$E3_{1}$ (β-Ag$_{2}$HgI$_{4}$) Structure: A2BC4_tP7_111_e_b_n-001
| Prototype | Ag$_{2}$HgI$_{4}$ |
| AFLOW prototype label | A2BC4_tP7_111_e_b_n-001 |
| Strukturbericht designation | $E3_{1}$ |
| ICSD | 30264 |
| Pearson symbol | tP7 |
| Space group number | 111 |
| Space group symbol | $P\overline{4}2m$ |
| AFLOW prototype command |
aflow --proto=A2BC4_tP7_111_e_b_n-001
--params=$a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak z_{3}$ |
Other compounds with this structure
CdIn$_{2}$Se$_{4}$, CuHg$_{2}$I$_{4}$
- (Ketelaar, 1931) determined this pseudo-cubic structure for $\beta$–Ag$_{2}$HgI$_{4}$, and (Hermann, 1937) assigned it the Strukturbericht symbol $E3_{1}$. Later, (Browall, 1974) showed that $\beta$–Ag$_{2}$HgI$_{4}$ takes the Al$_{2}$CdS$_{4}$ structure, which (Pearson, 1967) listed as Strukturbericht $E3$.
- The CdIn$_{2}$Se$_{4}$ structure found by (Hahn, 1955) does seem to be in this phase, so we have removed the
obsolete
label.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Hg I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}$ | (2e) | Ag I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}$ | (2e) | Ag I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4n) | I I |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (4n) | I I |
| $\mathbf{B_{6}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4n) | I I |
| $\mathbf{B_{7}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (4n) | I I |
References
- J. A. A. Ketelaar, Strukturbestimmung der komplexen Quecksilberverbindungen Ag$_{2}$HgJ$_{4}$ und Cu$_{2}$HgJ$_{4}$, Z. Krystallogr. 60, 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).
- H. Hahn, G. Frank, W. Klingler, A. D. Störger, and G. Störger, Untersuchungen über ternäre Chalkogenide. VI. Über Ternäre Chalkogenide des Aluminiums, Galliums und Indiums mit Zink, Cadmium und Quecksilber, Z. Anorganische und Allgemeine Chemie 279, 241–270 (1955), doi:10.1002/zaac.19552790502.
- W. B. Pearson, A Handbook of Lattice Spacings and Structures of Metals and Alloys, Volume 2, International Series of Monographs on Metal Physics and Physical Metallurgy, vol. 8 (Pergamon Press, Oxford, London, Edinburgh, New York, Toronto, Sydney, Paris, Braunschweig, 1967).
Found in
- K. W. Browall, J. S. Kasper, and H. Wiedemeier, Single-crystal studies of $\beta$-Ag$_{2}$HgI$_{4}$, J. Solid State Chem. 10, 20–28 (1974), doi:10.1016/0022-4596(74)90004-8.
Prototype Generator
aflow --proto=A2BC4_tP7_111_e_b_n --params=$a,c/a,x_{3},z_{3}$