Trigonometric gradient microstructures in additively manufactured single crystals enable strength-ductility synergy and programmable performance.

Additively manufactured (AM) single crystals (SXs) show great promise for extreme-environment applications. AM process enhances gradient microstructures around dendrites, including dislocation densities, matrix channel width, precipitate area, and elemental concentrations. Here, we leverage a unified trigonometric function describing all gradient microstructures in AM SXs, to quantify their effects and enable programmable performance. We reveal that trigonometric gradient microstructures (TGMs) can overcome strength-ductility trade-off, particularly at elevated temperatures. In contrast, conventional gradient microstructures requiring post-treatment improve strength at the expense of ductility. This benefit is attributed to the superposition relationship between initial density-graded dislocations and other TGMs, rather than geometrically necessary dislocations in conventional understanding. High-throughput simulations reveal linear correlations between TGM intensity and mechanical properties. By mapping performance against TGMs, we can tailor strength and elongation by tuning TGMs. This study deepens the understanding of gradient microstructures around columnar dendrites in AM alloys and provides guidance for tailoring mechanical properties.