Sheldrickite (NaCa$_{3}$[CO$_{3}$]$_{2}$F$_{3}$[H$_{2}$O]) Structure: A2B3C3DE7_hP48_145_2a_3a_3a_a_7a-001
| Prototype | C$_{2}$Ca$_{3}$F$_{3}$NaO$_{7}$ |
| AFLOW prototype label | A2B3C3DE7_hP48_145_2a_3a_3a_a_7a-001 |
| Mineral name | sheldrickite |
| ICSD | 89257 |
| Pearson symbol | hP48 |
| Space group number | 145 |
| Space group symbol | $P3_2$ |
| AFLOW prototype command |
aflow --proto=A2B3C3DE7_hP48_145_2a_3a_3a_a_7a-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak y_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak y_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak y_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak y_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak y_{15}, \allowbreak z_{15}, \allowbreak x_{16}, \allowbreak y_{16}, \allowbreak z_{16}$ |
- The H$_{2}$O molecule is centered on one of the oxygen (3a) sites; however it is only listed as O in this prototype.
- This structure can also be found in the enantiomorphic space group $P3_{1}$ #144.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} + y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (3a) | C I |
| $\mathbf{B_{2}}$ | = | $- y_{1} \, \mathbf{a}_{1}+\left(x_{1} - y_{1}\right) \, \mathbf{a}_{2}+\left(z_{1} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - 2 y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{1} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{1} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | C I |
| $\mathbf{B_{3}}$ | = | $- \left(x_{1} - y_{1}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(z_{1} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{1} - y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{1} \,\mathbf{\hat{y}}+c \left(z_{1} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | C I |
| $\mathbf{B_{4}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} + y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (3a) | C II |
| $\mathbf{B_{5}}$ | = | $- y_{2} \, \mathbf{a}_{1}+\left(x_{2} - y_{2}\right) \, \mathbf{a}_{2}+\left(z_{2} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - 2 y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{2} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{2} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | C II |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - y_{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(z_{2} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{2} \,\mathbf{\hat{y}}+c \left(z_{2} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | C II |
| $\mathbf{B_{7}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} + y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (3a) | Ca I |
| $\mathbf{B_{8}}$ | = | $- y_{3} \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - 2 y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{3} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{3} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | Ca I |
| $\mathbf{B_{9}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | Ca I |
| $\mathbf{B_{10}}$ | = | $x_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} + y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{4} - y_{4}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (3a) | Ca II |
| $\mathbf{B_{11}}$ | = | $- y_{4} \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{4} - 2 y_{4}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{4} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{4} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | Ca II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{4} - y_{4}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | Ca II |
| $\mathbf{B_{13}}$ | = | $x_{5} \, \mathbf{a}_{1}+y_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} + y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{5} - y_{5}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (3a) | Ca III |
| $\mathbf{B_{14}}$ | = | $- y_{5} \, \mathbf{a}_{1}+\left(x_{5} - y_{5}\right) \, \mathbf{a}_{2}+\left(z_{5} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{5} - 2 y_{5}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{5} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{5} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | Ca III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{5} - y_{5}\right) \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}+\left(z_{5} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{5} - y_{5}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{5} \,\mathbf{\hat{y}}+c \left(z_{5} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | Ca III |
| $\mathbf{B_{16}}$ | = | $x_{6} \, \mathbf{a}_{1}+y_{6} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} + y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{6} - y_{6}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (3a) | F I |
| $\mathbf{B_{17}}$ | = | $- y_{6} \, \mathbf{a}_{1}+\left(x_{6} - y_{6}\right) \, \mathbf{a}_{2}+\left(z_{6} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{6} - 2 y_{6}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{6} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{6} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | F I |
| $\mathbf{B_{18}}$ | = | $- \left(x_{6} - y_{6}\right) \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}+\left(z_{6} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{6} - y_{6}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{6} \,\mathbf{\hat{y}}+c \left(z_{6} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | F I |
| $\mathbf{B_{19}}$ | = | $x_{7} \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} + y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{7} - y_{7}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (3a) | F II |
| $\mathbf{B_{20}}$ | = | $- y_{7} \, \mathbf{a}_{1}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{2}+\left(z_{7} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{7} - 2 y_{7}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{7} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{7} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | F II |
| $\mathbf{B_{21}}$ | = | $- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\left(z_{7} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{7} - y_{7}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | F II |
| $\mathbf{B_{22}}$ | = | $x_{8} \, \mathbf{a}_{1}+y_{8} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} + y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{8} - y_{8}\right) \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (3a) | F III |
| $\mathbf{B_{23}}$ | = | $- y_{8} \, \mathbf{a}_{1}+\left(x_{8} - y_{8}\right) \, \mathbf{a}_{2}+\left(z_{8} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{8} - 2 y_{8}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{8} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{8} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | F III |
| $\mathbf{B_{24}}$ | = | $- \left(x_{8} - y_{8}\right) \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\left(z_{8} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{8} - y_{8}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{8} \,\mathbf{\hat{y}}+c \left(z_{8} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | F III |
| $\mathbf{B_{25}}$ | = | $x_{9} \, \mathbf{a}_{1}+y_{9} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} + y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{9} - y_{9}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (3a) | Na I |
| $\mathbf{B_{26}}$ | = | $- y_{9} \, \mathbf{a}_{1}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{2}+\left(z_{9} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{9} - 2 y_{9}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{9} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{9} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | Na I |
| $\mathbf{B_{27}}$ | = | $- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{1}- x_{9} \, \mathbf{a}_{2}+\left(z_{9} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{9} - y_{9}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{9} \,\mathbf{\hat{y}}+c \left(z_{9} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | Na I |
| $\mathbf{B_{28}}$ | = | $x_{10} \, \mathbf{a}_{1}+y_{10} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} + y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{10} - y_{10}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (3a) | O I |
| $\mathbf{B_{29}}$ | = | $- y_{10} \, \mathbf{a}_{1}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{2}+\left(z_{10} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{10} - 2 y_{10}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{10} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{10} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O I |
| $\mathbf{B_{30}}$ | = | $- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{1}- x_{10} \, \mathbf{a}_{2}+\left(z_{10} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{10} - y_{10}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{10} \,\mathbf{\hat{y}}+c \left(z_{10} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O I |
| $\mathbf{B_{31}}$ | = | $x_{11} \, \mathbf{a}_{1}+y_{11} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} + y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{11} - y_{11}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (3a) | O II |
| $\mathbf{B_{32}}$ | = | $- y_{11} \, \mathbf{a}_{1}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{2}+\left(z_{11} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{11} - 2 y_{11}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{11} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{11} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O II |
| $\mathbf{B_{33}}$ | = | $- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{1}- x_{11} \, \mathbf{a}_{2}+\left(z_{11} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{11} - y_{11}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{11} \,\mathbf{\hat{y}}+c \left(z_{11} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O II |
| $\mathbf{B_{34}}$ | = | $x_{12} \, \mathbf{a}_{1}+y_{12} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} + y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{12} - y_{12}\right) \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (3a) | O III |
