LiCuVO4 Structure : ABC4D_oI28_74_a_d_hi_e

Picture of Structure; Click for Big Picture
Prototype : CuLiO4V
AFLOW prototype label : ABC4D_oI28_74_a_d_hi_e
Strukturbericht designation : None
Pearson symbol : oI28
Space group number : 74
Space group symbol : $Imma$
AFLOW prototype command : aflow --proto=ABC4D_oI28_74_a_d_hi_e
--params=
$a$,$b/a$,$c/a$,$z_{3}$,$y_{4}$,$z_{4}$,$x_{5}$,$z_{5}$


Body-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 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{Cu} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}b \, \mathbf{\hat{y}} & \left(4a\right) & \mbox{Cu} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Li} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}}- \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \mbox{Li} \\ \mathbf{B}_{5} & = & \left(\frac{1}{4} +z_{3}\right) \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{V} \\ \mathbf{B}_{6} & = & \left(\frac{3}{4} - z_{3}\right) \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}b \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{V} \\ \mathbf{B}_{7} & = & \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O I} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{4}\right)b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O I} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{1}-z_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & \left(\frac{1}{4} +z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O II} \\ \mathbf{B}_{12} & = & \left(\frac{1}{4} +z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O II} \\ \mathbf{B}_{13} & = & \left(\frac{3}{4} - z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O II} \\ \mathbf{B}_{14} & = & \left(\frac{3}{4} - z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O II} \\ \end{array} \]

References

  • M. A. Lafontaine, M. Leblanc, and G. Ferey, New refinement of the room–temperature structure of LiCuVO4, Acta Crystallogr. C 45, 1205–1206 (1989), doi:10.1107/S0108270189001551.

Found in

  • A. V. Prokofiev, I. G. Vasilyeva, V. N. Ikorskii, V. V. Malakhov, I. P. Asanov, and W. Assmus, Structure, stoichiometry and magnetic properties of the low–dimensional structure phase LiCuVO4, J. Solid State Chem. 177, 3131–3139 (2004), doi:10.1016/j.jssc.2004.05.031.

Geometry files


Prototype Generator

aflow --proto=ABC4D_oI28_74_a_d_hi_e --params=

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