Cr$_{3}$Si ($A15$) Structure: A3B_cP8_223_c_a-001
| Prototype | Cr$_{3}$Si |
| AFLOW prototype label | A3B_cP8_223_c_a-001 |
| Strukturbericht designation | $A15$ |
| ICSD | 53218 |
| Pearson symbol | cP8 |
| Space group number | 223 |
| Space group symbol | $Pm\overline{3}n$ |
| AFLOW prototype command |
aflow --proto=A3B_cP8_223_c_a-001
--params=$a$ |
Other compounds with this structure
$\beta$-W, Cr$_{3}$Ga, Cr$_{3}$Ge, Cr$_{3}$Ir, Cr$_{3}$O, Cr$_{3}$Os, Cr$_{3}$Pt, Cr$_{3}$Rh, Cr$_{3}$Ru, Cr$_{3}$Si, Mo$_{3}$Al, Mo$_{3}$Be, Mo$_{3}$Ga, Mo$_{3}$Ge, Mo$_{3}$Ir, Mo$_{3}$O, Mo$_{3}$Os, Mo$_{3}$Pt, Mo$_{3}$Si, Mo$_{3}$Sn, Nb$_{3}$Al, Nb$_{3}$Au, Nb$_{3}$Bi, Nb$_{3}$Ga, Nb$_{3}$Ge, Nb$_{3}$In, Nb$_{3}$Ir, Nb$_{3}$Os, Nb$_{3}$Pb, Nb$_{3}$Pt, Nb$_{3}$Rh, Nb$_{3}$Sb, Nb$_{3}$Sn, Ta$_{3}$Au, Ta$_{3}$Sb, Ta$_{3}$Sn, Ti$_{3}$Au, Ti$_{3}$Hg, Ti$_{3}$Ir, Ti$_{3}$Sb, Tl$_{3}$Pt, V$_{3}$Al, $\alpha$-UH$_{3}$, V$_{3}$As, V$_{3}$Au, V$_{3}$Cd, V$_{3}$Co, V$_{3}$Ga, V$_{3}$Ge, V$_{3}$Ir, V$_{3}$Ni, V$_{3}$Pb, V$_{3}$Pd, V$_{3}$Pt, V$_{3}$Rh, V$_{3}$Sb, V$_{3}$Si, V$_{3}$Sn, W$_{3}$O, W$_{3}$Si, Zr$_{3}$Au, Zr$_{3}$Hg, Zr$_{3}$Sn
- The
A
Strukturbericht designation comes from the fact that this is also the structure of $\beta$–W.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&a \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Si I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (2a) | Si I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Cr I |
| $\mathbf{B_{4}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{z}}$ | (6c) | Cr I |
| $\mathbf{B_{5}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}$ | (6c) | Cr I |
| $\mathbf{B_{6}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{3}{4} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{3}{4}a \,\mathbf{\hat{y}}$ | (6c) | Cr I |
| $\mathbf{B_{7}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}a \,\mathbf{\hat{z}}$ | (6c) | Cr I |
| $\mathbf{B_{8}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{3}{4}a \,\mathbf{\hat{z}}$ | (6c) | Cr I |
References
- W. Jauch, A. J. Schultz, and G. Heger, Single-crystal time-of-flight neutron diffraction of Cr$_3$Si and MnF$_2$ comparison with monochromatic-beam techniques, J. Appl. Crystallogr. 20, 117–119 (1987), doi:10.1107/S002188988708703X.
Found in
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
Prototype Generator
aflow --proto=A3B_cP8_223_c_a --params=$a$