The Alpha Manganese Crystal Structure

Last modified 5 April 2001

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• Prototype: Alpha Mn (X-phase)
• Pearson Symbol: cI58
• Strukturbericht Designation: A12
• Space Group: I(-4)3m (Cartesian and lattice coordinate listings available)
• Number: 217
• Other Elements with this Structure: None
• Primitive Vectors:
  • A₁ = -½ a X + ½ a Y + ½ a Z
  • A₂ = +½ a X - ½ a Y + ½ a Z
  • A₃ = +½ a X + ½ a Y - ½ a Z
• Basis Vectors:

  The twenty-nine Manganese atoms in the primitive cell occupy four symmetry sites in the I(-4)3m space group. We'll number the types by the index j, and basis vector B_i(j) represents the i^th atom on the j^th symmetry site. To summarize the sites first:

  Index	Wyckoff Notation	Number of Atoms	Internal Parameters
  j = 1	(2a)	1	None
  j = 2	(8c)	4	[x2]
  j = 3	(24g)	12	[x3,z3]
  j = 4	(24g)	12	[x4,z4]

  And now the vectors:
  
  

  • j = 1 (2a)

    B1(1) = 0

  • j = 2 (8c)

    B1(2)	=	+ 2 x2 A1 + 2 x2 A2 + 2 x2 A3	=	+ x2 X + x2 Y + x2 Z
    B2(2)	=	- 2 x2 A1	=	+ x2 X - x2 Y - x2 Z
    B3(2)	=	- 2 x2 A2	=	- x2 X + x2 Y - x2 Z
    B4(2)	=	- 2 x2 A3	=	- x2 X - x2 Y + x2 Z

  • j = 3 and j = 4 (24g)

    B1(j)	=	+ (xj + zj) A1 + (xj + zj) A2 + 2 xj A3	=	+ xj X + xj Y + zj Z
    B2(j)	=	+ 2 xj A1 + (xj + zj) A2 + (xj + zj) A3	=	+ zj X + xj Y + xj Z
    B3(j)	=	+ (xj + zj) A1 + 2 xj A2 + (xj + zj) A3	=	+ xj X + zj Y + xj Z
    B4(j)	=	+ (xj - zj) A1 - (xj + zj) A2	=	- xj X + xj Y - zj Z
    B5(j)	=	- (xj + zj) A2 + (xj - zj) A3	=	- zj X + xj Y - xj Z
    B6(j)	=	- (xj - zj) A1 - 2 xj A2 - (xj - zj) A3	=	- xj X + zj Y - xj Z
    B7(j)	=	- (xj + zj) A1 + (xj - zj) A2	=	+ xj X - xj Y - zj Z
    B8(j)	=	+ 2 xj A1 - (xj - zj) A2 - (xj - zj) A3	=	+ zj X - xj Y - xj Z
    B9(j)	=	- (xj + zj) A1 + (xj - zj) A3	=	+ xj X - zj Y - xj Z
    B10(j)	=	- (xj - zj) A1 - (xj - zj) A2- 2 xj A3	=	- xj X - xj Y + zj Z
    B11(j)	=	+ (xj - zj) A2 - (xj + zj) A3	=	- zj X - xj Y + xj Z
    B12(j)	=	+ (xj - zj) A1 - (xj + zj) A3	=	- xj X - zj Y + xj Z

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