Crystal Lattice Structures:	Creation Date: 22 Dec 2002
	Last Modified:  9 Jul 2008

The Keatite (SiO₂) 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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• This has been an interesting detective story. All references, including Shropshire et al., Demuth et al., and Wyckoff, note that keatite can exist in both space group P4₁2₁2-D₄⁴ (#92) and its enantiomorph P4₃2₁2-D₄⁸ (#96). Wyckoff uses the coordinates proposed by Shropshire and assumes the space group is P4₁2₁2. He then notes that one of the Si-O bonds in this structure is very long (3.69 Å), and so improbable that there is something wrong either with the parameters as stated or the structure itself. (Wyckoff, Vol. I, p. 322).
  
  If we use space group P4₃2₁2 while retaining Shropshire's coordinates we obtain a much more convincing structure, one that looks much like the structure in Shropshire's Fig. 3.
  
  Demuth uses Shropshire's coordinates and claims to use space group P4₁2₁2, but close examination of the distances and angles in the paper show that the space group must be P4₃2₁2 if the coordinates given in Table 7 are correct.
  
  Our previous attempt at this structure followed Wyckoff, and we have retained the previous version here. However, note that the coordinates of the (8b) Si atoms are wrong, so the picture makes no sense even for the P4₁2₁ space group.
  
  In this version we use Shropshire's coordinates and space group P4₃2₁2.
• In order to distinguish the various types of atoms, the XYZ coordinate file relabels Si-I as Ge, O-II as N, and O-III as F.
• Note that going from P4₁2₁2 to P4₃2₁2 interchanges the ¼ and ¾ coordinates on the z axis. All other formulas remain the same.
• The Silicon atoms form a widely separated ST12 structure, so it is probably fair to call this ST12 with Oxygen atoms placed between the Silicons.

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• Prototype: Keatite SiO₂
• Pearson Symbol: tP36
• Space Group: P4₃2₁2 (Cartesian and lattice coordinate listings available)
• Number: 96
• Reference: J. Shropshire, et al., Zeitschrift für Kristallographie 112, 409-413 (1959).
• 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 + ¾ A3	=	(½ - x1) a X + (½ + x1) a Y + ¾ c Z	(Si-I)	(4a)
  B4	=	(½ + x1) A1 + (½ - x1) A2 + ¼ A3	=	(½ + x1) a X + (½ - x1) a Y + ¼ 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 + (¾ + z2) A3	=	(½ - y2) a X + (½ + x2) a Y + (¾ + z2) c Z	(Si-II)	(8b)
  B8	=	(½ + y2) A1 + (½ - x2) A2 + (¼ + z2) A3	=	(½ + y2) a X + (½ - x2) a Y + (¼ + 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 + (¾ - z2) A3	=	(½ - x2) a X + (½ + y2) a Y + (¾ - z2) c Z	(Si-II)	(8b)
  B12	=	(½ + x2) A1 + (½ - y2) A2 + (¼ - z2) A3	=	(½ + x2) a X + (½ - y2) a Y + (¼ - 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 + (¾ + z3) A3	=	(½ - y3) a X + (½ + x3) a Y + (¾ + z3) c Z	(O-I)	(8b)
  B16	=	(½ + y3) A1 + (½ - x3) A2 + (¼ + z3) A3	=	(½ + y3) a X + (½ - x3) a Y + (¼ + 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 + (¾ - z3) A3	=	(½ - x3) a X + (½ + y3) a Y + (¾ - z3) c Z	(O-I)	(8b)
  B20	=	(½ + x3) A1 + (½ - y3) A2 + (¼ - z3) A3	=	(½ + x3) a X + (½ - y3) a Y + (¼ - 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 + (¾ + z4) A3	=	(½ - y4) a X + (½ + x4) a Y + (¾ + z4) c Z	(O-II)	(8b)
  B24	=	(½ + y4) A1 + (½ - x4) A2 + (¼ + z4) A3	=	(½ + y4) a X + (½ - x4) a Y + (¼ + 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 + (¾ - z4) A3	=	(½ - x4) a X + (½ + y4) a Y + (¾ - z4) c Z	(O-II)	(8b)
  B28	=	(½ + x4) A1 + (½ - y4) A2 + (¼ - z4) A3	=	(½ + x4) a X + (½ - y4) a Y + (¼ - 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 + (¾ + z5) A3	=	(½ - y5) a X + (½ + x5) a Y + (¾ + z5) c Z	(O-III)	(8b)
  B32	=	(½ + y5) A1 + (½ - x5) A2 + (¼ + z5) A3	=	(½ + y5) a X + (½ - x5) a Y + (¼ + 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 + (¾ - z5) A3	=	(½ - x5) a X + (½ + y5) a Y + (¾ - z5) c Z	(O-III)	(8b)
  B36	=	(½ + x5) A1 + (½ - y5) A2 + (¼ - z5) A3	=	(½ + x5) a X + (½ - y5) a Y + (¼ - 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).