The Spinel (Al2 Mg O4) Structure
Last modified 19 July 2001
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In an inverse spinel, four of the Al atoms would be on the (8a) sites, and four Al and four Mg atoms would sit on the (16d) sites, presumably in a random fashion.
Note that we place the origin between the 2 Mg atoms. Pearson
places the origin on one of the Mg atoms. Thus Pearson's Oxygen
parameter x = 0.361 is transformed to our x parameter of 0.236
(=.361-1/8).
| B1 | = | - 1/8 A1 - 1/8 A2 - 1/8 A3 | = | - 1/8 a X - 1/8 a Y - 1/8 a Z | (Mg) | (8a) |
| B2 | = | + 1/8 A1 + 1/8 A2 + 1/8 A3 | = | + 1/8 a X + 1/8 a Y + 1/8 a Z | (Mg) | (8a) |
| B3 | = | + ½ A1 + ½ A2 + ½ A3 | = | + ½ a X + ½ a Y + ½ a Z | (Al) | (16d) |
| B4 | = | + ½ A2 + ½ A3 | = | + ½ a X + ¼ a Y + ¼ a Z | (Al) | (16d) |
| B5 | = | + ½ A1 + ½ A3 | = | + ¼ a X + ½ a Y + ¼ a Z | (Al) | (16d) |
| B6 | = | + ½ A1 + ½ A2 | = | + ¼ a X + ¼ a Y + ½ a Z | (Al) | (16d) |
| B7 | = | + x A1 + x A2 + x A3 | = | + x a X + x a Y + x a Z | (O) | (32e) |
| B8 | = | + (½ - 3 x) A1 + x A2 + x A3 | = | + x a X + (¼ - x) a Y + (¼ - x) a Z | (O) | (32e) |
| B9 | = | + x A1 + (½ - 3 x) A2 + x A3 | = | + (¼ - x) a X + x a Y + (¼ - x) a Z | (O) | (32e) |
| B10 | = | + x A1 + x A2 + (½ - 3 x) A3 | = | + (¼ - x) a X + (¼ - x) a Y + x a Z | (O) | (32e) |
| B11 | = | - x A1 - x A2 - x A3 | = | - x a X - x a Y - x a Z | (O) | (32e) |
| B12 | = | - (½ - 3 x) A1 - x A2 - x A3 | = | - x a X - (¼ - x) a Y - (¼ - x) a Z | (O) | (32e) |
| B13 | = | - x A1 - (½ - 3 x) A2 - x A3 | = | - (¼ - x) a X - x a Y - (¼ - x) a Z | (O) | (32e) |
| B14 | = | - x A1 - x A2 - (½ - 3 x) A3 | = | - (¼ - x) a X - (¼ - x) a Y - x a Z | (O) | (32e) |
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