In addition to spinel and alumina layer stacking sequences, Table 1 also shows the layer ‘blocks’ that have been found to comprise {111} and (0001) inter­stitial dislocation loops in spinel and alumina, respec­tively. An interstitial loop in spinel is composed of four layers such that the magnitude of the Burgers vector, b, along (111) is 1/6 (111). The composition of each of these blocks has stoichiometry M3O4, where M represents a cation (either Mg or Al) and O is an oxygen anion. The upper 1/6 (111) block in Table 1 has an actual composition of Al3O4, while the lower 1/6 (111) block has a composition of Mg2AlO4. If Mg and Al cations assume their formal valences (2+ and 3+, respectively), and O anions are 2—, then the blocks described here are charged: (Al3O4)1+and (Mg2AlO4)1-. This may result in an untenable situation of excess Coulombic energy, as each molecular unit in the block possesses an elec­trostatic charge of 1 esu. It has been proposed that this charge imbalance is overcome by partial inver­sion of the cation layers in the 1/6 (111 ) blocks.12 (Inversion in spinel refers to exchanging Mg and Al lattice positions such that some Mg cations reside on o sites, while a similar number of Al cations move to t sites.) If a random cation distribution is inserted into either the upper or lower 1/6 (111) block shown in Table 1 , then the block becomes charge neutral, that is, (MgAl2O4)x.

Table 1 Layer stacking of {111} planes along (111) in cubic spinel and (0001) planes along [0001] in hexagonal alumina

Layer # Layer height Spinel (MgAi2O4) {111}-layer stacking along (111) direction Alumina (а-АІ20з) (0001)-layer stacking along [0001] direction

Frank loop Burgers vectors

O = oxygen t = tetrahedral interstices o = octahedral interstices Layer registry (ABCABC-type O-stacking) Layer Frank loop composition Burgers vectors O=oxygen t = tetrahedral interstices o = octahedral interstices Layer registry (BCBC-type O-stacking) Layer composition 24 23/24 t C — t — 23 22/24 (11/12) O B O4 O C O3 22 21/24 (7/8) t A Mg1 t — 21 20/24 (5/6) o C AI1 o a3 Al2 20 19/24 t B Mg1 t — 19 18/24 (3/4) O A O4 г O B O3 18 17/24 t C — 1/6<111> t — 17 16/24 (2/3) o B AI3 =4 layers o a2 Al2 16 15/24 (5/8) t A — (Al3O4)1 + t — 15 14/24 (7/12) O C O4 L O C O3 14 13/24 t B Mg1 t — 13 12/24 (1/2) o A Al1 o a1 Al2 12 11/24 t C Mg1 t — 11 10/24 (5/12) O B O4 O B O3 10 9/24 t A — t — 9 8/24 (1/3) o C Al3 o a3 Al2 8 7/24 t B — t — 7 6/24 (1/4) O A O4 r O C O3 6 5/24 t C Mg1 1/6<111> t — 5 4/24 (1/6) o B Al1 =4 layers o a2 Al2 4 3/24 (1/8) t A Mg1 (Mg2AlO4)1- t — 3 2/24 (1/12) O C O4 L O B O3 2 1/24 t B — t — 1 0/24 o A Al3 o a1 Al2 0 -1/24 t C — t —

1/3 [0001] = 4 layers (excluding empty tetrahedral layers) (Al2O3)x

Table 1 indicates that an (0001) interstitial dislo­cation loop in alumina consists of a four-layer block (excluding the empty t layers) such that the magni­tude of the Burgers vector, b, along [0001] is 1/3 [0001]. The composition of each of these blocks is Al2O3, which is charge neutral, that is, (Al2O3)x. Thus, there are no Coulombic charge issues asso­ciated with interstitial dislocation loops along 3 in alumina. These dislocation loops consist simply of a pair of Al layers interleaved with two O layers.