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In this work, a long-established but sparsely documented method of obtaining semi-analytic derivatives of thermodynamic properties with respect to equilibrium conditions is briefly reviewed and rigorously derived. This procedure is then leveraged to construct general forms of derivatives of the residual driving force, a metric for measuring phase stability used in CALPHAD model optimization, with respect to overall system and individual phase compositions. Applied examples – calculating heat capacity in the Al-Fe system, thermodynamic factors in the Nb-V-W system, and residual driving force derivatives in the Ni-Ti system – demonstrate the versatility, accuracy, and extensibility of this method. Using the developed method, residual driving force gradients can be applied directly in CALPHAD model optimizers, as well as in materials design frameworks, to identify regions of phase stability with an efficient, gradient-based approach. 

Interface free energy is a fundamental material parameter needed to predict the nucleation and growth of new phases. The high cost of experimentally determining this parameter makes it an ideal target for calculation through a physically informed simulation. Direct determination of interface free energy has many challenges, especially for solid–solid transformations. Indirect determination of the interface free energy from the nucleation data has been done in the case of solidification. However, a slow on molecular dynamics (MD) simulation time scale atomic diffusion makes this method not applicable to the case of nucleation from the solid phase when precipitate composition is different from that in matrix. To address this challenge, we outline the development of a new technique for determining the critical nucleus size from an MD simulation using a recently developed method to accelerate solid-state diffusion. The accuracy of our approach for the Ni–Al system for Ni3Al (γ′) precipitates in a Ni–Al (γ) matrix is demonstrated well within experimental accuracy and greatly improves upon previous computational methods [Herrnring et al., Acta Mater. 215(8), 117053 (2021)]. 

A database for the Cr-Ni-V system was constructed by modeling the binary Cr-V and ternary Cr-Ni-V systems using the CALPHAD approach aided by density functional theory (DFT)-based first-principles calculations and ab initio molecular dynamics (AIMD) simulations. To validate this new database, a functionally graded material (FGM) using Ni-20Cr and V was fabricated using directed energy deposition additive manufacturing (DED AM) and experimentally characterized. The deposited Ni-20Cr was pure fcc phase, while increasing V content across the gradient resulted in sigma phase formation, followed by bcc phase formation. The experimentally measured phases were compared with CALPHAD computations made using a Cr-Ni-V thermodynamic database from the literature and the database developed in the present work. The newly developed database was shown to better predict the experimentally observed phases due to its accurate modeling of binary systems within the database and the ternary liquid phase, which is critical for accurate Scheil calculations. 

Abstract The design of materials and identification of optimal processing parameters constitute a complex and challenging task, necessitating efficient utilization of available data. Bayesian Optimization (BO) has gained popularity in materials design due to its ability to work with minimal data. However, many BO-based frameworks predominantly rely on statistical information, in the form of input-output data, and assume black-box objective functions. In practice, designers often possess knowledge of the underlying physical laws governing a material system, rendering the objective function not entirely black-box, as some information is partially observable. In this study, we propose a physics-informed BO approach that integrates physics-infused kernels to effectively leverage both statistical and physical information in the decision-making process. We demonstrate that this method significantly improves decision-making efficiency and enables more data-efficient BO. The applicability of this approach is showcased through the design of NiTi shape memory alloys, where the optimal processing parameters are identified to maximize the transformation temperature.