1212C [YBa2Cu3O7–x] High–Tc Structure: A2B3C7D_oP13_47_t_aq_eqrs_h

Picture of Structure; Click for Big Picture
Prototype : YBa2Cu3O7–x
AFLOW prototype label : A2B3C7D_oP13_47_t_aq_eqrs_h
Strukturbericht designation : None
Pearson symbol : oP13
Space group number : 47
Space group symbol : $\mbox{Pmmm}$
AFLOW prototype command : aflow --proto=A2B3C7D_oP13_47_t_aq_eqrs_h
--params=
$a$,$b/a$,$c/a$,$z_{4}$,$z_{5}$,$z_{6}$,$z_{7}$,$z_{8}$


Other compounds with this structure

  • GaSr2(Y,Ca)Cu2O7

  • The designation 1212C is from (Shaked, 1994). We will assume that the oxygen concentration is exactly 7. In experiment the O (2s) site is 92% occupied.

Simple Orthorhombic primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & b \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B_1} & = & 0 \, \mathbf{a}_{1} + 0 \, \mathbf{a}_{2} + 0 \, \mathbf{a}_{3} & = & 0 \mathbf{\hat{x}} + 0 \mathbf{\hat{y}} + 0 \mathbf{\hat{z}} & \left(1a\right) & \mbox{Cu I} \\ \mathbf{B}_{2} & =& \frac12 \, \mathbf{a}_{2}& =& \frac12 \, b \, \mathbf{\hat{y}}& \left(1e\right) & \mbox{O I} \\ \mathbf{B}_{3} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{2} + \frac12 \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}}+ \frac12 \, c \, \mathbf{\hat{z}}& \left(1h\right) & \mbox{Y} \\ \mathbf{B}_{4} & =& z_{4} \, \mathbf{a}_{3}& =& z_{4} \, c \, \mathbf{\hat{z}}& \left(2q\right) & \mbox{Cu II} \\ \mathbf{B}_{5} & =& - z_{4} \, \mathbf{a}_{3}& =& - z_{4} \, c \, \mathbf{\hat{z}}& \left(2q\right) & \mbox{Cu II} \\ \mathbf{B}_{6} & =& z_{5} \, \mathbf{a}_{3}& =& z_{5} \, c \, \mathbf{\hat{z}}& \left(2q\right) & \mbox{O II} \\ \mathbf{B}_{7} & =& - z_{5} \, \mathbf{a}_{3}& =& - z_{5} \, c \, \mathbf{\hat{z}}& \left(2q\right) & \mbox{O II} \\ \mathbf{B}_{8} & =& \frac12 \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3}& =& \frac12 \, b \, \mathbf{\hat{y}} + z_{6} \, c \, \mathbf{\hat{z}}& \left(2r\right) & \mbox{O III} \\ \mathbf{B}_{9} & =& \frac12 \, \mathbf{a}_{2} - z_{6} \, \mathbf{a}_{3}& =& \frac12 \, b \, \mathbf{\hat{y}} - z_{6} \, c \, \mathbf{\hat{z}}& \left(2r\right) & \mbox{O III} \\ \mathbf{B}_{10} & =& \frac12 \, \mathbf{a}_{1} + z_{7} \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + z_{7} \, c \, \mathbf{\hat{z}}& \left(2s\right) & \mbox{O IV} \\ \mathbf{B}_{11} & =& \frac12 \, \mathbf{a}_{1} - z_{7} \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} - z_{7} \, c \, \mathbf{\hat{z}}& \left(2s\right) & \mbox{O IV} \\ \mathbf{B}_{12} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{2} + z_{8} \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} + z_{8} \, c \, \mathbf{\hat{z}}& \left(2t\right) & \mbox{Ba} \\ \mathbf{B}_{13} & =& \frac12 \, \mathbf{a}_{1} + \frac12 \, \mathbf{a}_{2} - z_{8} \, \mathbf{a}_{3}& =& \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} - z_{8} \, c \, \mathbf{\hat{z}}& \left(2t\right) & \mbox{Ba} \\ \end{array} \]

References

  • W. I. F. David, W. T. A. Harrison, J. M. F. Gunn, O. Moze, A. K. Soper, P. Day, J. D. Jorgensen, D. G. Hinks, M. A. Beno, L. Soderholm, D. W. Capone II, I. K. Schuller, C. U. Segre, K. Zhang, and J. D. Grace, Structure and crystal chemistry of the high–Tc superconductor YBa2Cu3O7–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–Tc Superconducting Copper–Oxides (Elsevier Science B. V., Amsterdam, 1994).

Geometry files


Prototype Generator

aflow --proto=A2B3C7D_oP13_47_t_aq_eqrs_h --params=

Species:

Running:

Output: