Erroneous $L'1_{0}$ Structure: A4B_cP5_221_bc_a-001
| Prototype | Fe$_{4}$N |
| AFLOW prototype label | A4B_cP5_221_bc_a-001 |
| Strukturbericht designation | $L'1_{0}$ |
| ICSD | none |
| Pearson symbol | cP5 |
| Space group number | 221 |
| Space group symbol | $Pm\overline{3}m$ |
| AFLOW prototype command |
aflow --proto=A4B_cP5_221_bc_a-001
--params=$a$ |
- We (Hicks, 2019) accidentally misplaced the nickel atom in the $L'1_{0}$ structure. The correct structure can be found at $\gamma$'-Fe$_{4}$N $L'1_{0}$ page.
- Despite our error, this is a binary form of the cubic perovskite structure (AB3C_cP5_221_a_c_b), Strukturbericht designation $E2_{1}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (1b) | Fe I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Fe II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (3c) | Fe II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}$ | (3c) | Fe II |
References
- H. Jacobs, R. Rechenbach, and U. Zachwieja, Structure determination of $\gamma'$-Fe$_{4}$N and ε-Fe$_{3}$Na, J. Alloys Compd. 227, 10–17 (1995), doi:10.1016/0925-8388(95)01610-4.
- D. Hicks, M. J.Mehl, M. Esters, C. Oses, O. Levy, G. L. W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comput. Mater. Sci. 199, 110450 (2021), doi:10.1016/j.commatsci.2021.110450.
Prototype Generator
aflow --proto=A4B_cP5_221_bc_a --params=$a$