UP$_{2}$ Structure: A2B_tI24_107_2abc_2ab-001
| Prototype | P$_{2}$U |
| AFLOW prototype label | A2B_tI24_107_2abc_2ab-001 |
| ICSD | 87138 |
| Pearson symbol | tI24 |
| Space group number | 107 |
| Space group symbol | $I4mm$ |
| AFLOW prototype command |
aflow --proto=A2B_tI24_107_2abc_2ab-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak z_{3}, \allowbreak z_{4}, \allowbreak z_{5}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak z_{7}$ |
- This is very close to the Cu$_{2}$Sb ($C38)$ structure. Indeed, if we allow an uncertainty of 0.3Å FINDSYM puts this in the $C38$ structure.
- The ICSD entery is from the earlier work of (Pietrasko, 1971).
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (2a) | P I |
| $\mathbf{B_{2}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (2a) | P II |
| $\mathbf{B_{3}}$ | = | $z_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}$ | = | $c z_{3} \,\mathbf{\hat{z}}$ | (2a) | U I |
| $\mathbf{B_{4}}$ | = | $z_{4} \, \mathbf{a}_{1}+z_{4} \, \mathbf{a}_{2}$ | = | $c z_{4} \,\mathbf{\hat{z}}$ | (2a) | U II |
| $\mathbf{B_{5}}$ | = | $\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{5} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | P III |
| $\mathbf{B_{6}}$ | = | $z_{5} \, \mathbf{a}_{1}+\left(z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{5} \,\mathbf{\hat{z}}$ | (4b) | P III |
| $\mathbf{B_{7}}$ | = | $\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+z_{6} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (4b) | U III |
| $\mathbf{B_{8}}$ | = | $z_{6} \, \mathbf{a}_{1}+\left(z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+c z_{6} \,\mathbf{\hat{z}}$ | (4b) | U III |
| $\mathbf{B_{9}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+2 x_{7} \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8c) | P IV |
| $\mathbf{B_{10}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- 2 x_{7} \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8c) | P IV |
| $\mathbf{B_{11}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8c) | P IV |
| $\mathbf{B_{12}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (8c) | P IV |
References
- P. Wiśniewski, D. Aoki, N. Watanabe, R. Settai, Y. Haga, E. Yamamoto, and Y. . {O}nuki, Shubnikov–de Haas Effect Study of Cylindrical Fermi Surfaces in UP$_{2}$, J. Phys. Soc. Jpn. 70, 278–283 (2001), doi:10.1143/JPSJ.70.278.
- D. Pietrasko and K. Lukaszewicz, The crystal structure of uranium diphosphide UP$_{2}$, Bull. l'Academie Polo. Sci., Ser. Chim. 19, 237–242 (1971).
Found in
- Z. E. Brubaker, Y. Xiao, P. Chow, C. Kenney-Benson, J. S. Smith, H. Cynn, C. Reynolds, N. P. Butch, R. J. Zieve, and J. R. Jeffries, Valence instability across magnetostructural transition in USb$_{2}$, Phys. Rev. B 101, 085123 (2020), doi:10.1103/PhysRevB.101.085123.
Prototype Generator
aflow --proto=A2B_tI24_107_2abc_2ab --params=$a,c/a,z_{1},z_{2},z_{3},z_{4},z_{5},z_{6},x_{7},z_{7}$