Scheelite (CaWO4, $H0_{4}$) Structure : AB4C_tI24_88_b_f_a

Picture of Structure; Click for Big Picture
Prototype : CaO4W
AFLOW prototype label : AB4C_tI24_88_b_f_a
Strukturbericht designation : $H0_{4}$
Pearson symbol : tI24
Space group number : 88
Space group symbol : $I4_{1}/a$
AFLOW prototype command : aflow --proto=AB4C_tI24_88_b_f_a
--params=
$a$,$c/a$,$x_{3}$,$y_{3}$,$z_{3}$


Other compounds with this structure

  • ZrSiO4, LaNbO4, YNbO4, (Y,RE)NbO4 (fergusonite), YVO4, BiVO4, BaWO4, PbWO4 (wulfenite), SrWO4, EuWO4, PbMoO4 (stolzite), SrMoO4, CaMoO4 (powellite), CdMoO4, KReO4, TlReO4, AgReO4, and NaAlH4

  • (Ewald, 1931) originally gave this structure the Strukturbericht designation $H4$, but this was changed to $H0_{4}$ in (Gottfried, 1937).

Body-centered Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{W} \\ \mathbf{B}_{2} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{W} \\ \mathbf{B}_{3} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{5}{8}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ca} \\ \mathbf{B}_{4} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{7}{8}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Ca} \\ \mathbf{B}_{5} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} +x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - x_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{3}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{9} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}-y_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} + y_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} - x_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-x_{3}+y_{3}\right) \, \mathbf{a}_{3} & = & \left(- \frac{1}{4} +y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +x_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3} - y_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-y_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{3}\right)c \, \mathbf{\hat{z}} & \left(16f\right) & \mbox{O} \\ \end{array} \]

References

  • R. M. Hazen, L. W. Finger, and J. W. E. Mariathasan, High–pressure crystal chemistry of scheelite–type tungstates and molybdates, J. Phys. Chem. Solids 46, 253–263 (1985), doi:10.1016/0022-3697(85)90039-3.
  • P. P. Ewald and C. Hermann, eds., Strukturbericht 1913–1928 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1931).
  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933–1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • Y. Zhang, N. A. W. Holzwarth, and R. T. Williams, Electronic band structures of the scheelite materials CaMoO4, CaWO4, PbMoO4, and PbWO4, Phys. Rev. B 57, 12738–12750 (1988), doi:10.1103/PhysRevB.57.12738.

Geometry files


Prototype Generator

aflow --proto=AB4C_tI24_88_b_f_a --params=

Species:

Running:

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