124 Superconductor
(YBa$_{2}$Cu$_{4}$O$_{8}$) Structure: A2B4C8D_oC30_65_h_2g_3gh_c-001
| Prototype | Ba$_{2}$Cu$_{4}$O$_{8}$Y |
| AFLOW prototype label | A2B4C8D_oC30_65_h_2g_3gh_c-001 |
| ICSD | none |
| Pearson symbol | oC30 |
| Space group number | 65 |
| Space group symbol | $Cmmm$ |
| AFLOW prototype command |
aflow --proto=A2B4C8D_oC30_65_h_2g_3gh_c-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{2}, \allowbreak x_{3}, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}$ |
- Unlike most BCO-type superconductors, the stoichiometry of YBa$_{2}$Cu$_{4}$O$_{8}$ is fixed.
- We use the ambient pressure data from (Bordet, 1989) taken at room temperature.
- Although it is never explicitly stated by (Bordet, 1989), (Nelmes, 1990) notes that this data is given in the $Ammm$ setting of space group #65, making the long axis in the $z$-direction. The standard orientation is $Cmmm$, and we use FINDSYM to rotate the structure, putting the long axis in the $x$-direction.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2c) | Y I |
| $\mathbf{B_{2}}$ | = | $x_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}$ | = | $a x_{2} \,\mathbf{\hat{x}}$ | (4g) | Cu I |
| $\mathbf{B_{3}}$ | = | $- x_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}$ | = | $- a x_{2} \,\mathbf{\hat{x}}$ | (4g) | Cu I |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Cu II |
| $\mathbf{B_{5}}$ | = | $- x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (4g) | Cu II |
| $\mathbf{B_{6}}$ | = | $x_{4} \, \mathbf{a}_{1}+x_{4} \, \mathbf{a}_{2}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (4g) | O I |
| $\mathbf{B_{7}}$ | = | $- x_{4} \, \mathbf{a}_{1}- x_{4} \, \mathbf{a}_{2}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (4g) | O I |
| $\mathbf{B_{8}}$ | = | $x_{5} \, \mathbf{a}_{1}+x_{5} \, \mathbf{a}_{2}$ | = | $a x_{5} \,\mathbf{\hat{x}}$ | (4g) | O II |
| $\mathbf{B_{9}}$ | = | $- x_{5} \, \mathbf{a}_{1}- x_{5} \, \mathbf{a}_{2}$ | = | $- a x_{5} \,\mathbf{\hat{x}}$ | (4g) | O II |
| $\mathbf{B_{10}}$ | = | $x_{6} \, \mathbf{a}_{1}+x_{6} \, \mathbf{a}_{2}$ | = | $a x_{6} \,\mathbf{\hat{x}}$ | (4g) | O III |
| $\mathbf{B_{11}}$ | = | $- x_{6} \, \mathbf{a}_{1}- x_{6} \, \mathbf{a}_{2}$ | = | $- a x_{6} \,\mathbf{\hat{x}}$ | (4g) | O III |
| $\mathbf{B_{12}}$ | = | $x_{7} \, \mathbf{a}_{1}+x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Ba I |
| $\mathbf{B_{13}}$ | = | $- x_{7} \, \mathbf{a}_{1}- x_{7} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | Ba I |
| $\mathbf{B_{14}}$ | = | $x_{8} \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O IV |
| $\mathbf{B_{15}}$ | = | $- x_{8} \, \mathbf{a}_{1}- x_{8} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4h) | O IV |
References
- P. Bordet, J. L. Hodeau, R. Argoud, J. Muller, M. Marezio, , J. C. Martinez, J. J. Prejean, J. Karpinski, E. Kaldis, S. Rusiecki, and B. Bucher, Single crystal study of the 80K superconductor YBa$_{2}$Cu$_{4}$O$_{8}$}, Prog. Solid State Chem. \textbf{162-164, 524–525 (1989), doi:10.1016/0921-4534(89)91137-4.
Found in
- R. J. Nelmes, J. S. Loveday, E. Kaldis, and J. Karpinski, The crystal structure of YBa$_{2}$Cu$_{4}$O$_{8}$ as a function of pressure up to 5 GPa, Prog. Solid State Chem. 172, 311–324 (1990), doi:10.1016/0921-4534(90)90622-L.
Prototype Generator
aflow --proto=A2B4C8D_oC30_65_h_2g_3gh_c --params=$a,b/a,c/a,x_{2},x_{3},x_{4},x_{5},x_{6},x_{7},x_{8}$