LiNb$_{6}$O$_{15}$F Structure: ABC6D15_oP46_51_f_b_2e2i_cef4i2j-001
| Prototype | FLiNb$_{6}$O$_{15}$ |
| AFLOW prototype label | ABC6D15_oP46_51_f_b_2e2i_cef4i2j-001 |
| ICSD | 2910 |
| Pearson symbol | oP46 |
| Space group number | 51 |
| Space group symbol | $Pmma$ |
| AFLOW prototype command |
aflow --proto=ABC6D15_oP46_51_f_b_2e2i_cef4i2j-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak z_{11}, \allowbreak x_{12}, \allowbreak z_{12}, \allowbreak x_{13}, \allowbreak z_{13}, \allowbreak x_{14}, \allowbreak z_{14}, \allowbreak x_{15}, \allowbreak z_{15}$ |
- (Lundberg, 1965) suggests that the lithium atoms are either on the (2d) site or are statistically distributed on a (4f) site with approximate coordinates (0.08,1/2,0.10). For simplicity we place the atoms on the (2d) site.
- The X-ray scattering of an F$^-$ ion is almost identical to that of O$^{-2}$, and Lundberg was not able to distinguish between them. She arbitrarily designated the (2f) site she called O$_{4}$ as the location of the fluorine ion and we follow this, but in reality we have no idea if the F$^-$ ions are located on this site, are ordered on another site, or are statistically distributed on the oxygen sites.
- The ICSD entry does not place the lithium atoms.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Li I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2b) | Li I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | O I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Nb I |
| $\mathbf{B_{6}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{3} \,\mathbf{\hat{z}}$ | (2e) | Nb I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{4} \,\mathbf{\hat{z}}$ | (2e) | Nb II |
| $\mathbf{B_{8}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{4} \,\mathbf{\hat{z}}$ | (2e) | Nb II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{10}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- c z_{5} \,\mathbf{\hat{z}}$ | (2e) | O II |
| $\mathbf{B_{11}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2f) | F I |
| $\mathbf{B_{12}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (2f) | F I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (2f) | O III |
| $\mathbf{B_{14}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (2f) | O III |
| $\mathbf{B_{15}}$ | = | $x_{8} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{16}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{17}}$ | = | $- x_{8} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{18}}$ | = | $\left(x_{8} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $a \left(x_{8} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (4i) | Nb III |
| $\mathbf{B_{19}}$ | = | $x_{9} \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{20}}$ | = | $- \left(x_{9} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{9} \, \mathbf{a}_{3}$ | = | $- a \left(x_{9} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{21}}$ | = | $- x_{9} \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{22}}$ | = | $\left(x_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{9} \, \mathbf{a}_{3}$ | = | $a \left(x_{9} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{9} \,\mathbf{\hat{z}}$ | (4i) | Nb IV |
| $\mathbf{B_{23}}$ | = | $x_{10} \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{24}}$ | = | $- \left(x_{10} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{10} \, \mathbf{a}_{3}$ | = | $- a \left(x_{10} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{10} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{25}}$ | = | $- x_{10} \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- c z_{10} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{26}}$ | = | $\left(x_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{10} \, \mathbf{a}_{3}$ | = | $a \left(x_{10} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{10} \,\mathbf{\hat{z}}$ | (4i) | O IV |
| $\mathbf{B_{27}}$ | = | $x_{11} \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{28}}$ | = | $- \left(x_{11} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{11} \, \mathbf{a}_{3}$ | = | $- a \left(x_{11} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{11} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{29}}$ | = | $- x_{11} \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- c z_{11} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{30}}$ | = | $\left(x_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{11} \, \mathbf{a}_{3}$ | = | $a \left(x_{11} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{11} \,\mathbf{\hat{z}}$ | (4i) | O V |
| $\mathbf{B_{31}}$ | = | $x_{12} \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $a x_{12} \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{32}}$ | = | $- \left(x_{12} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{12} \, \mathbf{a}_{3}$ | = | $- a \left(x_{12} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{12} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{33}}$ | = | $- x_{12} \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{3}$ | = | $- a x_{12} \,\mathbf{\hat{x}}- c z_{12} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{34}}$ | = | $\left(x_{12} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{12} \, \mathbf{a}_{3}$ | = | $a \left(x_{12} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{12} \,\mathbf{\hat{z}}$ | (4i) | O VI |
| $\mathbf{B_{35}}$ | = | $x_{13} \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{3}$ | = | $a x_{13} \,\mathbf{\hat{x}}+c z_{13} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{36}}$ | = | $- \left(x_{13} - \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{13} \, \mathbf{a}_{3}$ | = | $- a \left(x_{13} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+c z_{13} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{37}}$ | = | $- x_{13} \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{3}$ | = | $- a x_{13} \,\mathbf{\hat{x}}- c z_{13} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{38}}$ | = | $\left(x_{13} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{13} \, \mathbf{a}_{3}$ | = | $a \left(x_{13} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- c z_{13} \,\mathbf{\hat{z}}$ | (4i) | O VII |
| $\mathbf{B_{39}}$ | = | $x_{14} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $a x_{14} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O VIII |
| $\mathbf{B_{40}}$ | = | $- \left(x_{14} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{14} \, \mathbf{a}_{3}$ | = | $- a \left(x_{14} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O VIII |
| $\mathbf{B_{41}}$ | = | $- x_{14} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $- a x_{14} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O VIII |
| $\mathbf{B_{42}}$ | = | $\left(x_{14} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{14} \, \mathbf{a}_{3}$ | = | $a \left(x_{14} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{14} \,\mathbf{\hat{z}}$ | (4j) | O VIII |
| $\mathbf{B_{43}}$ | = | $x_{15} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $a x_{15} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O IX |
| $\mathbf{B_{44}}$ | = | $- \left(x_{15} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{15} \, \mathbf{a}_{3}$ | = | $- a \left(x_{15} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O IX |
| $\mathbf{B_{45}}$ | = | $- x_{15} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $- a x_{15} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O IX |
| $\mathbf{B_{46}}$ | = | $\left(x_{15} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{15} \, \mathbf{a}_{3}$ | = | $a \left(x_{15} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- c z_{15} \,\mathbf{\hat{z}}$ | (4j) | O IX |
References
- M. Lundberg, The Crystal Structure of LiNb$_{6}$O$_{15}$F, Acta Chem. Scand. 19, 2274–2284 (1965), doi:10.3891/acta.chem.scand.19-2274.
Prototype Generator
aflow --proto=ABC6D15_oP46_51_f_b_2e2i_cef4i2j --params=$a,b/a,c/a,z_{3},z_{4},z_{5},z_{6},z_{7},x_{8},z_{8},x_{9},z_{9},x_{10},z_{10},x_{11},z_{11},x_{12},z_{12},x_{13},z_{13},x_{14},z_{14},x_{15},z_{15}$