Crystal Lattice Structures:	Reference Date:  1 Jan 2001
	Last Modified: 21 Oct 2004

The Spinel (Al₂ Mg O₄ - H1₁) Structure

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• see the structure from several perspectives;
• examine the structure with an external viewer; or
• download the coordinates of the atoms in these pictures in XYZ format.
• visualize the structure (Uses the JMOL Applet)

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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).

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• Prototype: Al₂MgO₄ (Spinel)
• Pearson Symbol: cF56
• Strukturbericht Designation: H1₁
• Space Group: Fd3m (Cartesian and lattice coordinate listings available)
• Number: 227
• Reference: Villars and Calvert, Pearson's Handbook, Vol. I, p. 906
• Other Compounds with this Structure: Al₂Se₄Zn, Al₂CrS₄, CaIn₂S₄, Al₂CdS₄, Cr₂Se₄Zr, Mn₂Te₄Zn, many others.
• Primitive Vectors:

  A1	=	½ a Y + ½ a Z
  A2	=	½ a X + ½ a Z
  A3	=	½ a X + ½ a Y

• Basis Vectors:

  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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Structures indexed by: Strukturbericht Symbol Pearson Symbol Space Group Prototype

This is a mirror of an old page created at the Naval Research Laboratory Center for Computational Materials Science The maintained successor is hosted at http://www.aflowlib.org/CrystalDatabase/ and published as M. Mehl et al., Comput. Mater. Sci. 136 (Supp.), S1-S828 (2017).