$L'3_{0}$ (approximate Fe$_{2}$N) Structure: AB_hP4_194_c_a-003
| Prototype | Fe$_{2}$N |
| AFLOW prototype label | AB_hP4_194_c_a-003 |
| Strukturbericht designation | $L'3_{0}$ |
| ICSD | none |
| Pearson symbol | hP4 |
| Space group number | 194 |
| Space group symbol | $P6_3/mmc$ |
| AFLOW prototype command |
aflow --proto=AB_hP4_194_c_a-003
--params=$a, \allowbreak c/a$ |
Other compounds with this structure
$\beta$-CTa$_{2}$, CV$_{2}$, CW$_{2}$, Mn$_{2}$N, Nb$_{2}$N, Ta$_{\approx 2}$N
- The $L'3_{0}$ designation is only found in (Smithells, 1955) and (Pearson, 1958), as well as their following volumes.
- Smithells gives two possible positions of the nitrogen atoms. We use the one that matches Pearson, which (Parthé, 1993) notes is equivalent to the NiAs $B8_{1}$ structure, but here the (2a) nitrogen site is only half-filled to maintain stoichiometry.
- Neither of the defining references gives a source for the structure.
- It is likely an approximation to $\epsilon$–Fe$_{2}$N, which has the $\beta$–V$_{2}$N $L'3_{2}$ structure.
- We take the lattice constants for this structure from the Fe-Fe distances in $\epsilon$–Fe$_{2}$N provided by (Hendricks, 1930), though this is not the structure described by Hendricks.
- The similar compounds list is taken from (Pearson, 1967). As it is quite similar to the list for $\beta$–V$_{2}$N, it is likely that this structure is only an approximation to the correct structure for these compounds as well.
- Fe$_{2}$N is also observed in the $\zeta$–Fe$_{2}$N structure.
- This structure has the same AFLOW designation, AB_hP4_194_c_a_Fe2N, as $B8_{1}$. The two structures differ by their lattice constants and the half-occupancy of the (2a) site in $L'3_{0}$.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | N I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2a) | N I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Fe I |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (2c) | Fe I |
References
- C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 4 (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.
- E. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzula, and R. Gladyshevskii, Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Gmelin Handbook of Inorganic and Organometallic Chemistry, vol. 2 (Springer-Verlag, Berlin, Heidelberg, 1993), 8 edn., doi:10.1007/978-3-662-02909-1_3.
- S. B. Hendricks and P. R. Kosting, The Crystal Structure of Fe$_2$P, Fe$_2$N, Fe$_3$N and FeB, Z. ristallogr. 74, 511–533 (1930), doi:10.1524/zkri.1930.74.1.511.
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Prototype Generator
aflow --proto=AB_hP4_194_c_a --params=$a,c/a$