Sr$_{5}$Si$_{3}$ Structure (Obsolete): A3B5_tI32_108_ac_a2c-001
| Prototype | Si$_{3}$Sr$_{5}$ |
| AFLOW prototype label | A3B5_tI32_108_ac_a2c-001 |
| ICSD | 15639 |
| Pearson symbol | tI32 |
| Space group number | 108 |
| Space group symbol | $I4cm$ |
| AFLOW prototype command |
aflow --proto=A3B5_tI32_108_ac_a2c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}$ |
- This is the original determination of the Sr$_{5}$Si$_{3}$ (Nagorsen, 1967). Later(Nesper, 1999) re-examined the system and found that it is actually in the $D8_{l}$ Cr$_{5}$B$_{3}$ structure, space group $I4/mcm$ #140.
- We include this here as our first example of a structure in space group $I4cm$ #108.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Sr I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Si II |
| $\mathbf{B_{6}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Si II |
| $\mathbf{B_{7}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Si II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | Si II |
| $\mathbf{B_{9}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{10}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{11}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{12}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | Sr II |
| $\mathbf{B_{13}}$ | = | $\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(2 x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | Sr III |
| $\mathbf{B_{14}}$ | = | $\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(2 x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | Sr III |
| $\mathbf{B_{15}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | Sr III |
| $\mathbf{B_{16}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | Sr III |
References
- G. Nagorsen, G. Rocktäschel, H. Schäfer, and A. Weiss, Notizen: Die Kristallstruktur der Phase Sr$_{5}$Si$_{3}$, Z. Naturforsch. B 22, 101–102 (1967), doi:10.1515/znb-1967-0122.
- R. Nesper and F. Zürcher, Redetermination of the crystal structure of pentastrontium trisilicide, Sr$_{5}$Si$_{3}$, Z. Kristallogr. 214, 19 (1999), doi:10.1515/ncrs-1999-0112.
Found in
- P. Villars and K. Cenzual, Pearson's Crystal Data – Crystal Structure Database for Inorganic Compounds (2013). ASM International.
Prototype Generator
aflow --proto=A3B5_tI32_108_ac_a2c --params=$a,c/a,z_{1},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5}$