$E3_{1}$ ($\beta$–Ag2HgI4) (obsolete) Structure : A2BC4_tP7_111_f_a_n

Picture of Structure; Click for Big Picture
Prototype : Ag2HgI4
AFLOW prototype label : A2BC4_tP7_111_f_a_n
Strukturbericht designation : $E3_{1}$
Pearson symbol : tP7
Space group number : 111
Space group symbol : $P\bar{4}2m$
AFLOW prototype command : aflow --proto=A2BC4_tP7_111_f_a_n
--params=
$a$,$c/a$,$x_{3}$,$z_{3}$


  • (Ketelaar, 1931) determined this pseudo–cubic structure for $\beta$–Ag2HgI4, and (Hermann, 1937) assigned it the Strukturbericht symbol $E3_{1}$. Later, (Browall, 1974) showed that $\beta$–Ag2HgI4 takes the Al2CdS4 structure, which some authorities give as Strukturbericht $E3$.

Simple Tetragonal primitive vectors:

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

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \, \mathbf{\hat{x}} + 0 \, \mathbf{\hat{y}} + 0 \, \mathbf{\hat{z}} & \left(1a\right) & \mbox{Hg} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{Ag} \\ \mathbf{B}_{3} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(2f\right) & \mbox{Ag} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{I} \\ \mathbf{B}_{5} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2} + z_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{I} \\ \mathbf{B}_{6} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{I} \\ \mathbf{B}_{7} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2}-z_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(4n\right) & \mbox{I} \\ \end{array} \]

References

  • J. A. A. Ketelaar, Strukturbestimmung der komplexen Quecksilberverbindungen Ag2HgJ4 und Cu2HgJ4, Zeitschrift für Kristallographie – Crystalline Materials 80, 190–203 (1931), doi:10.1524/zkri.1931.80.1.190.
  • C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928–1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).

Found in

  • K. W. Browall, J. S. Kasper, and H. Wiedemeier, Single–crystal studies of $\beta$–Ag2HgI4, J. Solid State Chem. 10, 20–28 (1974), doi:10.1016/0022-4596(74)90004-8.

Geometry files


Prototype Generator

aflow --proto=A2BC4_tP7_111_f_a_n --params=

Species:

Running:

Output: