CaBe$_{2}$Ge$_{2}$ Structure: A2BC2_tP10_129_ac_c_bc-001
| Prototype | Be$_{2}$CaGe$_{2}$ |
| AFLOW prototype label | A2BC2_tP10_129_ac_c_bc-001 |
| ICSD | 25337 |
| Pearson symbol | tP10 |
| Space group number | 129 |
| Space group symbol | $P4/nmm$ |
| AFLOW prototype command |
aflow --proto=A2BC2_tP10_129_ac_c_bc-001
--params=$a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}$ |
Other compounds with this structure
BaAu$_{2}$Sn$_{2}$, BaMg$_{2}$Pb$_{2}$, BaPd$_{2}$Sb$_{2}$, BaZn$_{2}$Sn$_{2}$, CeCu$_{2}$Sn$_{2}$, CeRh$_{2}$As$_{2}$, CeRh$_{2}$P$_{2}$, EuAu$_{2}$Al$_{2}$, EuPd$_{2}$Sb$_{2}$, EuPt$_{2}$Ge$_{2}$, HoPt$_{2}$Si$_{2}$, LaCu$_{2}$Sn$_{2}$, LaPt$_{2}$Bi$_{2}$, LaPt$_{2}$Ge$_{2}$, LaPt$_{2}$Si$_{2}$, LaRh$_{2}$As$_{2}$, LaRh$_{2}$P$_{2}$, LiPd$_{2}$Bi$_{2}$, NdRh$_{2}$As$_{2}$, NdRh$_{2}$P$_{2}$, PrRh$_{2}$As$_{2}$, PrRh$_{2}$P$_{2}$, SrAu$_{2}$Sn$_{2}$, SrCu$_{2}$Sn$_{2}$, SrPd$_{2}$Sb$_{2}$, SrPt$_{2}$As$_{2}$, ThIr$_{2}$Si$_{2}$, ThPt$_{2}$Si$_{2}$, UIr$_{2}$Si$_{2}$, UPt$_{2}$Si$_{2}$
- This is a ternary form of the $D1_{3}$ (BaAl$_{4}$) structure. The atomic positions are approximately the same as in the conventional cell of BaAl$_{4}$, but the distribution of the atoms on those sites and the resulting relaxation leads to a different structure.
- Space group $P4/nmm$ #129 has two settings, but both have the same $z$-axis origin, so either setting will do here. We chose our standard setting 2.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (2a) | Be I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (2a) | Be I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ge I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Ge I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2c) | Be II |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2c) | Be II |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (2c) | Ca I |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (2c) | Ca I |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (2c) | Ge II |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (2c) | Ge II |
References
- B. Eisenmann, N. May, W. Müller, and H. Schäfer, Eine neue strukturelle Variante des BaAl$_{4}$-Typs: Der CaBe$_{2}$Ge$_{2}$-Typ, Z. Naturforsch. B 27 (1972), doi:10.1515/znb-1972-1008. 1155-1157.
Prototype Generator
aflow --proto=A2BC2_tP10_129_ac_c_bc --params=$a,c/a,z_{3},z_{4},z_{5}$