Cr3Si ($A15$) Structure: A3B_cP8_223_c_a
| Prototype | : | Cr3Si |
| AFLOW prototype label | : | A3B_cP8_223_c_a |
| Strukturbericht designation | : | $A15$ |
| Pearson symbol | : | cP8 |
| Space group number | : | 223 |
| Space group symbol | : | $\text{Pm}\bar{3}\text{n}$ |
| AFLOW prototype command | : | aflow --proto=A3B_cP8_223_c_a --params=$a$ |
Other compounds with this structure
- beta–W, Nb3Al, CdV3, Cr3O, Ti3Sb, Ti3Au, many more
- The
A
Strukturbericht designation comes from the fact that this is also the structure of $\beta$–W.
Simple Cubic primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & a \, \mathbf{\hat{z}} \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = &0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \text{Si} \\ \mathbf{B}_{2} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(2a\right) & \text{Si} \\ \mathbf{B}_{3} & = &\frac14 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cr} \\ \mathbf{B}_{4} & = &\frac34 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cr} \\ \mathbf{B}_{5} & = &\frac12 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(6c\right) & \text{Cr} \\ \mathbf{B}_{6} & = &\frac12 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}& \left(6c\right) & \text{Cr} \\ \mathbf{B}_{7} & = &\frac12 \, \mathbf{a}_{2}+ \frac14 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cr} \\ \mathbf{B}_{8} & = &\frac12 \, \mathbf{a}_{2}+ \frac34 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \text{Cr} \\ \end{array} \]References
- W. Jauch, A. J. Schultz, and G. Heger, Single–crystal time–of–flight neutron diffraction of Cr3Si and MnF2 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., pp. 2742.