Next, we must consider the lattice registry of the layer blocks inserted into alumina and spinel to form interstitial dislocation loops along 3. Registry refers to the relative translational displacements between successive layers in a stack. In alumina, O anion layers are fully dense triangular atom nets, stacked in an hcp, BCBCBC… geometry. B and C represent two distinct layer registries (displaced lat­erally with respect to one another). All the Al cation layers occur within the same registry, labeled a in Table 1 (a is displaced laterally relative to B and C). These Al layers are 2/3 dense, relative to the fully dense O layers, forming honeycomb atomic patterns. The successive Al layers are differentiated by where the cation ‘vacancies’ occur within each a layer. There are three possibilities that occur sequentially, hence the subscripted labels in Table 1 (a1, a2, a3).11 Thus, the registry of cation/anion stacking in alumina follows the sequence: a1 B a2 C a3 B a1 C a2 B a3 C.

When extra pairs of Al and O layers are inserted into the stacking sequence, a1 Ba2 C a3 Ba1 C a2 B a3 C, a mistake in the stacking sequence is introduced. In other words, the dislocation loop formed by the block insertion is faulted (contains a stacking fault). Let us see how this works by inserting a 1/3 [0001] four-layer block, Al2-O3-Al2-O3, into the stacking sequence described above. We obtain:

a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a3 B

a1 C a2 B a3 C (before) a1 B a2 C a3 B a1 C a2 B a3 C a1 B a2 C a1 B

a2 C a3 B a1 C a2 B a3 C (after)

a1 a2 a3 a1 a2 a3 a1 a2 a1 a2 a3 a1 a2 a3

(after, showing only cations and showing stacking fault position) [2]

Notice in eqn [2] that after block insertion, the anion sublattice is not faulted (BCBC… layer stacking is preserved), whereas the cation sublattice is faulted, specifically at the position of the red vertical line in the last sequence. Kronberg13 refers to this as an unsymmetrical electrostatic fault. This fault is seen to be intrinsic and only in the cation sublattice; the anion sublattice is undisturbed. In summary, the dis­location loop formed by 1/3 [0001] block insertion in alumina is an intrinsic, cation-faulted, interstitial Frank loop. This is also a sessile loop.