Mechanical Origin of High-Temperature Thermal Stability in Platinum Oxides

Abstract

Platinum oxides are vital catalysts, but their limited thermal stability hinders applications. Recent studies have uncovered a structural transition in two-dimensional platinum oxides that significantly enhances their thermal resilience by several hundred Kelvin. Herein, we demonstrate that this enhanced stability stems from the mechanical robustness of the elastic network at the atomic scale. Prior to the transition, an over-constrained lattice generates localized states of self-stress through an incommensurate Moiré pattern with the platinum substrate, reducing thermal endurance. After the transition, the oxide shifts to a mechanically flexible structure with balanced degrees of freedom and constraints. The isostatic network, together with the platinum substrate, forms a commensurate Moiré superlattice that relaxes elastic energy and enhances stability. These findings highlight the fundamental role of network connectivity in governing thermal stability, and provide a design principle for catalysts in extreme environments.

Figures (9)

• Figure 1: Elastic network modeling of two-dimensional platinum oxide sheets based on in situ experiments wang2024NM. (a) Atomic structures of dice-lattice (left) and six-pointed star-lattice (right). In side view, oxygen atoms near the vacuum interface (purple) and near the platinum layer (red) are indicated. (b) Unit cell of the dice lattice, containing a platinum atom (green) at $\bm{A}=\ell_0(0,0,2.3)$ and oxygen atoms (red, purple) at $\bm{B}=\ell_0(\cos \tfrac{2\pi}{3}, \sin \tfrac{2\pi}{3},1.71)$ and $\bm{C}=\ell_0(\cos \tfrac{5\pi}{3}, \sin \tfrac{5\pi}{3},2.85)$. Here $\ell_0=1.726\,\text{\AA}$ is the horizontal projection of the nearest-neighbor edge length (solid red lines). Bending constraints are shown as red arcs. Primitive vectors are indicated by black arrows: $\bm{a}_{\rm dice}^{(1)}=\ell_0(\sqrt{3}\cos \tfrac{\pi}{6}, \sqrt{3}\sin \tfrac{\pi}{6},0)$ and $\bm{a}_{\rm dice}^{(2)}=\ell_0(0,\sqrt{3},0)$. (c) Unit cell of the star lattice, hosting two platinum atoms at $\bm{A}_1 = \ell_0(\sqrt{3}\cos \tfrac{4\pi}{3}, \sqrt{3}\sin \tfrac{4\pi}{3}, 2.3)$ and $\bm{A}_2 =\ell_0(0,0,2.3)$. Each platinum atom is coordinated by six oxygen atoms. Lower and upper oxygen atoms (red and purple dots) are located at $\bm{B}_i = \ell_0(\cos \tfrac{(4i-7)\pi}{6}, \sin \tfrac{(4i-7)\pi}{6}, 1.71)$ and $\bm{C}_i = \ell_0(\cos \tfrac{(4i-9)\pi}{6}, \sin \tfrac{(4i-9)\pi}{6}, 2.85)$ for $i=1,2,3$. Primitive vectors are $\bm{a}_{\rm star}^{(1)} = \ell_0(3\cos \frac{\pi}{6}, 3\sin \frac{\pi}{6}, 0)$ and $\bm{a}_{\rm star}^{(2)} = \ell_0(0,3,0)$. (d) Spatial profile of a self-stress state in the dice lattice, with color indicating stress intensity. Self-stress in bonds and bending constraints is represented by edges and diagonal lines. (e) The star lattice, being mechanically isostatic, exhibits no self-stress states.
• Figure 2: Initial bilayer structures prior to mechanical relaxation. (a) Geometry of the substrate: The primitive vectors of the triangular surface lattice are $\bm{a}_{\mathrm{Pt}}^{(1)} = \ell_0(1.606, 0, 0)$ and $\bm{a}_{\mathrm{Pt}}^{(2)} = \ell_0\bigl(1.606\cos\frac{\pi}{3},1.606\sin\frac{\pi}{3},0\bigr)$. The top platinum (111) layer (height $= 0$) evolves dynamically, while the subsurface layer (height $= -1.311\ell_0$) is fixed to model the rigid bulk of the platinum substrate. (b,c) Top views of the dice (b) and star (c) bilayers on the substrate. The rhombuses $\alpha_{\mathrm{dice}}^{(\mathrm{real})}$ and $\alpha_{\mathrm{star}}^{(\mathrm{real})}$ mark oxide unit cells; $\beta^{(\mathrm{real})}$ denotes the substrate unit cell. Side views (bottom) show the bonding of the lowest oxygen atoms (red dots) to the substrate platinum atoms. (d,e) Arrangement of the lowest oxygen atoms (oxide layer) and the top platinum atoms (substrate layer) forming interlayer bonds, generating (d) an incommensurate Moiré quasicrystal for the dice bilayer and (e) a commensurate Moiré superlattice for the star bilayer. The superlattice unit cell is outlined by black rhombus $\gamma_{\mathrm{star}}^{(\mathrm{real})}$ in (e).
• Figure 3: Bilayer structures after mechanical relaxation. (a) Platinum oxides with star lattice, shown left to right: atomic model, STM simulation, STM experiment, and electron density distribution. (b,c) Spatial profiles of elastic energy in the dice and star lattices, with colors on nearest-/next-nearest-neighbor edges indicating stretching and bending contributions. (d,e) Reciprocal lattices of the two Moiré bilayer patterns of site positions. Here, $\alpha_{\rm dice}^{(\rm rec)}$ and $\alpha_{\rm star}^{(\rm rec)}$ represent reciprocal lattice vectors of dice and star lattices, while $\beta^{(\rm rec)}$ corresponds to those of the platinum substrate. The reciprocal vector of the Moiré superlattice, highlighted in the enlarged square of (e), is denoted by $\gamma_{\rm star}^{(\rm rec)}$.
• Figure 4: Percentage distributions of stretching and bending energies per bond in bilayer structures at different temperatures: $0\,\text{K}$ in (a), $700\,\text{K}$ in (b), and $1200\,\text{K}$ in (c). Each bilayer is modeled as a rhombus with side length $104.0\,\text{\AA} = 60.25\ell_0$, comprising $35 \times 35$ unit cells with $2.3 \times 10^{4}$ bonds in the dice-bilayer, and $20 \times 20$ unit cells with $1.3 \times 10^{4}$ bonds in the star-bilayer. For statistical sampling, 10 dice-lattice and 10 star-lattice bilayers were generated by varying $\delta \bm{r}_{\rm Pt} = \xi^{(1)} \bm{a}_{\rm Pt}^{(1)} + \xi^{(2)} \bm{a}_{\rm Pt}^{(2)}$, which denotes the coordinate origin of the platinum substrate relative to the top platinum-oxide sheets, where $\xi^{(1,2)} \in [0,1]$ are uniformly distributed random variables. The horizontal axis shows elastic energies per constraint, while the vertical axis gives the normalized fraction (percentage population) of bonds/angles within each energy interval. Each data point corresponds to $E \pm \delta E/2$, with spacing $\delta E = 0.02\,\text{eV}$; the vertical axis is in units of one-thousandths. Distributions are truncated below $0.5\,\text{eV}$ to emphasize high-energy components (full statistics in Supplementary Information SIPtOx). Blue and red curves denote dice and star bilayers, respectively. Triangular and circular markers indicate mean values, with error bars showing standard deviations. Insets in (a-c) present the maximum stretching and bending energies per bond across the 10 random configurations for dice and star lattices at the corresponding temperatures.
• Figure 5: Three adjacent sites in a spring-mass model.