$H5_{6}$ [Tychite, Na6Mg2SO4(CO3)4)] (obsolete) Structure : A4B2C6D16E_cF232_227_e_d_f_eg_a

Picture of Structure; Click for Big Picture
Prototype : C4Mg2Na6O16S
AFLOW prototype label : A4B2C6D16E_cF232_227_e_d_f_eg_a
Strukturbericht designation : $H5_{6}$
Pearson symbol : cF232
Space group number : 227
Space group symbol : $Fd\bar{3}m$
AFLOW prototype command : aflow --proto=A4B2C6D16E_cF232_227_e_d_f_eg_a
--params=
$a$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$z_{6}$


  • This is the original structure determined by (Shiba, 1931) and given the designation $H5_{6}$ in (Hermann, 1937). (Schmidt, 2006) showed that the true structure is in space group $Fd\overline{3}$ #203, however the two structures are very similar, and a displacement of the oxygen atoms by less than 1 Å brings the two structures into agreement.
  • (Hermann, 1937) gives the chemical formula as Na6Mg2SO4(CO3)2, but the given Wyckoff positions are in agreement with the correct formula, Na6Mg2SO4(CO3)4.

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} & = & \frac{1}{8} \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \frac{1}{8} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{S} \\ \mathbf{B}_{2} & = & \frac{7}{8} \, \mathbf{a}_{1} + \frac{7}{8} \, \mathbf{a}_{2} + \frac{7}{8} \, \mathbf{a}_{3} & = & \frac{7}{8}a \, \mathbf{\hat{x}} + \frac{7}{8}a \, \mathbf{\hat{y}} + \frac{7}{8}a \, \mathbf{\hat{z}} & \left(8a\right) & \mbox{S} \\ \mathbf{B}_{3} & = & \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(16d\right) & \mbox{Mg} \\ \mathbf{B}_{4} & = & \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(16d\right) & \mbox{Mg} \\ \mathbf{B}_{5} & = & \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(16d\right) & \mbox{Mg} \\ \mathbf{B}_{6} & = & \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(16d\right) & \mbox{Mg} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{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(32e\right) & \mbox{C} \\ \mathbf{B}_{8} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - 3x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{12} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{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(32e\right) & \mbox{C} \\ \mathbf{B}_{13} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +3x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{C} \\ \mathbf{B}_{15} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{17} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - 3x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{19} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{20} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{21} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +3x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(32e\right) & \mbox{O I} \\ \mathbf{B}_{23} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{24} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{26} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{y}} + \frac{1}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{27} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{28} & = & \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \frac{1}{8}a \, \mathbf{\hat{x}} + \frac{1}{8}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{29} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{30} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{31} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{32} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \frac{3}{8}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{33} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{34} & = & \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{3}{4} +x_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \frac{3}{8}a \, \mathbf{\hat{x}} + \frac{3}{8}a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(48f\right) & \mbox{Na} \\ \mathbf{B}_{35} & = & z_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{36} & = & z_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{37} & = & \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{1} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{39} & = & \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{41} & = & z_{6} \, \mathbf{a}_{1} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{42} & = & z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{43} & = & z_{6} \, \mathbf{a}_{1} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{44} & = & z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{45} & = & \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{46} & = & \left(2x_{6}-z_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{6} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4}-z_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{47} & = & -z_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{48} & = & -z_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{49} & = & \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{50} & = & \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{1} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{51} & = & \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{53} & = & -z_{6} \, \mathbf{a}_{1} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{54} & = & -z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{55} & = & -z_{6} \, \mathbf{a}_{1} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{56} & = & -z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{2} + \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{4} +z_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{57} & = & \left(\frac{1}{2} +2x_{6} + z_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \mathbf{B}_{58} & = & \left(-2x_{6}+z_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(96g\right) & \mbox{O II} \\ \end{array} \]

References

  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • G. R. Schmidt, J. Reynard, H. Yang, and R. T. Downs, Tychite, Na6Mg2(SO4)(CO3)4: Structure analysis and Raman spectroscopic data, Acta Crystallogr. E 62, i207–i209 (2006), doi:10.1107/S160053680603491X.

Geometry files


Prototype Generator

aflow --proto=A4B2C6D16E_cF232_227_e_d_f_eg_a --params=

Species:

Running:

Output: