A conduction plane in the crystal lattice structure of β-alumina (Na2nAl2O3, see A misnomer in chemistry and materials science) separates two blocks of close packed layers of O2− ions. A block consists of a stack of four layers of O2− ions. Inside a block a selection of tetrahedral and octahedral interstices between pairs of adjacent layers are occupied by Al3+ ions. In the conduction layer three-quarters of the O2− are missing, leaving room for Na+ ions to reside and move.

β-alumina exists over a range of compositions. It is a two-dimensional solid electrolyte, in which conduction occurs via Na+ ions migrating within the conduction layer, but not across the insulating, spinel-structured blocks.

The following drawing shows the conduction plane in perpendicular view. The close packed block layer of O2− ions (light pink) represents the top layer of the block underneath the conduction layer. In β-alumina, this layer is superimposed by the close packed layer on top of the conduction layer. The layer sequence is ABA: The two A layers sandwich the conduction layer B, of which only a quarter of the sites are occupied by O2− ions (dark pink).

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Three types of locations are typically distinguished in the conduction layer: m, the mid-oxygen site (vacant O2− site); br, the Beevers Ross site; and abr, the anti-Beevers-Ross site. The abr sites, located between two O2− ions of opposite close layers, are much smaller than the br and m sites. Crystallographic data suggests that the Na+ ions are most likely to be found on br and m sites. But they must pass abr sites during migration and excess Na+ ions may stay in stable abr configurations.

Details of site occupation and ion movement depend on the stoichiometry of a particular β-alumina material and polymorphs thereof. For example, the modification β′′-alumina exhibits a non-symmetric stacking geometry at the conduction plane, and therefore the site geometry and coordination patterns deviate from those found in the β-modification. Variation in stoichiometry and ion substitution (doping) can lead to an even more complex mechanism of ion conduction.

References, Notes and Links

[1] Anthony R. West: Solid State Chemistry And Its Applications, John Wiley & Sons, Chichester, 1984.
The section entitled β-Alumina (pages 467 to 474) provides an excellent introduction to structure and properties of β- and β′′-alumina. Text and drawing of this webpage are based on that section and on selected research articles referenced below. Notice that in the literature, instead of m, br, and abr (used herein), the notations mO, BR and a-BR are used to represent a mid-oxygen, Beevers Ross and anti-Beevers-Ross site, respectively.
[2] J. R. Walker and C. R. A. Catlow: Structure and transport in non-stoichiometric β Al2O3. J. Phys. C: Solid State Phys., 1982, 15 ( 30), 6151. doi: 10.1088/0022-3719/15/30/009.
[3] P. Boolchand, K. C. Mishra, M. Raukas, A. Ellens and P. C. Schmidt: Occupancy and site distribution of europium in barium magnesium aluminate by 151Eu Mössbauer spectroscopy. Phys. Rev. B, 2002, 66, 134429. doi: 10.1103/PhysRevB.66.134429, pdf: http://secs.ceas.uc.edu/~pboolcha/papers/2002/PRB_02_66_134429.pdf.
FIG. 1 therein shows the three-dimensional crystal structure of BaMgAl10O17, depicting blocks and conduction layers with mO, BR and a-BR sites for this compound with β-alumina structure.
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