CaBe2Ge2 Structure : A2BC2_tP10_129_ac_c_bc
| Prototype | : | Be2CaGe2 |
| AFLOW prototype label | : | A2BC2_tP10_129_ac_c_bc |
| Strukturbericht designation | : | None |
| Pearson symbol | : | tP10 |
| Space group number | : | 129 |
| Space group symbol | : | $P4/nmm$ |
| AFLOW prototype command | : | aflow --proto=A2BC2_tP10_129_ac_c_bc --params=$a$,$c/a$,$z_{3}$,$z_{4}$,$z_{5}$ |
Other compounds with this structure
- BaMg2Pb2, BaPd2Sb2, BaZn2Sn2, EuAu2Al2, EuPd2Sb2, EuPt2Ge2, LaPt2Bi2, LaPt2Ge2, LiPd2Bi2, SrPd2Sb2, SrPt2As2, and ThIr2Si2
- This is a ternary form of the $D1_{3}$ (BaAl4) structure. The atomic positions are approximately the same as in the conventional cell of BaAl4, 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 origin of the $z$–axis, so either setting will do here. We chose our standard setting 2 here.
Simple Tetragonal primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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}} & \left(2a\right) & \text{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}} & \left(2a\right) & \text{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}} & \left(2b\right) & \text{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}} & \left(2b\right) & \text{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}} + z_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{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}}-z_{3}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{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}} + z_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Ca} \\ \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}}-z_{4}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Ca} \\ \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}} + z_{5}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{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}}-z_{5}c \, \mathbf{\hat{z}} & \left(2c\right) & \text{Ge II} \\ \end{array} \]References
- B. Eisenmann, N. May, W. Müller, and H. Schäfer, Eine neue strukturelle Variante des BaAl4–Typs: Der CaBe2Ge2–Typ, Z. Naturforsch. B 27, 1155–1157 (1972), doi:10.1515/znb-1972-1008.