Encyclopedia of Crystallographic Prototypes

AFLOW Prototype: A2B7C2_tI44_119_i_bdefgh_i

  • 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)
  • D. Hicks, M. J. Mehl, E. Gossett, C. Toher, O. Levy, R. M. Hanson, G. L. W. Hart, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 2, Comp. Mat. Sci. 161, S1-S1011 (2019). (doi=10.1016/j.commatsci.2018.10.043)
  • D. Hicks, M.J. Mehl, M. Esters, C. Oses, O. Levy, G.L.W. Hart, C. Toher, and S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 3, Comp. Mat. Sci. 199, 110450 (2021). (doi=10.1016/j.commatsci.2021.110450)

Phase II Cd2Re2O7 Structure : A2B7C2_tI44_119_i_bdefgh_i

Picture of Structure; Click for Big Picture
Prototype : Cd2O7Re2
AFLOW prototype label : A2B7C2_tI44_119_i_bdefgh_i
Strukturbericht designation : None
Pearson symbol : tI44
Space group number : 119
Space group symbol : $I\bar{4}m2$
AFLOW prototype command : aflow --proto=A2B7C2_tI44_119_i_bdefgh_i
--params=
$a$,$c/a$,$z_{3}$,$z_{4}$,$x_{5}$,$x_{6}$,$x_{7}$,$z_{7}$,$x_{8}$,$z_{8}$


  • 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 allows a tolerance of 0.2 Å and FINDSYM allows a tolerance of 0.2 Å for both the lattice vectors and atomic positions both of the tetragonal phases become cubic.
  • Phase IV is extremely close to Phase II. If AFLOW-SYM allows a tolerance of 0.002 Å and FINDSYM allows a tolerance 0.002 Å for both the lattice vectors and atomic positions the orthorhombic phase becomes tetragonal.
  • Data for the Phase II structure was taken at 160 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} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{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(2b\right) & \text{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(2d\right) & \text{O II} \\ \mathbf{B}_{3} & = & z_{3} \, \mathbf{a}_{1} + z_{3} \, \mathbf{a}_{2} & = & z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O III} \\ \mathbf{B}_{4} & = & -z_{3} \, \mathbf{a}_{1}-z_{3} \, \mathbf{a}_{2} & = & -z_{3}c \, \mathbf{\hat{z}} & \left(4e\right) & \text{O III} \\ \mathbf{B}_{5} & = & \left(\frac{1}{2} +z_{4}\right) \, \mathbf{a}_{1} + z_{4} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{y}} + z_{4}c \, \mathbf{\hat{z}} & \left(4f\right) & \text{O IV} \\ \mathbf{B}_{6} & = & -z_{4} \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{4}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}}-z_{4}c \, \mathbf{\hat{z}} & \left(4f\right) & \text{O IV} \\ \mathbf{B}_{7} & = & x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} + 2x_{5} \, \mathbf{a}_{3} & = & x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{8} & = & -x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2}-2x_{5} \, \mathbf{a}_{3} & = & -x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{9} & = & -x_{5} \, \mathbf{a}_{1} + x_{5} \, \mathbf{a}_{2} & = & x_{5}a \, \mathbf{\hat{x}}-x_{5}a \, \mathbf{\hat{y}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{10} & = & x_{5} \, \mathbf{a}_{1}-x_{5} \, \mathbf{a}_{2} & = & -x_{5}a \, \mathbf{\hat{x}} + x_{5}a \, \mathbf{\hat{y}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{11} & = & \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} +2x_{6}\right) \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{12} & = & \left(\frac{3}{4} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - 2x_{6}\right) \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{13} & = & \left(\frac{3}{4} - x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} +x_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{14} & = & \left(\frac{3}{4} +x_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{4} - x_{6}\right) \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{6}a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{6}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{15} & = & z_{7} \, \mathbf{a}_{1} + \left(x_{7}+z_{7}\right) \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{x}} + z_{7}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Cd} \\ \mathbf{B}_{16} & = & z_{7} \, \mathbf{a}_{1} + \left(-x_{7}+z_{7}\right) \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{x}} + z_{7}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Cd} \\ \mathbf{B}_{17} & = & \left(-x_{7}-z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2}-x_{7} \, \mathbf{a}_{3} & = & -x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Cd} \\ \mathbf{B}_{18} & = & \left(x_{7}-z_{7}\right) \, \mathbf{a}_{1}-z_{7} \, \mathbf{a}_{2} + x_{7} \, \mathbf{a}_{3} & = & x_{7}a \, \mathbf{\hat{y}}-z_{7}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Cd} \\ \mathbf{B}_{19} & = & z_{8} \, \mathbf{a}_{1} + \left(x_{8}+z_{8}\right) \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + z_{8}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Re} \\ \mathbf{B}_{20} & = & z_{8} \, \mathbf{a}_{1} + \left(-x_{8}+z_{8}\right) \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{x}} + z_{8}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Re} \\ \mathbf{B}_{21} & = & \left(-x_{8}-z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2}-x_{8} \, \mathbf{a}_{3} & = & -x_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{Re} \\ \mathbf{B}_{22} & = & \left(x_{8}-z_{8}\right) \, \mathbf{a}_{1}-z_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{y}}-z_{8}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{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_119_i_bdefgh_i --params=

Species:

Running:

Output: