Crystal Lattice Structures:	Creation Date:  2 Jun 2006
	Last Modified:  2 Jun 2006

The Cr₂₃C₆ (D8₄) 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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• Note that the pictures are drawn with different species of atoms for each of the Wyckoff positions [(4a), (8c), (32f), (48h)] occupied by the Cr atoms in the prototype material.

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• Prototype: Cr₂₃C₆
• Pearson Symbol: cF116
• Strukturbericht Designation: D8₄
• Space Group: Fm(-3)m (Cartesian and lattice coordinate listings available)
• Number: 225
• Reference: Villars and Calvert, Pearson's Handbook, Vol. II, p. 1873
• Other compounds with this Structure: The general structure of this compound is M₂₃X₆, where M = Fe, Cr, Ni, Mn, V, W ... , or combinations thereof, and X = C or B.
• 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	=	0			(Cr-I)	(4a)
  B2	=	¼ A1 + ¼ A2 + ¼ A3	=	¼ a X + ¼ a Y + ¼ c Z	(Cr-II)	(8c)
  B3	=	¾ A1 + ¾ A2 + ¾ A3	=	¾ a X + ¾ a Y + ¾ c Z	(Cr-II)	(8c)
  B4	=	- xC A1 + xC A2 + xC A3	=	+ xC a X	(C)	(24e)
  B5	=	+ xC A1 - xC A2 - xC A3	=	- xC a X	(C)	(24e)
  B6	=	+ xC A1 - xC A2 + xC A3	=	+ xC a Y	(C)	(24e)
  B7	=	- xC A1 + xC A2 - xC A3	=	- xC a Y	(C)	(24e)
  B8	=	+ xC A1 + xC A2 - xC A3	=	+ xC a Y	(C)	(24e)
  B9	=	- xC A1 - xC A2 + xC A3	=	- xC a Z	(C)	(24e)
  B10	=	+ xIII A1 + xIII A2 + xIII A3	=	+ xIII a X + xIII a Y + xIII a Z	(Cr-III)	(32f)
  B11	=	- xIII A1 - xIII A2 + xIII A3	=	+ xIII a X + xIII a Y - 3 xIII a Z	(Cr-III)	(32f)
  B12	=	- xIII A1 + xIII A2 - xIII A3	=	+ xIII a X - 3 xIII a Y + xIII a Z	(Cr-III)	(32f)
  B13	=	+ xIII A1 - xIII A2 - xIII A3	=	- 3 xIII a X + xIII a Y + xIII a Z	(Cr-III)	(32f)
  B14	=	- xIII A1 - xIII A2 - xIII A3	=	- xIII a X - xIII a Y - xIII a Z	(Cr-III)	(32f)
  B15	=	+ xIII A1 + xIII A2 - xIII A3	=	- xIII a X - xIII a Y + 3 xIII a Z	(Cr-III)	(32f)
  B16	=	+ xIII A1 - xIII A2 + xIII A3	=	- xIII a X + 3 xIII a Y - xIII a Z	(Cr-III)	(32f)
  B17	=	- xIII A1 + xIII A2 + xIII A3	=	+ 3 xIII a X - xIII a Y - xIII a Z	(Cr-III)	(32f)
  B18	=	+ 2 yIV A1	=	+ yIV a Y + yIV a Z	(Cr-IV)	(48h)
  B19	=	+ 2 yIV A2	=	+ yIV a X + yIV a Z	(Cr-IV)	(48h)
  B20	=	+ 2 yIV A3	=	+ yIV a X + yIV a Y	(Cr-IV)	(48h)
  B21	=	- 2 yIV A1	=	- yIV a Y - yIV a Z	(Cr-IV)	(48h)
  B22	=	- 2 yIV A2	=	- yIV a X - yIV a Z	(Cr-IV)	(48h)
  B23	=	- 2 yIV A3	=	- yIV a X - yIV a Y	(Cr-IV)	(48h)
  B24	=	- 2 yIV A2 + 2 yIV A3	=	+ yIV a Y - yIV a Z	(Cr-IV)	(48h)
  B25	=	+ 2 yIV A2 - 2 yIV A3	=	- yIV a Y + yIV a Z	(Cr-IV)	(48h)
  B26	=	- 2 yIV A1 + 2 yIV A3	=	+ yIV a X - yIV a Z	(Cr-IV)	(48h)
  B27	=	+ 2 yIV A1 - 2 yIV A3	=	- yIV a X + yIV a Z	(Cr-IV)	(48h)
  B28	=	- 2 yIV A1 + 2 yIV A2	=	+ yIV a X - yIV a Y	(Cr-IV)	(48h)
  B29	=	+ 2 yIV A1 - 2 yIV A2	=	- yIV a X + yIV a Y	(Cr-IV)	(48h)

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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).