Base-Centered Orthorhombic La$_{2}$CuO$_{4}$ Structure: AB2C4_oC28_64_a_f_ef-003
| Prototype | CuLa$_{2}$O$_{4}$ |
| AFLOW prototype label | AB2C4_oC28_64_a_f_ef-003 |
| ICSD | 155496 |
| Pearson symbol | oC28 |
| Space group number | 64 |
| Space group symbol | $Cmce$ |
| AFLOW prototype command |
aflow --proto=AB2C4_oC28_64_a_f_ef-003
--params=$a, \allowbreak b/a, \allowbreak c/a, \allowbreak y_{2}, \allowbreak y_{3}, \allowbreak z_{3}, \allowbreak y_{4}, \allowbreak z_{4}$ |
Other compounds with this structure
La$_{2}$NiO$_{4}$, Nd$_{2}$CeO$_{4}$
- We have found three possible structures for La$_{2}$CuO$_{4}$, the parent compound of the high-temperature cuprate superconductors.
- All are distortions of the tetragonal K$_{2}$NiF$_{4}$/0201 [(La,Ba)$_{2}$CuO$_{4}$] High-T$_{c}$ Structure, and reduce to that structure with doping of the lanthanum site:
- (Longo, 1973) proposed a face-centered orthorhombic structure.
- Later other workers, including (Reehuis, 2006) and references therein, proposed a base-centered orthorhombic structure (this structure).
- (Reehuis, 2006) found that a base-centered monoclinic structure was a better fit to their neutron diffraction data.
- As the two orthorhombic structures are both referenced in the literature, we present them, as well as the more recent monoclinic structure.
- (Reehuis, 2006) gave the structure of the base-centered phase in the $Bmab$ setting of space group #64. We used FINDSYM to transform it to the standard $Cmca$ setting.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}b \,\mathbf{\hat{y}}\\\mathbf{a_{3}}&=&c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $0$ | = | $0$ | (4a) | Cu I |
| $\mathbf{B_{2}}$ | = | $\frac{1}{2} \, \mathbf{a}_{1}+\frac{1}{2} \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}c \,\mathbf{\hat{z}}$ | (4a) | Cu I |
| $\mathbf{B_{3}}$ | = | $- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{4}}$ | = | $\left(y_{2} + \frac{1}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{1}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{1}{4}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{5}}$ | = | $\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{1}- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{3}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}- b y_{2} \,\mathbf{\hat{y}}+\frac{3}{4}c \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{6}}$ | = | $- \left(y_{2} - \frac{3}{4}\right) \, \mathbf{a}_{1}+\left(y_{2} + \frac{3}{4}\right) \, \mathbf{a}_{2}+\frac{1}{4} \, \mathbf{a}_{3}$ | = | $\frac{3}{4}a \,\mathbf{\hat{x}}+b y_{2} \,\mathbf{\hat{y}}+\frac{1}{4}c \,\mathbf{\hat{z}}$ | (8e) | O I |
| $\mathbf{B_{7}}$ | = | $- y_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $b y_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8f) | La I |
| $\mathbf{B_{8}}$ | = | $\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{3} \,\mathbf{\hat{y}}+c \left(z_{3} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La I |
| $\mathbf{B_{9}}$ | = | $- \left(y_{3} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{3} \,\mathbf{\hat{y}}- c \left(z_{3} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | La I |
| $\mathbf{B_{10}}$ | = | $y_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- b y_{3} \,\mathbf{\hat{y}}- c z_{3} \,\mathbf{\hat{z}}$ | (8f) | La I |
| $\mathbf{B_{11}}$ | = | $- y_{4} \, \mathbf{a}_{1}+y_{4} \, \mathbf{a}_{2}+z_{4} \, \mathbf{a}_{3}$ | = | $b y_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{12}}$ | = | $\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}- b y_{4} \,\mathbf{\hat{y}}+c \left(z_{4} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{13}}$ | = | $- \left(y_{4} - \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(z_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \,\mathbf{\hat{x}}+b y_{4} \,\mathbf{\hat{y}}- c \left(z_{4} - \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (8f) | O II |
| $\mathbf{B_{14}}$ | = | $y_{4} \, \mathbf{a}_{1}- y_{4} \, \mathbf{a}_{2}- z_{4} \, \mathbf{a}_{3}$ | = | $- b y_{4} \,\mathbf{\hat{y}}- c z_{4} \,\mathbf{\hat{z}}$ | (8f) | O II |
References
- M. Reehuis, C. Ulrich, K. Prokeš, A. Gozar, G. Blumberg, S. Komiya, Y. Ando, P. Pattison, and B. Keimer, Crystal structure and high-field magnetism of La$_{2}$CuO$_{4}$, Phys. Rev. B 73, 144513 (2006), doi:10.1103/PhysRevB.73.144513.
- J. M. Longo and P. M. Raccah, The structure of La$_{2}$CuO$_{4}$ and LaSrVO$_{4}$, J. Solid State Chem. 6, 526–531 (1973), doi:10.1016/S0022-4596(73)80010-6.
Prototype Generator
aflow --proto=AB2C4_oC28_64_a_f_ef --params=$a,b/a,c/a,y_{2},y_{3},z_{3},y_{4},z_{4}$