Predicted Phase IV Cd$_{2}$Re$_{2}$O$_{7}$ Structure: A2B7C2_oF88_22_k_acefghij_k-001
| Prototype | Cd$_{2}$O$_{7}$Re$_{2}$ |
| AFLOW prototype label | A2B7C2_oF88_22_k_acefghij_k-001 |
| ICSD | none |
| Pearson symbol | oF88 |
| Space group number | 22 |
| Space group symbol | $F222$ |
| AFLOW prototype command |
aflow --proto=A2B7C2_oF88_22_k_acefghij_k-001
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak x_{3}, \allowbreak y_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak y_{7}, \allowbreak x_{8}, \allowbreak x_{9}, \allowbreak y_{9}, \allowbreak z_{9}, \allowbreak x_{10}, \allowbreak y_{10}, \allowbreak z_{10}$ |
- Cd$_{2}$Re$_{2}$O$_{7}$ exhibits a number of phases. We will use the notation of (Kapcia, 2020) to describe them:
- Phase I: Above 200K the system takes on the cubic pyrochlore ($E8_{1}$) structure.
- Phase II: in the range 120-200K the system is in the tetragonal $I\overline{4}m2$ #119 structure.
- Phase III: in the range 80-120K the system is in the tetragonal $I4_{1}22$ #98 structure.
- Phase IV: (Kapcia, 2020) did a first-principles study of this system and found that below 80K Phase III develops a soft phonon mode which transforms the system into an orthorhombic $F222$ #22 structure. (This structure)
- There are many issues with all of these structures (Norman, 2020):
- Phases II, III, and IV are all close to phase I. If we loosen the tolerance using AFLOW-SYM or FINDSYM the structures are seen to be equivalent to cubic pyrochlore.
- Using the default tolerance, Phase II and Phase IV are equivalent.
- Although the default AFLOW tolerance makes this structure equivalent to Phase II, the published structure can be recovered using the command:
- aflow--proto=A2B7C2_oF88_22_k_acefghij_k:Cd:O:Re --params=a,c/a,z$_{3}$,z$_{4}$,x$_{5}$,x$_{6}$,x$_{7}$,z$_{7}$,x$_{8}$,z$_{8}$ --tolerance=0.001.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}b \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | O I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{4} \, \mathbf{a}_{1}+\frac{1}{4} \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (4c) | O II |
| $\mathbf{B_{3}}$ | = | $- x_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}$ | (8e) | O III |
| $\mathbf{B_{4}}$ | = | $x_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}$ | (8e) | O III |
| $\mathbf{B_{5}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}+y_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}$ | (8f) | O IV |
| $\mathbf{B_{6}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}- y_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}$ | (8f) | O IV |
| $\mathbf{B_{7}}$ | = | $z_{5} \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}- z_{5} \, \mathbf{a}_{3}$ | = | $c z_{5} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{8}}$ | = | $- z_{5} \, \mathbf{a}_{1}- z_{5} \, \mathbf{a}_{2}+z_{5} \, \mathbf{a}_{3}$ | = | $- c z_{5} \,\mathbf{\hat{z}}$ | (8g) | O V |
| $\mathbf{B_{9}}$ | = | $z_{6} \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8h) | O VI |
| $\mathbf{B_{10}}$ | = | $- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(z_{6} - \frac{1}{2}\right) \, \mathbf{a}_{2}+z_{6} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}- c \left(z_{6} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8h) | O VI |
| $\mathbf{B_{11}}$ | = | $y_{7} \, \mathbf{a}_{1}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{2}+y_{7} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{7} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{12}}$ | = | $- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{1}+y_{7} \, \mathbf{a}_{2}- \left(y_{7} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b \left(y_{7} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8i) | O VII |
| $\mathbf{B_{13}}$ | = | $- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{1}+x_{8} \, \mathbf{a}_{2}+x_{8} \, \mathbf{a}_{3}$ | = | $a x_{8} \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{14}}$ | = | $x_{8} \, \mathbf{a}_{1}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{8} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a \left(x_{8} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+\frac{1}{4}b \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8j) | O VIII |
| $\mathbf{B_{15}}$ | = | $\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16k) | Cd I |
| $\mathbf{B_{16}}$ | = | $\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{2}- \left(x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}+c z_{9} \,\mathbf{\hat{z}}$ | (16k) | Cd I |
| $\mathbf{B_{17}}$ | = | $\left(x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{1}- \left(x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{2}+\left(- x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $- a x_{9} \,\mathbf{\hat{x}}+b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16k) | Cd I |
| $\mathbf{B_{18}}$ | = | $- \left(x_{9} + y_{9} + z_{9}\right) \, \mathbf{a}_{1}+\left(x_{9} + y_{9} - z_{9}\right) \, \mathbf{a}_{2}+\left(x_{9} - y_{9} + z_{9}\right) \, \mathbf{a}_{3}$ | = | $a x_{9} \,\mathbf{\hat{x}}- b y_{9} \,\mathbf{\hat{y}}- c z_{9} \,\mathbf{\hat{z}}$ | (16k) | Cd I |
| $\mathbf{B_{19}}$ | = | $\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16k) | Re I |
| $\mathbf{B_{20}}$ | = | $\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{2}- \left(x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}+c z_{10} \,\mathbf{\hat{z}}$ | (16k) | Re I |
| $\mathbf{B_{21}}$ | = | $\left(x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{1}- \left(x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{2}+\left(- x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $- a x_{10} \,\mathbf{\hat{x}}+b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16k) | Re I |
| $\mathbf{B_{22}}$ | = | $- \left(x_{10} + y_{10} + z_{10}\right) \, \mathbf{a}_{1}+\left(x_{10} + y_{10} - z_{10}\right) \, \mathbf{a}_{2}+\left(x_{10} - y_{10} + z_{10}\right) \, \mathbf{a}_{3}$ | = | $a x_{10} \,\mathbf{\hat{x}}- b y_{10} \,\mathbf{\hat{y}}- c z_{10} \,\mathbf{\hat{z}}$ | (16k) | Re I |
References
- K. J. Kapcia, M. Reedyk, M. Hajialamdari, A. Ptok, P. Piekarz, A. Schulz, F. S. Razavi, R. K. Kremer, and A. M. Oleś, Discovery of a low-temperature orthorhombic phase of the Cd$_{2}$Re$_{2}$O$_{7}$ superconductor, Phys. Rev. Res. 2, 033108 (2020), doi:10.1103/PhysRevResearch.2.033108.
Prototype Generator
aflow --proto=A2B7C2_oF88_22_k_acefghij_k --params=$a,b/a,c/a,x_{3},y_{4},z_{5},z_{6},y_{7},x_{8},x_{9},y_{9},z_{9},x_{10},y_{10},z_{10}$