Sc$_{11}$Al$_{2}$Ge$_{8}$ Structure: A2B8C11_tI84_139_h_deim_eh2n-001
| Prototype | Al$_{2}$Ge$_{8}$Sc$_{11}$ |
| AFLOW prototype label | A2B8C11_tI84_139_h_deim_eh2n-001 |
| ICSD | 184236 |
| CCDC | 1693480 |
| Pearson symbol | tI84 |
| Space group number | 139 |
| Space group symbol | $I4/mmm$ |
| AFLOW prototype command |
aflow --proto=A2B8C11_tI84_139_h_deim_eh2n-001
--params=$a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak z_{7}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak y_{9}, \allowbreak z_{9}$ |
Other compounds with this structure
Er$_{11}$Al$_{2}$Ge$_{8}$, Gd$_{11}$In$_{2}$Ge$_{8}$, Yb$_{11}$Sn$_{2}$Bi$_{8}$
- This is a tenary form of Ho$_{11}$Ge$_{10}$. The ICSD lists all these compounds using the Ho$_{11}$Ge$_{10}$ prototype. We arbitrarily chose Sc$_{11}$Al$_{2}$Ge$_{8}$ as the prototype.
- Tb$_{11}$Si$_{4}$In$_{6}$ is a second ternary form of Ho$_{11}$Ge$_{10}$.
- The AFLOW standard labeling algorithm shifts the origin by (0.5 a, 0.5 b, 0), moving the Ge III atom from the published (8j) Wyckoff position to (8i).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Ge I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4d) | Ge I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Ge II |
| $\mathbf{B_{4}}$ | = | $- z_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}$ | = | $- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | Ge II |
| $\mathbf{B_{5}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Sc I |
| $\mathbf{B_{6}}$ | = | $- z_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}$ | = | $- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | Sc I |
| $\mathbf{B_{7}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+2 x_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{8}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}- 2 x_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}$ | (8h) | Al I |
| $\mathbf{B_{11}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+2 x_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Sc II |
| $\mathbf{B_{12}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}- 2 x_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Sc II |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Sc II |
| $\mathbf{B_{14}}$ | = | $- x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}$ | (8h) | Sc II |
| $\mathbf{B_{15}}$ | = | $x_{6} \, \mathbf{a}_{2}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}$ | (8i) | Ge III |
| $\mathbf{B_{16}}$ | = | $- x_{6} \, \mathbf{a}_{2}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}$ | (8i) | Ge III |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{y}}$ | (8i) | Ge III |
| $\mathbf{B_{18}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{y}}$ | (8i) | Ge III |
| $\mathbf{B_{19}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+2 x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{20}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- 2 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{21}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{22}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{23}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{24}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{25}}$ | = | $\left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}+2 x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{26}}$ | = | $- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}- 2 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (16m) | Ge IV |
| $\mathbf{B_{27}}$ | = | $\left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{28}}$ | = | $- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{29}}$ | = | $z_{8} \, \mathbf{a}_{1}- \left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{30}}$ | = | $z_{8} \, \mathbf{a}_{1}+\left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{31}}$ | = | $\left(y_{8} - z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{32}}$ | = | $- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{33}}$ | = | $- z_{8} \, \mathbf{a}_{1}+\left(y_{8} - z_{8}\right) \, \mathbf{a}_{2}+y_{8} \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{34}}$ | = | $- z_{8} \, \mathbf{a}_{1}- \left(y_{8} + z_{8}\right) \, \mathbf{a}_{2}- y_{8} \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (16n) | Sc III |
| $\mathbf{B_{35}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{36}}$ | = | $- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{37}}$ | = | $z_{9} \, \mathbf{a}_{1}- \left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{38}}$ | = | $z_{9} \, \mathbf{a}_{1}+\left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{39}}$ | = | $\left(y_{9} - z_{9}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{40}}$ | = | $- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{41}}$ | = | $- z_{9} \, \mathbf{a}_{1}+\left(y_{9} - z_{9}\right) \, \mathbf{a}_{2}+y_{9} \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
| $\mathbf{B_{42}}$ | = | $- z_{9} \, \mathbf{a}_{1}- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{2}- y_{9} \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (16n) | Sc IV |
References
- J. T. Zhao and E. Parthé, Sc$_{11}$Al$_{2}$Ge$_{8}$, a ternary substitution variant of the tetragonal Ho$_{11}$Ge$_{10}$ type, Acta Crystallogr. Sect. C 47, 4–6 (1991), doi:10.1107/S0108270190007314.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2B8C11_tI84_139_h_deim_eh2n --params=$a,c/a,z_{2},z_{3},x_{4},x_{5},x_{6},x_{7},z_{7},y_{8},z_{8},y_{9},z_{9}$