Al$_{6}$C$_{3}$N$_{2}$ Structure: A6B3C2_hR11_166_3c_ac_c-001
| Prototype | Al$_{6}$C$_{3}$N$_{2}$ |
| AFLOW prototype label | A6B3C2_hR11_166_3c_ac_c-001 |
| ICSD | 654993, 41260 |
| Pearson symbol | hR11 |
| Space group number | 166 |
| Space group symbol | $R\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A6B3C2_hR11_166_3c_ac_c-001
--params=$a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}$ |
- The structure presented by (Jeffrey, 1966) has problems similar to those of Al$_{8}$C$_{3}$N$_{4}$. See that page for a discussion of our resolution of the problems.
- The ICSD is rather confused about this compound. The entry associated with (Jeffrey, 1996), #41260, has the original structure. Entry #654993 gives a structure quite similar to ours, but it is attributed to (Suzuki, 1993), a paper concerning the structure of iron nitride. It is better associated with (Daams, 1993). We list both ICSDs, but consider #654993 the correct structure.
- Hexagonal settings of this structure can be obtained with the option
--hex.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | C I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $- c x_{2} \,\mathbf{\hat{z}}$ | (2c) | Al I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- c x_{3} \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+x_{4} \, \mathbf{a}_{3}$ | = | $c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Al III |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- x_{4} \, \mathbf{a}_{3}$ | = | $- c x_{4} \,\mathbf{\hat{z}}$ | (2c) | Al III |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+x_{5} \, \mathbf{a}_{3}$ | = | $c x_{5} \,\mathbf{\hat{z}}$ | (2c) | C II |
| $\mathbf{B_{9}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- x_{5} \, \mathbf{a}_{3}$ | = | $- c x_{5} \,\mathbf{\hat{z}}$ | (2c) | C II |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $c x_{6} \,\mathbf{\hat{z}}$ | (2c) | N I |
| $\mathbf{B_{11}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- c x_{6} \,\mathbf{\hat{z}}$ | (2c) | N I |
References
- G. A. Jeffrey and V. Y. Wu, The structure of the aluminum carbonitrides. II, Acta Cryst. 20, 538–547 (1966), doi:10.1107/S0365110X66001208.
- K. Suzuki, H. Morita, T. Kaneko, H. Yoshida, and H. Fujimori, Crystal structure and magnetic properties of the compound FeN, J. Alloys Compd. 201, 11–16 (1993), doi:10.1016/0925-8388(93)90854-G.
- J. L. C. Daams and P. Villars, Atomic environment classification of the rhombohedral
intermetallic
structure types, J. Alloys Compd. 197, 243–269 (1993), doi:10.1016/0925-8388(93)90046-P.
Found in
- P. Villars, Pearson's Handbook (ASM International, Materials Park OH, 1999), vol. 1, chap. Compound Table, pp. 296–297, desk edition edn.
Prototype Generator
aflow --proto=A6B3C2_hR11_166_3c_ac_c --params=$a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6}$