Decoding solute-vacancy binding in transition metals via first-principles and machine learning

Traditional solute-vacancy binding energy (SVBE) models based on atomic radii or electronegativity fail for transition metals. Through first-principles analysis, we show SVBE comprises solute-host bond energy and vacancy relaxation energy. For main-group solutes, both components align with parabolic trends, yielding predictable SVBE. In transition metals, solute-host bond energy remains parabolic, but vacancy relaxation energy shifts its peak due to d-orbital splitting-induced lattice distortion asymmetry, leading to non-parabolic SVBE. This coupling resolves historical discrepancies across alloy systems. A complementary data-driven approach identifies key electronic descriptors. The framework provides a universal principle for solute selection in diffusion-controlled alloy design.