Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A3B_cP8_223_c_a

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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 : $\text{Pm}\bar{3}\text{n}$
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.

Geometry files


Prototype Generator

aflow --proto=A3B_cP8_223_c_a --params=

Species:

Running:

Output: