# Encyclopedia of Crystallographic Prototypes

M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)

## Fe2N (approximate, $L'3_{0}$) Structure : AB_hP4_194_c_a

 Prototype : Fe2N AFLOW prototype label : AB_hP4_194_c_a Strukturbericht designation : $L'3_{0}$ Pearson symbol : hP4 Space group number : 194 Space group symbol : $P6_{3}/mmc$ AFLOW prototype command : aflow --proto=AB_hP4_194_c_a --params=$a$,$c/a$

### Other compounds with this structure

• $\beta$–CTa2, CV2, CW2, Mn2N, Nb2N, and Ta$_{≈ 2}$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 $\epsilon$–Fe2N, which has the $\beta$–V2N $L'3_{2}$ structure. We take the lattice constants for this structure from the Fe–Fe distances in $\epsilon$–Fe2N provided by (Hendricks, 1930).
• The similar compounds list is taken from (Pearson, 1967). As it is quite similar to the list for $\beta$–V2N, it is likely that this structure is only an approximation to the correct structure for these compounds as well.
• 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 $L'3_{0}$.

### Hexagonal primitive vectors:

$\begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{x}} - \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac{\sqrt3}2 \, a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array}$

Basis vectors:

$\begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{N} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2a\right) & \mbox{N} \\ \mathbf{B}_{3} & = & \frac{1}{3} \, \mathbf{a}_{1} + \frac{2}{3} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Fe} \\ \mathbf{B}_{4} & = & \frac{2}{3} \, \mathbf{a}_{1} + \frac{1}{3} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}- \frac{1}{2\sqrt{3}}a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Fe} \\ \end{array}$

### 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. N. R. C. No. 4303.
• E. Parthé, L. Gelato, B. Chabot, M. Penzo, K. Cenzual, and R. Gladyshevskii, in Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types (Springer–Verlag, Berlin, Heidelberg, 1993), Gmelin Handbook of Inorganic and Organometallic Chemistry, vol. 2, chap. Crystal Chemical Characterization of Inorganic Structure Types, 8 edn., doi:10.1007/978-3-662-02909-1_3.
• S. B. Hendricks and P. R. Kosting, The Crystal Structure of Fe2P, Fe2N, Fe3N and FeB, Zeitschrift für Kristallographie – Crystalline Materials 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). N. R. C. No. 8752.

### Prototype Generator

aflow --proto=AB_hP4_194_c_a --params=