$\gamma$–brass (Cu9Al4, $D8_{3}$) Structure: A4B9_cP52_215_ei_3efgi

Picture of Structure; Click for Big Picture
Prototype : Cu9Al4
AFLOW prototype label : A4B9_cP52_215_ei_3efgi
Strukturbericht designation : $D8_{3}$
Pearson symbol : cP52
Space group number : 215
Space group symbol : $P\bar{4}3m$
AFLOW prototype command : aflow --proto=A4B9_cP52_215_ei_3efgi
--params=
$a$,$x_{1}$,$x_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$


Other compounds with this structure

  • Cu9Ga4. (Pearson, 1958), pp. 252, gives a list of compounds which can take on the D81, D82, or D83 structure, depending on the exact composition.

  • (Arnberg, 1978) give the Wyckoff positions of the Cu IV and Cu V atoms as (6g) $(x , 1/2 , 1/2)$, but give the coordinates in the form $(x , 0 , 0)$ corresponding to the (6f) site. (Stokhuyzen, 1974) used (6f) for both types of atoms in the isostructural system Ga9Al4. (Pearson, 1958) places the Cu IV atoms on a (6f) site and Cu V on (6g), but does not give explicit coordinates. Placing the Cu V atoms on (6f) sites yields an interatomic distance of 1.8Å. This contradicts (Arnberg, 1978), who say that the minimum interatomic distance is 2.48 Å\ between the Cu IV and Cu V atoms. Placing the Cu V atoms on (6g) sites gives this distance, in agreement with (Pearson, 1958), so we make this choice for the crystal structure. This is a variety of $\gamma$-brass comparable to the $D8_{2}$ structure. In fact, if we
    • Replace the Al and Cu III atoms by Zn, while setting $x_{4} = x_{1} + 1/2$ ,
    • Replace the Al II and Cu VI atoms by Zn, with $x_{8} = x_{7} + 1/2$ and $z_{8} = z_{7} + 1/2$,
    • Set $x_{3} = x_{2} + 1/2$ and
    • Set $x_{6} = x_{5} + 1/2$,
    then this structure is identical to $D8_{2}$ $\gamma$-brass.

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} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al I} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + x_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + x_{1}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al I} \\ \mathbf{B}_{3} & = & -x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al I} \\ \mathbf{B}_{4} & = & x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2}-x_{1} \, \mathbf{a}_{3} & = & x_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}}-x_{1}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Al I} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu I} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu I} \\ \mathbf{B}_{7} & = & -x_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu I} \\ \mathbf{B}_{8} & = & x_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2}-x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu I} \\ \mathbf{B}_{9} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu II} \\ \mathbf{B}_{10} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu II} \\ \mathbf{B}_{11} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu II} \\ \mathbf{B}_{12} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-x_{3}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu II} \\ \mathbf{B}_{13} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu III} \\ \mathbf{B}_{14} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu III} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu III} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-x_{4}a \, \mathbf{\hat{z}} & \left(4e\right) & \mbox{Cu III} \\ \mathbf{B}_{17} & = & x_{5} \, \mathbf{a}_{1} & = & x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{18} & = & -x_{5} \, \mathbf{a}_{1} & = & -x_{5}a \, \mathbf{\hat{x}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{19} & = & x_{5} \, \mathbf{a}_{2} & = & x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{20} & = & -x_{5} \, \mathbf{a}_{2} & = & -x_{5}a \, \mathbf{\hat{y}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{21} & = & x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{22} & = & -x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{z}} & \left(6f\right) & \mbox{Cu IV} \\ \mathbf{B}_{23} & = & x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{24} & = & -x_{6} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{25} & = & \frac{1}{2} \, \mathbf{a}_{1} + x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{26} & = & \frac{1}{2} \, \mathbf{a}_{1}-x_{6} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{27} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{28} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2}-x_{6} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(6g\right) & \mbox{Cu V} \\ \mathbf{B}_{29} & = & x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{30} & = & -x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{31} & = & -x_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{32} & = & x_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-z_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-z_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{33} & = & z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{34} & = & z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{35} & = & -z_{7} \, \mathbf{a}_{1}-x_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}}-x_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{36} & = & -z_{7} \, \mathbf{a}_{1} + x_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -z_{7}a \, \mathbf{\hat{x}} + x_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{37} & = & x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{38} & = & -x_{7} \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{39} & = & x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}}-x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{40} & = & -x_{7} \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}}-z_{7}a \, \mathbf{\hat{y}} + x_{7}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Al II} \\ \mathbf{B}_{41} & = & x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{42} & = & -x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{43} & = & -x_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{44} & = & x_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-z_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-z_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{45} & = & z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{46} & = & z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{47} & = & -z_{8} \, \mathbf{a}_{1}-x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}}-x_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{48} & = & -z_{8} \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -z_{8}a \, \mathbf{\hat{x}} + x_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{49} & = & x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{50} & = & -x_{8} \, \mathbf{a}_{1} + z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{51} & = & x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}}-x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \mathbf{B}_{52} & = & -x_{8} \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}}-z_{8}a \, \mathbf{\hat{y}} + x_{8}a \, \mathbf{\hat{z}} & \left(12i\right) & \mbox{Cu VI} \\ \end{array} \]

References

  • L. Arnberg and S. Westman, Crystal perfection in a noncentrosymmetric alloy. Refinement and test of twinning of the γCu9Al4 structure, Acta Crystallogr. Sect. A 34, 399–404 (1978), doi:10.1107/S0567739478000807.
  • R. Stokhuyzen, J. K. Brandon, P. C. Chieh, and W. B. Pearson, Copper–Gallium, gamma1Cu9Ga4, Acta Crystallogr. Sect. B Struct. Sci. 30, 2910–2911 (1974), doi:10.1107/S0567740874008478.
  • W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, no. N.R.C. No. 4303 in International Series of Monographs on Metal Physics and Physical Metallurgy (Pergamon Press, Oxford, London, Edinburgh, New York, Paris, Frankfort, 1958), 1964 reprint with corrections edn.

Found in

  • P. Villars and K. Cenuzal, eds., Structure Types (Springer, Berlin, Heidelberg, 2005), Landolt–Börnstein – Group III Condensed Matter (Numerical Data and Functional Relationships in Science and Technology), vol. 43A2, chap. Cu9Al4 in Part 2: Space Groups (218) P–43n – (195) P23.

Geometry files


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