TeO6H6 Structure: A6B_cF224_228_h_c

Picture of Structure; Click for Big Picture
Prototype : TeO6H6
AFLOW prototype label : A6B_cF224_228_h_c
Strukturbericht designation : None
Pearson symbol : cF224
Space group number : 228
Space group symbol : $Fd\bar{3}c$
AFLOW prototype command : aflow --proto=A6B_cF224_228_h_c
--params=
$a$,$x_{2}$,$y_{2}$,$z_{2}$


  • Polytypes appear in space groups #14, #210 and #225. Only the non-hydrogen atoms are listed.

Face-centered Cubic primitive vectors:

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

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(32c\right) & \mbox{Te} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(32c\right) & \mbox{Te} \\ \mathbf{B}_{9} & = & \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{10} & = & \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + z_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{11} & = & \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{13} & = & \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & z_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{15} & = & \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + y_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{16} & = & \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{17} & = & \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{18} & = & \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + z_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{20} & = & \left(x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{21} & = & \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{24} & = & \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{25} & = & \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{26} & = & \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{29} & = & \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{31} & = & \left(x_{2}+y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} - x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} - z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{33} & = & \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{34} & = & \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}}-z_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{35} & = & \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{37} & = & \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -z_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{39} & = & \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{y}}-y_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{40} & = & \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{41} & = & \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{2} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{42} & = & \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}}-z_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{44} & = & \left(-x_{2}-y_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{2}\right)a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{45} & = & \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{46} & = & \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{48} & = & \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{49} & = & \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{50} & = & \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{51} & = & \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{53} & = & \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{54} & = & \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} - z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{55} & = & \left(-x_{2}-y_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} - y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} - x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \mathbf{B}_{56} & = & \left(\frac{1}{2} +x_{2} + y_{2} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2} - y_{2} + z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{2} + y_{2} + z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{z}} & \left(192h\right) & \mbox{O} \\ \end{array} \]

References

  • L. M. Kirkpatrick and L. Pauling, XXVIII. Über die Kristallstruktur der kubischen Tellursäure, Zeitschrift für Kristallographie – Crystalline Materials 63, 502–506 (1926), doi:10.1524/zkri.1926.63.1.502.

Found in

  • P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds, ASM International (2013).

Geometry files


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aflow --proto=A6B_cF224_228_h_c --params=

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