1212C [YBa$_{2}$Cu$_{3}$O$_{7-x}$] High-$T_{c}$ Structure: A2B3C7D_oP13_47_k_cj_aijl_f-001
| Prototype | Ba$_{2}$Cu$_{3}$O$_{7-x}$Y |
| AFLOW prototype label | A2B3C7D_oP13_47_k_cj_aijl_f-001 |
| ICSD | 62943 |
| CCDC | 1626100 |
| Pearson symbol | oP13 |
| Space group number | 47 |
| Space group symbol | $Pmmm$ |
| AFLOW prototype command |
aflow --proto=A2B3C7D_oP13_47_k_cj_aijl_f-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{4}, \allowbreak x_{5}, \allowbreak x_{6}, \allowbreak x_{7}, \allowbreak x_{8}$ |
Other compounds with this structure
GaSr$_{2}$(Y, Ca)Cu$_{2}$O$_{7}$, DyBa$_{2}$Cu$_{3}$O$_{7-x}$
- This is the superconducting phase of Ba$_{2}$YCu$_{3-x}$O$_{7-y}$. Above 575$^\circ$C it transforms into the tetragonal phase. (Nakai, 1987)
- The designation 1212C is from (Shaked, 1994). In experiment the Ba (2k) site is 80% occupied, and the O (2l) site is 92% occupied, so $x$ = 0.16. Excess oxygen may appear on the (2b) (1/2 0 ) site, i.e., along the long axis.
- AFLOW rotates the lattice taking ($x \rightarrow y \rightarrow z \rightarrow x$) and also shifts the origin to move the single oxygen atom from the (1e) to the (1a) site.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&a \,\mathbf{\hat{x}}\\\mathbf{a_{2}}&=&b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (1a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}c \,\mathbf{\hat{z}}$ | (1c) | Cu I |
| $\mathbf{B_{3}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (1f) | Y I |
| $\mathbf{B_{4}}$ | = | $x_{4} \, \mathbf{a}_{1}$ | = | $a x_{4} \,\mathbf{\hat{x}}$ | (2i) | O II |
| $\mathbf{B_{5}}$ | = | $- x_{4} \, \mathbf{a}_{1}$ | = | $- a x_{4} \,\mathbf{\hat{x}}$ | (2i) | O II |
| $\mathbf{B_{6}}$ | = | $x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2j) | Cu II |
| $\mathbf{B_{7}}$ | = | $- x_{5} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2j) | Cu II |
| $\mathbf{B_{8}}$ | = | $x_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2j) | O III |
| $\mathbf{B_{9}}$ | = | $- x_{6} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2j) | O III |
| $\mathbf{B_{10}}$ | = | $x_{7} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2k) | Ba I |
| $\mathbf{B_{11}}$ | = | $- x_{7} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}$ | (2k) | Ba I |
| $\mathbf{B_{12}}$ | = | $x_{8} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2l) | O IV |
| $\mathbf{B_{13}}$ | = | $- x_{8} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a x_{8} \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (2l) | O IV |
References
- W. I. F. David, W. T. A. Harrison, J. M. F. Gunn, A. K. S. O. Moze, P. Day, J. D. Jorgensen, D. G. Hinks, M. A. Beno, L. Soderholm, D. W. C. Ii, I. K. Schuller, C. U. Segre, K. Zhang, and J. D. Grace, Structure and crystal chemistry of the high-Tc superconductor YBa$_2$Cu$_3$O$_{7-x}$, Nature 327, 310–312 (1987), doi:10.1038/327310a0.
- H. Shaked, P. M. Keane, J. C. Rodrigues, F. F. Owen, R. L. Hitterman, and J. D. Jorgensen, Crystal Structures of the High-T$_c$ Superconducting Copper Oxides, Elsevier Science B. V., Amsterdam (1994).
- I. Nakai, S. Sueno, F. P. Okamura, and A. Ono, X-Ray Single Crystal Structure Analysis of Tetragonal Ba$_{2}$YCu$_{3-x}$O$_{7-y}$, a High Temperature Form of the Superconductor, Japn. J. Appl. Phys. 26, L788–L790 (1987), doi:10.1143/JJAP.26.L788.
First cited in
- M. J. Mehl, D. Hicks, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 1, Comp. Mat. Sci. 136, S1-S828 (2017). (doi=10.1016/j.commatsci.2017.01.017)
Geometry files
Prototype Generator
aflow --proto=A2B3C7D_oP13_47_k_cj_aijl_f --params=$a,b/a,c/a,x_{4},x_{5},x_{6},x_{7},x_{8}$