Santite (KB5O8·4H2O, $K3_{5}$) Structure : A5B8CD12_oC104_41_a2b_4b_a_6b

Picture of Structure; Click for Big Picture
Prototype : B5H8KO12
AFLOW prototype label : A5B8CD12_oC104_41_a2b_4b_a_6b
Strukturbericht designation : $K3_{5}$
Pearson symbol : oC104
Space group number : 41
Space group symbol : $Aba2$
AFLOW prototype command : aflow --proto=A5B8CD12_oC104_41_a2b_4b_a_6b
--params=
$a$,$b/a$,$c/a$,$z_{1}$,$z_{2}$,$x_{3}$,$y_{3}$,$z_{3}$,$x_{4}$,$y_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$,$x_{6}$,$y_{6}$,$z_{6}$,$x_{7}$,$y_{7}$,$z_{7}$,$x_{8}$,$y_{8}$,$z_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$,$x_{11}$,$y_{11}$,$z_{11}$,$x_{12}$,$y_{12}$,$z_{12}$,$x_{13}$,$y_{13}$,$z_{13}$,$x_{14}$,$y_{14}$,$z_{14}$


  • (Zachariasen, 1938) originally determined the structure of this compound, without knowing the positions of the hydrogens, but believed the structure to be correctly written as KH2(H3O)2B5O10. (Gottfried, 1940) gave this the Strukturbericht designation $K3_{5}$. (Zachariasen, 1963) did a refinement of the structure, including the hydrogen positions, noting that the structure should properly be written K[B5O6(OH)4]·2H2O. As neither the positions of the heavy atoms nor the space group have changed, we retain the $K3_{5}$ designation, but we give the prototype as KB5O8·4H2O, which seems to be the standard formula even though it is not structurally correct.

Base-centered Orthorhombic primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & -z_{1} \, \mathbf{a}_{2} + z_{1} \, \mathbf{a}_{3} & = & z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{B I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{1}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{1}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{1}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{B I} \\ \mathbf{B}_{3} & = & -z_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{K} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \mbox{K} \\ \mathbf{B}_{5} & = & x_{3} \, \mathbf{a}_{1} + \left(y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B II} \\ \mathbf{B}_{6} & = & -x_{3} \, \mathbf{a}_{1} + \left(-y_{3}-z_{3}\right) \, \mathbf{a}_{2} + \left(-y_{3}+z_{3}\right) \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-y_{3}b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B II} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{3}\right)b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B II} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{3} - z_{3}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{3} + z_{3}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{3}\right)b \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B II} \\ \mathbf{B}_{9} & = & x_{4} \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B III} \\ \mathbf{B}_{10} & = & -x_{4} \, \mathbf{a}_{1} + \left(-y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(-y_{4}+z_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-y_{4}b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B III} \\ \mathbf{B}_{11} & = & \left(\frac{1}{2} +x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{4}\right)b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B III} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{4} - z_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{4} + z_{4}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{4}\right)b \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{B III} \\ \mathbf{B}_{13} & = & x_{5} \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H I} \\ \mathbf{B}_{14} & = & -x_{5} \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H I} \\ \mathbf{B}_{15} & = & \left(\frac{1}{2} +x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{5}\right)b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H I} \\ \mathbf{B}_{16} & = & \left(\frac{1}{2} - x_{5}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{5} - z_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{5} + z_{5}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{5}\right)b \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H I} \\ \mathbf{B}_{17} & = & x_{6} \, \mathbf{a}_{1} + \left(y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H II} \\ \mathbf{B}_{18} & = & -x_{6} \, \mathbf{a}_{1} + \left(-y_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-y_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-y_{6}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H II} \\ \mathbf{B}_{19} & = & \left(\frac{1}{2} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{6}\right)b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H II} \\ \mathbf{B}_{20} & = & \left(\frac{1}{2} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{6} - z_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{6} + z_{6}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{6}\right)b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H II} \\ \mathbf{B}_{21} & = & x_{7} \, \mathbf{a}_{1} + \left(y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H III} \\ \mathbf{B}_{22} & = & -x_{7} \, \mathbf{a}_{1} + \left(-y_{7}-z_{7}\right) \, \mathbf{a}_{2} + \left(-y_{7}+z_{7}\right) \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-y_{7}b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H III} \\ \mathbf{B}_{23} & = & \left(\frac{1}{2} +x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7} - z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{7} + z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{7}\right)b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H III} \\ \mathbf{B}_{24} & = & \left(\frac{1}{2} - x_{7}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{7} - z_{7}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{7} + z_{7}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{7}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{7}\right)b \, \mathbf{\hat{y}} + z_{7}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H III} \\ \mathbf{B}_{25} & = & x_{8} \, \mathbf{a}_{1} + \left(y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H IV} \\ \mathbf{B}_{26} & = & -x_{8} \, \mathbf{a}_{1} + \left(-y_{8}-z_{8}\right) \, \mathbf{a}_{2} + \left(-y_{8}+z_{8}\right) \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-y_{8}b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H IV} \\ \mathbf{B}_{27} & = & \left(\frac{1}{2} +x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{8} - z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{8} + z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{8}\right)b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H IV} \\ \mathbf{B}_{28} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{8} - z_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{8} + z_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{8}\right)b \, \mathbf{\hat{y}} + z_{8}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{H IV} \\ \mathbf{B}_{29} & = & x_{9} \, \mathbf{a}_{1} + \left(y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{30} & = & -x_{9} \, \mathbf{a}_{1} + \left(-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{31} & = & \left(\frac{1}{2} +x_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{9} - z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{9} + z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{9}\right)b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{32} & = & \left(\frac{1}{2} - x_{9}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{9} - z_{9}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{9} + z_{9}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{9}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{9}\right)b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O I} \\ \mathbf{B}_{33} & = & x_{10} \, \mathbf{a}_{1} + \left(y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{34} & = & -x_{10} \, \mathbf{a}_{1} + \left(-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{35} & = & \left(\frac{1}{2} +x_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{10} - z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{10} + z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{10}\right)b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{36} & = & \left(\frac{1}{2} - x_{10}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{10} - z_{10}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{10} + z_{10}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{10}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{10}\right)b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O II} \\ \mathbf{B}_{37} & = & x_{11} \, \mathbf{a}_{1} + \left(y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & x_{11}a \, \mathbf{\hat{x}} + y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{38} & = & -x_{11} \, \mathbf{a}_{1} + \left(-y_{11}-z_{11}\right) \, \mathbf{a}_{2} + \left(-y_{11}+z_{11}\right) \, \mathbf{a}_{3} & = & -x_{11}a \, \mathbf{\hat{x}}-y_{11}b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{39} & = & \left(\frac{1}{2} +x_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{11} - z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{11} + z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{11}\right)b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{40} & = & \left(\frac{1}{2} - x_{11}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{11} - z_{11}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{11} + z_{11}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{11}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{11}\right)b \, \mathbf{\hat{y}} + z_{11}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O III} \\ \mathbf{B}_{41} & = & x_{12} \, \mathbf{a}_{1} + \left(y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & x_{12}a \, \mathbf{\hat{x}} + y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \mathbf{B}_{42} & = & -x_{12} \, \mathbf{a}_{1} + \left(-y_{12}-z_{12}\right) \, \mathbf{a}_{2} + \left(-y_{12}+z_{12}\right) \, \mathbf{a}_{3} & = & -x_{12}a \, \mathbf{\hat{x}}-y_{12}b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \mathbf{B}_{43} & = & \left(\frac{1}{2} +x_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{12} - z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{12} + z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{12}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{12}\right)b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \mathbf{B}_{44} & = & \left(\frac{1}{2} - x_{12}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{12} - z_{12}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{12} + z_{12}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{12}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{12}\right)b \, \mathbf{\hat{y}} + z_{12}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O IV} \\ \mathbf{B}_{45} & = & x_{13} \, \mathbf{a}_{1} + \left(y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & x_{13}a \, \mathbf{\hat{x}} + y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O V} \\ \mathbf{B}_{46} & = & -x_{13} \, \mathbf{a}_{1} + \left(-y_{13}-z_{13}\right) \, \mathbf{a}_{2} + \left(-y_{13}+z_{13}\right) \, \mathbf{a}_{3} & = & -x_{13}a \, \mathbf{\hat{x}}-y_{13}b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O V} \\ \mathbf{B}_{47} & = & \left(\frac{1}{2} +x_{13}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{13} - z_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{13} + z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{13}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{13}\right)b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O V} \\ \mathbf{B}_{48} & = & \left(\frac{1}{2} - x_{13}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{13} - z_{13}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{13} + z_{13}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{13}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{13}\right)b \, \mathbf{\hat{y}} + z_{13}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O V} \\ \mathbf{B}_{49} & = & x_{14} \, \mathbf{a}_{1} + \left(y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & x_{14}a \, \mathbf{\hat{x}} + y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O VI} \\ \mathbf{B}_{50} & = & -x_{14} \, \mathbf{a}_{1} + \left(-y_{14}-z_{14}\right) \, \mathbf{a}_{2} + \left(-y_{14}+z_{14}\right) \, \mathbf{a}_{3} & = & -x_{14}a \, \mathbf{\hat{x}}-y_{14}b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O VI} \\ \mathbf{B}_{51} & = & \left(\frac{1}{2} +x_{14}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{14} - z_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{14} + z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{14}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{14}\right)b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O VI} \\ \mathbf{B}_{52} & = & \left(\frac{1}{2} - x_{14}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{14} - z_{14}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +y_{14} + z_{14}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{14}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{14}\right)b \, \mathbf{\hat{y}} + z_{14}c \, \mathbf{\hat{z}} & \left(8b\right) & \mbox{O VI} \\ \end{array} \]

References

  • W. H. Zachariasen and H. A. Plettinger, Refinement of the structure of potassium pentaborate tetrahydrate, Acta Cryst. 16, 376–379 (1963), doi:10.1107/S0365110X63001006.
  • W. H. Zachariasen, The Crystal Structure of Potassium Acid Dihydronium Pentaborate KH2(H3O)2B5O10, (Potassium Pentaborate Tetrahydrate), Zeitschrift für Kristallographie – Crystalline Materials 98, 266–274 (1938), doi:10.1524/zkri.1938.98.1.266.
  • C. Gottfried, ed., Strukturbericht Band V 1937 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1940).

Geometry files


Prototype Generator

aflow --proto=A5B8CD12_oC104_41_a2b_4b_a_6b --params=

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