$D1_{3}$ (BaAl$_{4}$) Structure: A4B_tI10_139_de_a-001
| Prototype | Al$_{4}$Ba |
| AFLOW prototype label | A4B_tI10_139_de_a-001 |
| Strukturbericht designation | $D1_{3}$ |
| ICSD | 57513 |
| Pearson symbol | tI10 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A4B_tI10_139_de_a-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}$ |
Other compounds with this structure
BaGa$_{4}$, BaIn$_{4}$, CaAl$_{4}$, CaGa$_{4}$, CeAl$_{4}$, EuAl$_{4}$, EuGa$_{4}$, KIn$_{4}$, LaAl$_{4}$, NdAl$_{4}$, PrAl$_{4}$, SmAl$_{4}$, SrAl$_{4}$, SrGa$_{4}$, ThZn$_{4}$, TlGa$_{4}$, YAl$_{4}$
- BaAl$_{4}$ is the parent structure of a number of ternary compounds (Shatruk, 2019):
- ThCr$_{2}$Si$_{2}$, space group $I4/mmm$ #139, with $c/a < 3$.
- TlCo$_{2}$S$_{2}$, also in space group $I4/mmm$ #139 but with $c/a > 3$.
- CaBe$_{2}$Ge$_{2}$, space group $P4/nmm$ #129.
- BaNiSn$_{3}$, space group $I4mm$ #107.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Ba I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Al I |
| $\mathbf{B_{4}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Al II |
| $\mathbf{B_{5}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Al II |
References
- K. R. Andress and E. Alberti, Röntgenographische Untersuchung der Legierungsreihe Aluminium-Barium, Z. Metallkd. 27, 126–128 (1935).
- M. Shatruk, ThCr$_{2}$Si$_{2}$ structure type: The
perovskite
of intermetallics, J. Solid State Chem. 272, 198–209 (2019), doi:10.1016/j.jssc.2019.02.012.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=A4B_tI10_139_de_a --params=$a,c/a,z_{3}$