Hexagonal WO3 Structure : A3B_hP12_191_gl_f

Picture of Structure; Click for Big Picture
Prototype : O3W
AFLOW prototype label : A3B_hP12_191_gl_f
Strukturbericht designation : None
Pearson symbol : hP12
Space group number : 191
Space group symbol : $P6/mmm$
AFLOW prototype command : aflow --proto=A3B_hP12_191_gl_f
--params=
$a$,$c/a$,$x_{3}$



Hexagonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{W} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} & \left(3f\right) & \mbox{W} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(3f\right) & \mbox{W} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{O I} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{O I} \\ \mathbf{B}_{6} & = & \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}c \, \mathbf{\hat{z}} & \left(3g\right) & \mbox{O I} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + 2x_{3} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{8} & = & -2x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}} + \frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} & = & -\sqrt{3}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-2x_{3} \, \mathbf{a}_{2} & = & -\frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{11} & = & 2x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & \frac{3}{2}x_{3}a \, \mathbf{\hat{x}}-\frac{\sqrt{3}}{2}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} & = & \sqrt{3}x_{3}a \, \mathbf{\hat{y}} & \left(6l\right) & \mbox{O 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_hP12_191_gl_f --params=

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