Orange (I) HgI$_{2}$ Structure: AB2_tI48_141_h_2eg-001
| Prototype | HgI$_{2}$ |
| AFLOW prototype label | AB2_tI48_141_h_2eg-001 |
| ICSD | 18126 |
| Pearson symbol | tI48 |
| Space group number | 141 |
| Space group symbol | $I4_1/amd$ |
| AFLOW prototype command |
aflow --proto=AB2_tI48_141_h_2eg-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
- HgI$_{2}$ can be found in a variety of forms (Gumiński, 1997):
- The ground state, coccinite, also known as red or $\alpha$–HgI$_{2}$ and given the Strukturbericht designation $C13$. It is stable up to 135$^\circ$C.
- At higher temperatures this transforms into yellow or $\beta$–HgI$_{2}$ in the HgBr$_{2}$ ($C24$) structure. This is stable up to the melting point at 258$^\circ$C.
- (Schwarzenbach, 1969) studied the metastable orange HgI$_{2}$ (this structure) body-centered tetragonal ($I4_{1}/amd$ #141) phase. This structure was refined by (Hostettler, 2002).
- (Hostettler, 2002) also found a second orange HgI$_{2}$ phase in a simple tetragonal ($P4_{2}/nmc$ #137) cell.
- The last two structures differ by stacking order. (Hostettler, 2002) used them to produce an averaged orange HgI$_{2}$ structure, space group $P\overline{4}m2$ #115.
- The ICSD entry for this structure is from the earlier work of (Schwarzenbach, 1969).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (8e) | I I |
| $\mathbf{B_{2}}$ | = | $z_{1} \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | I I |
| $\mathbf{B_{3}}$ | = | $- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (8e) | I I |
| $\mathbf{B_{4}}$ | = | $- z_{1} \, \mathbf{a}_{1}- \left(z_{1} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{1} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | I I |
| $\mathbf{B_{5}}$ | = | $\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (8e) | I II |
| $\mathbf{B_{6}}$ | = | $z_{2} \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | I II |
| $\mathbf{B_{7}}$ | = | $- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (8e) | I II |
| $\mathbf{B_{8}}$ | = | $- z_{2} \, \mathbf{a}_{1}- \left(z_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{2} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (8e) | I II |
| $\mathbf{B_{9}}$ | = | $\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{10}}$ | = | $- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{4}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{11}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{12}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{13}}$ | = | $- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{14}}$ | = | $\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{3}{4}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{3}{4}\right) \,\mathbf{\hat{y}}+\frac{1}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{15}}$ | = | $- \left(x_{3} - \frac{1}{8}\right) \, \mathbf{a}_{1}+\left(x_{3} + \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a \left(x_{3} + \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{16}}$ | = | $\left(x_{3} + \frac{1}{8}\right) \, \mathbf{a}_{1}- \left(x_{3} - \frac{7}{8}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a \left(x_{3} - \frac{1}{4}\right) \,\mathbf{\hat{y}}+\frac{3}{8}c \,\mathbf{\hat{z}}$ | (16g) | I III |
| $\mathbf{B_{17}}$ | = | $\left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{18}}$ | = | $\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{19}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(- y_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{20}}$ | = | $z_{4} \, \mathbf{a}_{1}+\left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}+c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{21}}$ | = | $\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{22}}$ | = | $- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{1}- z_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- a y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{23}}$ | = | $- z_{4} \, \mathbf{a}_{1}+\left(y_{4} - z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $a \left(y_{4} + \frac{1}{4}\right) \,\mathbf{\hat{x}}- \frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Hg I |
| $\mathbf{B_{24}}$ | = | $- z_{4} \, \mathbf{a}_{1}- \left(y_{4} + z_{4}\right) \, \mathbf{a}_{2}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(y_{4} - \frac{1}{4}\right) \,\mathbf{\hat{x}}+\frac{1}{4}a \,\mathbf{\hat{y}}- c \left(z_{4} + \frac{1}{4}\right) \,\mathbf{\hat{z}}$ | (16h) | Hg I |
References
- M. Hostettler, H. Birkedal, and D. Schwarzenbach, The structure of orange HgI$_{2}$. I. Polytypic layer structure, Acta Crystallogr. Sect. B 58, 903–913 (2002), doi:10.1107/S010876810201618X.
- D. Schwarzenbach, The crystal structure and one-dimensional disorder of the orange modification of HgI$_{2}$, Z. Kristallogr. 128, 97–114 (1969), doi:10.1524/zkri.1969.128.1-2.97.
- D. Schwarzenbach, H. Birkedal, M. Hostettler, and P. Fischer, Neutron diffraction investigation of the temperature dependence of crystal structure and thermal motions of red HgI$_{2}$, Acta Crystallogr. Sect. B 63, 826–835 (2007), doi:10.1107/S0108768107043327.
Prototype Generator
aflow --proto=AB2_tI48_141_h_2eg --params=$a,c/a,z_{1},z_{2},x_{3},y_{4},z_{4}$