Cr3Si (A15) Structure: A3B_cP8_223_c_a

Picture of Structure; Click for Big Picture
Prototype : Cr3Si
AFLOW prototype label : A3B_cP8_223_c_a
Strukturbericht designation : A15
Pearson symbol : cP8
Space group number : 223
Space group symbol : Pm3n
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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_{1}} & = &0 \, \mathbf{a_1} + 0 \, \mathbf{a_2} + 0 \, \mathbf{a_3} & = &0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Si} \\ \mathbf{B_{2}} & = &\frac12 \, \mathbf{a_1}+ \frac12 \, \mathbf{a_2}+ \frac12 \, \mathbf{a_3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{y}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(2a\right) & \mbox{Si} \\ \mathbf{B_{3}} & = &\frac14 \, \mathbf{a_1}+ \frac12 \, \mathbf{a_3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cr} \\ \mathbf{B_{4}} & = &\frac34 \, \mathbf{a_1}+ \frac12 \, \mathbf{a_3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \frac12 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cr} \\ \mathbf{B_{5}} & = &\frac12 \, \mathbf{a_1}+ \frac14 \, \mathbf{a_2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}& \left(6c\right) & \mbox{Cr} \\ \mathbf{B_{6}} & = &\frac12 \, \mathbf{a_1}+ \frac34 \, \mathbf{a_2}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}& \left(6c\right) & \mbox{Cr} \\ \mathbf{B_{7}} & = &\frac12 \, \mathbf{a_2}+ \frac14 \, \mathbf{a_3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cr} \\ \mathbf{B_{8}} & = &\frac12 \, \mathbf{a_2}+ \frac34 \, \mathbf{a_3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac34 \, a \, \mathbf{\hat{z}}& \left(6c\right) & \mbox{Cr} \\ \end{array} \]

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.

Geometry files