CaBe2Ge2 Structure : A2BC2_tP10_129_ac_c_bc

Picture of Structure; Click for Big Picture
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} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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) & \mbox{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.

Geometry files


Prototype Generator

aflow --proto=A2BC2_tP10_129_ac_c_bc --params=

Species:

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