CdAl2S4 ($E3$) Structure: A2BC4_tI14_82_bc_a_g

Picture of Structure; Click for Big Picture
Prototype : CdAl2S4
AFLOW prototype label : A2BC4_tI14_82_bc_a_g
Strukturbericht designation : $E3$
Pearson symbol : tI14
Space group number : 82
Space group symbol : $\mbox{I}\bar{4}$
AFLOW prototype command : aflow --proto=A2BC4_tI14_82_bc_a_g
--params=
$a$,$c/a$,$x_{4}$,$y_{4}$,$z_{4}$


Other compounds with this structure

  • CoGa2S4, FeGa2S4, HgGa2Te4, ZnGa2S4, HgAl2S4, numerous others.

  • When $c = 2a$ and $x = y = 1/4$, and $z = 1/8$ the atoms are on the sites of the diamond (A4) structure, but of course there are defects. Removing the Al–I (2b) atom transforms this to the BPO4 (H07) 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:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(2a\right) & \mbox{Cd} \\ \mathbf{B_2} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{2}& = & \frac12 \, c \, \mathbf{\hat{z}} & \left(2b\right) & \mbox{Al I} \\ \mathbf{B_3} & =& \frac34 \, \mathbf{a}_{1} + \frac14 \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{y}} + \frac14 \, c \, \mathbf{\hat{z}}& \left(2c\right) & \mbox{Al II} \\ \mathbf{B}_{4} & =& \left(y_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(z_{4}+x_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3}& =& x_{4} \, a \, \mathbf{\hat{x}} + y_{4} \, a \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{S} \\ \mathbf{B_5} & =& \left(z_{4}-y_{4}\right) \, \mathbf{a}_{1} + \left(z_{4}-x_{4}\right) \, \mathbf{a}_{2} - \left(x_{4}+y_{4}\right) \, \mathbf{a}_{3}& =& - x_{4} \, a \, \mathbf{\hat{x}} - y_{4} \, a \, \mathbf{\hat{y}} + z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{S} \\ \mathbf{B_6} & =& - \left(z_{4}+x_{4}\right) \, \mathbf{a}_{1} + \left(y_{4}-z_{4}\right) \, \mathbf{a}_{2} + \left(y_{4}-x_{4}\right) \, \mathbf{a}_{3}& =& y_{4} \, a \, \mathbf{\hat{x}} - x_{4} \, a \, \mathbf{\hat{y}} - z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{S} \\ \mathbf{B_7} & =& \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} - \left(y_{4}+z_{4}\right) \, \mathbf{a}_{2} + \left(x_{4}-y_{4}\right) \, \mathbf{a}_{3}& =& - y_{4} \, a \, \mathbf{\hat{x}} + x_{4} \, a \, \mathbf{\hat{y}} - z_{4} \, c \, \mathbf{\hat{z}}& \left(8g\right) & \mbox{S} \\ \end{array} \]

References

  • H. Hahn, G. Frank, W. Klingler, A. Störger, and G. Störger, Untersuchungen über ternäre Chalkogenide. VI. Über ternäre Chalogenide des Aluminiums, Galliums und Indiums mit Zink, Cadmium und Quecksilber, Z. Anorg. Allg. Chem. 279, 241–270 (1955), doi:10.1002/zaac.19552790502.

Found in

  • P. Villars, Material Phases Data System ((MPDS), CH–6354 Vitznau, Switzerland, 2014). Accessed through the Springer Materials site.

Geometry files


Prototype Generator

aflow --proto=A2BC4_tI14_82_bc_a_g --params=

Species:

Running:

Output: