Ion intercalation, particularly with small ions, plays a pivotal role in a plethora of contemporary technologies, ranging from the realm of energy storage and conversion to physical neural networks in machine learning applications. The process involves the insertion and removal of ions into a host material without causing significant structural deformations. For example, in rechargeable metal-ion batteries, metal ions like lithium ions and sodium ions shuffle between the anode and cathode during charge and discharge cycles. Proton percolation in inorganic materials is adopted in various applications, for example, hydrogen storage, electrolyzers, fuel cells, and sensors. Similarly, proton transportation process is also essential in machine learning devices. Understanding the dynamics of ion intercalation is vital because it directly affects the performance, efficiency, and durability of systems. Typically, researchers harness the capabilities of density functional theory (DFT) and molecular dynamics (MD) simulations to attain fundamental understandings. Yet, the derived ion migration barriers and diffusivities are only average measures that inadequately elucidate complex intercalation mechanisms at the atomistic level, particularly in materials with complex structures and multiple dopants. Such approaches tend to overlook atomic dynamics as analyzing the typically vast simulation datasets remains a daunting task. Thus, while ion intercalation is undeniably significant, there remains much to uncover about its underlying intricacies.

This work focuses on understanding small ion intercalation dynamics in host microstructure at the electronic and atomistic levels, leveraging MD and advanced machine learning algorithms. We particularly focus on the proton intercalation process in scandium (Sc)-doped barium zirconate (BaZrO₃) perovskite lattice, denoted as H_xBZSc. MD simulations form the backbone of understanding real-time atomic interactions in our system. They provided insights by mapping the translation and reorientation jumps of protons under different operational scenarios. Given the complexity and characteristics of the trajectory data, we have applied clustering algorithms to segment the trajectory data, effectively identifying distinct patterns that highlight the dynamic interactions of protons. Additionally, visualization tools have been instrumental in deciphering these clusters, unveiling unique proton behaviors and patterns within the H_xBZSc lattice models. The identified patterns indicate the existence of potential proton transfer pathways within the lattice, offering profound insights that correlate with experimental observations such as conductivity and stability. This foundational study paves the way for the development of advanced materials by enhancing our understanding of their underlying mechanisms.