Beta Manganese Crystal Structure

Last modified 5 April 2001

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• Prototype: Beta Mn
• Pearson Symbol: cP20
• Strukturbericht Designation: A13
• Space Group: P4₁32 (Cartesian and lattice coordinate listings available)
• Number: 213
• Other Elements with this Structure: None
• Primitive Vectors:
  • A₁ = a X
  • A₂ = a Y
  • A₃ = a Z
• Basis Vectors:

  Since this is a simple cubic unit cell, we will only list the Cartesian coordinates of the atoms in the basis.

  B1	=	+ x1 a X + x1 a Y + x1 a Z	(8c)
  B2	=	+ (¾ - x1) a X + (¾ - x1) a Y + (¾ - x1) a Z	(8c)
  B3	=	+ (½ + x1) a X + (½ - x1) a Y - x1 a Z	(8c)
  B4	=	+ (¼ - x1) a X + (¾ + x1) a Y + (¼ + x1) a Z	(8c)
  B5	=	- x1 a X + (½ + x1) a Y + (½ - x1)a Z	(8c)
  B6	=	+ (¼ + x1) a X + (¼ - x1) a Y + (¾ + x1) a Z	(8c)
  B7	=	+ (½ - x1) a X + - x1 a Y + (½ + x1)a Z	(8c)
  B8	=	+ (¾ + x1) a X + (¼ + x1) a Y + (¼ - x1) a Z	(8c)
  B9	=	+ 1/8 a X + x2 a Y + (¼ + x2) a Z	(12d)
  B10	=	+ 3/8 a X - x2 a Y + (¾ + x2) a Z	(12d)
  B11	=	+ 7/8 a X + (½ + x2) a Y + (¼ - x2) a Z	(12d)
  B12	=	+ 5/8 a X + (½ - x2) a Y + (¾ - x2) a Z	(12d)
  B13	=	+ (¼ + x2) a X + 1/8 a Y + x2 a Z	(12d)
  B14	=	+ (¾ + x2) a X + 3/8 a Y - x2 a Z	(12d)
  B15	=	+ (¼ - x2) a X + 7/8 a Y + (½ + x2) a Z	(12d)
  B16	=	+ (¾ - x2) a X + 5/8 a Y + (½ - x2) a Z	(12d)
  B17	=	+ x2 a X + (¼ + x2) a Y + 1/8 a Z	(12d)
  B18	=	- x2 a X + (¾ + x2) a Y + 3/8 a Z	(12d)
  B19	=	+ (½ + x2) a X + (¼ - x2) a Y + 7/8 a Z	(12d)
  B20	=	+ (½ - x2) a X + (¾ - x2) a Y + 5/8 a Z	(12d)

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