The Brookite (C21) Structure

Last modified 18 April 2001

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• see the structure from several perspectives;
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• Prototype: TiO₂
• Pearson Symbol: oP24
• Strukturbericht Designation: C21
• Space Group: Pbca (Cartesian and lattice coordinate listings available)
• Number: 61
• Primitive Vectors:
  • A₁ = a X
  • A₂ = b Y
  • A₃ = c Z
• Basis Vectors:

  Since there are a lot of atoms here, and the conversion from Cartesian to orthorhombic lattice coordinates is obvious, we'll only list the Cartesian positions of the atoms here:

  B1	=	+ x1 a X + y1 b Y + z1 c Z	(8c)	(Ti)
  B2	=	(½ + x1) a X + (½ - y1) b Y - z1 c Z	(8c)	(Ti)
  B3	=	- x1 a X + (½ + y1) b Y + (½ - z1) c Z	(8c)	(Ti)
  B4	=	(½ - x1) a X - y1 b Y + (½ + z1) c Z	(8c)	(Ti)
  B5	=	- x1 a X - y1 b Y - z1 c Z	(8c)	(Ti)
  B6	=	(½ - x1) a X + (½ + y1) b Y + z1 c Z	(8c)	(Ti)
  B7	=	+ x1 a X + (½ - y1) b Y + (½ + z1) c Z	(8c)	(Ti)
  B8	=	(½ + x1) a X + y1 b Y + (½ - z1) c Z	(8c)	(Ti)
  B9	=	+ x2 a X + y2 b Y + z2 c Z	(8c)	(O-I)
  B10	=	(½ + x2) a X + (½ - y2) b Y - z2 c Z	(8c)	(O-I)
  B11	=	- x2 a X + (½ + y2) b Y + (½ - z2) c Z	(8c)	(O-I)
  B12	=	(½ - x2) a X - y2 b Y + (½ + z2) c Z	(8c)	(O-I)
  B13	=	- x2 a X - y2 b Y - z2 c Z	(8c)	(O-I)
  B14	=	(½ - x2) a X + (½ + y2) b Y + z2 c Z	(8c)	(O-I)
  B15	=	+ x2 a X + (½ - y2) b Y + (½ + z2) c Z	(8c)	(O-I)
  B16	=	(½ + x2) a X + y2 b Y + (½ - z2) c Z	(8c)	(O-I)
  B17	=	+ x3 a X + y3 b Y + z3 c Z	(8c)	(O-II)
  B18	=	(½ + x3) a X + (½ - y3) b Y - z3 c Z	(8c)	(O-II)
  B19	=	- x3 a X + (½ + y3) b Y + (½ - z3) c Z	(8c)	(O-II)
  B20	=	(½ - x3) a X - y3 b Y + (½ + z3) c Z	(8c)	(O-II)
  B21	=	- x3 a X - y3 b Y - z3 c Z	(8c)	(O-II)
  B22	=	(½ - x3) a X + (½ + y3) b Y + z3 c Z	(8c)	(O-II)
  B23	=	+ x3 a X + (½ - y3) b Y + (½ + z3) c Z	(8c)	(O-II)
  B24	=	(½ + x3) a X + y3 b Y + (½ - z3) c Z	(8c)	(O-II)

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