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

# The βU (Ab) Structure

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• 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: Ab
• 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)

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 Structures indexed by: This is a mirror of an old page created at theNaval Research LaboratoryCenter for Computational Materials ScienceThe 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).