β-PdCl$_{2}$ Structure: A2B_hR18_148_2f_f-001
| Prototype | Cl$_{2}$Pd |
| AFLOW prototype label | A2B_hR18_148_2f_f-001 |
| ICSD | 404624 |
| Pearson symbol | hR18 |
| Space group number | 148 |
| Space group symbol | $R\overline{3}$ |
| AFLOW prototype command |
aflow --proto=A2B_hR18_148_2f_f-001
--params=$a, \allowbreak c/a, \allowbreak x_{1}, \allowbreak y_{1}, \allowbreak z_{1}, \allowbreak x_{2}, \allowbreak y_{2}, \allowbreak z_{2}, \allowbreak x_{3}, \allowbreak y_{3}, \allowbreak z_{3}$ |
- PdCl$_{2}$ is known to exist in four different structures at ambient pressure (Evers, 2010):
- (Dell'Amico, 1996) did the original assessment of the crystal structure of $\beta$–PdCl$_{2}$, but it is difficult to determine the Wyckoff positions from this paper. We relied on (Villars, 2010) for the Wyckoff positions.
\[ \begin{array}{ccc}
\mathbf{a_{1}}&=&\frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{2}}&=&\frac{1}{\sqrt{3}}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}\\\mathbf{a_{3}}&=&- \frac{1}{2}a \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \,\mathbf{\hat{y}}+\frac{1}{3}c \,\mathbf{\hat{z}}
\end{array}\]
Basis vectors
| Lattice coordinates | Cartesian coordinates | Wyckoff position | Atom type | |||
|---|---|---|---|---|---|---|
| $\mathbf{B_{1}}$ | = | $x_{1} \, \mathbf{a}_{1}+y_{1} \, \mathbf{a}_{2}+z_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{1} - 2 y_{1} + z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{2}}$ | = | $z_{1} \, \mathbf{a}_{1}+x_{1} \, \mathbf{a}_{2}+y_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{1} - y_{1} - z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{3}}$ | = | $y_{1} \, \mathbf{a}_{1}+z_{1} \, \mathbf{a}_{2}+x_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{1} + y_{1} - 2 z_{1}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{4}}$ | = | $- x_{1} \, \mathbf{a}_{1}- y_{1} \, \mathbf{a}_{2}- z_{1} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{1} - z_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} - 2 y_{1} + z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{5}}$ | = | $- z_{1} \, \mathbf{a}_{1}- x_{1} \, \mathbf{a}_{2}- y_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{1} - z_{1}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{1} - y_{1} - z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{6}}$ | = | $- y_{1} \, \mathbf{a}_{1}- z_{1} \, \mathbf{a}_{2}- x_{1} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{1} - y_{1}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{1} + y_{1} - 2 z_{1}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{1} + y_{1} + z_{1}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl I |
| $\mathbf{B_{7}}$ | = | $x_{2} \, \mathbf{a}_{1}+y_{2} \, \mathbf{a}_{2}+z_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{8}}$ | = | $z_{2} \, \mathbf{a}_{1}+x_{2} \, \mathbf{a}_{2}+y_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{9}}$ | = | $y_{2} \, \mathbf{a}_{1}+z_{2} \, \mathbf{a}_{2}+x_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{10}}$ | = | $- x_{2} \, \mathbf{a}_{1}- y_{2} \, \mathbf{a}_{2}- z_{2} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{2} - z_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} - 2 y_{2} + z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{11}}$ | = | $- z_{2} \, \mathbf{a}_{1}- x_{2} \, \mathbf{a}_{2}- y_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{2} - z_{2}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{2} - y_{2} - z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{12}}$ | = | $- y_{2} \, \mathbf{a}_{1}- z_{2} \, \mathbf{a}_{2}- x_{2} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{2} - y_{2}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{2} + y_{2} - 2 z_{2}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{2} + y_{2} + z_{2}\right) \,\mathbf{\hat{z}}$ | (6f) | Cl II |
| $\mathbf{B_{13}}$ | = | $x_{3} \, \mathbf{a}_{1}+y_{3} \, \mathbf{a}_{2}+z_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
| $\mathbf{B_{14}}$ | = | $z_{3} \, \mathbf{a}_{1}+x_{3} \, \mathbf{a}_{2}+y_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
| $\mathbf{B_{15}}$ | = | $y_{3} \, \mathbf{a}_{1}+z_{3} \, \mathbf{a}_{2}+x_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}+\frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
| $\mathbf{B_{16}}$ | = | $- x_{3} \, \mathbf{a}_{1}- y_{3} \, \mathbf{a}_{2}- z_{3} \, \mathbf{a}_{3}$ | = | $- \frac{1}{2}a \left(x_{3} - z_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} - 2 y_{3} + z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
| $\mathbf{B_{17}}$ | = | $- z_{3} \, \mathbf{a}_{1}- x_{3} \, \mathbf{a}_{2}- y_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(y_{3} - z_{3}\right) \,\mathbf{\hat{x}}- \frac{\sqrt{3}}{6}a \left(2 x_{3} - y_{3} - z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
| $\mathbf{B_{18}}$ | = | $- y_{3} \, \mathbf{a}_{1}- z_{3} \, \mathbf{a}_{2}- x_{3} \, \mathbf{a}_{3}$ | = | $\frac{1}{2}a \left(x_{3} - y_{3}\right) \,\mathbf{\hat{x}}+\frac{\sqrt{3}}{6}a \left(x_{3} + y_{3} - 2 z_{3}\right) \,\mathbf{\hat{y}}- \frac{1}{3}c \left(x_{3} + y_{3} + z_{3}\right) \,\mathbf{\hat{z}}$ | (6f) | Pd I |
References
- D. B. Dell'Amico, F. Calderazzo, F. Marchetti, and S. Ramello, Molecular Structure of [Pd$_{6}$Cl$_{12}$] in Single Crystals Chemically Grown at Room Temperature, Angew. Chem. Int. Ed. 35, 1131–1133 (1996), doi:10.1002/anie.199613311.
- J.Evers, W. Beck, M. Göbel, S. Jakob, P. Mayer, G. Oehlinger, M. Rotter, and T. Klapötke, The Structures of δ-PdCl$_{2}$ and γ-PdCl$_{2}$: Phases with Negative Thermal Expansion in One Direction, Angew. Chem. Int. Ed. 49, 5677–5682 (2010), doi:10.1002/anie.201000680.
- P. Villars and K. Cenzual, eds., Structure Types (Springer, Berlin, Heidelberg, 2010), Landolt-Börnstein – Group III Condensed Matter, vol. 43A8, chap. Part 8: SpaceGroups (156) P3m1 – (148) R-3, doi:10.1007/978-3-540-70892-6_423.
Prototype Generator
aflow --proto=A2B_hR18_148_2f_f --params=$a,c/a,x_{1},y_{1},z_{1},x_{2},y_{2},z_{2},x_{3},y_{3},z_{3}$