Moskvinite (Na$_{2}$KYSi$_{6}$O$_{15}$) Structure: AB2C15D6E_oI100_74_e_g_e2hi2j_hj_a-001
| Prototype | KNa$_{2}$O$_{15}$Si$_{6}$Y |
| AFLOW prototype label | AB2C15D6E_oI100_74_e_g_e2hi2j_hj_a-001 |
| Mineral name | moskvinite |
| ICSD | 97289 |
| Pearson symbol | oI100 |
| Space group number | 74 |
| Space group symbol | $Imma$ |
| AFLOW prototype command |
aflow --proto=AB2C15D6E_oI100_74_e_g_e2hi2j_hj_a-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak y_{5}, \allowbreak z_{5}, \allowbreak y_{6}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak z_{7}, \allowbreak x_{8}, \allowbreak z_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}, \allowbreak x_{11}, \allowbreak y_{11}, \allowbreak z_{11}$ |
- This is technically named moskvinite-(Y). The yttrium on the (4a) site can be replaced rare-earth elements. The composition of this sample is actually Na$_{2.06}$K$_{0.95}$(Y$_{0.77}$Dy$_{0.09}$Gd$_{0.04}$Er$_{0.04}$Ho$_{0.02}$Sm$_{0.02}$Nd$_{0.01}$Tb$_{0.01}$)$_{\Sigma 1.00}$Si$_{6}$O$_{15}$.
- (Sokolova, 2003) give the data for this structure in the $Ibmm$ setting of space group #74. We used FINDSYM to shift this to the standard $Imma$ setting. This involved rotation of the axes and shifting the Y-I atom from (1/4 1/4 1/4) to the origin.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Y I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}b \,\mathbf{\hat{y}}$ | (4a) | Y I |
| $\mathbf{B_{3}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (4e) | K I |
| $\mathbf{B_{4}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (4e) | K I |
| $\mathbf{B_{5}}$ | = | $\left(z_{3} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{6}}$ | = | $- \left(z_{3} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4e) | O I |
| $\mathbf{B_{7}}$ | = | $\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Na I |
| $\mathbf{B_{8}}$ | = | $- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- \frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Na I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- \left(y_{4} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Na I |
| $\mathbf{B_{10}}$ | = | $\left(y_{4} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- \frac{1}{4}c \,\mathbf{\hat{z}}$ | (8g) | Na I |
| $\mathbf{B_{11}}$ | = | $\left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+y_{5} \, \mathbf{a}_{3}$ | = | $b y_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8h) | O II |
| $\mathbf{B_{12}}$ | = | $\left(- y_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- \left(y_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8h) | O II |
| $\mathbf{B_{13}}$ | = | $\left(y_{5} - z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+\left(y_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8h) | O II |
| $\mathbf{B_{14}}$ | = | $- \left(y_{5} + z_{5}\right) \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}- y_{5} \, \mathbf{a}_{3}$ | = | $- b y_{5} \,\mathbf{\hat{y}}- c z_{5} \,\mathbf{\hat{z}}$ | (8h) | O II |
| $\mathbf{B_{15}}$ | = | $\left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+y_{6} \, \mathbf{a}_{3}$ | = | $b y_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8h) | O III |
| $\mathbf{B_{16}}$ | = | $\left(- y_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(y_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8h) | O III |
| $\mathbf{B_{17}}$ | = | $\left(y_{6} - z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}+\left(y_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8h) | O III |
| $\mathbf{B_{18}}$ | = | $- \left(y_{6} + z_{6}\right) \, \mathbf{a}_{1}- z_{6} \, \mathbf{a}_{2}- y_{6} \, \mathbf{a}_{3}$ | = | $- b y_{6} \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (8h) | O III |
| $\mathbf{B_{19}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $b y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8h) | Si I |
| $\mathbf{B_{20}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{7} \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8h) | Si I |
| $\mathbf{B_{21}}$ | = | $\left(y_{7} - z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}+\left(y_{7} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b \left(y_{7} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8h) | Si I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}- z_{7} \, \mathbf{a}_{2}- y_{7} \, \mathbf{a}_{3}$ | = | $- b y_{7} \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (8h) | Si I |
| $\mathbf{B_{23}}$ | = | $\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | O IV |
| $\mathbf{B_{24}}$ | = | $\left(z_{8} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (8i) | O IV |
| $\mathbf{B_{25}}$ | = | $- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(x_{8} + z_{8}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | O IV |
| $\mathbf{B_{26}}$ | = | $- \left(z_{8} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(x_{8} - z_{8}\right) \, \mathbf{a}_{2}+\left(x_{8} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{3}{4}b \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (8i) | O IV |
| $\mathbf{B_{27}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{28}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{29}}$ | = | $\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{30}}$ | = | $- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{31}}$ | = | $- \left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{32}}$ | = | $\left(y_{9} - z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b \left(y_{9} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{33}}$ | = | $\left(- y_{9} + z_{9} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- b \left(y_{9} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{34}}$ | = | $\left(y_{9} + z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} - z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} - y_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16j) | O V |
| $\mathbf{B_{35}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{36}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{37}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{38}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{39}}$ | = | $- \left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{40}}$ | = | $\left(y_{10} - z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b \left(y_{10} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{41}}$ | = | $\left(- y_{10} + z_{10} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b \left(y_{10} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{42}}$ | = | $\left(y_{10} + z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} - z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} - y_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16j) | O VI |
| $\mathbf{B_{43}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{44}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{45}}$ | = | $\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(- x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{46}}$ | = | $- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{47}}$ | = | $- \left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} + y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}- b y_{11} \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{48}}$ | = | $\left(y_{11} - z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} + y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}+b \left(y_{11} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{49}}$ | = | $\left(- y_{11} + z_{11} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{11} + z_{11}\right) \, \mathbf{a}_{2}+\left(x_{11} - y_{11} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{11} \,\mathbf{\hat{x}}- b \left(y_{11} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
| $\mathbf{B_{50}}$ | = | $\left(y_{11} + z_{11}\right) \, \mathbf{a}_{1}- \left(x_{11} - z_{11}\right) \, \mathbf{a}_{2}- \left(x_{11} - y_{11}\right) \, \mathbf{a}_{3}$ | = | $- a x_{11} \,\mathbf{\hat{x}}+b y_{11} \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (16j) | Si II |
References
- E. Sokolova, F. C. Hawthorne, A. A. Agakhanov, and L. A. Pautov, The crystal structure of Moskvinite-(Y), Na$_{2}$K(Y,REE)[Si$_{6}$O$_{15}$], a new silicate mineral with [Si$_{6}$O$_{15}$] three-membered double rings from the Dara-I-Pioz Moraine, Tien-Shan Mountains, Tajikistan, Can. Mineral. 41, 513–520 (2003), doi:10.2113/gscanmin.41.2.513.
Prototype Generator
aflow --proto=AB2C15D6E_oI100_74_e_g_e2hi2j_hj_a --params=$a,b/a,c/a,z_{2},z_{3},y_{4},y_{5},z_{5},y_{6},z_{6},y_{7},z_{7},x_{8},z_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10},x_{11},y_{11},z_{11}$