrix translations, ordered-phase antiphase boundaries and paired dislocations]{ref}
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