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Defining heat treatments for compositionally functionally graded materials (FGMs) is challenging due to varying processing conditions in terminal alloys and gradient regions. In the present work, we studied the impact of heat treatments on phase transformations and the resulting mechanical properties along an FGM grading from stainless steel 304L (SS304L) to Inconel 625 (IN625) FGM fabricated using directed energy deposition (DED) additive manufacturing (AM). We applied heat treatments at 700 °C, 900 °C, and 1150 °C and the microstructure and hardness, as a function of layer-wise composition and applied heat treatment, were characterized. The applicability of computational methods previously developed by the team to predict experimentally observed phases by the hybrid Scheil-equilibrium approach was evaluated. This approach improves the accuracy of predicting phases formed after heat treatment compared to equilibrium thermodynamic calculations using the overall layer compositions and provides a simple pathway to assist in designing heat treatment for FGMs. 

The Fe-Nb and Fe-Nb-Ni systems are remodeled using updated sublattice models for the topologically close packed (TCP) phases of Laves_C14, δ and μ with new experimental data and first-principles and phonon calculations based on density functional theory (DFT). Experimental techniques are used to determine phase compositions and tie-lines in the Fe-Nb-Ni system. The three-, three-, and five- sublattice models are used for Laves_C14, δ, and μ phases, respectively. DFT calculations are employed to predict thermochemical data as a function of temperature for Laves_C14, δ, and μ phases. The new thermodynamic description of the Fe-Nb-Ni system includes a new hexagonal phase named - hP24 - and the updates for the Fe-Nb system and reproduces better the experimental and computational thermochemical and phase equilibrium data from the present study and the literature. The new results will improve thermodynamic predictions of TCP and other phases in both Fe-based and Ni-based alloy systems. 

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. 

It has been observed in both natural and man-made materials that volume sometimes decreases with increasing temperature. Though mechanistic understanding has been gained for some individual materials, a general answer to the question “Why does volume sometimes decrease with the increase of temperature?” remains lacking. Based on the thermodynamic relation that the derivative of volume with respect to temperature, i.e., thermal expansion, is equal to the negative derivative of entropy with respect to pressure, we developed a general theory in terms of multiscale entropy to understand and predict the change of volume as a function of temperature, which is termed as zentropy theory in the present work. It is shown that a phase at high temperatures is a statistical representation of the ground-state stable and multiple nonground-state metastable configurations. It is demonstrated that when the volumes of the nonground-state configurations with high probabilities are smaller than that of the ground-state configuration, the volume of the phase may decrease with the increase of temperature in certain ranges of temperature-pressure combinations, depicting the negative divergency of thermal expansion at the critical point. As examples, positive and negative divergencies of thermal expansion are predicted at the critical points of Ce and Fe3Pt, respectively, along with the temperature and pressure ranges for abnormally positive and negative thermal expansions. The authors believe that the zentropy theory is applicable to predict anomalies of other physical properties of phases because the change of entropy drives the responses of a system to external stimuli.