Crystal Lattice Structures:	Creation Date: 26 Sep 2000
	Last Modified: 21 Oct 2004

Si₃₄ Clathrate

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• Silicon clathrates are open structures of pentagonal dodecahedra connected so that all of the silicon atoms have sp³ bonding. In nature these structures are stabilized by alkali impurity atoms. This structure and the Si₄₆ structure are proposed ``pure'' silicon clathrate structures. For more information about these structures and their possible stability, see G. B. Adams, M. O'Keeffe A. A. Demkov, O. F. Sankey, and Y.-M. Huang, Phys. Rev. B 49, 8048-8053 (1994).
• This structure has recently been obtained experimentally. See J. Gryko, P. F. McMillan, R. F. Marzke, G. K. Ramachandran, D. Patton, S. K. Deb, and O. F. Sankey, ``Low-density framework from of crystalline silicon with a wide optical band gap,'' Phys. Rev. B 62 R7707-R7710 (2000).

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• Prototype: Si₃₄ Clathrate
• Pearson Symbol: cF136
• Space Group: Fd3m (Cartesian and lattice coordinate listings available)
• Number: 227
• Reference: G. B. Adams et al., Phys. Rev. B 49, 8048 (1994).
• 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	(Si)	(8a)
  B2	=	- 1/8 A1- 1/8 A2- 1/8 A3	=	- 1/8 a X - 1/8 a Y- 1/8 a Z	(Si)	(8a)
  B3	=	+ x1 A1+ x1 A2+ x1 A3	=	+ x1 a X + x1 a Y + x1 a Z	(Si)	(32e)
  B4	=	- x1 A1- x1 A2- x1 A3	=	- x1 a X - x1 a Y - x1 a Z	(Si)	(32e)
  B5	=	+ (½-3x1) A1 + x1 A2+ x1 A3	=	+ x1 a X + (¼-x1) a Y + (¼-x1) a Z	(Si)	(32e)
  B6	=	- (½-3x1) A1 - x1 A2- x1 A3	=	- x1 a X - (¼-x1) a Y - (¼-x1) a Z	(Si)	(32e)
  B7	=	+ x1 A1+ (½-3x1) A2+ x1 A3	=	+ (¼-x1) a X + x1 a Y + (¼-x1) a Z	(Si)	(32e)
  B8	=	- x1 A1- (½-3x1) A2- x1 A3	=	- (¼-x1) a X - x1 a Y - (¼-x1) a Z	(Si)	(32e)
  B9	=	+ x1 A1+ x1 A2+ (½-3x1) A3	=	+ (¼-x1) a X + (¼-x1) a Y + x1 a Z	(Si)	(32e)
  B10	=	- x1 A1- x1 A2- (½-3x1) A3	=	- (¼-x1) a X - (¼-x1) a Y - x1 a Z	(Si)	(32e)
  B11	=	+ z2 A1+ z2 A2+ (2x2-z2) A3	=	+ x2 a X + x2 a Y + z2 a Z	(Si)	(96g)
  B12	=	- z2 A1- z2 A2- (2x2-z2) A3	=	- x2 a X - x2 a Y - z2 a Z	(Si)	(96g)
  B13	=	+ (2x2-z2) A1+ z2 A2+ z2 A3	=	+ z2 a X + x2 a Y + x2 a Z	(Si)	(96g)
  B14	=	- (2x2-z2) A1- z2 A2- z2 A3	=	- z2 a X - x2 a Y - x2 a Z	(Si)	(96g)
  B15	=	+ z2 A1+ (2x2-z2) A2+ z2 A3	=	+ x2 a X + z2 a Y + x2 a Z	(Si)	(96g)
  B16	=	- z2 A1- (2x2-z2) A2- z2 A3	=	- x2 a X - z2 a Y - x2 a Z	(Si)	(96g)
  B17	=	+ (½-2x2-z2) A1+ (2x2-z2) A2+ z2 A3	=	+ x2 a X + (¼-x2) a Y + (¼-z2) a Z	(Si)	(96g)
  B18	=	- (½-2x2-z2) A1- (2x2-z2) A2- z2 A3	=	- x2a X - (¼-x2) a Y - (¼-z2) a Z	(Si)	(96g)
  B19	=	+ (½-2x2-z2) A1+ z2 A2+ z2 A3	=	+ z2 a X + (¼-x2) a Y + (¼-x2) a Z	(Si)	(96g)
  B20	=	- (½-2x2-z2) A1- z2 A2- z2 A3	=	- z2 a X - (¼-x2) a Y - (¼-x2) a Z	(Si)	(96g)
  B21	=	+ (½-2x2-z2) A1+ z2 A2+ (2x2-z2) A3	=	+ x2 a X + (¼-z2) a Y + (¼-x2) a Z	(Si)	(96g)
  B22	=	- (½-2x2-z2) A1- z2 A2- (2x2-z2) A3	=	- x2 a X - (¼-z2) a Y - (¼-x2) a Z	(Si)	(96g)
  B23	=	+ (2x2-z2) A1+ (½-2x2-z2) A2 + z2 A3	=	+ (¼-x2) a X + x2 a Y + (¼-z2) a Z	(Si)	(96g)
  B24	=	- (2x2-z2) A1- (½-2x2-z2) A2 - z2 A3	=	- (¼-x2) a X - x2 a Y - (¼-z2) a Z	(Si)	(96g)
  B25	=	+ z2 A1+ (½-2x2-z2) A2 + (2x2-z2) A3	=	+ (¼-z2) a X + x2 a Y + (¼-x2) a Z	(Si)	(96g)
  B26	=	- z2 A1- (½-2x2-z2) A2 - (2x2-z2) A3	=	- (¼-z2) a X - x2 a Y - (¼-x2) a Z	(Si)	(96g)
  B27	=	+ z2 A1+ (½-2x2-z2) A2 + z2 A3	=	+ (¼-x2) a X + z2 a Y + (¼-x2) a Z	(Si)	(96g)
  B28	=	- z2 A1- (½-2x2-z2) A2 - z2 A3	=	- (¼-x2) a X - z2 a Y - (¼-x2) a Z	(Si)	(96g)
  B29	=	+ z2 A1+ z2 A2+ (½-2x2-z2) A3	=	+ (¼-x2) a X + (¼-x2) a Y + z2 a Z	(Si)	(96g)
  B30	=	- z2 A1- z2 A2- (½-2x2-z2) A3	=	- (¼-x2) a X - (¼-x2) a Y - z2 a Z	(Si)	(96g)
  B31	=	+ z2 A1+ (2x2-z2) A2+ (½-2x2-z2) A3	=	+ (¼-z2) a X + (¼-x2) a Y + x2 a Z	(Si)	(96g)
  B32	=	- z2 A1- (2x2-z2) A2- (½-2x2-z2) A3	=	- (¼-z2) a X - (¼-x2) a Y - x2 a Z	(Si)	(96g)
  B33	=	+ (2x2-z2) A1+ z2 A2+ (½-2x2-z2) A3	=	+ (¼-x2) a X + (¼-z2) a Y + x2 a Z	(Si)	(96g)
  B34	=	- (2x2-z2) A1- z2 A2- (½-2x2-z2) A3	=	- (¼-x2) a X - (¼-z2) a Y - x2 a Z	(Si)	(96g)

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