Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2BC4_tI14_82_bc_a_g

  • M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

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 : $\text{I}\bar{4}$
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:

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

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=

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