Now, we consider the formation of an interstitial dislocation loop along 3 in spinel. In spinel, O anion layers are fully dense triangular atom nets stacked in a ccp, ABCABC… geometry (A, B, and C are all distinct layer registries). Between adjacent O layers, 3/4 dense Al and MgAlMg layers are inserted, with regis­tries labeled a, b, and c in Table 1 (a cations have the same registry as A anions; likewise, b same as B, c same as C). For stacking fault layer stacking assessments in spinel, it is conventional to simplify the layer notation for the cations (see, e. g., Clinard et al6). The successive kagome Al layers are labeled a, p, g, while the MgAlMg mixed atom slabs are each pro­jected onto one layer and labeled a0, p0, g0. With these definitions, the registry of cation/anion stacking in spinel follows the sequence: a C p0 A g B a0 C p A g0 B.

As with alumina, when extra pairs of cation and anion layers are inserted into the spinel 3 stacking sequence, a C p0 A g B a0 C p A g0 B, a fault in the stacking sequence is introduced. One can demon­strate how this works by inserting a 1/6 (111) p A block into the stacking sequence described above (this is equivalent to the upper Burgers vector for spinel shown in Table 1, which uses a kagome Al cation layer). We obtain:

a C p0 A g B a0 C p A g0 B a C p0 A g B a0 C p A g0 B (before) a C p0 A g B a0 C p A g0 B p A a C p0 A g B a0 C p A g0 B (after) a C p0 A g B a0 C p A g0 B p A a C p0 A g B a0 C p A g0 B (after, showing stacking fault positions) [3]

Notice in eqn [3] that after block insertion, both the anion sublattice (CABCAB… stacking is not preserved) and the cation sublattice are faulted. Also, notice that the cation and anion stacking sequences are faulted on both sides of the inserted p A block (the layer sequences are broken approach­ing the block from both the left and the right). Thus, the p A block actually contains two stacking faults, on either side of the block. The positions of these stack­ing faults are denoted by vertical red lines in eqn [3]. The dislocation loop formed by 1/6 (111) block insertion in spinel is an extrinsic, cation+anion faulted, sessile interstitial Frank loop.

We can also consider inserting a 1/6 (111) p’ A block into the spinel stacking sequence (i. e., the lower spinel Burgers vector shown in Table 1, which uses a mixed MgAlMg cation slab). We obtain:

a C p’ A g B a’ C p A g’ B a C p’ A g B a’ C p A g’ B (before)

a C p’ A g B a’ C p A g’ B p’ A a C p’ A g B a’ C p A g’ B (after) a C p’ A g B a’ C p A g’ B | p’ A | a C p’ A g B a’ C p A g’ B (after, showing stacking fault positions) [4]

Once again, both the anion and cation sublattices are faulted, and we obtain an extrinsic, cation+anion faulted, sessile interstitial Frank loop.