AlN (cF40) Structure : AB_cF40_216_ce_de
| Prototype | : | AlN |
| AFLOW prototype label | : | AB_cF40_216_ce_de |
| Strukturbericht designation | : | None |
| Pearson symbol | : | cF40 |
| Space group number | : | 216 |
| Space group symbol | : | $F\bar{4}3m$ |
| AFLOW prototype command | : | aflow --proto=AB_cF40_216_ce_de --params=$a$,$x_{3}$,$x_{4}$ |
- AlN naturally occurs in two forms (Liu, 2019): the stable wz–AlN wurtzite ($B4$) structure, and the high–pressure rs–AlN rock salt ($B1$) structure. A metastable zb–AlN zincblende (zb–AlN) structure can be synthesized via a solid–state reaction.
- (Liu, 2019) used a first–principles evolutionary technique to find four possible metastable phases: one in the SC16 structure, and three novel cubic structures, cF40, cI16, and cI24.
Face-centered Cubic primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]
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{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(4c\right) & \mbox{Al I} \\ \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(4d\right) & \mbox{N I} \\ \mathbf{B}_{3} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Al II} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-3x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Al II} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1}-3x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Al II} \\ \mathbf{B}_{6} & = & -3x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{Al II} \\ \mathbf{B}_{7} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{N II} \\ \mathbf{B}_{8} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-3x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{N II} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1}-3x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{N II} \\ \mathbf{B}_{10} & = & -3x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(16e\right) & \mbox{N II} \\ \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.