Crystal Lattice Structures: Reference Date:  1 Jan 2000 Last Modified: 21 Oct 2004

# Corundum (D51)

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• Although corundum has a rhombohedral primitive unit cell, Pearson's Handbook and other references use the equivalent hexagonal lattice, which contains 3 primitive cells. Since we're more interested in the primitive cell we'll use the rhombohedral structure.
• Pearson's Handbook lists ahcp = 4.758 Å and chcp = 12.99Å. In terms of the lattice below, this translates to a = 3.621Å and b = 0.257 Å, with an angle between the vectors of 55.3o. For the internal parameters, in terms of the hexagonal lattice, xAl(hex) = 0.35228 and xO(hex) = 0.3064. On the rhombohedral lattice this translates to z1 = xAl(hex) = 0.35228 and x1 = ¼ - xO(hex) = -.0564.
• If the angle between the primitive vectors was 60o instead of 55.3o, the primitive vectors would be fcc. This occurs when b = 0, below.

• Prototype: αAl2O3
• Pearson Symbol: hR10
• Strukturbericht Designation: D51
• Space Group: R3c (Cartesian and lattice coordinate listings available)
• Number: 167
• Reference: Villars and Calvert, Pearson's Handbook, Vol. I, pp. 970-1
• Primitive Vectors:  A1 = b X + a Y + a Z A2 = a X + b Y + a Z A3 = a X + a Y + b Z
• Basis Vectors:  B1 = + z1 (A1 + A2 + A3) = + z1 (2a + b) (X + Y + Z) (Al) (4c) B2 = - z1 (A1 + A2 + A3) = - z1 (2a + b) (X + Y + Z) (Al) (4c) B3 = + (½ + z1) (A1 + A2 + A3) = + (½ + z1) (2a + b) (X + Y + Z) (Al) (4c) B4 = - (½ + z1) (A1 + A2 + A3) = - (½ + z1) (2a + b) (X + Y + Z) (Al) (4c) B5 = + x1 A1 + (½ -x1) A2 + ¼ A3 = + [(¾ - x1) a + x1 b] X + [(¼ + x1) a + (½ - x1) b] Y + [½ a + ¼ b] Z (O) (6e) B6 = - x1 A1 - (½ -x1) A2 - ¼ A3 = - [(¾ - x1) a + x1 b] X - [(¼ + x1) a + (½ - x1) b] Y - [½ a + ¼ b] Z (O) (6e) B7 = + (½ -x1) A1 + ¼ A2 + x1 A3 = + [(¼ + x1) a + (½ - x1) b] X + [½ a + ¼ b] Y + [(¾ - x1) a + x1 b] Z (O) (6e) B8 = - (½ -x1) A1 - ¼ A2 - x1 A3 = - [(¼ + x1) a + (½ - x1) b] X - [½ a + ¼ b] Y - [(¾ - x1) a + x1 b] Z (O) (6e) B9 = + ¼ A1 + x1 A2 + (½ -x1) A3 = + [½ a + ¼ b] X + [(¾ - x1) a + x1 b] Y + [(¼ + x1) a + (½ - x1) b] Z (O) (6e) B10 = - ¼ A1 - x1 A2 - (½ -x1) A3 = - [½ a + ¼ b] X - [(¾ - x1) a + x1 b] Y - [(¼ + x1) a + (½ - x1) b] Z (O) (6e)

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