Crystal Lattice Structures:	Creation Date: 10 Mar 2002
	Last Modified: 21 Oct 2004

The βU (A_b) 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)

---

• According to Donohue, there are three possible space groups which fit the diffraction data for βU. This is the highest symmetry space group of the three.
• This structure is identical to the disordered σCrFe phase.

---

• Prototype: βU
• Strukturbericht Designation: A_b
• Pearson Symbol: tP30
• Space Group: P4₂/mnm (Cartesian and lattice coordinate listings available)
• Number: 136
• Reference: Donohue, Structures of the Elements, p. 141.
• Primitive Vectors:

  A1	=	a X
  A2	=	a Y
  A3	=	c Z

• Basis Vectors:
  
  Since this is a tetragonal lattice, we'll only list the Cartesian coordinates of the atoms, leaving the conversion to lattice coordinates as an exercise.
  
  

  B1	=	½ c Z	(U-I)	(2b)
  B2	=	½ a X + ½ a Y	(U-I)	(2b)
  B3	=	+ x2 a X + x2 a Y	(U-II)	(4f)
  B4	=	- x2 a X - x2 a Y	(U-II)	(4f)
  B5	=	(½ + x2) a X + (½ - x2) a Y + ½ c Z	(U-II)	(4f)
  B6	=	(½ - x2) a X + (½ + x2) a Y + ½ c Z	(U-II)	(4f)
  B7	=	+ x3 a X + x3 a Y + z3 c Z	(U-III)	(8j)
  B8	=	- x3 a X - x3 a Y + z3 c Z	(U-III)	(8j)
  B9	=	+ x3 a X + x3 a Y - z3 c Z	(U-III)	(8j)
  B10	=	- x3 a X - x3 a Y - z3 c Z	(U-III)	(8j)
  B11	=	(½ + x3) a X + (½ - x3) a Y + (½ + z3) c Z	(U-III)	(8j)
  B12	=	(½ - x3) a X + (½ + x3) a Y + (½ + z3) c Z	(U-III)	(8j)
  B13	=	(½ + x3) a X + (½ - x3) a Y + (½ - z3) c Z	(U-III)	(8j)
  B14	=	(½ - x3) a X + (½ + x3) a Y + (½ - z3) c Z	(U-III)	(8j)
  B15	=	+ x4 a X + y4 a Y	(U-IV)	(8i)
  B16	=	+ y4 a X + x4 a Y	(U-IV)	(8i)
  B17	=	- x4 a X - y4 a Y	(U-IV)	(8i)
  B18	=	- y4 a X - x4 a Y	(U-IV)	(8i)
  B19	=	(½ + x4) a X + (½ - y4) a Y + ½ c Z	(U-IV)	(8i)
  B20	=	(½ - x4) a X + (½ + y4) a Y + ½ c Z	(U-IV)	(8i)
  B21	=	(½ + y4) a X + (½ - x4) a Y + ½ c Z	(U-IV)	(8i)
  B22	=	(½ - y4) a X + (½ + x4) a Y + ½ c Z	(U-IV)	(8i)
  B23	=	+ x5 a X + y5 a Y	(U-V)	(8i)
  B24	=	+ y5 a X + x5 a Y	(U-V)	(8i)
  B25	=	- x5 a X - y5 a Y	(U-V)	(8i)
  B26	=	- y5 a X - x5 a Y	(U-V)	(8i)
  B27	=	(½ + x5) a X + (½ - y5) a Y + ½ c Z	(U-V)	(8i)
  B28	=	(½ - x5) a X + (½ + y5) a Y + ½ c Z	(U-V)	(8i)
  B29	=	(½ + y5) a X + (½ - x5) a Y + ½ c Z	(U-V)	(8i)
  B30	=	(½ - y5) a X + (½ + x5) a Y + ½ c Z	(U-V)	(8i)

---

Go back to the Lanthanides & Actinides page.

Go back to Crystal Lattice Structure page.

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).