Predicted Phase IV Cd2Re2O7 Structure : A2B7C2_oF88_22_k_bdefghij_k
| Prototype | : | Cd2O7Re2 |
| AFLOW prototype label | : | A2B7C2_oF88_22_k_bdefghij_k |
| Strukturbericht designation | : | None |
| Pearson symbol | : | oF88 |
| Space group number | : | 22 |
| Space group symbol | : | $F222$ |
| AFLOW prototype command | : | aflow --proto=A2B7C2_oF88_22_k_bdefghij_k --params=$a$,$b/a$,$c/a$,$x_{3}$,$y_{4}$,$z_{5}$,$z_{6}$,$y_{7}$,$x_{8}$,$x_{9}$,$y_{9}$,$z_{9}$,$x_{10}$,$y_{10}$,$z_{10}$ |
- Cd2Re2O7 exhibits a number of phases. We will use the notation of (Kapcia, 2019) to describe them:
- Phase I: above 200 K, the system takes on the cubic pyrochlore ($E8_{1}$) structure.
- Phase II: in the range 120–200 K the system is in the tetragonal $I\overline{4}m2$ #119 structure.
- Phase III: in the range 80–120 K the system is in the tetragonal $I4_{1}22$ #98 structure.
- Phase IV: (Kapcia, 2019) did a first–principles study of this system and found that below 80 K Phase III develops a soft phonon mode which transforms the system into an orthorhombic $F222$ #22 structure. (This structure)
- (Norman, 2019) points out that both Phase III and Phase IV structures have issues.
- Phase IV is extremely close to Phase II. If AFLOW-SYM and FINDSYM allow symmetry tolerances of 0.002 Å, the orthorhombic phase becomes tetragonal.
Face-centered Orthorhombic primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & \frac12 \, b \, \mathbf{\hat{y}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_2 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, c \, \mathbf{\hat{z}} \\ \mathbf{a}_3 & = & \frac12 \, a \, \mathbf{\hat{x}} + \frac12 \, b \, \mathbf{\hat{y}} \\ \end{array} \]
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} \, \mathbf{a}_{3} & = & \frac{1}{2}a \, \mathbf{\hat{x}} + \frac{1}{2}b \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4b\right) & \text{O I} \\ \mathbf{B}_{2} & = & \frac{3}{4} \, \mathbf{a}_{1} + \frac{3}{4} \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \frac{3}{4}a \, \mathbf{\hat{x}} + \frac{3}{4}b \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4d\right) & \text{O II} \\ \mathbf{B}_{3} & = & -x_{3} \, \mathbf{a}_{1} + x_{3} \, \mathbf{a}_{2} + x_{3} \, \mathbf{a}_{3} & = & x_{3}a \, \mathbf{\hat{x}} & \left(8e\right) & \text{O III} \\ \mathbf{B}_{4} & = & x_{3} \, \mathbf{a}_{1}-x_{3} \, \mathbf{a}_{2}-x_{3} \, \mathbf{a}_{3} & = & -x_{3}a \, \mathbf{\hat{x}} & \left(8e\right) & \text{O III} \\ \mathbf{B}_{5} & = & y_{4} \, \mathbf{a}_{1}-y_{4} \, \mathbf{a}_{2} + y_{4} \, \mathbf{a}_{3} & = & y_{4}b \, \mathbf{\hat{y}} & \left(8f\right) & \text{O IV} \\ \mathbf{B}_{6} & = & -y_{4} \, \mathbf{a}_{1} + y_{4} \, \mathbf{a}_{2}-y_{4} \, \mathbf{a}_{3} & = & -y_{4}b \, \mathbf{\hat{y}} & \left(8f\right) & \text{O IV} \\ \mathbf{B}_{7} & = & z_{5} \, \mathbf{a}_{1} + z_{5} \, \mathbf{a}_{2}-z_{5} \, \mathbf{a}_{3} & = & z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{8} & = & -z_{5} \, \mathbf{a}_{1}-z_{5} \, \mathbf{a}_{2} + z_{5} \, \mathbf{a}_{3} & = & -z_{5}c \, \mathbf{\hat{z}} & \left(8g\right) & \text{O V} \\ \mathbf{B}_{9} & = & z_{6} \, \mathbf{a}_{1} + z_{6} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + z_{6}c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - z_{6}\right) \, \mathbf{a}_{2} + z_{6} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{6}\right)c \, \mathbf{\hat{z}} & \left(8h\right) & \text{O VI} \\ \mathbf{B}_{11} & = & y_{7} \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{2} + y_{7} \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + y_{7}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{O VII} \\ \mathbf{B}_{12} & = & \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{1} + y_{7} \, \mathbf{a}_{2} + \left(\frac{1}{2} - y_{7}\right) \, \mathbf{a}_{3} & = & \frac{1}{4}a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{7}\right)b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8i\right) & \text{O VII} \\ \mathbf{B}_{13} & = & \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{1} + x_{8} \, \mathbf{a}_{2} + x_{8} \, \mathbf{a}_{3} & = & x_{8}a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8j\right) & \text{O VIII} \\ \mathbf{B}_{14} & = & x_{8} \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{2} + \left(\frac{1}{2} - x_{8}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{8}\right)a \, \mathbf{\hat{x}} + \frac{1}{4}b \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(8j\right) & \text{O VIII} \\ \mathbf{B}_{15} & = & \left(-x_{9}+y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}-y_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}+y_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Cd} \\ \mathbf{B}_{16} & = & \left(x_{9}-y_{9}+z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}+y_{9}+z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}-y_{9}-z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}} + z_{9}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Cd} \\ \mathbf{B}_{17} & = & \left(x_{9}+y_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(-x_{9}-y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(-x_{9}+y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & -x_{9}a \, \mathbf{\hat{x}} + y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Cd} \\ \mathbf{B}_{18} & = & \left(-x_{9}-y_{9}-z_{9}\right) \, \mathbf{a}_{1} + \left(x_{9}+y_{9}-z_{9}\right) \, \mathbf{a}_{2} + \left(x_{9}-y_{9}+z_{9}\right) \, \mathbf{a}_{3} & = & x_{9}a \, \mathbf{\hat{x}}-y_{9}b \, \mathbf{\hat{y}}-z_{9}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Cd} \\ \mathbf{B}_{19} & = & \left(-x_{10}+y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}-y_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(x_{10}+y_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Re} \\ \mathbf{B}_{20} & = & \left(x_{10}-y_{10}+z_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}+y_{10}+z_{10}\right) \, \mathbf{a}_{2} + \left(-x_{10}-y_{10}-z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}} + z_{10}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Re} \\ \mathbf{B}_{21} & = & \left(x_{10}+y_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(-x_{10}-y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(-x_{10}+y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & -x_{10}a \, \mathbf{\hat{x}} + y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Re} \\ \mathbf{B}_{22} & = & \left(-x_{10}-y_{10}-z_{10}\right) \, \mathbf{a}_{1} + \left(x_{10}+y_{10}-z_{10}\right) \, \mathbf{a}_{2} + \left(x_{10}-y_{10}+z_{10}\right) \, \mathbf{a}_{3} & = & x_{10}a \, \mathbf{\hat{x}}-y_{10}b \, \mathbf{\hat{y}}-z_{10}c \, \mathbf{\hat{z}} & \left(16k\right) & \text{Re} \\ \end{array} \]References
- 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.