Crystal Lattice Structures:	Creation Date: 22 Dec 2002
	Last Modified: 21 Oct 2004

The Keatite (SiO₂) Structure

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• One of the Si-O bonds in this structure is very long (3.69 Å). Wyckoff considers this ``so improbable that there is something wrong either with the parameters as stated or the structure itself.'' (Wyckoff, Vol. I, p. 322)

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• Prototype: Keatite SiO₂
• Pearson Symbol: tP36
• Space Group: P4₁2₁2 (Cartesian and lattice coordinate listings available)
• Number: 92
• Reference: Wyckoff, Vol. I, p. 321
• Primitive Vectors:

  A1	=	a X
  A2	=	a Y
  A3	=	c Z

• Basis Vectors:

  B1	=	x1 A1 + x1 A2	=	x1 a X + x1 a Y	(Si-I)	(4a)
  B2	=	- x1 A1 - x1 A2 + ½ A3	=	- x1 a X - x1 a Y + ½ c Z	(Si-I)	(4a)
  B3	=	(½ - x1) A1 + (½ + x1) A2 + ¼ A3	=	(½ - x1) a X + (½ + x1) a Y + ¼ c Z	(Si-I)	(4a)
  B4	=	(½ + x1) A1 + (½ - x1) A2 + ¾ A3	=	(½ + x1) a X + (½ - x1) a Y + ¾ c Z	(Si-I)	(4a)
  B5	=	x2 A1 + y2 A2 + z2 A3	=	x2 a X + y2 a Y + z2 c Z	(Si-II)	(8b)
  B6	=	- x2 A1 - y2 A2 + (½ + z2) A3	=	- x2 a X - y2 a Y + (½ + z2) c Z	(Si-II)	(8b)
  B7	=	(½ - y2) A1 + (½ + x2) A2 + (¼ + z2) A3	=	(½ - y2) a X + (½ + x2) a Y + (¼ + z2) c Z	(Si-II)	(8b)
  B8	=	(½ + y2) A1 + (½ - x2) A2 + (¾ + z2) A3	=	(½ + y2) a X + (½ - x2) a Y + (¾ + z2) c Z	(Si-II)	(8b)
  B9	=	y2 A1 + x2 A2 - z2 A3	=	y2 a X + x2 a Y - z2 c Z	(Si-II)	(8b)
  B10	=	- y2 A1 - x2 A2 + (½ - z2) A3	=	- y2 a X - x2 a Y + (½ - z2) c Z	(Si-II)	(8b)
  B11	=	(½ - x2) A1 + (½ + y2) A2 + (¼ - z2) A3	=	(½ - x2) a X + (½ + y2) a Y + (¼ - z2) c Z	(Si-II)	(8b)
  B12	=	(½ + x2) A1 + (½ - y2) A2 + (¾ - z2) A3	=	(½ + x2) a X + (½ - y2) a Y + (¾ - z2) c Z	(Si-II)	(8b)
  B13	=	x3 A1 + y3 A2 + z3 A3	=	x3 a X + y3 a Y + z3 c Z	(O-I)	(8b)
  B14	=	- x3 A1 - y3 A2 + (½ + z3) A3	=	- x3 a X - y3 a Y + (½ + z3) c Z	(O-I)	(8b)
  B15	=	(½ - y3) A1 + (½ + x3) A2 + (¼ + z3) A3	=	(½ - y3) a X + (½ + x3) a Y + (¼ + z3) c Z	(O-I)	(8b)
  B16	=	(½ + y3) A1 + (½ - x3) A2 + (¾ + z3) A3	=	(½ + y3) a X + (½ - x3) a Y + (¾ + z3) c Z	(O-I)	(8b)
  B17	=	y3 A1 + x3 A2 - z3 A3	=	y3 a X + x3 a Y - z3 c Z	(O-I)	(8b)
  B18	=	- y3 A1 - x3 A2 + (½ - z3) A3	=	- y3 a X - x3 a Y + (½ - z3) c Z	(O-I)	(8b)
  B19	=	(½ - x3) A1 + (½ + y3) A2 + (¼ - z3) A3	=	(½ - x3) a X + (½ + y3) a Y + (¼ - z3) c Z	(O-I)	(8b)
  B20	=	(½ + x3) A1 + (½ - y3) A2 + (¾ - z3) A3	=	(½ + x3) a X + (½ - y3) a Y + (¾ - z3) c Z	(O-I)	(8b)
  B21	=	x4 A1 + y4 A2 + z4 A3	=	x4 a X + y4 a Y + z4 c Z	(O-II)	(8b)
  B22	=	- x4 A1 - y4 A2 + (½ + z4) A3	=	- x4 a X - y4 a Y + (½ + z4) c Z	(O-II)	(8b)
  B23	=	(½ - y4) A1 + (½ + x4) A2 + (¼ + z4) A3	=	(½ - y4) a X + (½ + x4) a Y + (¼ + z4) c Z	(O-II)	(8b)
  B24	=	(½ + y4) A1 + (½ - x4) A2 + (¾ + z4) A3	=	(½ + y4) a X + (½ - x4) a Y + (¾ + z4) c Z	(O-II)	(8b)
  B25	=	y4 A1 + x4 A2 - z4 A3	=	y4 a X + x4 a Y - z4 c Z	(O-II)	(8b)
  B26	=	- y4 A1 - x4 A2 + (½ - z4) A3	=	- y4 a X - x4 a Y + (½ - z4) c Z	(O-II)	(8b)
  B27	=	(½ - x4) A1 + (½ + y4) A2 + (¼ - z4) A3	=	(½ - x4) a X + (½ + y4) a Y + (¼ - z4) c Z	(O-II)	(8b)
  B28	=	(½ + x4) A1 + (½ - y4) A2 + (¾ - z4) A3	=	(½ + x4) a X + (½ - y4) a Y + (¾ - z4) c Z	(O-II)	(8b)
  B29	=	x5 A1 + y5 A2 + z5 A3	=	x5 a X + y5 a Y + z5 c Z	(O-III)	(8b)
  B30	=	- x5 A1 - y5 A2 + (½ + z5) A3	=	- x5 a X - y5 a Y + (½ + z5) c Z	(O-III)	(8b)
  B31	=	(½ - y5) A1 + (½ + x5) A2 + (¼ + z5) A3	=	(½ - y5) a X + (½ + x5) a Y + (¼ + z5) c Z	(O-III)	(8b)
  B32	=	(½ + y5) A1 + (½ - x5) A2 + (¾ + z5) A3	=	(½ + y5) a X + (½ - x5) a Y + (¾ + z5) c Z	(O-III)	(8b)
  B33	=	y5 A1 + x5 A2 - z5 A3	=	y5 a X + x5 a Y - z5 c Z	(O-III)	(8b)
  B34	=	- y5 A1 - x5 A2 + (½ - z5) A3	=	- y5 a X - x5 a Y + (½ - z5) c Z	(O-III)	(8b)
  B35	=	(½ - x5) A1 + (½ + y5) A2 + (¼ - z5) A3	=	(½ - x5) a X + (½ + y5) a Y + (¼ - z5) c Z	(O-III)	(8b)
  B36	=	(½ + x5) A1 + (½ - y5) A2 + (¾ - z5) A3	=	(½ + x5) a X + (½ - y5) a Y + (¾ - z5) c Z	(O-III)	(8b)

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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).