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Abstract Today’s thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author’s group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined law for nonequilibrium systems presented by Hillert, the author developed the theory of cross phenomena beyond the phenomenological Onsager Theorem. The zentropy theory and theory of cross phenomena jointly provide quantitative predictive theories for systems from electronic to any observable scales as reviewed in the present work. 

Additive manufacturing (AM) can be used to fabricate functionally graded materials (FGMs) in which composition, and therefore properties, vary spatially within a component. A practical consideration for FGM fabrication is the effects of dilution. In the gradient region of vertically graded FGMs, dilution from the previous layer with a different composition from that being newly deposited can result in the composition of the newly solidified layer deviating from the feedstock composition from the nozzles. In this study, a dilution model for multi-layer FGM samples is proposed and validated experimentally with an Inconel625 (IN625)-Monel400 FGM sample. Factors that affect the deviation from the designed compositional path are discussed and methods for mitigating dilution effects to produce designed path are provided and experimentally demonstrated in a stainless steel 316 L (SS316L)-50/50 wt% SS316L/Ni-Monel400 FGM sample, aiding in precise production of the designed FGM path. 

In joining Fe-alloys and Cu-containing alloys to access the high strength of steels and corrosion resistance of Cu-alloy, cracking is widely observed due to the significant Cu microsegregation during the solidification process, resulting in an interdendritic Cu-rich liquid film at the end of solidification. By fabricating functionally graded materials (FGMs) that incorporate additional elements like Ni in the transition region between these terminal alloy classes, the hot cracking can be reduced. In the present work, the joining of stainless steel 316L (SS316L) and Monel400 by modifying the Ni concentration in the gradient region was studied. A new hot cracking criterion based on hybrid Scheil-equilibrium approach was developed and validated with monolithic multi-layer samples within the SS316L-Ni-Monel400 three-alloy system and a SS316L to 55/45 wt% SS316L/Ni to Monel400 FGM sample fabricated by direct energy deposition (DED). The new hot cracking criterion, based on the hybrid Scheil-equilibrium approach, is expected to help design FGM paths between other Fe-alloys and Cu-containing alloys as well. 

Functionally graded materials enable the spatial tailoring of properties through controlling compositions and phases that appear as a function of position within a component. The present study investigates the ability to reduce the coefficient of thermal expansion (CTE) of an aluminum alloy, Al 2219, through additions of Ti-6Al-4V. Thermodynamic simulations were used for phase predictions, and homogenization methods were used for CTE predictions of the bulk CTE of samples spanning compositions between 100 wt% Al 2219 and 70 wt% Al 2219 (balance Ti-6Al-4V) in 10 wt% increments. The samples were fabricated using directed energy deposition (DED) additive manufacturing (AM). Al2Cu and fcc phases were experimentally identified in all samples, and aluminides were shown to form in the samples containing Ti-6Al-4V. Thermomechanical analysis was used to measure the CTE of the samples, which agreed with the predicted CTE values from homogenization methods. The present study demonstrates the ability to tailor the CTEs of samples through compositional modification, thermodynamic calculations, and homogenization methods for property predictions. 

Unraveling mechanical properties from fundamentals is far from complete despite their vital role in determining applicability and longevity for a given material. Here, we perform a comprehensive study related to mechanical properties of 60 pure elements in bcc, fcc, hcp, and/or diamond structures by means of pure alias shear and pure tensile deformations via density functional theory (DFT) based calculations alongside a broad review of existing literature. The present data compilation enables a detailed correlation analysis of mechanical properties, focusing on DFT-based ideal shear and tensile strengths (τis and σit), stable and unstable stacking fault energies (γsf and γus), surface energy (γs), and vacancy activation energy (QV); and experimental hardness (HB), ultimate tensile strength (σUT), fracture toughness (KIc), and elongation (εEL). The present work examines models, identifies outliers, and provides insights into mechanical properties, for example, (i) HB is correlated by QV, σUT by γs or γus, and KIc by γs; (ii) data outliers are identified for Cr (related to τis, γs, QV, and σUT), Be (τis, γsf, γus, and QV), Hf (HB and KIc), Yb (all properties), and Pt (γsf vs. γus); and (iii) τis σit, γsf, γus, γs, QV, and HB are highly correlated to elemental attributes, while σUT, KIc, and especially εEL are less correlated due mainly to experimental uncertainty. In particular, the present data compilation provides a solid foundation to model properties such as γs and τis of multicomponent alloys and τis of unstable structures like bcc Ti, Zr, and Hf. 

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. 

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. 

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. 

Density functional theory (DFT) prescribes the existence of a ground-state configuration at 0 K for a given system. However, the ground-state configuration alone is insufficient to describe a phase at finite temperatures as symmetry-breaking non-ground-state configurations are excited statistically at temperatures above 0 K. Our multiscale entropy approach, Zentropy, postulates that the entropy of a phase is composed of the sum of the entropy of each configuration weighted by its probability plus the configurational entropy among all configurations. Consequently, the partition function of each configuration in statistical mechanics needs to be evaluated by its free energy rather than total energy. The combination of the ground-state and symmetry-breaking non-ground-state configurations represents the building blocks of materials and can be used to quantitatively predict free energy of individual phases with the free energy of each configuration predicted from DFT as well as all properties derived from free energy of individual phases.