AFLOW Prototype: AB13_cF112_226_a_bi
Prototype | : | NaZn |
AFLOW prototype label | : | AB13_cF112_226_a_bi |
Strukturbericht designation | : | $D2_{3}$ |
Pearson symbol | : | cF112 |
Space group number | : | 226 |
Space group symbol | : | $Fm\bar{3}c$ |
AFLOW prototype command | : | aflow --proto=AB13_cF112_226_a_bi --params=$a$,$y_{3}$,$z_{3}$ |
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} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Na} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(8a\right) & \text{Na} \\ \mathbf{B}_{3} & = & 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(8b\right) & \text{Zn I} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(8b\right) & \text{Zn I} \\ \mathbf{B}_{5} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{6} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}} + z_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{7} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{8} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{y}}-z_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{9} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{10} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{11} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}} + y_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{12} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -z_{3}a \, \mathbf{\hat{x}}-y_{3}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{13} & = & \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{14} & = & \left(y_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}} + z_{3}a \, \mathbf{\hat{y}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{15} & = & \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{16} & = & \left(y_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{3} & = & -y_{3}a \, \mathbf{\hat{x}}-z_{3}a \, \mathbf{\hat{y}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{17} & = & \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(96i\right) & \text{Zn II} \\ \end{array} \]