FeSi ($B20$) Structure: AB_cP8_198_a_a-002
| Prototype | FeSi |
| AFLOW prototype label | AB_cP8_198_a_a-002 |
| Strukturbericht designation | $B20$ |
| ICSD | 5250 |
| Pearson symbol | cP8 |
| Space group number | 198 |
| Space group symbol | $P2_13$ |
| AFLOW prototype command |
aflow --proto=AB_cP8_198_a_a-002
--params=$a, \allowbreak x_{1}, \allowbreak x_{2}$ |
Other compounds with this structure
AlPt, AuBe, CoGe, CoSi, CrGe, CrSi, FeGe, FeSi, GaPd, GaPt, GeMn, GeRh, GeRu, HfSb, HfSn, HgPd, MgPt, MnSi, OsSi, ReSi, RhS, RhSi, RhSn, RuSi, SbZr, SiTc
- When $x_{1}=0$ and $x_{2}=1/2$, or $x_{1}=1/4$ and $x_{2}=3/4$, this lattice reduces to the rock salt ($B1$) structure. When $x_{1}=-x_{2}=1/8(\sqrt{5}-1)$ we have an
idea
structure where every atom is seven-fold coordinated. - FeSi ($B20$) and $\alpha$–CO ($B21$) have the same AFLOW prototype label, AB_cP8_198_a_a. They are generated by the same symmetry operations with different sets of parameters (
--params) specified in their corresponding CIF files.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $a x_{1} \,\mathbf{\hat{x}}+a x_{1} \,\mathbf{\hat{y}}+a x_{1} \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{2}}$ | = | $- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{1} \,\mathbf{\hat{y}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{3}}$ | = | $- x_{1} \, \mathbf{a}_{1}+\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{1} \,\mathbf{\hat{x}}+a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{4}}$ | = | $\left(x_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{1} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $a \left(x_{1} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{1} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{1} \,\mathbf{\hat{z}}$ | (4a) | Fe I |
| $\mathbf{B_{5}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+a x_{2} \,\mathbf{\hat{y}}+a x_{2} \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{2} \,\mathbf{\hat{y}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{7}}$ | = | $- x_{2} \, \mathbf{a}_{1}+\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | Si I |
| $\mathbf{B_{8}}$ | = | $\left(x_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{2} - \frac{1}{2}\right) \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{2} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{2} - \frac{1}{2}\right) \,\mathbf{\hat{y}}- a x_{2} \,\mathbf{\hat{z}}$ | (4a) | Si I |
References
- L. Vočadlo, K. S. Knight, G. D. Price, and I. G. Wood, Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction, Phys. Chem. Miner. 29, 132–139 (2002), doi:10.1007/s002690100202.
Prototype Generator
aflow --proto=AB_cP8_198_a_a --params=$a,x_{1},x_{2}$