SrCu2(BO3)2 Structure : A2B2C6D_tI44_121_i_i_ij_c

Picture of Structure; Click for Big Picture
Prototype : B2Cu2O6Sr
AFLOW prototype label : A2B2C6D_tI44_121_i_i_ij_c
Strukturbericht designation : None
Pearson symbol : tI44
Space group number : 121
Space group symbol : $I\bar{4}2m$
AFLOW prototype command : aflow --proto=A2B2C6D_tI44_121_i_i_ij_c
--params=
$a$,$c/a$,$x_{2}$,$z_{2}$,$x_{3}$,$z_{3}$,$x_{4}$,$z_{4}$,$x_{5}$,$y_{5}$,$z_{5}$


Body-centered Tetragonal primitive vectors:

\[ \begin{array}{ccc} \mathbf{a}_1 & = & - \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} - \frac12 \, a \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & ~ \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, a \, \mathbf{\hat{y}} - \frac12 \, c \, \mathbf{\hat{z}} \\ \end{array} \]

Basis vectors:

\[ \begin{array}{ccccccc} & & \mbox{Lattice Coordinates} & & \mbox{Cartesian Coordinates} &\mbox{Wyckoff Position} & \mbox{Atom Type} \\ \mathbf{B}_{1} & = & \frac{1}{2} \, \mathbf{a}_{1} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} & \left(4c\right) & \mbox{Sr} \\ \mathbf{B}_{2} & = & \frac{1}{2} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} & \left(4c\right) & \mbox{Sr} \\ \mathbf{B}_{3} & = & \left(x_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}+z_{2}\right) \, \mathbf{a}_{2} + 2x_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B} \\ \mathbf{B}_{4} & = & \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}+z_{2}\right) \, \mathbf{a}_{2}-2x_{2} \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B} \\ \mathbf{B}_{5} & = & \left(-x_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(x_{2}-z_{2}\right) \, \mathbf{a}_{2} & = & x_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B} \\ \mathbf{B}_{6} & = & \left(x_{2}-z_{2}\right) \, \mathbf{a}_{1} + \left(-x_{2}-z_{2}\right) \, \mathbf{a}_{2} & = & -x_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{B} \\ \mathbf{B}_{7} & = & \left(x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}+z_{3}\right) \, \mathbf{a}_{2} + 2x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Cu} \\ \mathbf{B}_{8} & = & \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}+z_{3}\right) \, \mathbf{a}_{2}-2x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} + z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Cu} \\ \mathbf{B}_{9} & = & \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(x_{3}-z_{3}\right) \, \mathbf{a}_{2} & = & x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Cu} \\ \mathbf{B}_{10} & = & \left(x_{3}-z_{3}\right) \, \mathbf{a}_{1} + \left(-x_{3}-z_{3}\right) \, \mathbf{a}_{2} & = & -x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}}-z_{3}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{Cu} \\ \mathbf{B}_{11} & = & \left(x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}+z_{4}\right) \, \mathbf{a}_{2} + 2x_{4} \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O I} \\ \mathbf{B}_{12} & = & \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}+z_{4}\right) \, \mathbf{a}_{2}-2x_{4} \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O I} \\ \mathbf{B}_{13} & = & \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(x_{4}-z_{4}\right) \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O I} \\ \mathbf{B}_{14} & = & \left(x_{4}-z_{4}\right) \, \mathbf{a}_{1} + \left(-x_{4}-z_{4}\right) \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}}-z_{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \mbox{O I} \\ \mathbf{B}_{15} & = & \left(y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{16} & = & \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{17} & = & \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{18} & = & \left(x_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{19} & = & \left(y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(-x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{20} & = & \left(-y_{5}-z_{5}\right) \, \mathbf{a}_{1} + \left(x_{5}-z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}}-y_{5}a \, \mathbf{\hat{y}}-z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{21} & = & \left(-x_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(-y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(-x_{5}-y_{5}\right) \, \mathbf{a}_{3} & = & -y_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \mathbf{B}_{22} & = & \left(x_{5}+z_{5}\right) \, \mathbf{a}_{1} + \left(y_{5}+z_{5}\right) \, \mathbf{a}_{2} + \left(x_{5}+y_{5}\right) \, \mathbf{a}_{3} & = & y_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} + z_{5}c \, \mathbf{\hat{z}} & \left(16j\right) & \mbox{O II} \\ \end{array} \]

References

  • R. W. Smith and D. A. Keszler, Synthesis, structure, and properties of the orthoborate SrCu2(BO3)2, J. Solid State Chem. 93, 430–435 (1991), doi:10.1016/0022-4596(91)90316-A.

Found in

  • H. Kageyama, K. Yoshimura, R. Stern, N. V. Mushnikov, K. Onizuka, M. Kato, K. Kosuge, C. P. Slichter, T. Goto, and Y. Ueda, Exact Dimer Ground State and Quantized Magnetization Plateaus in the Two–Dimensional Spin System SrCu2(BO3)2, Phys. Rev. Lett. 82, 3168–3171 (1999), doi:10.1103/PhysRevLett.82.3168.

Geometry files


Prototype Generator

aflow --proto=A2B2C6D_tI44_121_i_i_ij_c --params=

Species:

Running:

Output: