NbP (40
) Structure: AB_tI8_141_a_b-001
| Prototype | NbP |
| AFLOW prototype label | AB_tI8_141_a_b-001 |
| Strukturbericht designation | ``40'' |
| ICSD | 76027 |
| CCDC | 1636665 |
| Pearson symbol | tI8 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=AB_tI8_141_a_b-001
--params=$a, \allowbreak c/a$ |
- When $c/a=2$, the atoms in this lattice are on the sites of the face-centered cubic lattice. Thus (Lu, 1991) use this lattice for their structural stability studies, and arbitrarily assign this lattice a Strukturbericht designation of
40.
Note that (Schönberg, 1954) gives the space group as $I4_{1}22$ #98 but, as (Villars, 1991) notes, the coordinates given increase the symmetry to $I4_{1}/amd$ #141.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4a) | Nb I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4a) | Nb I |
| $\mathbf{B_{3}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (4b) | P I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (4b) | P I |
References
- N. Schönberg, An X-Ray Investigation of Transition Metal Phosphides, Acta Chem. Scand. 8, 226–239 (1954), doi:10.3891/acta.chem.scand.08-0221.
- Z. W. Lu, S.-H. Wei, and A. Zunger, Long-Range Order in Binary Late-Transition-Metal Alloys, Phys. Rev. Lett. 66, 1753–1756 (1991), doi:10.1103/PhysRevLett.66.1753.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
First cited in
- 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)
Geometry files
Prototype Generator
aflow --proto=AB_tI8_141_a_b --params=$a,c/a$