AFLOW Prototype: ABC6D15_oC46_38_b_b_2a2d_2ab4d2e
Prototype | : | FNaNb6O15 |
AFLOW prototype label | : | ABC6D15_oC46_38_b_b_2a2d_2ab4d2e |
Strukturbericht designation | : | None |
Pearson symbol | : | oC46 |
Space group number | : | 38 |
Space group symbol | : | $Amm2$ |
AFLOW prototype command | : | aflow --proto=ABC6D15_oC46_38_b_b_2a2d_2ab4d2e --params=$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$z_{3}$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$y_{8}$,$z_{8}$,$y_{9}$,$z_{9}$,$y_{10}$,$z_{10}$,$y_{11}$,$z_{11}$,$y_{12}$,$z_{12}$,$y_{13}$,$z_{13}$,$y_{14}$,$z_{14}$,$y_{15}$,$z_{15}$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Nb I} \\ \mathbf{B}_{2} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Nb II} \\ \mathbf{B}_{3} & = & -z_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & z_{3}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{O I} \\ \mathbf{B}_{4} & = & -z_{4} \, \mathbf{a}_{2} + z_{4} \, \mathbf{a}_{3} & = & z_{4}c \, \mathbf{\hat{z}} & \left(2a\right) & \text{O II} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{5}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{F} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{6}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{Na} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + z_{7}c \, \mathbf{\hat{z}} & \left(2b\right) & \text{O III} \\ \mathbf{B}_{8} & = & \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb III} \\ \mathbf{B}_{9} & = & \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & -y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb III} \\ \mathbf{B}_{10} & = & \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb IV} \\ \mathbf{B}_{11} & = & \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{Nb IV} \\ \mathbf{B}_{12} & = & \left(y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O IV} \\ \mathbf{B}_{13} & = & \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O IV} \\ \mathbf{B}_{14} & = & \left(y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O V} \\ \mathbf{B}_{15} & = & \left(-y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O V} \\ \mathbf{B}_{16} & = & \left(y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VI} \\ \mathbf{B}_{17} & = & \left(-y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & -y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VI} \\ \mathbf{B}_{18} & = & \left(y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VII} \\ \mathbf{B}_{19} & = & \left(-y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & -y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O VII} \\ \mathbf{B}_{20} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O VIII} \\ \mathbf{B}_{21} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O VIII} \\ \mathbf{B}_{22} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O IX} \\ \mathbf{B}_{23} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(-y_{15}-z_{15}\right) \, \mathbf{a}_{2} + \left(-y_{15}+z_{15}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-y_{15}b \, \mathbf{\hat{y}} + z_{15}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O IX} \\ \end{array} \]