Sb2Tl7 ($L2_{2}$) Structure: A2B7_cI54_229_e_afh

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Prototype : Sb2Tl7
AFLOW prototype label : A2B7_cI54_229_e_afh
Strukturbericht designation : $L2_{2}$
Pearson symbol : cI54
Space group number : 229
Space group symbol : $\mbox{Im}\bar{3}\mbox{m}$
AFLOW prototype command : aflow --proto=A2B7_cI54_229_e_afh
--params=
$a$,$x_{2}$,$x_{3}$,$y_{4}$


Body-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, a \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Tl I} \\ \mathbf{B}_{2} & = &x_{2} \, \mathbf{a}_{2}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{x}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{3} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{3}& = &x_{2} \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{4} & = &x_{2} \, \mathbf{a}_{1}+ x_{2} \, \mathbf{a}_{2}& = &x_{2} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{5} & = &- x_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{x}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{6} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{3}& = &- x_{2} \, a \, \mathbf{\hat{y}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{7} & = &- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}& = &- x_{2} \, a \, \mathbf{\hat{z}}& \left(12e\right) & \mbox{Sb} \\ \mathbf{B}_{8} & = &2 x_{3} \, \mathbf{a}_{1}+ 2 x_{3} \, \mathbf{a}_{2}+ 2 x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{9} & = &- 2 x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{10} & = &- 2 x_{3} \, \mathbf{a}_{2}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{11} & = &- 2 x_{3} \, \mathbf{a}_{1}& = &x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{12} & = &2 x_{3} \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{13} & = &- 2 x_{3} \, \mathbf{a}_{1}- 2 x_{3} \, \mathbf{a}_{2}- 2 x_{3} \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}- x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{14} & = &2 x_{3} \, \mathbf{a}_{2}& = &x_{3} \, a \, \mathbf{\hat{x}}- x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{15} & = &2 x_{3} \, \mathbf{a}_{1}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ x_{3} \, a \, \mathbf{\hat{y}}+ x_{3} \, a \, \mathbf{\hat{z}}& \left(16f\right) & \mbox{Tl II} \\ \mathbf{B}_{16} & = &2 y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{y}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{17} & = &y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{y}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{18} & = &- y_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{y}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{19} & = &- 2 y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{y}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{20} & = &y_{4} \, \mathbf{a}_{1}+ 2 y_{4} \, \mathbf{a}_{2}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{21} & = &- y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{22} & = &y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{23} & = &- y_{4} \, \mathbf{a}_{1}- 2 y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{z}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{24} & = &y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}+ 2 y_{4} \, \mathbf{a}_{3}& = &y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{25} & = &y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}& = &- y_{4} \, a \, \mathbf{\hat{x}}+ y_{4} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{26} & = &- y_{4} \, \mathbf{a}_{1}+ y_{4} \, \mathbf{a}_{2}& = &y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Tl III} \\ \mathbf{B}_{27} & = &- y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- 2 y_{4} \, \mathbf{a}_{3}& = &- y_{4} \, a \, \mathbf{\hat{x}}- y_{4} \, a \, \mathbf{\hat{y}}& \left(24h\right) & \mbox{Tl III} \\ \end{array} \]

References

  • R. Stokhuyzen, C. Chieh, and W. B. Pearson, Crystal Structure of Sb2Tl7, Can. J. Chem. 55, 1120–1122 (1977), doi:10.1139/v77-157.

Found in

  • P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn., pp. 5199.

Geometry files


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