Crystal Lattice Structures:	Creation Date: 24 Feb 2007
	Last Modified: 24 Feb 2007

The Bixbyite (Mn₂O₃, D5₃) Structure

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Notes:

• A search for “Bixbyite” on the American Mineralogist Crystal Structure Database shows two structures with the Mn atoms on the (8a) sites and one with Mn on the (8b) site. We use the structure that agrees with the data in Pearson's Handbook, Vol. IV, pp. 4346-7, placing the Mn atoms on the (8b) sites.
• The referenced data is for (Mn,Fe)₂O₃, with Mn and Fe randomly populating the (8b) and (24d) sites. The pictures are drawn with Fe atoms on the (8b) sites and Mn atoms on the (24d) sites in order to better delineate the difference in the crystallographic behavior of the sites, but both sites are randomly occupied.
• This can be viewed as a Fluorite (C1) structure with defects, i.e., Fluorite MnO₂ with one-fourth of the Oxygen atoms removed.
• The picture shown is drawn with the (8b) sites at the corners and at the center of the cube. Note that none of these sites is the actual origin as given using the basis vectors below.
• The basis vector representation is chosen so that all lattice coordinates are in the range - ½ < α <½.

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• Prototype: Mn₂ O₃
• Pearson Symbol: cI80
• Strukturbericht Designation: D5₃
• Space Group: Ia3 (Cartesian and lattice coordinate listings available)
• Number: 206
• Reference: H. Dachs, Z.f. Kristal. 107, 370 (1956).
• Other Compounds with this Structure: Am₂O₃, As₂Mg₃, As₂Zn₃, Cd₃P₂, Ce₂O₃, Fe₂O₃, La₂O₃, Lu₂O₃, Tb₂O₃, Tm₂O₃, P₂Zn₃, many others.
• 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:

