Chalcopyrite (CuFeS2, $E1_{1}$) Structure: ABC2_tI16_122_a_b_d

Picture of Structure; Click for Big Picture
Prototype : CuFeS2
AFLOW prototype label : ABC2_tI16_122_a_b_d
Strukturbericht designation : $E1_{1}$
Pearson symbol : tI16
Space group number : 122
Space group symbol : $\mbox{I}\bar{4}\mbox{2d}$
AFLOW prototype command : aflow --proto=ABC2_tI16_122_a_b_d
--params=
$a$,$c/a$,$x_{3}$


Other compounds with this structure

  • CuInS2, CuInSe2

  • When $c = 2a$ and $x_{3} = 1/8$ the atoms are on the sites of the diamond (A4) structure. In this case, if we replace the Fe atoms by Cu, we get the zincblende (B3) structure.

Body-centered Tetragonal primitive vectors:

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

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(4a\right) & \mbox{Cu} \\ \mathbf{B_2} & = &\frac34 \, \mathbf{a}_{1}+ \frac14 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{y}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4a\right) & \mbox{Cu} \\ \mathbf{B_3} & = &\frac12 \, \mathbf{a}_{1}+ \frac12 \, \mathbf{a}_{2}& = &\frac12 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Fe} \\ \mathbf{B_4} & = &\frac14 \, \mathbf{a}_{1}+ \frac34 \, \mathbf{a}_{2}+ \frac12 \, \mathbf{a}_{3}& = &\frac12 \, a \, \mathbf{\hat{x}}+ \frac14 \, c \, \mathbf{\hat{z}}& \left(4b\right) & \mbox{Fe} \\ \mathbf{B_5} & = &\frac38 \, \mathbf{a}_{1}+ \left(\frac18 + x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac14 + x_{3}\right) \, \mathbf{a}_{3}& = &x_{3} \, a \, \mathbf{\hat{x}}+ \frac14 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{S} \\ \mathbf{B_6} & = &\frac78 \, \mathbf{a}_{1}+ \left(\frac18 - x_{3}\right) \, \mathbf{a}_{2}+ \left(\frac34 - x_{3}\right) \, \mathbf{a}_{3}& = &- x_{3} \, a \, \mathbf{\hat{x}}+ \frac34 \, a \, \mathbf{\hat{y}}+ \frac18 \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{S} \\ \mathbf{B_7} & = &\left(\frac78 - x_{3}\right) \, \mathbf{a}_{1}+ \frac18 \, \mathbf{a}_{2}+ \left(\frac14 - x_{3}\right) \, \mathbf{a}_{3}& = &\frac34 \, a \, \mathbf{\hat{x}}+ \left(\frac12 - x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{S} \\ \mathbf{B_8} & = &\left(\frac78 + x_{3}\right) \, \mathbf{a}_{1}+ \frac58 \, \mathbf{a}_{2}+ \left(\frac34 + x_{3}\right) \, \mathbf{a}_{3}& = &\frac14 \, a \, \mathbf{\hat{x}}+ \left(\frac12 + x_{3}\right) \, a \, \mathbf{\hat{y}}+ \frac38 \, c \, \mathbf{\hat{z}}& \left(8d\right) & \mbox{S} \\ \end{array} \]

References

  • S. R. Hall and J. M. Stewart, The Crystal Structure Refinement of Chalcopyrite, CuFeS2, Acta Crystallogr. Sect. B Struct. Sci. 29, 579–585 (1973), doi:10.1107/S0567740873002943.
  • S. C. Abrahams and J. L. Bernstein, Piezoelectric nonlinear optic CuGaS2 and CuInS2 crystal structure: Sublattice distortion in AIBIIC2VI and AIIBIVC2V type chalcopyrites, J. Chem. Phys. 59, 5415–5422 (1973), doi:10.1063/1.1679891.

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. 2808.

Geometry files


Prototype Generator

aflow --proto=ABC2_tI16_122_a_b_d --params=

Species:

Running:

Output: