ZrNiAl Structure: ABC_hP9_189_f_bc_g-003
| Prototype | AlNiZr |
| AFLOW prototype label | ABC_hP9_189_f_bc_g-003 |
| ICSD | 152131 |
| Pearson symbol | hP9 |
| Space group number | 189 |
| Space group symbol | $P\overline{6}2m$ |
| AFLOW prototype command |
aflow --proto=ABC_hP9_189_f_bc_g-003
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak x_{4}$ |
Other compounds with this structure
AgAsCa, AgSiYb, AlCoPu, AlCuTm, AlNiTb, DyNiIn, DyNiSn, ErNiAl, FeCoAs, FeGaU, FeNiP, GaNiZr, GaPdSc, GdNiIn, GdNiSn, HoNiIn, RhSnZr, RuSiZr, ScIrP, TbNiIn, TiFeP, ZrRuAs, BSi$_{2}$Ni$_{6}$
- This a the ternary form of the Fe$_{2}$P structure. While (Shved, 2019) placed the nickel atoms on the (1a) and (2d) sites, as in Fe$_{2}$P, we have shifted to origin by $\frac12 c \hat{z}$ to place them on the (1b) and (2c) sites. Otherwise the structures are nearly identical.
- (Shved, 2019) found evidence of 6-10% mixing between the Ni-II (2d) and Al (3g) sites.
- (Shved, 2019) has no entry in the ICSD, so we reference the ZrNiAl entry from (Zumdick, 1999).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Ni I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Ni II |
| $\mathbf{B_{3}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}$ | (2c) | Ni II |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | Al I |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a x_{3} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}$ | (3f) | Al I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (3f) | Al I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Zr I |
| $\mathbf{B_{8}}$ | = | $x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a x_{4} \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Zr I |
| $\mathbf{B_{9}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (3g) | Zr I |
References
- O. Shved, L. P. Salamakha, S. Mudry, O. Sologub, P. F. Rogl, and E. Bauer, Zr-based nickel aluminides: crystal structure and electronic properties, J. Alloys Compd. p. 153326 (2019), doi:10.1016/j.jallcom.2019.153326. In press.
- M. F. Zumdick, R.-D. Hoffmann, and R. Pöttgen, The Intermetallic Zirconium Compounds ZrNiAl, ZrRhSn, and ZrPtGa - Structural Distortions and Metal-Metal Bonding in Fe$_{2}$P Related Compounds, Z. Naturforsch. B 54, 45–53 (1999), doi:10.1515/znb-1999-0111.
Prototype Generator
aflow --proto=ABC_hP9_189_f_bc_g --params=$a,c/a,x_{3},x_{4}$