HgBa$_{2}$Ca$_{2}$Cu$_{3}$O$_{8}$ (Hg-1223) Structure: A2B2C3DE8_tP16_123_h_h_bg_a_egi-001
| Prototype | Ba$_{2}$Ca$_{2}$Cu$_{3}$HgO$_{6}$ |
| AFLOW prototype label | A2B2C3DE8_tP16_123_h_h_bg_a_egi-001 |
| ICSD | 75730 |
| CCDC | 1636374 |
| Pearson symbol | tP16 |
| Space group number | 123 |
| Space group symbol | $P4/mmm$ |
| AFLOW prototype command |
aflow --proto=A2B2C3DE8_tP16_123_h_h_bg_a_egi-001
--params=$a, \allowbreak c/a, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak z_{7}, \allowbreak z_{8}$ |
- The Hg-$12(n-1)n$, or $n$HBCCO in the notation of (Bacq-Labreuil, 2025), cuprates have the general formula HgBa$_{2}$Ca$_{n-1}$Cu$_{n}$O$_{2n+2+\delta}$. These are tetragonally-stacked perovskite-like compounds similar to tetragonal YBa$_{2}$Cu$_{3}$O$_{7}-x$, and all are superconducting at temperatures near or above 100K. Although compounds have been structured for $n \le 16$ (Bacq-Labreuil, 2025) we will limit ourselves to tabluating the first three. In addition, we will only list the zero-pressure structures and assume perfect stoiciometry. In practice the can be additional oxygen ($\delta > 0$) and a deficit of barium.
- We include the structures
- Hg1201/1HBCCO: HgBa$_{2}$CuO$_{4}$,
- Hg1212/2HBCCO: HgBa$_{2}$CaCu$_{2}$O$_{6}$, and
- Hg1223/3HBCCO: HgBa$_{2}$Ca$_{2}$Cu$_{3}$O$_{8}$. (this structure)
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&a \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | Hg I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1b) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{4}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2e) | O I |
| $\mathbf{B_{5}}$ | = | $z_{4} \, \mathbf{a}_{3}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (2g) | Cu II |
| $\mathbf{B_{6}}$ | = | $- z_{4} \, \mathbf{a}_{3}$ | = | $- c z_{4} \,\mathbf{\hat{z}}$ | (2g) | Cu II |
| $\mathbf{B_{7}}$ | = | $z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (2g) | O II |
| $\mathbf{B_{8}}$ | = | $- z_{5} \, \mathbf{a}_{3}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (2g) | O II |
| $\mathbf{B_{9}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (2h) | Ba I |
| $\mathbf{B_{10}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{6} \,\mathbf{\hat{z}}$ | (2h) | Ba I |
| $\mathbf{B_{11}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (2h) | Ca I |
| $\mathbf{B_{12}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}- z_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{7} \,\mathbf{\hat{z}}$ | (2h) | Ca I |
| $\mathbf{B_{13}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{8} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{14}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{8} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{15}}$ | = | $\frac{1}{2} \, \mathbf{a}_{2}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}- c z_{8} \,\mathbf{\hat{z}}$ | (4i) | O III |
| $\mathbf{B_{16}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}- z_{8} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- c z_{8} \,\mathbf{\hat{z}}$ | (4i) | O III |
References
- B. A. Hunter, J. D. Jorgensen, J. L. Wagner, P. G. Radaelli, D. G. Hinks, H. Shaked, R. L. Hitterman, and R. B. V. Dreele, Pressure-induced structural changes in superconducting HgBa$_{2}$Ca$_{n-1}$CunO$_{2n+2+\delta}$ (n = 1, 2, 3) compounds, Physica C 221, 1–10 (1994), doi:10.1016/0921-4534(94)90659-9.
Found in
- B. Bacq-Labreuil, B. Lacasse, A.-M. S. Tremblay, D. Sénéchal, and K. Haule, Towards an {\em ab initio} theory of high-temperature superconductors: a study of multilayer cuprates, Phys. Rev. X 15, 021071 (2025), doi:10.1103/PhysRevX.15.021071.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A2B2C3DE8_tP16_123_h_h_bg_a_egi --params=$a,c/a,z_{4},z_{5},z_{6},z_{7},z_{8}$