On-the-fly path planning for the design of compositional gradients in high dimensions

Functional gradients have recently experienced a surge in research activity due to advances in manufacturing, where compositions can now be spatially varied on-the-fly during fabrication. In addition, modern computational thermodynamics has reached sufficient maturity – with respect to property databases and the availability of commercial software – that gradients can be designed with specific sets of properties. Despite these successes, there are practical limitations on the calculation speeds of these thermodynamic tools that make it intractable to model every element in an alloy. As a result, most path planning is carried out via surrogate models on simplified systems (e.g., approximating Inconel 718 as Ni₅₉Cr₂₃Fe₁₈ instead of Ni₅₃Cr₂₃Fe₁₈Nb₃Mo₂Ti₁). In this work, it is demonstrated that this limitation can be overcome using a combination of on-the-fly sampling and a conjectured corollary of the lever rule for transformations of isothermal paths in arbitrary compositional dimensions. The effectiveness of this new method is quantitatively benchmarked, and it is found that it can be as much as 10⁶ times more efficient than surrogate modeling.