Zn$_{2}$VO(PO$_{4}$)$_{2}$ Structure: A9B2CD2_tI56_108_a2cd_c_a_c-001
| Prototype | O$_{9}$P$_{2}$VZn$_{2}$ |
| AFLOW prototype label | A9B2CD2_tI56_108_a2cd_c_a_c-001 |
| ICSD | 69768 |
| CCDC | 1631618 |
| Pearson symbol | tI56 |
| Space group number | 108 |
| Space group symbol | $I4cm$ |
| AFLOW prototype command |
aflow --proto=A9B2CD2_tI56_108_a2cd_c_a_c-001
--params=$a, \allowbreak c/a, \allowbreak z_{1}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak z_{3}, \allowbreak x_{4}, \allowbreak z_{4}, \allowbreak x_{5}, \allowbreak z_{5}, \allowbreak x_{6}, \allowbreak z_{6}, \allowbreak x_{7}, \allowbreak y_{7}, \allowbreak z_{7}$ |
- We could not reproduce all of the interatomic distances in Table III of (Lii, 1991). While we found the correct nearest neighbor distances for Zn-O, P-O, and the first three V-O distances, we find that what they call the V-O(3) (our V-O I) distance is 1.57Å rather than the published value of 3.149Å. The 1.57Å value can be easily confirmed from the published lattice constants, the Wyckoff positions in the paper, and by estimating the V-O(3) distance in Fig. 1 and comparing it to the P-O distances in the same figure. We are not certain what distances the other entries in the table represent, as we cannot find them in our reconstruction of the crystal, which agrees with the ICSD entry and the Wyckoff parameters in Table II.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{1}{2}a \,\mathbf{\hat{y}}+\frac{1}{2}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}+\frac{1}{2}a \,\mathbf{\hat{y}}- \frac{1}{2}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $z_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}$ | = | $c z_{1} \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{2}}$ | = | $\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{1} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{1} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | O I |
| $\mathbf{B_{3}}$ | = | $z_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}$ | = | $c z_{2} \,\mathbf{\hat{z}}$ | (4a) | V I |
| $\mathbf{B_{4}}$ | = | $\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(z_{2} + \frac{1}{2}\right) \, \mathbf{a}_{2}$ | = | $c \left(z_{2} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (4a) | V I |
| $\mathbf{B_{5}}$ | = | $\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3}\right) \, \mathbf{a}_{2}+\left(2 x_{3} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{3} \,\mathbf{\hat{x}}+a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{6}}$ | = | $\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{2}- \left(2 x_{3} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{3} \,\mathbf{\hat{x}}- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{7}}$ | = | $\left(x_{3} + z_{3}\right) \, \mathbf{a}_{1}+\left(- x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{3} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{8}}$ | = | $- \left(x_{3} - z_{3}\right) \, \mathbf{a}_{1}+\left(x_{3} + z_{3} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{3} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{3} \,\mathbf{\hat{y}}+c z_{3} \,\mathbf{\hat{z}}$ | (8c) | O II |
| $\mathbf{B_{9}}$ | = | $\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4}\right) \, \mathbf{a}_{2}+\left(2 x_{4} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{4} \,\mathbf{\hat{x}}+a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{10}}$ | = | $\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{2}- \left(2 x_{4} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{4} \,\mathbf{\hat{x}}- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{11}}$ | = | $\left(x_{4} + z_{4}\right) \, \mathbf{a}_{1}+\left(- x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{4} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{12}}$ | = | $- \left(x_{4} - z_{4}\right) \, \mathbf{a}_{1}+\left(x_{4} + z_{4} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{4} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{4} \,\mathbf{\hat{y}}+c z_{4} \,\mathbf{\hat{z}}$ | (8c) | O III |
| $\mathbf{B_{13}}$ | = | $\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5}\right) \, \mathbf{a}_{2}+\left(2 x_{5} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{5} \,\mathbf{\hat{x}}+a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | P I |
| $\mathbf{B_{14}}$ | = | $\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{2}- \left(2 x_{5} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{5} \,\mathbf{\hat{x}}- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | P I |
| $\mathbf{B_{15}}$ | = | $\left(x_{5} + z_{5}\right) \, \mathbf{a}_{1}+\left(- x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{5} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | P I |
| $\mathbf{B_{16}}$ | = | $- \left(x_{5} - z_{5}\right) \, \mathbf{a}_{1}+\left(x_{5} + z_{5} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{5} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{5} \,\mathbf{\hat{y}}+c z_{5} \,\mathbf{\hat{z}}$ | (8c) | P I |
| $\mathbf{B_{17}}$ | = | $\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6}\right) \, \mathbf{a}_{2}+\left(2 x_{6} + \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $a x_{6} \,\mathbf{\hat{x}}+a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{18}}$ | = | $\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{1}- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{2}- \left(2 x_{6} - \frac{1}{2}\right) \, \mathbf{a}_{3}$ | = | $- a x_{6} \,\mathbf{\hat{x}}- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{19}}$ | = | $\left(x_{6} + z_{6}\right) \, \mathbf{a}_{1}+\left(- x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $- a \left(x_{6} - \frac{1}{2}\right) \,\mathbf{\hat{x}}+a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{20}}$ | = | $- \left(x_{6} - z_{6}\right) \, \mathbf{a}_{1}+\left(x_{6} + z_{6} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\frac{1}{2} \, \mathbf{a}_{3}$ | = | $a \left(x_{6} + \frac{1}{2}\right) \,\mathbf{\hat{x}}- a x_{6} \,\mathbf{\hat{y}}+c z_{6} \,\mathbf{\hat{z}}$ | (8c) | Zn I |
| $\mathbf{B_{21}}$ | = | $\left(y_{7} + z_{7}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{22}}$ | = | $- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{1}- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{23}}$ | = | $\left(x_{7} + z_{7}\right) \, \mathbf{a}_{1}- \left(y_{7} - z_{7}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{24}}$ | = | $- \left(x_{7} - z_{7}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c z_{7} \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{25}}$ | = | $\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $a x_{7} \,\mathbf{\hat{x}}- a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{26}}$ | = | $\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} - y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a x_{7} \,\mathbf{\hat{x}}+a y_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{27}}$ | = | $\left(- x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(- y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}- \left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $- a y_{7} \,\mathbf{\hat{x}}- a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | O IV |
| $\mathbf{B_{28}}$ | = | $\left(x_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{1}+\left(y_{7} + z_{7} + \frac{1}{2}\right) \, \mathbf{a}_{2}+\left(x_{7} + y_{7}\right) \, \mathbf{a}_{3}$ | = | $a y_{7} \,\mathbf{\hat{x}}+a x_{7} \,\mathbf{\hat{y}}+c \left(z_{7} + \frac{1}{2}\right) \,\mathbf{\hat{z}}$ | (16d) | O IV |
References
- K. H. Lii and H. J. Tsai, Synthesis and crystal structure of Zn$_{2}$VO(PO$_{4}$)$_{2}$, a vanadyl(IV) orthophosphate containing a dimer of edge-sharing ZnO$_{5}$ square pyramids, J. Solid State Chem. 90, 291–295 (1991), doi:10.1016/0022-4596(91)90145-8.
Found in
- N. S. Kini, E. E. Kaul, and C. Geibel, Zn$_{2}$VO(PO$_{4}$)$_{2}$: an $S = 1/2$ Heisenberg antiferromagnetic square lattice system, J. Phys.: Condens. Matter 18, 1303–1311 (2006), doi:10.1088/0953-8984/18/4/015.
First cited in
- N. Anderson, M. J. Mehl, H. Eckert, S. Divilov, X. Campilongo, S. Curtarolo, The AFLOW Library of Crystallographic Prototypes: Part 5. Submitted to Computational Materials Science (2026).
Geometry files
Prototype Generator
aflow --proto=A9B2CD2_tI56_108_a2cd_c_a_c --params=$a,c/a,z_{1},z_{2},x_{3},z_{3},x_{4},z_{4},x_{5},z_{5},x_{6},z_{6},x_{7},y_{7},z_{7}$