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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. 

This study presents a framework for mapping the effects of composition and phase fractions on the coefficient of thermal expansion (CTE) and elastic properties in the Al-Fe-Ni ternary, using thermodynamic phase calculations, first-principles property calculations, and experimental validation. The calculation of phase diagrams (CALPHAD) method was used to predict phases within the Al-Fe-Ni ternary, and the CTE and elastic constants of the phases were computed using DFT-based calculations, which were used to determine P-wave modulus and wave speed values. For multi-phase compositions, anticipated bulk CTE and P-wave modulus values were calculated using homogenization equations and individual phase properties. Arc-melted samples of compositions within the ternary were fabricated, and their phases, CTE, and wave speeds were measured, showing agreement with predicted phases and property trends. The approach presented in this work can be used towards property-informed design of alloys, joints, and functionally graded materials. 

Multi-phase alloys may achieve superior performance over single-phase alloys through synergistic combinations of the properties of the individual phases. An understanding of the individual phase properties aids in alloy design and optimization. However, experimental methods for directly characterizing the constitutive behavior of individual phases are limited. In this work, an inverse analysis based on representative volume element (RVE) finite element simulations was used to extract phase-wise constitutive behavior based on micrographs and macroscale constitutive response of two-phase microstructures. Both 2D and 3D RVE simulations were performed and compared to identify the most appropriate boundary conditions for the more time-efficient 2D simulations. The proposed method for extracting phase-specific constitutive behavior was validated by determining phase properties in a range of two-phase materials, including dual phase steel, steel welds, and Al-Ni alloys. This approach provides a means for extracting phase-specific mechanical properties using the microstructure, experimental tensile test data, and phase elastic moduli as input, providing insight into the contributions of individual phases to properties of multi-phase alloys toward new alloy development or microstructure optimization. 

Compositionally complex materials (CCMs), such as functionally graded materials (FGMs) made by additive manufacturing (AM) often form undesired phases or cracks, negatively affecting the build. Equilibrium thermodynamic calculations and solidification simulations, such as Scheil–Gulliver, can be used to predict feasible compositions or compositional paths, acting as constraints before empirical or machine learning models are applied to predict properties of interest. In addition, additional analysis of solidification simulations can be used to predict hot-cracking using various criteria to further account for manufacturability. To define and navigate the high order chemical systems of CCMs/FGMs, the open-source tool, AMMap, has been developed utilizing open models and CALPHAD methods for thermodynamic computation. AMMap explores spaces constructed with the nimplex library, using a novel algorithm to represent high-dimensional systems as graphs that can be joined into homogeneous structures and explored with graph traversal algorithms to automate the path-design process. This method allows the use of existing high-performance gradient descent, graph traversal search, and other path optimization algorithms to automate the path-design process with as little prior bias as possible. 

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.