CdAl$_{2}$S$_{4}$ ($E3$) Structure: A2BC4_tI14_82_bc_a_g-001
| Prototype | Al$_{2}$CdS$_{4}$ |
| AFLOW prototype label | A2BC4_tI14_82_bc_a_g-001 |
| Strukturbericht designation | $E3$ |
| ICSD | 25634 |
| Pearson symbol | tI14 |
| Space group number | 82 |
| Space group symbol | $I\overline{4}$ |
| AFLOW prototype command |
aflow --proto=A2BC4_tI14_82_bc_a_g-001
--params=$a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
CdAl$_{2}$Se$_{4}$, CdAl$_{2}$Te$_{4}$, CdGa$_{2}$S$_{4}$, CdGa$_{2}$Se$_{4}$, CdGa$_{2}$Te$_{4}$, CoGa$_{2}$S$_{4}$, FeGa$_{2}$S$_{4}$, HfGa$_{2}$Se$_{4}$, $\beta$-HgAg$_{2}$I$_{4}$, HgAl$_{2}$S$_{4}$, HgAl$_{2}$Se$_{4}$, HgAl$_{2}$Te$_{4}$, HgGa$_{2}$S$_{4}$, HgGa$_{2}$Te$_{4}$, HgIn$_{2}$Se$_{4}$, HgIn$_{2}$Te$_{4}$, ZnGa$_{2}$S$_{4}$, ZnGa$_{2}$Se$_{4}$, ZnGa$_{2}$Te$_{4}$, ZnIn$_{2}$Se$_{4}$, ZnIn$_{2}$Te$_{4}$
- 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 BPO$_{4}$ ($H0_{7}$) structure.
- (Pearson, 1967) gives this the designation $E3$, without any subscript. It should be defined as $E3_{a}$, but as he did not put any other structures into this subcategory, we will leave it as is.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Cd I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2b) | Al I |
| $\mathbf{B_{3}}$ | = | $\frac{3}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (2c) | Al II |
| $\mathbf{B_{4}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8g) | S I |
| $\mathbf{B_{5}}$ | = | $- \left(y_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8g) | S I |
| $\mathbf{B_{6}}$ | = | $- \left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(y_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8g) | S I |
| $\mathbf{B_{7}}$ | = | $\left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8g) | S I |
References
- H. Hahn, G. Frank, W. Klingler, A.-D. Störger, and G. Störger, Über ternäre Chalogenide des Aluminiums, Galliums und Indiums mit Zink, Cadmium und Quecksilber}, Z. Anorganische und Allgemeine Chemie 279, 241–270 (1955), doi:10.1002/zaac.19552790502. \bibitem{parthe93:TYPIXE. Parthé, L. Gelato, B. Chabot, M. Penso, K. Cenzula, and R. Gladyshevskii, Standardized Data and Crystal Chemical Characterization of Inorganic Structure Types, Gmelin Handbook of Inorganic and Organometallic Chemistry}, vol. 2 (Springer-Verlag, Berlin, Heidelberg, 1993), 8 edn., doi:10.1007/978-3-662-02909-1_3.\bibAnnoteFile{parthe93:TYPIX
- P. Villars and L. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases (ASM International, Materials Park, OH, 1991), 2nd edn.
- C. Hermann, O. Lohrmann, and H. Philipp, eds., Strukturbericht Band II 1928-1932 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1937).
- 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
- P. Villars, CdAl$_{2}$S$_{4}$ Crystal Structure (2016). PAULING FILE in: Inorganic Solid Phases, SpringerMaterials (online database), Springer, Heidelberg (ed.) SpringerMaterials.
Prototype Generator
aflow --proto=A2BC4_tI14_82_bc_a_g --params=$a,c/a,x_{4},y_{4},z_{4}$