| $\mathbf{B_{35}}$ | = | $- y_{12} \, \mathbf{a}_{1}+\left(x_{12} - y_{12}\right) \, \mathbf{a}_{2}+\left(z_{12} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{12} - 2 y_{12}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{12} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{12} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O III |
| $\mathbf{B_{36}}$ | = | $- \left(x_{12} - y_{12}\right) \, \mathbf{a}_{1}- x_{12} \, \mathbf{a}_{2}+\left(z_{12} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{12} - y_{12}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{12} \,\mathbf{\hat{y}}+c \left(z_{12} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O III |
| $\mathbf{B_{37}}$ | = | $x_{13} \, \mathbf{a}_{1}+y_{13} \, \mathbf{a}_{2}+z_{13} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} + y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{13} - y_{13}\right) \,\mathbf{\hat{y}}+c z_{13} \,\mathbf{\hat{z}}$ | (3a) | O IV |
| $\mathbf{B_{38}}$ | = | $- y_{13} \, \mathbf{a}_{1}+\left(x_{13} - y_{13}\right) \, \mathbf{a}_{2}+\left(z_{13} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{13} - 2 y_{13}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{13} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{13} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O IV |
| $\mathbf{B_{39}}$ | = | $- \left(x_{13} - y_{13}\right) \, \mathbf{a}_{1}- x_{13} \, \mathbf{a}_{2}+\left(z_{13} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{13} - y_{13}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{13} \,\mathbf{\hat{y}}+c \left(z_{13} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O IV |
| $\mathbf{B_{40}}$ | = | $x_{14} \, \mathbf{a}_{1}+y_{14} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} + y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{14} - y_{14}\right) \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (3a) | O V |
| $\mathbf{B_{41}}$ | = | $- y_{14} \, \mathbf{a}_{1}+\left(x_{14} - y_{14}\right) \, \mathbf{a}_{2}+\left(z_{14} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{14} - 2 y_{14}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{14} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{14} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O V |
| $\mathbf{B_{42}}$ | = | $- \left(x_{14} - y_{14}\right) \, \mathbf{a}_{1}- x_{14} \, \mathbf{a}_{2}+\left(z_{14} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{14} - y_{14}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{14} \,\mathbf{\hat{y}}+c \left(z_{14} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O V |
| $\mathbf{B_{43}}$ | = | $x_{15} \, \mathbf{a}_{1}+y_{15} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} + y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{15} - y_{15}\right) \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (3a) | O VI |
| $\mathbf{B_{44}}$ | = | $- y_{15} \, \mathbf{a}_{1}+\left(x_{15} - y_{15}\right) \, \mathbf{a}_{2}+\left(z_{15} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{15} - 2 y_{15}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{15} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{15} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O VI |
| $\mathbf{B_{45}}$ | = | $- \left(x_{15} - y_{15}\right) \, \mathbf{a}_{1}- x_{15} \, \mathbf{a}_{2}+\left(z_{15} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{15} - y_{15}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{15} \,\mathbf{\hat{y}}+c \left(z_{15} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O VI |
| $\mathbf{B_{46}}$ | = | $x_{16} \, \mathbf{a}_{1}+y_{16} \, \mathbf{a}_{2}+z_{16} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} + y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \left(x_{16} - y_{16}\right) \,\mathbf{\hat{y}}+c z_{16} \,\mathbf{\hat{z}}$ | (3a) | O VII |
| $\mathbf{B_{47}}$ | = | $- y_{16} \, \mathbf{a}_{1}+\left(x_{16} - y_{16}\right) \, \mathbf{a}_{2}+\left(z_{16} + \frac{2}{3}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{16} - 2 y_{16}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a x_{16} \,\mathbf{\hat{y}}+\frac{1}{3}c \left(3 z_{16} + 2\right) \,\mathbf{\hat{z}}$ | (3a) | O VII |
| $\mathbf{B_{48}}$ | = | $- \left(x_{16} - y_{16}\right) \, \mathbf{a}_{1}- x_{16} \, \mathbf{a}_{2}+\left(z_{16} + \frac{1}{3}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(2 x_{16} - y_{16}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a y_{16} \,\mathbf{\hat{y}}+c \left(z_{16} + \frac{1}{3}\right) \,\mathbf{\hat{z}}$ | (3a) | O VII |
References
- J. D. Grice, R. A. Gault, and J. van Velthuizen, Sheldrickite, a new sodium-calcium-fluorocarbonate mineral species from Mont Saint-Hilaire, Quebec, Can. Mineral. 35, 181–187 (1997).
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A2B3C3DE7_hP48_145_2a_3a_3a_a_7a --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3},x_{4},y_{4},z_{4},x_{5},y_{5},z_{5},x_{6},y_{6},z_{6},x_{7},y_{7},z_{7},x_{8},y_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11},x_{12},y_{12},z_{12},x_{13},y_{13},z_{13},x_{14},y_{14},z_{14},x_{15},y_{15},z_{15},x_{16},y_{16},z_{16}$