Bayesian Optimization of the Experimental Parameters of Material Synthesis: Application to the Magnesioreduction of Rare-Earth-Free (Mn_1–<i>x</i>Fe_<i>x</i>)₅Si₃ Magnetocalorics

Optimizing complex synthesis processes remains a significant challenge in materials science, particularly when high phase purity must be achieved in complex multivariable systems with restricted experimental throughput. Here, we demonstrate the application of a fully experimental Bayesian Optimization (BO) framework to efficiently optimize the synthesis conditions of (Mn1–xFex)5Si3, a rare-earth-free magnetocaloric material. Using magnesioreduction as the synthesis route, seven experimental parameters were iteratively refined via active learning to maximize phase purity. Phase-pure samples, including the challenging peritectoid-forming Fe5Si3, were obtained within five active learning iterations. The approach generalizes to unseen compositions and yields chemically meaningful insights via SHAP analysis of the trained Gaussian Process model, identifying maximum temperature and SiO2 excess as key drivers of phase purity. X-ray diffraction and scanning electron microscopy confirmed high crystallinity, uniform submicron grain size, and accurate compositional control in the optimized samples. Magnetic measurements revealed a near-room-temperature magnetocaloric effect in ferromagnetic Mn1.25Fe3.75Si3, with a peak −ΔSmag of 1.06 J kg–1 K–1 at 275 K under a 2 T magnetic field change. This study establishes BO as a powerful and data-efficient framework for accelerating the synthesis of functional materials from small experimental data sets.