Mechanisms and modelling of diffusion in solids: a multiscale framework with industrial case studies and AI enhancements

Diffusion in solids is a fundamental mechanism governing mass transport, phase transformations, and microstructural evolution in metals, alloys, and functional materials. This review presents a comprehensive overview of key atomic-scale diffusion mechanisms, including substitutional, interstitial, grain boundary, and surface/pipe pathways, within the classical framework of Fick’s steady-state and non-steady-state laws. The roles of temperature, crystal structure, defect density, and concentration gradients in controlling diffusivity are critically analyzed, with emphasis on activation energies and transport regimes. The limitations of classical Fickian models at the nanoscale are examined, where transport often deviates from equilibrium behaviour and becomes dominated by interfaces, anisotropy, and confinement effects. Addressing these challenges requires alternative modelling frameworks and multiscale simulation strategies. Recent advances are highlighted in computational-experimental integration, including first-principles calculations, phase-field modelling, and in situ characterization under service-relevant conditions. The review also explores the emerging role of artificial intelligence (AI) and machine learning (ML) in predicting diffusion coefficients, activation barriers, and optimal processing conditions. These tools enable inverse design workflows and are increasingly applied in surface treatment design, grain boundary engineering, and coating development. Case studies in carburization, alloy homogenization, and high-temperature coating systems illustrate how diffusion modelling informs real-world process optimization. Looking forward, the convergence of physics-based models, AI-driven analytics, and experimental feedback loops is expected to accelerate the development of diffusion-aware materials design strategies, advancing applications in structural alloys, protective coatings, and digital manufacturing.