Kesterite [Cu2(Zn,Fe)SnS4] Structure : A2BCD4_tI16_82_ac_b_d_g

Picture of Structure; Click for Big Picture
Prototype : Cu2(Fe,Zn)SnS4
AFLOW prototype label : A2BCD4_tI16_82_ac_b_d_g
Strukturbericht designation : None
Pearson symbol : tI16
Space group number : 82
Space group symbol : $I\bar{4}$
AFLOW prototype command : aflow --proto=A2BCD4_tI16_82_ac_b_d_g
--params=
$a$,$c/a$,$x_{5}$,$y_{5}$,$z_{5}$


  • The kesterite structure is related to the stannite structure, with differences occurring due to the positioning of the Cu atoms (Hall, 1978). The ($2b$) Wyckoff position is partially occupied with Zn and Fe; however, we decorate it with Fe only.

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(2a\right) & \mbox{Cu I} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Fe} \\ \mathbf{B}_{3} & = & \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}c \, \mathbf{\hat{z}} & \left(2c\right) & \mbox{Cu II} \\ \mathbf{B}_{4} & = & \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}c \, \mathbf{\hat{z}} & \left(2d\right) & \mbox{S} \\ \mathbf{B}_{5} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Sn} \\ \mathbf{B}_{6} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Sn} \\ \mathbf{B}_{7} & = & \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Sn} \\ \mathbf{B}_{8} & = & \left(x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \mbox{Sn} \\ \end{array} \]

References

  • S. R. Hall, J. T. Szyma\'nski, and J. M. Stewart, Kesterite, Cu2(Zn,Fe)SnS4, and stannite, Cu2(Fe,Zn)SnS4, structurally similar but distinct minerals, Can. Mineral. 16, 131–137 (1978).
  • S. Schorr, H.–J. Hoebler, and M. Tovar, A neutron diffraction study of the stannite–kesterite solid solution series, Eur. J. Mineral. 19, 65–73 (2007), doi:10.1127/0935-1221/2007/0019-0065.
  • S. Schorr, The crystal structure of kesterite type compounds: A neutron and X–ray diffraction study, Sol. Energy Mater. Sol. Cells 95, 1482–1488 (2011), doi:10.1016/j.solmat.2011.01.002.

Geometry files


Prototype Generator

aflow --proto=A2BCD4_tI16_82_ac_b_d_g --params=

Species:

Running:

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