AFLOW Prototype: AB7CD2_oI44_24_a_b3d_c_ac
Prototype | : | Na2MgAlF7 |
AFLOW prototype label | : | AB7CD2_oI44_24_a_b3d_c_ac |
Strukturbericht designation | : | None |
Pearson symbol | : | oI44 |
Space group number | : | 24 |
Space group symbol | : | $I2_{1}2_{1}2_{1}$ |
AFLOW prototype command | : | aflow --proto=AB7CD2_oI44_24_a_b3d_c_ac --params=$a$,$b/a$,$c/a$,$x_{1}$,$x_{2}$,$y_{3}$,$z_{4}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{1}\right) \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Al} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Al} \\ \mathbf{B}_{3} & = & \frac{1}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{2}\right) \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Na I} \\ \mathbf{B}_{4} & = & \frac{3}{4} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Na I} \\ \mathbf{B}_{5} & = & y_{3} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} +y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} & \left(4b\right) & \text{F I} \\ \mathbf{B}_{6} & = & \left(\frac{1}{2} - y_{3}\right) \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \left(\frac{1}{4} - y_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \text{F I} \\ \mathbf{B}_{7} & = & \left(\frac{1}{4} +z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Mg} \\ \mathbf{B}_{8} & = & \left(\frac{1}{4} - z_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Mg} \\ \mathbf{B}_{9} & = & \left(\frac{1}{4} +z_{5}\right) \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Na II} \\ \mathbf{B}_{10} & = & \left(\frac{1}{4} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(4c\right) & \text{Na II} \\ \mathbf{B}_{11} & = & \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} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F II} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - y_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} - y_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{6}\right)b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F II} \\ \mathbf{B}_{13} & = & \left(y_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6} + y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{6}\right)a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}}-z_{6}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F II} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - y_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}-y_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{6}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F II} \\ \mathbf{B}_{15} & = & \left(y_{7}+z_{7}\right) \, \mathbf{a}_{1} + \left(x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}+y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F III} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - y_{7} + z_{7}\right) \, \mathbf{a}_{1} + \left(-x_{7}+z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7} - y_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{7}\right)b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F III} \\ \mathbf{B}_{17} & = & \left(y_{7}-z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7} - z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7} + y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{7}\right)a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F III} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - y_{7} - z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7} - z_{7}\right) \, \mathbf{a}_{2} + \left(x_{7}-y_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{7}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F III} \\ \mathbf{B}_{19} & = & \left(y_{8}+z_{8}\right) \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}+y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F IV} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - y_{8} + z_{8}\right) \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8} - y_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{8}\right)b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F IV} \\ \mathbf{B}_{21} & = & \left(y_{8}-z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8} - z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8} + y_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{8}\right)a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F IV} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - y_{8} - z_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{8} - z_{8}\right) \, \mathbf{a}_{2} + \left(x_{8}-y_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{8}\right)c \, \mathbf{\hat{z}} & \left(8d\right) & \text{F IV} \\ \end{array} \]