NaCr(SO4)2·12H2O Alum Structure : AB12CD8E2_cP96_205_a_2d_b_cd_c

Picture of Structure; Click for Big Picture
Prototype : Cr(H2O)12NaO8S2
AFLOW prototype label : AB12CD8E2_cP96_205_a_2d_b_cd_c
Strukturbericht designation : None
Pearson symbol : cP96
Space group number : 205
Space group symbol : $Pa\bar{3}$
AFLOW prototype command : aflow --proto=AB12CD8E2_cP96_205_a_2d_b_cd_c
--params=
$a$,$x_{3}$,$x_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$


Other compounds with this structure

  • CsCr(SO4)2·12H2O

  • The alums have the general formula $AB$($X$O4)2·12H2O, where $A$ is a monovalent ion, $B$ is a trivalent ion, and $X$ is a chalcogen. In most cases atom $B$ is aluminum and atom $X$ is sulfur, leading to the name alum.
  • All alums have their room–temperature form in space group $Pa\overline{3}$ #205, but the bonding between the $A$ and $B$ ions and the $X$O4 complex can be quite different.
  • (Lipson, 1935ab) described three general forms of alum based on the sizes of the monovalent ions. Each of these forms was given a Strukturbericht designation by (Gottfried, 1937):
    • $\alpha$–alum, with intermediate sized ions, prototype KAl(SO4)2·12H2O, $H4_{13}$,
    • $\beta$–alum, with large ions, prototype (NH3CH3)Al(SO4)2·12H2O, $H4_{14}$, and
    • $\gamma$–alum, with small ions, prototype NaAl(SO4)2·12H2O, $H4_{15}$.
  • This classification scheme is not complete, e.g., (Ledsham, 1968) points out that NaCr(SO4)2·12H2O (this structure) does not fit into any of these categories, and that the actual structure depends on the combination of monovalent and trivalent ions.
  • As noted above, the $Pa\overline{3}$ structures of alum are the room temperature form. As the temperature decreases the alum structure may transform. For example, in the temperature range 150–170 K the $\beta$–alum (NH3CH3)Al(SO4)2·12H2O transforms into an orthorhombic structure with fully ordered NH3CH3 ions.
  • The positions of the hydrogen atoms in the water molecules were not determined, so we only provide the positions of the oxygen atoms (labeled as H2O).

Simple Cubic primitive vectors:

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

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(4a\right) & \mbox{Cr} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cr} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{Cr} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4a\right) & \mbox{Cr} \\ \mathbf{B}_{5} & = & \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(4b\right) & \mbox{Na} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4b\right) & \mbox{Na} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4b\right) & \mbox{Na} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{Na} \\ \mathbf{B}_{9} & = & 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(8c\right) & \mbox{O I} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & -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(8c\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & x_{3} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O I} \\ \mathbf{B}_{17} & = & 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(8c\right) & \mbox{S} \\ \mathbf{B}_{18} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{19} & = & -x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{21} & = & -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(8c\right) & \mbox{S} \\ \mathbf{B}_{22} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{23} & = & x_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{S} \\ \mathbf{B}_{25} & = & x_{5} \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{26} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{27} & = & -x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{29} & = & z_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + y_{5} \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{30} & = & \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2}-y_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{32} & = & -z_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{33} & = & y_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{34} & = & -y_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{37} & = & -x_{5} \, \mathbf{a}_{1}-y_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{38} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + y_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{39} & = & x_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{41} & = & -z_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-y_{5} \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-y_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{42} & = & \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{2} + y_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + y_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{44} & = & z_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{45} & = & -y_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2}-x_{5} \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{46} & = & y_{5} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{5}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} - y_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{5}\right) \, \mathbf{a}_{2} + x_{5} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{5}\right)a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} +y_{5}\right) \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{5}\right)a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O I} \\ \mathbf{B}_{49} & = & x_{6} \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{50} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{51} & = & -x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{53} & = & z_{6} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{54} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{55} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{56} & = & -z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{57} & = & y_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{58} & = & -y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{59} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{60} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{61} & = & -x_{6} \, \mathbf{a}_{1}-y_{6} \, \mathbf{a}_{2}-z_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{62} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + y_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + y_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{63} & = & x_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{64} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{65} & = & -z_{6} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2}-y_{6} \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-y_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{66} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{2} + y_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + y_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{67} & = & \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{68} & = & z_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{69} & = & -y_{6} \, \mathbf{a}_{1}-z_{6} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & -y_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{70} & = & y_{6} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{3} & = & y_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{6}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{71} & = & \left(\frac{1}{2} - y_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{6}\right) \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{6}\right)a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{72} & = & \left(\frac{1}{2} +y_{6}\right) \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{6}\right)a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{H$_{2}$O II} \\ \mathbf{B}_{73} & = & x_{7} \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{74} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{75} & = & -x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{76} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{77} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + y_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + y_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{78} & = & \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2}-y_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}}-y_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{79} & = & \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{80} & = & -z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{81} & = & y_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{82} & = & -y_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{83} & = & \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{84} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{85} & = & -x_{7} \, \mathbf{a}_{1}-y_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{86} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + y_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{87} & = & x_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{88} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{89} & = & -z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-y_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-y_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{90} & = & \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{2} + y_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{y}} + y_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{91} & = & \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{92} & = & z_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{93} & = & -y_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -y_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{94} & = & y_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{3} & = & y_{7}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-z_{7}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{95} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +z_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +z_{7}\right)a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \mathbf{B}_{96} & = & \left(\frac{1}{2} +y_{7}\right) \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{7}\right)a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{z}} & \left(24d\right) & \mbox{O II} \\ \end{array} \]

References

  • A. H. C. Ledsham and H. Steeple, The crystal structure of sodium chromium alum and caesium chromium alum, Acta Crystallogr. Sect. B Struct. Sci. 24, 1287–1289 (1968), doi:10.1107/S0567740868004188.
  • C. Gottfried and F. Schossberger, eds., Strukturbericht Band III 1933–1935 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
  • R. O. W. Fletcher and H. Steeple, The crystal structure of the low–temperature phase of methylammonium alum, Acta Cryst. 17, 290–294 (1964), doi:10.1107/S0365110X64000706.

Geometry files


Prototype Generator

aflow --proto=AB12CD8E2_cP96_205_a_2d_b_cd_c --params=

Species:

Running:

Output: