Pinnoite (MgB$_{2}$O[OH]$_{6}$) Structure: A2B6CD7_tP64_77_2d_6d_d_ab6d-001
| Prototype | B$_{2}$H$_{6}$MgO$_{7}$ |
| AFLOW prototype label | A2B6CD7_tP64_77_2d_6d_d_ab6d-001 |
| Mineral name | pinnoite |
| ICSD | 20662 |
| Pearson symbol | tP64 |
| Space group number | 77 |
| Space group symbol | $P4_2$ |
| AFLOW prototype command |
aflow --proto=A2B6CD7_tP64_77_2d_6d_d_ab6d-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}, \allowbreak x_{17}, \allowbreak y_{17}, \allowbreak z_{17}$ |
- (Genkina, 1983) state that their Wyckoff positions were to be multiplied by $10^{-4}$. This is not the case for the $z$-coordinates and the $x$- and $y$-coordinates of the hydrogen atoms: those coordinates should be multiplied by $10^{-3}$. This confusion led to incorrect hydrogen-oxygen distances in both our original page (Hicks, 2019) and in (Villars, 2016). We believe the current interpretation is correct, as our Mg-O and B-O distances agree with (Genkina, 1983) and all of our O-H bonds are on the order of 1Å. The ICSD CIF also interprets the coordinates in this fashion.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2a) | O I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2b) | O II |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (2b) | O II |
| $\mathbf{B_{5}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4d) | B I |
| $\mathbf{B_{6}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4d) | B I |
| $\mathbf{B_{7}}$ | = | $- y_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | B I |
| $\mathbf{B_{8}}$ | = | $y_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | B I |
| $\mathbf{B_{9}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4d) | B II |
| $\mathbf{B_{10}}$ | = | $- x_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (4d) | B II |
| $\mathbf{B_{11}}$ | = | $- y_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | B II |
| $\mathbf{B_{12}}$ | = | $y_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | B II |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4d) | H I |
| $\mathbf{B_{14}}$ | = | $- x_{5} \, \mathbf{a}_{1}- y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4d) | H I |
| $\mathbf{B_{15}}$ | = | $- y_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{5} \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H I |
| $\mathbf{B_{16}}$ | = | $y_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{5} \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H I |
| $\mathbf{B_{17}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4d) | H II |
| $\mathbf{B_{18}}$ | = | $- x_{6} \, \mathbf{a}_{1}- y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4d) | H II |
| $\mathbf{B_{19}}$ | = | $- y_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{6} \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H II |
| $\mathbf{B_{20}}$ | = | $y_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{6} \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H II |
| $\mathbf{B_{21}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4d) | H III |
| $\mathbf{B_{22}}$ | = | $- x_{7} \, \mathbf{a}_{1}- y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (4d) | H III |
| $\mathbf{B_{23}}$ | = | $- y_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H III |
| $\mathbf{B_{24}}$ | = | $y_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H III |
| $\mathbf{B_{25}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4d) | H IV |
| $\mathbf{B_{26}}$ | = | $- x_{8} \, \mathbf{a}_{1}- y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- a y_{8} \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4d) | H IV |
| $\mathbf{B_{27}}$ | = | $- y_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{8} \,\mathbf{\hat{x}}+a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H IV |
| $\mathbf{B_{28}}$ | = | $y_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{8} \,\mathbf{\hat{x}}- a x_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H IV |
| $\mathbf{B_{29}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4d) | H V |
| $\mathbf{B_{30}}$ | = | $- x_{9} \, \mathbf{a}_{1}- y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- a y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (4d) | H V |
| $\mathbf{B_{31}}$ | = | $- y_{9} \, \mathbf{a}_{1}+x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{9} \,\mathbf{\hat{x}}+a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H V |
| $\mathbf{B_{32}}$ | = | $y_{9} \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{9} \,\mathbf{\hat{x}}- a x_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H V |
| $\mathbf{B_{33}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4d) | H VI |
| $\mathbf{B_{34}}$ | = | $- x_{10} \, \mathbf{a}_{1}- y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- a y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (4d) | H VI |
| $\mathbf{B_{35}}$ | = | $- y_{10} \, \mathbf{a}_{1}+x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{10} \,\mathbf{\hat{x}}+a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H VI |
| $\mathbf{B_{36}}$ | = | $y_{10} \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{10} \,\mathbf{\hat{x}}- a x_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | H VI |
| $\mathbf{B_{37}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4d) | Mg I |
| $\mathbf{B_{38}}$ | = | $- x_{11} \, \mathbf{a}_{1}- y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- a y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (4d) | Mg I |
| $\mathbf{B_{39}}$ | = | $- y_{11} \, \mathbf{a}_{1}+x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{11} \,\mathbf{\hat{x}}+a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | Mg I |
| $\mathbf{B_{40}}$ | = | $y_{11} \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{11} \,\mathbf{\hat{x}}- a x_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | Mg I |
| $\mathbf{B_{41}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{42}}$ | = | $- x_{12} \, \mathbf{a}_{1}- y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- a y_{12} \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{43}}$ | = | $- y_{12} \, \mathbf{a}_{1}+x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{12} \,\mathbf{\hat{x}}+a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{44}}$ | = | $y_{12} \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{12} \,\mathbf{\hat{x}}- a x_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O III |
| $\mathbf{B_{45}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (4d) | O IV |
| $\mathbf{B_{46}}$ | = | $- x_{13} \, \mathbf{a}_{1}- y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- a y_{13} \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (4d) | O IV |
| $\mathbf{B_{47}}$ | = | $- y_{13} \, \mathbf{a}_{1}+x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{13} \,\mathbf{\hat{x}}+a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O IV |
| $\mathbf{B_{48}}$ | = | $y_{13} \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{13} \,\mathbf{\hat{x}}- a x_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O IV |
| $\mathbf{B_{49}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4d) | O V |
| $\mathbf{B_{50}}$ | = | $- x_{14} \, \mathbf{a}_{1}- y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}- a y_{14} \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4d) | O V |
| $\mathbf{B_{51}}$ | = | $- y_{14} \, \mathbf{a}_{1}+x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{14} \,\mathbf{\hat{x}}+a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O V |
| $\mathbf{B_{52}}$ | = | $y_{14} \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{14} \,\mathbf{\hat{x}}- a x_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O V |
| $\mathbf{B_{53}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (4d) | O VI |
| $\mathbf{B_{54}}$ | = | $- x_{15} \, \mathbf{a}_{1}- y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}- a y_{15} \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (4d) | O VI |
| $\mathbf{B_{55}}$ | = | $- y_{15} \, \mathbf{a}_{1}+x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{15} \,\mathbf{\hat{x}}+a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VI |
| $\mathbf{B_{56}}$ | = | $y_{15} \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{15} \,\mathbf{\hat{x}}- a x_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VI |
| $\mathbf{B_{57}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $a x_{16} \,\mathbf{\hat{x}}+a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (4d) | O VII |
| $\mathbf{B_{58}}$ | = | $- x_{16} \, \mathbf{a}_{1}- y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $- a x_{16} \,\mathbf{\hat{x}}- a y_{16} \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (4d) | O VII |
| $\mathbf{B_{59}}$ | = | $- y_{16} \, \mathbf{a}_{1}+x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{16} \,\mathbf{\hat{x}}+a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VII |
| $\mathbf{B_{60}}$ | = | $y_{16} \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{16} \,\mathbf{\hat{x}}- a x_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VII |
| $\mathbf{B_{61}}$ | = | $x_{17} \, \mathbf{a}_{1}+y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $a x_{17} \,\mathbf{\hat{x}}+a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (4d) | O VIII |
| $\mathbf{B_{62}}$ | = | $- x_{17} \, \mathbf{a}_{1}- y_{17} \, \mathbf{a}_{2}+z_{17} \, \mathbf{a}_{3}$ | = | $- a x_{17} \,\mathbf{\hat{x}}- a y_{17} \,\mathbf{\hat{y}}+c z_{17} \,\mathbf{\hat{z}}$ | (4d) | O VIII |
| $\mathbf{B_{63}}$ | = | $- y_{17} \, \mathbf{a}_{1}+x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{17} \,\mathbf{\hat{x}}+a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VIII |
| $\mathbf{B_{64}}$ | = | $y_{17} \, \mathbf{a}_{1}- x_{17} \, \mathbf{a}_{2}+\left(z_{17} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a y_{17} \,\mathbf{\hat{x}}- a x_{17} \,\mathbf{\hat{y}}+c \left(z_{17} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4d) | O VIII |
References
- E. A. Genkina and Y. A. Malinovskii, Refinement of the structure of pinnoite: Location of hydrogen atoms, Sov. Phys. Crystallogr. 28, 475–477 (1983). Translated from translated from Kristallografiya.
- D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comput. Mater. Sci. 161, S1–S1011 (2019), doi:10.1016/j.commatsci.2018.10.043.
Found in
- P. Villars, Mg[B$_{2}$O(OH)$_{6}$] (MgB$_{2}$O[OH]$_{6}$) Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Prototype Generator
aflow --proto=A2B6CD7_tP64_77_2d_6d_d_ab6d --params=$a,c/a,z_{1},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16},x_{17},y_{17},z_{17}$