Crystal Lattice Structures:	Creation Date: 15 Nov 2001
	Last Modified: 21 Oct 2004

The Ca₃₃Ge (CTi₂) Structure

You can now

• 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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• The real prototype of this system is Ca₃₃Ge, with the (32e) sites occupied by Ca atoms and the (16c) sites by random Ca and Ge atoms. CTi₂ is a fully ordered crystal with the same structure, so we'll use that compound to generate the structure.
• Pearson's Handbook uses the first origin site in the Space Group Tables. This places one of the (16c) atoms at (1/8,1/8,1/8). We'll use the second origin site, which places one of the (16c) atoms, as well as the inversion site, at the origin.
• For some reason, no one noticed that the original title of page file was ``The Ca₃₃Ga (CTi₂) Structure.''

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• Prototype: Ca₃₃Ge
• Pearson Symbol: cF48
• Space Group: Fd3m (Cartesian and lattice coordinate listings available)
• Number: 227
• Reference: Pearson's Handbook Vol. IV, p. 2057 (Ca₃₃Ge), p. 2022 (CTi₂)
• Other Compounds with this Structure: CTi₂
• 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		(16c)	(C)
  B2 =	½ A1	=	¼ a Y  + ¼ a Z	(16c)	(C)
  B3 =	½ A2	=	¼ a X  + ¼ a Z	(16c)	(C)
  B4 =	½ A3	=	¼ a X  + ¼ a Y	(16c)	(C)
  B5 =	+ x A1 + x A2 + x A3	=	+ x a X  + x a Y  + x a Z	(32e)	(Ti)
  B6 =	- x A1 - x A2 - x A3	=	- x a X  - x a Y  - x a Z	(32e)	(Ti)
  B7 =	+ x A1 + x A2 + (½ - 3 x) A3	=	(¼ - x) a X  + (¼ - x) a Y  + x a Z	(32e)	(Ti)
  B8 =	- x A1 - x A2 + (3 x - ½) A3	=	(x - ¼) a X  + (x - ¼) a Y  - x a Z	(32e)	(Ti)
  B9 =	+ x A1 + (½ - 3 x) A2 + x A3	=	(¼ - x) a X  + x a Y  + (¼ - x) a Z	(32e)	(Ti)
  B10 =	- x A1 + (3x - ½) A2 - x A3	=	(x - ¼) a X  - x a Y  + (x - ¼) a Z	(32e)	(Ti)
  B11 =	+ (½ - 3 x) A1 + x A2 + x A3	=	+ x a X  + (¼ - x) a Y  + (¼ - x) a Z	(32e)	(Ti)
  B12 =	+ (3 x - ½) A1 - x A2 - x A3	=	- x a X  + (x - ¼) a Y  + (x - ¼) a Z	(32e)	(Ti)

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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).