  B1	=	½ A1 + ½ A2 + ½ A3	=	+ ¼ a X + ¼ a Y + ¼ a Z	(Mn-I)	(8b)
  B2	=	½ A1	=	- ¼ a X + ¼ a Y + ¼ a Z	(Mn-I)	(8b)
  B3	=	½ A2	=	+ ¼ a X - ¼ a Y + ¼ a Z	(Mn-I)	(8b)
  B4	=	½ A3	=	+ ¼ a X + ¼ a Y - ¼ a Z	(Mn-I)	(8b)
  B5	=	+ ¼ A1 + (x1 + ¼) A2 + x1 A3	=	+ x1 a X + ¼ a Z	(Mn-II)	(24d)
  B6	=	- ¼ A1 - (x1 - ¼) A2 - (x1 + ½) A3	=	- x1 a X - ½ a Y + ¼ a Z	(Mn-II)	(24d)
  B7	=	+ x1 A1 + ¼ A2 + (x1 + ¼) A3	=	+ ¼ a X + x1 a Y	(Mn-II)	(24d)
  B8	=	- (x1 + ½) A1 - ¼ A2 - (x1 - ¼) A3	=	+ ¼ a X - x1 a Y - ½ a Z	(Mn-II)	(24d)
  B9	=	+ (x1 + ¼) A1 + x1 A2 + ¼ A3	=	+ ¼ a Y + x1 a Z	(Mn-II)	(24d)
  B10	=	- (x1 - ¼) A1 - (x1 + ½) A2 - ¼ A3	=	- ½ a X + ¼ a Y - x1 a Z	(Mn-II)	(24d)
  B11	=	- ¼ A1 - (x1 + ¼) A2 - x1 A3	=	- x1 a X - ¼ a Z	(Mn-II)	(24d)
  B12	=	+ ¼ A1 + (x1 - ¼) A2 + (x1 + ½) A3	=	+ x1 a X + ½ a Y - ¼ a Z	(Mn-II)	(24d)
  B13	=	- x1 A1 - ¼ A2 - (x1 + ¼) A3	=	- ¼ a X - x1 a Y	(Mn-II)	(24d)
  B14	=	+ (x1 + ½) A1 + ¼ A2 + (x1 - ¼) A3	=	- ¼ a X + x1 a Y + ½ a Z	(Mn-II)	(24d)
  B15	=	- (x1 + ¼) A1 - x1 A2 - ¼ A3	=	- ¼ a Y - x1 a Z	(Mn-II)	(24d)
  B16	=	+ (x1 - ¼) A1 + (x1 + ½) A2 + ¼ A3	=	+ ½ a X - ¼ a Y + x1 a Z	(Mn-II)	(24d)
  B17	=	+ (y2 + z2) A1 + (z2 + x2) A2 + (x2 + y2) A3	=	+ x2 a X + y2 a Y + z2 a Z	(O)	(48e)
  B18	=	- (y2 - z2 + ½) A1 + (z2 - x2) A2 - (x2 + y2 - ½) A3	=	- (x2 - ½) a X - y2 a Y + (z2 - ½) a Z	(O)	(48e)
  B19	=	+ (y2 - z2) A1 - (z2 + x2 - ½) A2 - (x2 - y2 - ½) A3	=	- (x2 - ½) a X + y2 a Y - z2 a Z	(O)	(48e)
  B20	=	- (y2 + z2 - ½) A1 - (z2 - x2 + ½) A2 + (x2 - y2) A3	=	+ (x2 - ½) a X - (y2 - ½) a Y - z2 a Z	(O)	(48e)
  B21	=	+ (x2 + y2) A1 + (y2 + z2) A2 + (z2 + x2) A3	=	+ z2 a X + x2 a Y + y2 a Z	(O)	(48e)
  B22	=	- (x2 + y2 - ½) A1 - (y2 - z2 + ½) A2 + (z2 - x2) A3	=	+ (z2 - ½) a X - (x2 - ½) a Y - y2 a Z	(O)	(48e)
  B23	=	- (x2 - y2 - ½) A1 + (y2 - z2) A2 - (z2 + x2 - ½) A3	=	- z2 a X - (x2 - ½) a Y + y2 a Z	(O)	(48e)
  B24	=	+ (x2 - y2) A1 - (y2 + z2 - ½) A2 - (z2 - x2 + ½) A3	=	- z2 a X + (x2 - ½) a Y - (y2 - ½) a Z	(O)	(48e)
  B25	=	+ (z2 + x2) A1 + (x2 + y2) A2 + (y2 + z2) A3	=	+ y2 a X + z2 a Y + x2 a Z	(O)	(48e)
  B26	=	+ (z2 - x2) A1 - (x2 + y2 - ½) A2 - (y2 - z2 + ½) A3	=	- y2 a X + (z2 - ½) a Y - (x2 - ½) a Z	(O)	(48e)
  B27	=	- (z2 + x2 - ½) A1 - (x2 - y2 - ½) A2 + (y2 - z2) A3	=	+ y2 a X - z2 a Y - (x2 - ½) a Z	(O)	(48e)
  B28	=	- (z2 - x2 + ½) A1 + (x2 - y2) A2 - (y2 + z2 - ½) A3	=	- (y2 - ½) a X - z2 a Y + (x2 - ½) a Z	(O)	(48e)
  B29	=	- (y2 + z2) A1 - (z2 + x2) A2 - (x2 + y2) A3	=	- x2 a X - y2 a Y - z2 a Z	(O)	(48e)
  B30	=	+ (y2 - z2 + ½) A1 - (z2 - x2) A2 + (x2 + y2 - ½) A3	=	+ (x2 - ½) a X + y2 a Y - (z2 - ½) a Z	(O)	(48e)
  B31	=	- (y2 - z2) A1 + (z2 + x2 - ½) A2 + (x2 - y2 - ½) A3	=	+ (x2 - ½) a X - y2 a Y + z2 a Z	(O)	(48e)
  B32	=	+ (y2 + z2 - ½) A1 + (z2 - x2 + ½) A2 - (x2 - y2) A3	=	- (x2 - ½) a X + (y2 - ½) a Y + z2 a Z	(O)	(48e)
  B33	=	- (x2 + y2) A1 - (y2 + z2) A2 - (z2 + x2) A3	=	- z2 a X - x2 a Y - y2 a Z	(O)	(48e)
  B34	=	+ (x2 + y2 - ½) A1 + (y2 - z2 + ½) A2 - (z2 - x2) A3	=	- (z2 - ½) a X + (x2 - ½) a Y + y2 a Z	(O)	(48e)
  B35	=	+ (x2 - y2 - ½) A1 - (y2 - z2) A2 + (z2 + x2 - ½) A3	=	+ z2 a X + (x2 - ½) a Y - y2 a Z	(O)	(48e)
  B36	=	- (x2 - y2) A1 + (y2 + z2 - ½) A2 + (z2 - x2 + ½) A3	=	+ z2 a X - (x2 - ½) a Y + (y2 - ½) a Z	(O)	(48e)
  B37	=	- (z2 + x2) A1 - (x2 + y2) A2 - (y2 + z2) A3	=	- y2 a X - z2 a Y - x2 a Z	(O)	(48e)
  B38	=	- (z2 - x2) A1 + (x2 + y2 - ½) A2 + (y2 - z2 + ½) A3	=	+ y2 a X - (z2 - ½) a Y + (x2 - ½) a Z	(O)	(48e)
  B39	=	+ (z2 + x2 - ½) A1 + (x2 - y2 - ½) A2 - (y2 - z2) A3	=	- y2 a X + z2 a Y + (x2 - ½) a Z	(O)	(48e)
  B40	=	+ (z2 - x2 + ½) A1 - (x2 - y2) A2 + (y2 + z2 - ½) A3	=	+ (y2 - ½) a X + z2 a Y - (x2 - ½) a Z	(O)	(48e)

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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).