- The paper demonstrates that thermodynamic surface reconstruction, rather than homogeneous models, fundamentally governs HEA catalytic activity.
- Monte Carlo annealing combined with spin-polarized DFT and CGCNN reveals pronounced Pd and Pt surface enrichment and optimal OH adsorption behavior.
- A novel surface compositional deviation metric (D) quantitatively links surface restructuring to catalytic performance, challenging traditional assumptions.
Introduction
This work systematically interrogates the governing factors underlying the catalytic activity of high-entropy alloys (HEAs) and directly challenges the prevalent homogeneous surface paradigm used in computational catalyst discovery. The investigation centers on Ru-Rh-Pd-Pt-Ir HEAs and provides robust experimental–computational correlation demonstrating that the catalytic behavior of HEAs is dictated by the thermodynamically reconstructed surface rather than by the nominal bulk composition or random surface models. The study employs high-throughput experimental measurements, Monte Carlo–annealed thermodynamic simulations driven by crystal graph convolutional neural networks (CGCNN), and compositional and spatial analysis to resolve the interplay of segregation energetics and entropy in HEA catalytic surfaces.
Methodology
The computational approach is anchored in spin-polarized DFT calculations with RPBE functionals, and a CGCNN trained on both bulk and slab DFT data (MAE ≈ 0.006 eV atom⁻¹), enabling efficient evaluation of formation energetics for large-scale Monte Carlo surface annealing. Surface configurations are generated via Metropolis Monte Carlo on (111) slabs with temperatures cooled from 4000 K to 298 K. The OH adsorption energy serves as the activity descriptor following linear scaling relationships, and the resultant activities are benchmarked against high-resolution experimental SECCM combinatorial data, with rigorous spatial registration for map-level comparison.
Homogeneous Surface Models Fail to Capture Catalytic Trends
Direct comparison reveals that homogeneous surface models—approximating HEA surfaces as statistically random mixtures reflective of bulk composition—fail to recover experimentally observed activity landscapes. The homogeneous models perform at or below a random-selection baseline for activity recall and display weak or negative Spearman and Kendall rank correlations to experiment (for homogeneous models: Spearman ρ = –0.09, Kendall τ = –0.06). This outcome indicates not merely predictive inaccuracy but systematic misranking of catalytic compositions—an unreliability that fundamentally undermines high-throughput screening protocols unless surface thermodynamics are explicitly considered.
Thermodynamic Surface Segregation and Short-Range Order
In contrast, Monte Carlo annealing incorporating energetics and entropy yields surfaces that faithfully reproduce key experimental activity features (Spearman ρ = 0.46, Kendall τ = 0.31). Segregation energy calculations show pronounced surface enrichment by Pd and Pt (with ΔH_seg ≈ –0.5 eV), moderate Rh preference, Ir neutrality, and Ru exclusion (ΔH_seg ≈ +0.5 eV), indicating strong elemental selectivity far exceeding configurational entropy stabilization at catalytic temperatures. Temperature-dependent simulations reveal a transition from partially mixed high-temperature surfaces to chemically stratified, catalytically relevant interfaces at 298 K—contravening the core assumption of entropy stabilization at the catalyst surface for HEAs.
Short-range ordering is quantified by the Warren-Cowley parameter, showing that local surface structures are governed by strongly pair-dependent associations/disassociations, particularly preferring Pt-containing motifs and separating Pd from Rh and Ir. Therefore, the catalyst interface is a non-random, thermodynamically selected ensemble—not a statistical sampling—of local atomic environments.
Impact of Surface Ordering on Active-Site Distribution
Thermodynamic surface reconstruction drastically alters the active-site landscape. The surface becomes Pd- and Pt-rich (e.g., at 298 K: ∼70% Pd, ∼30% Pt), while Ru, Rh, and Ir are largely expelled or restricted to subsurface/bulk layers. The distribution of adsorption energies sharply contracts from a broad, multimodal spectrum (in the homogeneous case) to narrowly distributed, catalytically favorable values centered near the Sabatier optimum. Thus, compositional complexity is reorganized into vertical chemical partitioning, functionally decoupling the catalytic interface from the compositional diversity of the bulk.
A strong quantitative correlation is established between the surface compositional deviation from the bulk state (D) and both the pixel-wise shift in mean OH binding energies (R² = 0.745) and recall of experimentally active compositions. Increased deviation translates directly into systematic modification of the adsorption descriptor space, mechanistically explaining the breakdown of homogeneous models as D increases.
Implications for Theory and Catalyst Design
The findings assert that HEA catalytic screening and design must incorporate thermodynamic surface reconstruction phenomena, even in systems previously assumed to be entropy stabilized at the surface. Homogeneous models can yield false positives and negatives, misdirecting materials exploration. The introduction of surface compositional deviation D as a physical metric provides a practical tool for determining the validity regime of random-surface approximations and for quantifying when predictive frameworks must explicitly model thermodynamic segregation.
These insights generalize beyond the studied Ru-Rh-Pd-Pt-Ir system. The balance of surface segregation energetics and configurational entropy as the determinant of multicomponent catalyst surface structure is relevant for the broader class of entropy-stabilized and complex solid-solution alloys. Future theoretical models and AI-accelerated catalyst discovery pipelines must explicitly incorporate surface state reconstructions to realize accurate and transferable catalyst predictions. Experimentally, the results motivate finer atomistic characterization of catalyst surfaces, especially following realistic synthesis and operational annealing protocols.
Conclusion
Thermodynamically driven surface reconstruction, not nominal bulk composition or random surface models, governs the catalytic performance of high-entropy alloys. Short-range order and chemical segregation selectively enrich catalytically active environments at the surface, producing sharply stratified interfaces and narrowing the active-site ensemble. Homogeneous models lose validity as surface compositional deviation rises, leading to systematic predictive errors. Accurate computational catalysis in HEAs and related multicomponent systems thus requires explicit modeling of surface thermodynamics to guide reliable catalyst discovery and rational compositional engineering.