ThFe$_{2}$SiC Structure: AB2CD_oC20_63_a_f_c_c-001
| Prototype | CFe$_{2}$SiTh |
| AFLOW prototype label | AB2CD_oC20_63_a_f_c_c-001 |
| ICSD | 75133 |
| Pearson symbol | oC20 |
| Space group number | 63 |
| Space group symbol | $Cmcm$ |
| AFLOW prototype command |
aflow --proto=AB2CD_oC20_63_a_f_c_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
ErFe$_{2}$SiC, GdFe$_{2}$SiC, HoFe$_{2}$SiC, LuFe$_{2}$SiC, SmFe$_{2}$SiC, TbFe$_{2}$SiC, TmFe$_{2}$SiC, UFe$_{2}$SiC, YFe$_{2}$SiC
- This structure is a filled version of the Re$_{3}$B structure, with carbon atoms sitting in the (4b) Wyckoff positions. This is the quaternary version of the structure. The ternary version, where one of the (4c) Wyckoff positions has the same atom type as the (8f) site, is designated the the V$_{3}$AsC structure.
- (Witte, 1994) does not designate a prototype for this structure, but as they only give full crystallographic data for the ThFe$_{2}$SiC structure we will use this as the prototype.
- (Witte, 1994) lists the occupation of each site as Th (100.2%), Fe (97.7%), Si (96.0%), and C (97.0%), indicating that there are vacancies on the Fe, Si, and C sites, and that some of the Th atoms are either interstitial or occuping the other (4c) site or the (8f) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | C I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | C I |
| $\mathbf{B_{3}}$ | = | $- y_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Si I |
| $\mathbf{B_{4}}$ | = | $y_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Si I |
| $\mathbf{B_{5}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | Th I |
| $\mathbf{B_{6}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (4c) | Th I |
| $\mathbf{B_{7}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Fe I |
| $\mathbf{B_{8}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Fe I |
| $\mathbf{B_{9}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | Fe I |
| $\mathbf{B_{10}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8f) | Fe I |
References
- A. M. Witte and W. Jeitschko, Carbides with Filled Re$_{3}$B-Type Structure, J. Solid State Chem. 112, 232–236 (1994), doi:10.1006/jssc.1994.1297.
Prototype Generator
aflow --proto=AB2CD_oC20_63_a_f_c_c --params=$a,b/a,c/a,y_{2},y_{3},y_{4},z_{4}$