Eulytine (Bi$_{4}$(SiO$_{4}$)$_{3}$, $S1_{5}$) Structure: A4B12C3_cI76_220_c_e_a-001
| Prototype | Bi$_{4}$O$_{12}$Si$_{3}$ |
| AFLOW prototype label | A4B12C3_cI76_220_c_e_a-001 |
| Strukturbericht designation | $S1_{5}$ |
| Mineral name | eulytine |
| ICSD | 402349 |
| Pearson symbol | cI76 |
| Space group number | 220 |
| Space group symbol | $I\overline{4}3d$ |
| AFLOW prototype command |
aflow --proto=A4B12C3_cI76_220_c_e_a-001
--params=$a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
Ba$_{3}$Bi(PO$_{4}$)$_{3}$, Ba$_{3}$Gd(PO$_{4}$)$_{3}$, Ba$_{3}$In(PO$_{4}$)$_{3}$, Ba$_{3}$La(PO$_{4}$)$_{3}$, Ba$_{3}$Lu(PO$_{4}$)$_{3}$, Ba$_{3}$Nd(PO$_{4}$)$_{3}$, Ba$_{3}$Y(PO$_{4}$)$_{3}$, Sr$_{3}$Bi(PO$_{4}$)$_{3}$, Sr$_{3}$Gd(PO$_{4}$)$_{3}$, Sr$_{3}$In(PO$_{4}$)$_{3}$, Sr$_{3}$La(PO$_{4}$)$_{3}$, Sr$_{3}$Lu(PO$_{4}$)$_{3}$, Sr$_{3}$Nd(PO$_{4}$)$_{3}$, Sr$_{3}$Y(PO$_{4}$)$_{3}$, Bi$_{4}$(GeO$_{4}$)$_{3}$, Ca$_{3}$Bi(PO$_{4}$)$_{3}$
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{5}{8} \, \mathbf{a}_{2}+\frac{3}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{8}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (12a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{7}{8} \, \mathbf{a}_{2}+\frac{1}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{8}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (12a) | Si I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{8} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{5}{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{3}{8}a \,\mathbf{\hat{y}}$ | (12a) | Si I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{8} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}+\frac{7}{8} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{8}a \,\mathbf{\hat{y}}$ | (12a) | Si I |
| $\mathbf{B_{5}}$ | = | $\frac{5}{8} \, \mathbf{a}_{1}+\frac{3}{8} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+\frac{3}{8}a \,\mathbf{\hat{z}}$ | (12a) | Si I |
| $\mathbf{B_{6}}$ | = | $\frac{7}{8} \, \mathbf{a}_{1}+\frac{1}{8} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}+\frac{1}{8}a \,\mathbf{\hat{z}}$ | (12a) | Si I |
| $\mathbf{B_{7}}$ | = | $2 x_{2} \, \mathbf{a}_{1}+2 x_{2} \, \mathbf{a}_{2}+2 x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{9}}$ | = | $- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{10}}$ | = | $- \left(2 x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{11}}$ | = | $\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(2 x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- 2 x_{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{13}}$ | = | $- 2 x_{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{14}}$ | = | $- 2 x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{2} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16c) | Bi I |
| $\mathbf{B_{15}}$ | = | $\left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{16}}$ | = | $\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{17}}$ | = | $\left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a y_{3} \,\mathbf{\hat{y}}- a z_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{18}}$ | = | $- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a y_{3} \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{19}}$ | = | $\left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{20}}$ | = | $- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a z_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{21}}$ | = | $\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a z_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{22}}$ | = | $\left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- a y_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{23}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{24}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(- y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a z_{3} \,\mathbf{\hat{y}}- a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{25}}$ | = | $- \left(x_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a y_{3} \,\mathbf{\hat{x}}- a z_{3} \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{26}}$ | = | $\left(x_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a y_{3} \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+a x_{3} \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{27}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{28}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{29}}$ | = | $- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{30}}$ | = | $\left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{31}}$ | = | $\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{32}}$ | = | $- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{2}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{33}}$ | = | $\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{2}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{34}}$ | = | $- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{35}}$ | = | $\left(x_{3} + y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(y_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{36}}$ | = | $- \left(x_{3} + y_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(y_{3} - z_{3}\right) \, \mathbf{a}_{3}$ | = | $a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{37}}$ | = | $- \left(x_{3} - y_{3}\right) \, \mathbf{a}_{1}- \left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(y_{3} - z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+a \left(y_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
| $\mathbf{B_{38}}$ | = | $\left(x_{3} - y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(y_{3} + z_{3}\right) \, \mathbf{a}_{3}$ | = | $- a \left(z_{3} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- a \left(y_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (48e) | O I |
References
- H. Liu and C. Kuo, Crystal structure of bismuth(III) silicate, Bi$_{4}$SiO$_{4}$)$_{3}$, Z. Kristallogr. 212, 48 (1997), doi:10.1524/zkri.1997.212.1.48.
Found in
- R. T. Downs and M. Hall-Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).
Prototype Generator
aflow --proto=A4B12C3_cI76_220_c_e_a --params=$a,x_{2},x_{3},y_{3},z_{3}$