Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: AB7_cF32_225_b_ad

  • 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)

$L1_{a}$ (disputed CuPt3) Structure : AB7_cF32_225_b_ad

Picture of Structure; Click for Big Picture
Prototype : CuPt3
AFLOW prototype label : AB7_cF32_225_b_ad
Strukturbericht designation : $L1_{a}$
Pearson symbol : cF32
Space group number : 225
Space group symbol : $Fm\bar{3}m$
AFLOW prototype command : aflow --proto=AB7_cF32_225_b_ad
--params=
$a$


  • According to (Tang, 1951), the ($24d$) sites have the composition Pt0.8Cu0.2 in stoichiometric CuPt3. Here we use Pt to specify the atoms on this site.
  • (Tang, 1951) states that the crystal structure of CuPt3 must be cubic, but (Mshumi, 2014) argue that it is orthorhombic, and in fact the $L1_{3}$ structure.
  • (Smithells, 1955) gave this structure the $L1_{a}$ designation as part of his extension of the original Strukturbericht labels. He does note that an alternative orthorhombic structure had been proposed.
  • (Smithells, 1955) assigns this structure to space group $F432$ #209, but the positions given by (Tang, 1951) are also consistent with $Fm\overline{3}m$ #225, so we assign this structure to the higher symmetry space group.
  • (Tang, 1951) does not give the lattice constant, so we use the value estimated by (Smithells, 1955).
  • The Wyckoff positions are identical to those of the Ca7Ge structure.

Face-centered Cubic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(4a\right) & \text{Pt I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(4b\right) & \text{Cu} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{1} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{Pt II} \\ \mathbf{B}_{4} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{Pt II} \\ \mathbf{B}_{5} & = & \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{Pt II} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{Pt II} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(24d\right) & \text{Pt II} \\ \mathbf{B}_{8} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(24d\right) & \text{Pt II} \\ \end{array} \]

References

  • C. J. Smithells, Metals Reference Book (Butterworths Scientific, London, 1955), second edn.

Found in

  • C. Mshumi, C. I. Lang, L. R. Richey, K. C. Erb, C. W. Rosenbrock, L. J. Nelson, R. R. Vanfleet, H. T. Stokes, B. J. Campbell, and G. L. W. Hart, Revisiting the CuPt3 prototype and the $L1_{3}$ structure, Acta Mater. 73, 326–336 (2014), doi:10.1016/j.actamat.2014.03.029.

Geometry files


Prototype Generator

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