Theoretical Study of Configurationally Disordered Bimetallic Surfaces Based on Machine Learning Force Field Aided Cluster Expansion Approach^†

Bimetallic surfaces play a pivotal role in heterogeneous catalysis, yet their theoretical modeling has long been hindered by the computational challenges of capturing configurational disorder, a critical feature governing their catalytic properties. Traditional approaches rely on oversimplified ordered surface models or restrict disorder to a few atomic layers, limiting their predictive power. Here, we present an accurate and efficient computational framework that integrates machine learning force fields (MLFFs) with the cluster expansion (CE) method to study configurationally disordered bimetallic surfaces at finite temperatures. We have developed an efficient workflow in which the MLFF is first trained iteratively via an active learning protocol, and then used to generate accurate energetic data for thousands of configurations that enable robust CE model construction. By treating bulk and surface clusters separately, we can build CE models for surface slabs with an arbitrary number of layers. Using \mathrmCu_1-x\mathrmZn_x as a case study, our CE-based Monte Carlo simulations reveal key structural insights that are relevant to the understanding of catalytic properties of \mathrmCu_1-x\mathrmZn_x surfaces. This work demonstrates how MLFF-aided CE can overcome traditional limitations in theoretical modeling of bimetallic surfaces and highlights pathways toward more realistic modeling of heterogeneous catalysts.