AlN (cI24) Structure : AB_cI24_220_a_b

Picture of Structure; Click for Big Picture
Prototype : AlN
AFLOW prototype label : AB_cI24_220_a_b
Strukturbericht designation : None
Pearson symbol : cI24
Space group number : 220
Space group symbol : $I\bar{4}3d$
AFLOW prototype command : aflow --proto=AB_cI24_220_a_b
--params=
$a$



Body-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, a \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{z}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{3} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{4} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{5} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{6} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12a\right) & \mbox{Al} \\ \mathbf{B}_{7} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}- \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{8} \, \mathbf{a}_{2} + \frac{5}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \mathbf{B}_{9} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & - \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \mathbf{B}_{10} & = & \frac{5}{8} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{8} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \mathbf{B}_{11} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \mathbf{B}_{12} & = & \frac{3}{8} \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(12b\right) & \mbox{N} \\ \end{array} \]

References

  • C. Liu, M. Chen, J. Li, L. Liu, P. Li, M. Ma, C. Shao, J. He, and T. Liang, A first–principles study of novel cubic AlN phases, J. Phys. Chem. Solids 130, 58–66 (2019), doi:10.1016/j.jpcs.2019.02.009.

Geometry files


Prototype Generator

aflow --proto=AB_cI24_220_a_b --params=

Species:

Running:

Output: