Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B4C_tI112_141_fg_2hi_h-001

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Li$_{2}$WO$_{4}$ (II) Structure: A2B4C_tI112_141_fg_2hi_h-001

Picture of Structure; Click for Big Picture
Prototype Li$_{2}$O$_{4}$W
AFLOW prototype label A2B4C_tI112_141_fg_2hi_h-001
ICSD 10479
CCDC 1595311
Pearson symbol tI112
Space group number 141
Space group symbol $I4_1/amd$
AFLOW prototype command aflow --proto=A2B4C_tI112_141_fg_2hi_h-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}$

  • Li$_{2}$WO$_{4}$ is found in a variety of phases at different pressures and temperatures (Yamaoka, 1973; Pistorius, 1975):
  • Li$_{2}$WO$_{4}$(I), which is in the Phenakite ($S1_{3}$) structure, is stable at low pressures and temperatures above 300$^\circ$C.
  • Tetragonal Li$_{2}$WO$_{4}$(II) (this structure) is the ground state, and is stable below a line from (300$^\circ$C, 0 kBar) to (650$^\circ$C, 2 kBar) to (550$^\circ$C, 12 kBar) to (380$^\circ$C, 15 kBar).
  • Orthorhombic Li$_{2}$WO$_{4}$(III) is the high temperature structure for all pressures above phases II and IV. Its exact crystal structure has not been determined. It has been conjectured to be in space group $Pna2_{1}$ #33, $Pnnm$ #58 or $Cmmm$ #65.
  • Monoclinic Li$_{2}$WO$_{4}$(IV), stable at pressures higher than phase II and temperatures lower than phase III.
  • Later (Hämmer, 2022) determined the structure of triclinic Li$_{2}$WO$_{4}$ (V) (this structure), which may be the phase (Belyaev, 1961) observed at ambient pressure above 660$^\circ$C.
  • (Horiuchi, 1979) state that this structure is similar to spinel ($H1_{4}$).
  • The ICSD assigns this structure to the Bi$_{2}$CdO$_{4}$ prototype, but these structures do not even have the same sets of occupied Wyckoff positions, so we give Li$_{2}$WO$_{4}$ (II) its own prototype.

\[ \begin{array}{ccc} \mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}} \end{array}\]

Basis vectors

Lattice coordinates Cartesian coordinates Wyckoff position Atom type
$\mathbf{B_{1}}$ = $x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}$ (16f) Li I
$\mathbf{B_{2}}$ = $\frac{1}{2} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ (16f) Li I
$\mathbf{B_{3}}$ = $x_{1} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (16f) Li I
$\mathbf{B_{4}}$ = $- x_{1} \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ (16f) Li I
$\mathbf{B_{5}}$ = $- x_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ = $- a x_{1} \,\mathbf{\hat{x}}$ (16f) Li I
$\mathbf{B_{6}}$ = $\frac{1}{2} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{1} \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ (16f) Li I
$\mathbf{B_{7}}$ = $- x_{1} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}- a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ (16f) Li I
$\mathbf{B_{8}}$ = $x_{1} \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $\frac{1}{4}a \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ (16f) Li I
$\mathbf{B_{9}}$ = $\left(x_{2} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{2} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{10}}$ = $- \left(x_{2} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{2} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{11}}$ = $\left(x_{2} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{12}}$ = $- \left(x_{2} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{13}}$ = $- \left(x_{2} - \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{2} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $- a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{14}}$ = $\left(x_{2} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{2} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ = $a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{15}}$ = $- \left(x_{2} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{2} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{16}}$ = $\left(x_{2} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ = $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ (16g) Li II
$\mathbf{B_{17}}$ = $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ = $a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{18}}$ = $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{19}}$ = $z_{3} \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{20}}$ = $z_{3} \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{21}}$ = $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{22}}$ = $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ = $- a y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{23}}$ = $- z_{3} \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ = $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{24}}$ = $- z_{3} \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O I
$\mathbf{B_{25}}$ = $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ = $a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{26}}$ = $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{27}}$ = $z_{4} \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ = $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{28}}$ = $z_{4} \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{29}}$ = $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{30}}$ = $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ = $- a y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{31}}$ = $- z_{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ = $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{32}}$ = $- z_{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) O II
$\mathbf{B_{33}}$ = $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ = $a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{34}}$ = $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{35}}$ = $z_{5} \, \mathbf{a}_{1}+\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{36}}$ = $z_{5} \, \mathbf{a}_{1}+\left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{37}}$ = $\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{38}}$ = $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ = $- a y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{39}}$ = $- z_{5} \, \mathbf{a}_{1}+\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ = $a \left(y_{5} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{5} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{40}}$ = $- z_{5} \, \mathbf{a}_{1}- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{5} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{5} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (16h) W I
$\mathbf{B_{41}}$ = $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{42}}$ = $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{43}}$ = $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{44}}$ = $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{45}}$ = $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(- x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{46}}$ = $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{47}}$ = $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{48}}$ = $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{49}}$ = $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{50}}$ = $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}+a \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{51}}$ = $- \left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{52}}$ = $\left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{53}}$ = $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} - y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a x_{6} \,\mathbf{\hat{x}}- a \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{54}}$ = $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{3}$ = $- a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{55}}$ = $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{6} + y_{6}\right) \, \mathbf{a}_{3}$ = $- a \left(y_{6} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III
$\mathbf{B_{56}}$ = $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(y_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(x_{6} + y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ = $a \left(y_{6} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+c \left(z_{6} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ (32i) O III

References

  • H. Horiuchi, N. Morimoto, and S. Yamaoka, The crystal structure of Li2WO4II: A structure related to spinel, J. Solid State Chem. 30, 129–135 (1979), doi:10.1016/0022-4596(79)90094-X.
  • S. Yamaoka, O. Fukunaga, T. Ono, E. Iizuka, and S. Asami, Phase Transformations of Li$_{2}$WO$_{4}$ at High Pressure, J. Solid State Chem. 6, 280–285 (1973), doi:10.1016/0022-4596(73)90191-6.
  • C. W. F. T. Pistorius, Phase Behavior of Li$_{2}$WO$_{4}$ at High Pressures and Temperatures, J. Solid State Chem. 13, 325–329 (1975), doi:10.1016/0022-4596(75)90147-4.
  • M. Hämmer and H. A. Höppe, New Insights into Alkali Metal Tungstates: The High Temperature Polymorphism of Na$_{2}$WO$_{4}$, the New Polymorph Li$_{2}$WO$_{4}$-V and the Redetermined Crystal Structure of Li$_{2}$W$_{2}$O$_{7}$, Z. Anorganische und Allgemeine Chemie 648, 202100373 (2022), doi:10.1002/zaac.202100373.
  • I. N. Belyaev, , Russ. J. Inorg. Chem. 6, 602 (1961).

Found in

  • H. Horiuchi, N. Morimoto, and S. Yamaoka, The crystal structure of Li$_{2}$WO$_{4}$(IV) and its relation to the wolframite-type structure, J. Solid State Chem. 35, 115–119 (1980), doi:10.1016/0022-4596(80)90554-X.

First cited in

  • N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).

Geometry files


Prototype Generator

aflow --proto=A2B4C_tI112_141_fg_2hi_h --params=$a,c/a,x_{1},x_{2},y_{3},z_{3},y_{4},z_{4},y_{5},z_{5},x_{6},y_{6},z_{6}$

Species:

Running:

Output: