Al$_{3}$Zr ($D0_{23}$) Structure: A3B_tI16_139_cde_e-001
| Prototype | Al$_{3}$Zr |
| AFLOW prototype label | A3B_tI16_139_cde_e-001 |
| Strukturbericht designation | $D0_{23}$ |
| ICSD | 107130 |
| Pearson symbol | tI16 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A3B_tI16_139_cde_e-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}$ |
Other compounds with this structure
Al$_{3}$Hf, Ga$_{3}$Zr
- When c=4a, z$_{3}$=3/8 and z$_{4}$=1/8 the atoms are on the sites of a face-centered cubic lattice. This phase can also be described as a set of alternating $L1_{2}$ and $D0_{22}$ lattices.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (4c) | Al I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (4c) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al II |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Al III |
| $\mathbf{B_{6}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Al III |
| $\mathbf{B_{7}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Zr I |
| $\mathbf{B_{8}}$ | = | $- z_{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (4e) | Zr I |
References
- Y. Ma, C. Romming, B. Lebech, J. Gjonnes, and J. Tafto, Structure Refinement of AI3Zr using Single-Crystal X-ray Diffraction, Powder Neutron Diffraction and CBED, Acta Crystallogr. Sect. B 48, 11–16 (1992), doi:10.1107/S0108768191010467.
Found in
- G. Ghosh and M. Asta, First-principles calculation of structural energetics of Al-TM (TM = Ti, Zr, Hf) intermetallics, Acta Mater. 53, 3225–3252 (2005), doi:10.1016/j.actamat.2005.03.028.
Prototype Generator
aflow --proto=A3B_tI16_139_cde_e --params=$a,c/a,z_{3},z_{4}$