AFLOW Prototype: A5B3C_hP18_186_2a3b_2ab_b
Prototype | : | Al5C3N |
AFLOW prototype label | : | A5B3C_hP18_186_2a3b_2ab_b |
Strukturbericht designation | : | $E9_{4}$ |
Pearson symbol | : | hP18 |
Space group number | : | 186 |
Space group symbol | : | $\text{P6}_{3}\text{mc}$ |
AFLOW prototype command | : | aflow --proto=A5B3C_hP18_186_2a3b_2ab_b --params=$a$,$c/a$,$z_1$,$z_2$,$z_3$,$z_4$,$z_5$,$z_6$,$z_7$,$z_8$,$z_9$ |
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B_1} & = & z_1 \, \mathbf{a}_{3} & = & z_1 \, \, c \, \mathbf{\hat{z}} &\left(2a\right) & \text{Al I} \\ \mathbf{B_2} & = & \left(\frac12 + z_1\right) \, \mathbf{a}_{3} & = & \left(\frac12 +z_1\right) \, \, c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Al I} \\ \mathbf{B_3} & = & z_2 \, \mathbf{a}_{3} & = & z_2 \, \, c \, \mathbf{\hat{z}} &\left(2a\right) & \text{Al II} \\ \mathbf{B_4} & = & \left(\frac12 + z_2\right) \, \mathbf{a}_{3} & = & \left(\frac12 +z_2\right) \, \, c \, \mathbf{\hat{z}} & \left(2a\right) & \text{Al II} \\ \mathbf{B_5} & = & z_3 \, \mathbf{a}_{3} & = & z_3 \, \, c \, \mathbf{\hat{z}} &\left(2a\right) & \text{C I} \\ \mathbf{B_6} & = & \left(\frac12 + z_3\right) \, \mathbf{a}_{3} & = & \left(\frac12 +z_3\right) \, \, c \, \mathbf{\hat{z}} & \left(2a\right) & \text{C I} \\ \mathbf{B_7} & = & z_4 \, \mathbf{a}_{3} & = & z_4 \, \, c \, \mathbf{\hat{z}} &\left(2a\right) & \text{C II} \\ \mathbf{B_8} & = & \left(\frac12 + z_4\right) \, \mathbf{a}_{3} & = & \left(\frac12 +z_4\right) \, \, c \, \mathbf{\hat{z}} & \left(2a\right) & \text{C II} \\ \mathbf{B_9} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_5 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_5 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al III} \\ \mathbf{B}_{10} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_5\right) \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_5\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al III} \\ \mathbf{B}_{11} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_6 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_6 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al IV} \\ \mathbf{B}_{12} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_6\right) \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_6\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al IV} \\ \mathbf{B}_{13} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_7 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_7 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al V} \\ \mathbf{B}_{14} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_7\right) \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_7\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{Al V} \\ \mathbf{B}_{15} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_8 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_8 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{C III} \\ \mathbf{B}_{16} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_8\right) \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_8\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{C III} \\ \mathbf{B}_{17} & =& \frac13 \mathbf{a}_{1} + \frac23 \mathbf{a}_{2} + z_9 \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ z_9 \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{N} \\ \mathbf{B}_{18} & =& \frac23 \mathbf{a}_{1} + \frac13 \mathbf{a}_{2} + \left(\frac12 + z_9\right) \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - \frac{1}{2\sqrt{3}} \, a \, \mathbf{\hat{y}}+ \left(\frac12 + z_9\right) \, c \, \mathbf{\hat{z}}& \left(2b\right) & \text{N} \\ \end{array} \]