Phase III Cd2Re2O7 Structure : A2B7C2_tI44_98_f_bcde_f

Picture of Structure; Click for Big Picture
Prototype : Cd2O7Re2
AFLOW prototype label : A2B7C2_tI44_98_f_bcde_f
Strukturbericht designation : None
Pearson symbol : tI44
Space group number : 98
Space group symbol : $I4_{1}22$
AFLOW prototype command : aflow --proto=A2B7C2_tI44_98_f_bcde_f
--params=
$a$,$c/a$,$z_{2}$,$x_{3}$,$x_{4}$,$x_{5}$,$x_{6}$


  • Cd2Re2O7 exhibits a number of phases. We will use the notation of (Kapcia, 2019) to describe them:
  • Both Phase II and Phase III are extremely close to Phase I. If AFLOW-SYM and FINDSYM allow a 0.2 Å uncertainty in lattice vectors and atomic positions both of the tetragonal phases become cubic.
  • Phase IV is extremely close to Phase II. If AFLOW-SYM and FINDSYM allow a 0.002 Å uncertainty in the lattice vectors and atomic positions the orthorhombic phase becomes tetragonal.
  • Data for the Phase III structure was taken at 90 K.

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}_{2} & = & \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O I} \\ \mathbf{B}_{2} & = & \frac{1}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4b\right) & \mbox{O I} \\ \mathbf{B}_{3} & = & z_{2} \, \mathbf{a}_{1} + z_{2} \, \mathbf{a}_{2} & = & z_{2}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{4} & = & \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{5} & = & \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{6} & = & -z_{2} \, \mathbf{a}_{1}-z_{2} \, \mathbf{a}_{2} & = & -z_{2}c \, \mathbf{\hat{z}} & \left(8c\right) & \mbox{O II} \\ \mathbf{B}_{7} & = & x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + 2x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + x_{3}a \, \mathbf{\hat{y}} & \left(8d\right) & \mbox{O III} \\ \mathbf{B}_{8} & = & -x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-2x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}}-x_{3}a \, \mathbf{\hat{y}} & \left(8d\right) & \mbox{O III} \\ \mathbf{B}_{9} & = & \left(\frac{3}{4} +x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{O III} \\ \mathbf{B}_{10} & = & \left(\frac{3}{4} - x_{3}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{3}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{3}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8d\right) & \mbox{O III} \\ \mathbf{B}_{11} & = & x_{4} \, \mathbf{a}_{1}-x_{4} \, \mathbf{a}_{2} & = & -x_{4}a \, \mathbf{\hat{x}} + x_{4}a \, \mathbf{\hat{y}} & \left(8e\right) & \mbox{O IV} \\ \mathbf{B}_{12} & = & -x_{4} \, \mathbf{a}_{1} + x_{4} \, \mathbf{a}_{2} & = & x_{4}a \, \mathbf{\hat{x}}-x_{4}a \, \mathbf{\hat{y}} & \left(8e\right) & \mbox{O IV} \\ \mathbf{B}_{13} & = & \left(\frac{3}{4} - x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{4}\right) \, \mathbf{a}_{3} & = & -x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O IV} \\ \mathbf{B}_{14} & = & \left(\frac{3}{4} +x_{4}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{4}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{4}\right) \, \mathbf{a}_{3} & = & x_{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{4}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8e\right) & \mbox{O IV} \\ \mathbf{B}_{15} & = & \frac{3}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} +x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Cd} \\ \mathbf{B}_{16} & = & \frac{7}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} - x_{5}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Cd} \\ \mathbf{B}_{17} & = & \left(\frac{7}{8} +x_{5}\right) \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{5}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Cd} \\ \mathbf{B}_{18} & = & \left(\frac{7}{8} - x_{5}\right) \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{5}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{5}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Cd} \\ \mathbf{B}_{19} & = & \frac{3}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \frac{1}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Re} \\ \mathbf{B}_{20} & = & \frac{7}{8} \, \mathbf{a}_{1} + \left(\frac{1}{8} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \frac{3}{4}a \, \mathbf{\hat{y}} + \frac{1}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Re} \\ \mathbf{B}_{21} & = & \left(\frac{7}{8} +x_{6}\right) \, \mathbf{a}_{1} + \frac{1}{8} \, \mathbf{a}_{2} + \left(\frac{1}{4} +x_{6}\right) \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Re} \\ \mathbf{B}_{22} & = & \left(\frac{7}{8} - x_{6}\right) \, \mathbf{a}_{1} + \frac{5}{8} \, \mathbf{a}_{2} + \left(\frac{3}{4} - x_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \frac{3}{8}c \, \mathbf{\hat{z}} & \left(8f\right) & \mbox{Re} \\ \end{array} \]

References

  • S.–W. Huang, H.–T. Jeng, J.–Y. Lin, W. J. Chang, J. M. Chen, G. H. Lee, H. Berger, H. D. Yang, and K. S. Liang, Electronic structure of pyrochlore Cd2Re2O7, J. Phys.: Condens. Matter 21, 195602 (2009), doi:10.1088/0953-8984/21/19/195602.
  • K. J. Kapcia, M. Reedyk, M. Hajialamdari, A. Ptok, P. Piekarz, F. S. Razavi, A. M. Oleś, and R. K. Kremer, Discovery of a low–temperature orthorhombic phase of the Cd2Re2O7 superconductor, Phys. Rev. Research 2, 033108 (2020), doi:10.1103/PhysRevResearch.2.033108.

Found in

Geometry files


Prototype Generator

aflow --proto=A2B7C2_tI44_98_f_bcde_f --params=

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