Density functional theory study of platinum oxides: From infinite crystals to nanoscopic particles

For over a century, platinum oxides find technologically relevant applications in various fields ranging from catalysis to electrochemistry and nanoelectronics. We have performed a density functional theory study of the PtO, ${\mathrm{Pt}}_3{\mathrm{O}}_4$, and $\mathrm{Pt}{\mathrm{O}}_2$ bulk oxide phases. In our calculations, PtO and ${\mathrm{Pt}}_3{\mathrm{O}}_4$ present metallic character at the simple generalized gradient approximation level. The application of Hubbard corrections to the Kohn-Sham Hamiltonian opens a small gap in the electronic band structure of PtO, but not of ${\mathrm{Pt}}_3{\mathrm{O}}_4$, in which metallic Pt-Pt bonds are revealed by a Bader analysis of the calculated electronic structure. These results, together with the noninteger oxidation number of the Pt ions, are indicative of metallicity of the ${\mathrm{Pt}}_3{\mathrm{O}}_4$ phase which may be consistent with the known metallic character of platinum bronzes. Moreover, we have calculated the relative thermodynamic stabilities of platinum oxide Wulff’s particles and discussed the results in the context of catalysis. Finally, we have predicted that the formation of $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ nanotubes could be energetically feasible. This result is of potential interest both for nanotechnological and catalytic applications and may explain the formation of curled $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ sheets observed in high-resolution transmission electron microscopy images.

Figure 1

(Color online) Crystal structures of the investigated Pt oxides: (a) $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$, (b) $\beta \text{−}\mathrm{Pt}{\mathrm{O}}_2$, (c) PtO, and (d) ${\mathrm{Pt}}_3{\mathrm{O}}_4$.

Figure 2

Electronic band structures of (a) $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ and (b) $\beta \text{−}\mathrm{Pt}{\mathrm{O}}_2$. The energy values are reported relative to the valence band top.

Figure 3

Electronic band structures of PtO and ${\mathrm{Pt}}_3{\mathrm{O}}_4$: (a) PtO within spin-paired GGA, (b) PtO within $\mathrm{GGA}+U$ and $U=4\mathrm{eV}$, (c) PtO within $\mathrm{GGA}+U$ and $U=9\mathrm{eV}$, (d) ${\mathrm{Pt}}_3{\mathrm{O}}_4$ within spin-paired GGA, (e) ${\mathrm{Pt}}_3{\mathrm{O}}_4$ within $\mathrm{GGA}+U$ and $U=4\mathrm{eV}$, and (f) ${\mathrm{Pt}}_3{\mathrm{O}}_4$ within $\mathrm{GGA}+U$ and $U=9\mathrm{eV}$. The energy values are reported relative to the Fermi level.

Figure 4

(Color online) Pt-Pt bonds (black lines) in (a) PtO and (b) ${\mathrm{Pt}}_3{\mathrm{O}}_4$, as found by Bader analysis of the computed electron densities.

Figure 5

Phase transition temperatures as function of Pt particle size at $1\mathrm{atm}$ oxygen pressure. The particle size is defined as the distance between two opposite (100) faces in a metallic Wulff’s nanoparticle.

Figure 6

HRTEM images of $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ specimens (at $100\mathrm{keV}$). [(a) and (b)] $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ specimen as produced in Ref. 11; [(c) and (d)] similar specimen after annealing for $3\mathrm{h}$ at $350°\mathrm{C}$ in a ${\mathrm{N}}_2$ atmosphere.

Figure 7

(Color online) $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ nanotubes. Nanotube with six Pt atoms in the unit cell, (a) nonrelaxed and (b) relaxed; nanotube with 12 Pt atoms in the unit cell, (c) nonrelaxed and (d) relaxed.

Figure 8

(Color online) Formation energies of $\alpha \text{−}\mathrm{Pt}{\mathrm{O}}_2$ nanotubes of increasing radius. (a) Unrelaxed system: circles, DFT results; solid line, fitted function $\frac{\alpha }{r^2}$, with $\alpha =33.31\mathrm{eV}{\mathrm{\AA }}^2$. (b) Relaxed system: circles, DFT results; solid line, fitted function $\frac{\alpha }{r^2}$, with $\alpha =19.70\mathrm{eV}{\mathrm{\AA }}^2$. Notice the different energy scales in the two diagrams.