β-CuI (Kurdyumova) Structure: AB_hP12_156_3a2bc_3a2bc-001
| Prototype | CuI |
| AFLOW prototype label | AB_hP12_156_3a2bc_3a2bc-001 |
| ICSD | 30363 |
| Pearson symbol | hP12 |
| Space group number | 156 |
| Space group symbol | $P3m1$ |
| AFLOW prototype command |
aflow --proto=AB_hP12_156_3a2bc_3a2bc-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}, \allowbreak z_{9}, \allowbreak z_{10}, \allowbreak z_{11}, \allowbreak z_{12}$ |
- Copper(I) iodide can be found in three forms (Keen, 1995):
- $\alpha$–CuI is stable above 673$\pm$8K, 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 $643 \pm 2$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, which is three times larger than the standard cell for this structure and is now considered erroneous, is the one listed on this page. (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, with a unit cell similar to (Bührer, 1977) and (Sakuma, 1988). Like the former paper, the oxygen positions are disordered.
- Space group $P3m1$ #156 allows an arbitary choice of origin for the $z$-axis. Used this freedom to place the I-III atom at the origin.
- This structure originally appeared in (Hicks, 2019). This page has been rewritten, but the structure itself has not changed.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{2}a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{3}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (1a) | Cu I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{3}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (1a) | Cu II |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{3}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (1a) | Cu III |
| $\mathbf{B_{4}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (1a) | I I |
| $\mathbf{B_{5}}$ | = | $z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (1a) | I II |
| $\mathbf{B_{6}}$ | = | $z_{6} \, \mathbf{a}_{3}$ | = | $c z_{6} \,\mathbf{\hat{z}}$ | (1a) | I III |
| $\mathbf{B_{7}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (1b) | Cu IV |
| $\mathbf{B_{8}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (1b) | Cu V |
| $\mathbf{B_{9}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{9} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (1b) | I IV |
| $\mathbf{B_{10}}$ | = | $\frac{1}{3} \, \mathbf{a}_{1}+\frac{2}{3} \, \mathbf{a}_{2}+z_{10} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (1b) | I V |
| $\mathbf{B_{11}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{11} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{11} \,\mathbf{\hat{z}}$ | (1c) | Cu VI |
| $\mathbf{B_{12}}$ | = | $\frac{2}{3} \, \mathbf{a}_{1}+\frac{1}{3} \, \mathbf{a}_{2}+z_{12} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+c z_{12} \,\mathbf{\hat{z}}$ | (1c) | I VI |
References
- 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.
- T. Sakuma, Crystal Structure of β-CuI, J. Phys. Soc. Jpn. 57, 565–569 (1988), doi:10.1143/JPSJ.57.565.
- 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.
- 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.
- D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comput. Mater. Sci. 161, S1–S1011 (2019), doi:10.1016/j.commatsci.2018.10.043.
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=AB_hP12_156_3a2bc_3a2bc --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},z_{7},z_{8},z_{9},z_{10},z_{11},z_{12}$