AFLOW Prototype: ABC4D_oI28_74_a_d_hi_e
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=$a$,$b/a$,$c/a$,$z_{3}$,$y_{4}$,$z_{4}$,$x_{5}$,$z_{5}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{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) & \text{O II} \\ \end{array} \]