β-CuI (Keen-Hull) Structure: A2B_hP6_164_2d_d-001
| Prototype | CuI |
| AFLOW prototype label | A2B_hP6_164_2d_d-001 |
| ICSD | 78429 |
| Pearson symbol | hP6 |
| Space group number | 164 |
| Space group symbol | $P\overline{3}m1$ |
| AFLOW prototype command |
aflow --proto=A2B_hP6_164_2d_d-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}$ |
- Copper(I) iodide can be found in three forms (Keen, 1995):
- $\alpha$–CuI is stable above $673\pm8$K, and is in the $\delta$–Bi$_{2}$O$_{3}$ structure, with the iodine atoms on the (2a) Wyckoff positions and the copper atoms occupying 1/8 of the (32f) positions.
- $\gamma$–CuI (marshite) is the ground state, stable below $643\pm2$K, and is also in the $\delta$–Bi$_{2}$O$_{3}$ structure.
- In the intermediate temperature range $\beta$–CuI is generally agreed to be trigonal or hexagonal, but the exact structure is under dispute:
- (Kurdyumova, 1961) placed it in trigonal space group $P3m1$ #156. Their unit cell is three times larger than the standard cell for this structure, and is now considered erroneous. (Abrahams, 2008).
- (Bührer, 1977) placed it in hexagonal space group $P\overline{6}m2$ #187, with the copper atoms partially occupying two sites.
- (Sakuma, 1988) placed it in trigonal space group $P3m1$ #156 with a smaller unit cell than (Kurdyumova, 1961) and no disorder on the copper sites.
- (Keen, 1994) placed it in trigonal space group $P\overline{3}m1$ #164 (this structure), with a unit cell similar to (Bührer, 1977) and (Sakuma, 1988). Like the former paper, the oxygen positions are disordered.
- The data from (Keen, 1994) was taken at 655K.
- The copper sites are only partially occupied: Cu-I (2d) is 85.1% filled, with the remaining 14.9% of the copper atoms going on the Cu-II (2d) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{1} \,\mathbf{\hat{z}}$ | (2d) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{1} \,\mathbf{\hat{z}}$ | (2d) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Cu II |
| $\mathbf{B_{4}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{2} \,\mathbf{\hat{z}}$ | (2d) | Cu II |
| $\mathbf{B_{5}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (2d) | I I |
| $\mathbf{B_{6}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (2d) | I I |
References
- D. A. Keen and S. Hull, Determination of the structure of β-CuI by high-resolution neutron powder diffraction, J. Phys.: Condens. Matter 6, 1637–1644 (1994), doi:10.1088/0953-8984/6/9/006.
- T. Sakuma, Crystal Structure of β-CuI, J. Phys. Soc. Jpn. 57, 565–569 (1988), doi:10.1143/JPSJ.57.565.
- R. N. Kurdyumova and R. V. Baranova, An electron diffraction study of thin films of cuprous iodide, Sov. Phys. Cryst. 6, 318–321 (1961).
- W. Bührer and W. Hälg, Crystal structure of high-temperature cuprous iodide and cuprous bromide, Electrochimica Acta 22, 701–704 (1977), doi:10.1016/0013-4686(77)80021-2.
- D. A. Keen and S. Hull, The high-temperature structural behaviour of copper(I) iodide, J. Phys.: Condens. Matter 7, 5793–5804 (1995), doi:10.1088/0953-8984/7/29/007.
Found in
- S. C. Abrahams, Inorganic structures in space group $P3m1$; coordinate analysis and systematic prediction of new ferroelectrics, Acta Crystallogr. Sect. B 64, 426–437 (2008), doi:10.1107/S0108768108018144.
Prototype Generator
aflow --proto=A2B_hP6_164_2d_d --params=$a,c/a,z_{1},z_{2},z_{3}$