Tennantite (Cu12As4S13) Structure : A4B24C13_cI82_217_c_deg_ag

Picture of Structure; Click for Big Picture
Prototype : As4Cu12S13
AFLOW prototype label : A4B24C13_cI82_217_c_deg_ag
Strukturbericht designation : None
Pearson symbol : cI82
Space group number : 217
Space group symbol : $I\bar{4}3m$
AFLOW prototype command : aflow --proto=A4B24C13_cI82_217_c_deg_ag
--params=
$a$,$x_{2}$,$x_{4}$,$x_{5}$,$z_{5}$,$x_{6}$,$z_{6}$


Other compounds with this structure

  • Cu14Sb4S13 (tetrahedrite)

  • The Cu–II ($12e$) site is only occupied 75.8% of the time, and the Cu–III site is occupied 12.1% of the time, so that these sites only contain twelve atoms.
  • Searching (Downs, 2003) shows that natural samples often have antimony substituting for arsenic. The antimony structures (tetrahedrites) contain higher concentrations of copper.
  • The AFLOW label models the structure as if the sites were fully occupied.

Body-centered Cubic primitive vectors:

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

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{S I} \\ \mathbf{B}_{2} & = & 2x_{2} \, \mathbf{a}_{1} + 2x_{2} \, \mathbf{a}_{2} + 2x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{As} \\ \mathbf{B}_{3} & = & -2x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + x_{2}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{As} \\ \mathbf{B}_{4} & = & -2x_{2} \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{As} \\ \mathbf{B}_{5} & = & -2x_{2} \, \mathbf{a}_{1} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-x_{2}a \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{As} \\ \mathbf{B}_{6} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{7} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{8} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{2}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{9} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{10} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{11} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{1}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{4}a \, \mathbf{\hat{z}} & \left(12d\right) & \mbox{Cu I} \\ \mathbf{B}_{12} & = & x_{4} \, \mathbf{a}_{2} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{13} & = & -x_{4} \, \mathbf{a}_{2}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{14} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{y}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{15} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{y}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{16} & = & x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{z}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{17} & = & -x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{z}} & \left(12e\right) & \mbox{Cu II} \\ \mathbf{B}_{18} & = & \left(x_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + 2x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{19} & = & \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2}-2x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + z_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{20} & = & \left(x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{2} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{21} & = & \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{2} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-z_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{22} & = & 2x_{5} \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{23} & = & -2x_{5} \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{24} & = & \left(x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{25} & = & \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -z_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{26} & = & \left(x_{5}+z_{5}\right) \, \mathbf{a}_{1} + 2x_{5} \, \mathbf{a}_{2} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{27} & = & \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{1}-2x_{5} \, \mathbf{a}_{2} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{28} & = & \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}}-x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{29} & = & \left(x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-z_{5}a \, \mathbf{\hat{y}} + x_{5}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{Cu III} \\ \mathbf{B}_{30} & = & \left(x_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{2} + 2x_{6} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{31} & = & \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{2}-2x_{6} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + z_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{32} & = & \left(x_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{2} & = & -x_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{33} & = & \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-z_{6}\right) \, \mathbf{a}_{2} & = & x_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-z_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{34} & = & 2x_{6} \, \mathbf{a}_{1} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{35} & = & -2x_{6} \, \mathbf{a}_{1} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{36} & = & \left(x_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}}-x_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{37} & = & \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{2} + \left(x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -z_{6}a \, \mathbf{\hat{x}} + x_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{38} & = & \left(x_{6}+z_{6}\right) \, \mathbf{a}_{1} + 2x_{6} \, \mathbf{a}_{2} + \left(x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{39} & = & \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{1}-2x_{6} \, \mathbf{a}_{2} + \left(-x_{6}+z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{40} & = & \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}}-x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \mathbf{B}_{41} & = & \left(x_{6}-z_{6}\right) \, \mathbf{a}_{1} + \left(-x_{6}-z_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}}-z_{6}a \, \mathbf{\hat{y}} + x_{6}a \, \mathbf{\hat{z}} & \left(24g\right) & \mbox{S II} \\ \end{array} \]

References

  • A. A. Yaroslavzev, A. V. Mironov, A. N. Kuznetsov, A. P. Dudka, and O. N. Khrykina, Tennantite: multi–temperature crystal structure, phase transition and electronic structure of synthetic Cu12As4S13, Acta Crystallogr. Sect. B Struct. Sci. 75, 634–642 (2019), doi:10.1107/S2052520619007595.
  • R. T. Downs and M. Hall–Wallace, The American Mineralogist Crystal Structure Database, Am. Mineral. 88, 247–250 (2003).

Geometry files


Prototype Generator

aflow --proto=A4B24C13_cI82_217_c_deg_ag --params=

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