Crystal Lattice Structures:	Creation Date: 25 Aug 2002
	Last Modified: 21 Oct 2004

The Ga₄Ni₃ Structure

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• This is a simple defect superstructure of the Cesium Chloride (B2) structure. The distortions of the (48f) and (48g) sites are minor, since x₁ is about zero and y₂ is about 3/8.
• Given those values of the internal parameters, you can convert this structure into B2 by adding Nickel atoms to the (16b) sites of space group Ia3d.

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• Prototype: Ga₄Ni₃
• Pearson Symbol: cI112
• Space Group: Ia3d (Cartesian and lattice coordinate listings available)
• Number: 230
• Other compounds with this structure: Al₄CoNi₂, Al₄Ni₃, Ga₃Ni₃Zn
• Primitive Vectors:

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

• Basis Vectors:

  B1	=		0		(Ga)	(16a)
  B2	=	½ A2 + ½ A3	=	½ a X	(Ga)	(16a)
  B3	=	½ A1 + ½ A3	=	½ a Y	(Ga)	(16a)
  B4	=	½ A1 + ½ A2	=	½ a Z	(Ga)	(16a)
  B5	=	½ A1	=	- ¼ a X + ¼ a Y + ¼ a Z	(Ga)	(16a)
  B6	=	½ A2	=	+ ¼ a X - ¼ a Y + ¼ a Z	(Ga)	(16a)
  B7	=	½ A3	=	+ ¼ a X + ¼ a Y - ¼ a Z	(Ga)	(16a)
  B8	=	+ ½ A1 + ½ A2 + ½ A3	=	+ ¾ a X + ¾ a Y + ¾ a Z	(Ga)	(16a)
  B9	=	+ ¼ A1 + (¼ + x1) A2 + x1 A3	=	+ x1 a X + ¼ a Z	(Ga)	(48f)
  B10	=	- ¼ A1 + (¼ - x1) A2 + (½ - x1) A3	=	+ (½ - x1) a X - ¼ a Z	(Ga)	(48f)
  B11	=	+ x1 A1 + ¼ A2 + (¼ + x1) A3	=	+ ¼ a X + x1 a Y	(Ga)	(48f)
  B12	=	+ (½ - x1) A1 - ¼ A2 + (¼ - x1) A3	=	- ¼ a X + (½ - x1) a Y	(Ga)	(48f)
  B13	=	+ (¼ + x1) A1 + x1 A2 + ¼ A3	=	+ ¼ a Y + x1 a Z	(Ga)	(48f)
  B14	=	+ (¼ - x1) A1 + (½ - x1) A2 - ¼ A3	=	- ¼ a Y + (½ - x1) a Z	(Ga)	(48f)
  B15	=	+ (¼ + x1) A1 - ¼ A2 + x1 A3	=	- ¼ a X + (¼ + x1) a Y	(Ga)	(48f)
  B16	=	+ (¼ - x1) A1 + ¼ A2 + (½ - x1) A3	=	+ ¼ a X + (¼ - x1) a Y	(Ga)	(48f)
  B17	=	- ¼ A1 + x1 A2 + (¼ + x1) A3	=	+ (¼ + x1) a X - ¼ a Z	(Ga)	(48f)
  B18	=	+ ¼ A1 + (½ - x1) A2 + (¼ - x1) A3	=	+ (¼ - x1) a X + ¼ a Z	(Ga)	(48f)
  B19	=	+ (½ - x1) A1 + (¼ - x1) A2 + ¼ A3	=	+ ¼ a Y + (¼ - x1) a Z	(Ga)	(48f)
  B20	=	+ x1 A1 + (¼ + x1) A2 - ¼ A3	=	- ¼ a Y + (¼ + x1) a Z	(Ga)	(48f)
  B21	=	- ¼ A1 - (¼ + x1) A2 - x1 A3	=	- x1 a X - ¼ a Z	(Ga)	(48f)
  B22	=	+ ¼ A1 - (¼ - x1) A2 - (½ - x1) A3	=	- (½ - x1) a X + ¼ a Z	(Ga)	(48f)
  B23	=	- x1 A1 - ¼ A2 - (¼ + x1) A3	=	- ¼ a X - x1 a Y	(Ga)	(48f)
  B24	=	- (½ - x1) A1 + ¼ A2 - (¼ - x1) A3	=	+ ¼ a X - (½ - x1) a Y	(Ga)	(48f)
  B25	=	- (¼ + x1) A1 - x1 A2 - ¼ A3	=	- ¼ a Y - x1 a Z	(Ga)	(48f)
  B26	=	- (¼ - x1) A1 - (½ - x1) A2 + ¼ A3	=	+ ¼ a Y - (½ - x1) a Z	(Ga)	(48f)
  B27	=	- (¼ + x1) A1 + ¼ A2 - x1 A3	=	+ ¼ a X - (¼ + x1) a Y	(Ga)	(48f)
  B28	=	- (¼ - x1) A1 - ¼ A2 - (½ - x1) A3	=	- ¼ a X - (¼ - x1) a Y	(Ga)	(48f)
  B29	=	+ ¼ A1 - x1 A2 - (¼ + x1) A3	=	- (¼ + x1) a X + ¼ a Z	(Ga)	(48f)
  B30	=	- ¼ A1 - (½ - x1) A2 - (¼ - x1) A3	=	- (¼ - x1) a X - ¼ a Z	(Ga)	(48f)
  B31	=	- (½ - x1) A1 - (¼ - x1) A2 - ¼ A3	=	- ¼ a Y - (¼ - x1) a Z	(Ga)	(48f)
  B32	=	- x1 A1 - (¼ + x1) A2 + ¼ A3	=	+ ¼ a Y - (¼ + x1) a Z	(Ga)	(48f)
  B33	=	+ ¼ A1 + (3/8 - y2) A2 + (1/8 + y2) A3	=	+ 1/8 a X + y2 a Y + (¼ - y2) a Z	(Ni)	(48g)
  B34	=	- (¼ + 2 y2) A1 + (1/8 - y2) A2 + (3/8 - y2) A3	=	+ 3/8 a X - y2 a Y - (¼ + y2) a Z	(Ni)	(48g)
  B35	=	- (¼ - 2 y2) A1 + (1/8 + y2) A2 + (3/8 + y2) A3	=	+ 3/8 a X + y2 a Y - (¼ - y2) a Z	(Ni)	(48g)
  B36	=	+ ¼ A1 + (3/8 + y2) A2 + (1/8 - y2) A3	=	+ 1/8 a X - y2 a Y + (¼ + y2) a Z	(Ni)	(48g)
  B37	=	+ (1/8 + y2) A1 + ¼ A2 + (3/8 - y2) A3	=	+ (¼ - y2) a X + 1/8 a Y + y2 a Z	(Ni)	(48g)
  B38	=	+ (3/8 - y2) A1 - (¼ + 2 y2) A2 + (1/8 - y2) A3	=	- (¼ + y2) a X + 3/8 a Y - y2 a Z	(Ni)	(48g)
  B39	=	+ (3/8 + y2) A1 - (¼ - 2 y2) A2 + (1/8 + y2) A3	=	- (¼ - y2) a X + 3/8 a Y + y2 a Z	(Ni)	(48g)
  B40	=	+ (1/8 - y2) A1 + ¼ A2 + (3/8 + y2) A3	=	+ (¼ + y2) a X + 1/8 a Y - y2 a Z	(Ni)	(48g)
  B41	=	+ (3/8 - y2) A1 + (1/8 + y2) A2 + ¼ A3	=	+ y2 a X + (¼ - y2) a Y + 1/8 a Z	(Ni)	(48g)
  B42	=	+ (1/8 - y2) A1 + (3/8 - y2) A2 - (¼ + 2 y2) A3	=	- y2 a X - (¼ + y2) a Y + 3/8 a Z	(Ni)	(48g)
  B43	=	+ (1/8 + y2) A1 + (3/8 + y2) A2 - (¼ - 2 y2) A3	=	+ y2 a X - (¼ - y2) a Y + 3/8 a Z	(Ni)	(48g)
  B44	=	+ (3/8 + y2) A1 + (1/8 - y2) A2 + ¼ A3	=	- y2 a X + (¼ + y2) a Y + 1/8 a Z	(Ni)	(48g)
  B45	=	- ¼ A1 - (3/8 - y2) A2 - (1/8 + y2) A3	=	- 1/8 a X - y2 a Y - (¼ - y2) a Z	(Ni)	(48g)
  B46	=	+ (¼ + 2 y2) A1 - (1/8 - y2) A2 - (3/8 - y2) A3	=	- 3/8 a X + y2 a Y + (¼ + y2) a Z	(Ni)	(48g)
  B47	=	+ (¼ - 2 y2) A1 - (1/8 + y2) A2 - (3/8 + y2) A3	=	- 3/8 a X - y2 a Y + (¼ - y2) a Z	(Ni)	(48g)
  B48	=	- ¼ A1 - (3/8 + y2) A2 - (1/8 - y2) A3	=	- 1/8 a X + y2 a Y - (¼ + y2) a Z	(Ni)	(48g)
  B49	=	- (1/8 + y2) A1 - ¼ A2 - (3/8 - y2) A3	=	- (¼ - y2) a X - 1/8 a Y - y2 a Z	(Ni)	(48g)
  B50	=	- (3/8 - y2) A1 + (¼ + 2 y2) A2 - (1/8 - y2) A3	=	+ (¼ + y2) a X - 3/8 a Y + y2 a Z	(Ni)	(48g)
  B51	=	- (3/8 + y2) A1 + (¼ - 2 y2) A2 - (1/8 + y2) A3	=	+ (¼ - y2) a X - 3/8 a Y - y2 a Z	(Ni)	(48g)
  B52	=	- (1/8 - y2) A1 - ¼ A2 - (3/8 + y2) A3	=	- (¼ + y2) a X - 1/8 a Y + y2 a Z	(Ni)	(48g)
  B53	=	- (3/8 - y2) A1 - (1/8 + y2) A2 - ¼ A3	=	- y2 a X - (¼ - y2) a Y - 1/8 a Z	(Ni)	(48g)
  B54	=	- (1/8 - y2) A1 - (3/8 - y2) A2 + (¼ + 2 y2) A3	=	+ y2 a X + (¼ + y2) a Y - 3/8 a Z	(Ni)	(48g)
  B55	=	- (1/8 + y2) A1 - (3/8 + y2) A2 + (¼ - 2 y2) A3	=	- y2 a X + (¼ - y2) a Y - 3/8 a Z	(Ni)	(48g)
  B56	=	- (3/8 + y2) A1 - (1/8 - y2) A2 - ¼ A3	=	+ y2 a X - (¼ + y2) a Y - 1/8 a Z	(Ni)	(48g)

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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).