Mg(NH$_{3}$)$_{2}$Cl$_{2}$ ($E1_{3}$) Structure: A2B8CD2_oC26_65_h_r_a_i-001
| Prototype | Cl$_{2}$H$_{6}$MgN$_{2}$ |
| AFLOW prototype label | A2B8CD2_oC26_65_h_r_a_i-001 |
| Strukturbericht designation | $E1_{3}$ |
| ICSD | 202459 |
| Pearson symbol | oC26 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=A2B8CD2_oC26_65_h_r_a_i-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak y_{3}, \allowbreak x_{4}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
Cd(NH$_{3}$)$_{2}$Cl$_{2}$, Mg(NH$_{3}$)$_{2}$Cl$_{2}$, Hg(NH$_{3}$)$_{2}$Cl$_{2}$, Ni(NH$_{3}$)$_{2}$Br$_{2}$, Ni(NH$_{3}$)$_{2}$Cl$_{2}$, Ni(NH$_{3}$)$_{2}$I$_{2}$
- (Gottfried, 1938) gave the $E1_{3}$ designation to Cd(NH$_{3}$)$_{2}$Cl$_{2}$, and gave coordinates in the $Cmm2$ #35 space group. However, the cited reference, (MacGillavry, 1936) noted that their coordinates allowed several different space groups, with $Cmmm$ #65 having the highest symmetry. We therefore follow most authors and use the $Cmmm$ representation.
- (MacGillavry, 1936) could not determine the positions of the hydrogen atoms, but (Leineweber, 1999) was able to do this using the isostructural compound Mg(NH$_{3}$)$_{2}$Cl$_{2}$. Accordingly we us Mg(NH$_{3}$)$_{2}$Cl$_{2}$ for the prototype of $E1_{3}$.
- Twelve hydrogen atoms are statistically distributed among the (16r) positions, giving each site 75% occupation.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (2a) | Mg I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cl I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{2} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Cl I |
| $\mathbf{B_{4}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}$ | = | $b y_{3} \,\mathbf{\hat{y}}$ | (4i) | N I |
| $\mathbf{B_{5}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}$ | = | $- b y_{3} \,\mathbf{\hat{y}}$ | (4i) | N I |
| $\mathbf{B_{6}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{7}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{8}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{9}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{10}}$ | = | $- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{11}}$ | = | $\left(x_{4} - y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + y_{4}\right) \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{12}}$ | = | $\left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
| $\mathbf{B_{13}}$ | = | $- \left(x_{4} + y_{4}\right) \, \mathbf{a}_{1}- \left(x_{4} - y_{4}\right) \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16r) | H I |
References
- A. Leineweber, M. W. Friedriszik, and H. Jacobs, Preparation and Crystal Structures of Mg(NH$_{3}$)$_{2}$Cl$_{2}$, Mg(NH$_{3}$)$_{2}$Br$_{2}$, and Mg(NH$_{3}$)$_{2}$I$_{2}$, J. Solid State Chem. 147, 229–234 (1999), doi:10.1006/jssc.1999.8238.
- C. H. MacGillavry and J. M. Bijvoet, Die Kristallstruktur von Zn(NH$_{3}$)$_{2}$Cl$_{2}$ und Zn(NH$_{3}$)$_{2}$Br$_{2}$, Z. Kristallogr. 94, 231–245 (1936), doi:10.1524/zkri.1936.94.1.249.
- C. Gottfried, ed., Strukturbericht Band IV 1936 (Akademische Verlagsgesellschaft M. B. H., Leipzig, 1938).
Prototype Generator
aflow --proto=A2B8CD2_oC26_65_h_r_a_i --params=$a,b/a,c/a,x_{2},y_{3},x_{4},y_{4},z_{4}$