Fe$_{8}$N ($D2_{g}$) Structure: A8B_tI18_139_deh_a-001
| Prototype | Fe$_{8}$N |
| AFLOW prototype label | A8B_tI18_139_deh_a-001 |
| Strukturbericht designation | $D2_{g}$ |
| ICSD | 654562 |
| Pearson symbol | tI18 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A8B_tI18_139_deh_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak x_{4}$ |
- (Jack, 1951) and others refer to this structure as $\alpha$-Fe$_{16}$N$_{2}$.
- (Yamashita, 2012) determined the structure by examining crystals containing various amounts of $\alpha$-Fe$_{16}$N$_{2}$ and $\alpha$–Fe (bcc iron). We use their data from the sample that was 90% $\alpha$-Fe$_{16}$N$_{2}$. Their measurements were confirmed by first principles calculations and are in agreement with the first principles calculations of (Sims, 2012).
- The ICSD entry is from (Jack, 1951).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Fe I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Fe I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Fe II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Fe II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Fe III |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Fe III |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Fe III |
| $\mathbf{B_{9}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Fe III |
References
- S. Yamashita, Y. Masubuchi, Y. Nakazawa, T. Okayama, M. Tsuchiya, and S. Kikkawa, Crystal structure and magnetic properties of “$\alpha$-Fe$_{16}$N$_{2}$” containing residual α-Fe prepared by low-temperature ammonia nitridation, J. Solid State Chem. 194, 76–79 (2012), doi:10.1016/j.jssc.2012.07.025.
- K. H. Jack, The occurrence and the crystal structure of $\alpha$-iron nitride; a new type of interstitial alloy formed during the tempering of nitrogen-martensite, Proc. R. Soc. A Math. Phys. Eng. Sci. 208, 216–217 (1951), doi:10.1098/rspa.1951.0155.
- H. Sims, W. H. Butler, M. Richter, K. Koepernik, E. Şaşioğlu, C. Friedrich, and S. Blügel, Theoretical investigation into the possibility of very large moments in Fe$_{16}$N$_{2}$, Phys. Rev. B 86, 174422 (2012), doi:10.1103/PhysRevB.86.174422.
Prototype Generator
aflow --proto=A8B_tI18_139_deh_a --params=$a,c/a,z_{3},x_{4}$