Original $\beta$–WO3 ( obsolete) Structure : A3B_oP32_62_ab4c_2c

Picture of Structure; Click for Big Picture
Prototype : O3W
AFLOW prototype label : A3B_oP32_62_ab4c_2c
Strukturbericht designation : None
Pearson symbol : oP32
Space group number : 62
Space group symbol : $Pnma$
AFLOW prototype command : aflow --proto=A3B_oP32_62_ab4c_2c
--params=
$a$,$b/a$,$c/a$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$



Simple Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}b \, \mathbf{\hat{y}} & \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} & \left(4b\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O III} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O IV} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{4}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O IV} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O IV} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{4}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O IV} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O V} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O V} \\ \mathbf{B}_{19} & = & -x_{5} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O V} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O V} \\ \mathbf{B}_{21} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O VI} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O VI} \\ \mathbf{B}_{23} & = & -x_{6} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O VI} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{O VI} \\ \mathbf{B}_{25} & = & x_{7} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W I} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W I} \\ \mathbf{B}_{27} & = & -x_{7} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W I} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W I} \\ \mathbf{B}_{29} & = & x_{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W II} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{8}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W II} \\ \mathbf{B}_{31} & = & -x_{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W II} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{8}\right)c \, \mathbf{\hat{z}} & \left(4c\right) & \mbox{W II} \\ \end{array} \]

References

  • P. M. Woodward, A. W. Sleight, and T. Vogt, Ferroelectric Tungsten Trioxide, J. Solid State Chem. 131, 9–17 (1997), doi:10.1006/jssc.1997.7268.
  • T. Vogt, P. M. Woodward, and B. A. Hunter, The High–Temperature Phases of WO3, J. Solid State Chem. 144, 209–215 (1999), doi:10.1006/jssc.1999.8173.
  • R. Diehl, G. Brandt, and E. Salje, The Crystal Structure of Triclinic WO3, Acta Crystallogr. Sect. B Struct. Sci. 34, 1105–1111 (1978), doi:10.1107/S0567740878005014.
  • H. Bräkken, Die Kristallstrukturen der Trioxyde von Chrom, Molybdän und Wolfram, Zeitschrift für Kristallographie – Crystalline Materials 78, 484–488 (1931), doi:10.1524/zkri.1931.78.1.484.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • B. Gerand, G. Nowogrocki, J. Guenot, and M. Figlarz, Structural study of a new hexagonal form of tungsten trioxide, J. Solid State Chem. 29, 429–434 (1979), doi:10.1016/0022-4596(79)90199-3.

Geometry files


Prototype Generator

aflow --proto=A3B_oP32_62_ab4c_2c --params=

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