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Eingeladener Vortrag (wissenschaftliche Konferenzen)
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Phase diagrams serve as fundamental blueprints for comprehending material behaviour and guiding material design. However, the phase diagrams are largely available only for the bulk phases. The thermodynamic properties and phase behaviour of defects, such as grain boundaries (GBs) and phase boundaries (PBs), are equally important for the safe design of materials. Recently, we developed CALPHAD-integrated density-based phase field model (DPF) to calculate the thermodynamic data of GBs. In the model, the GB was represented by a continuous relative atomic density field with reference to a single bulk density and a Gibbs free energy functional was derived. In this work, we extend the DPF model by re-deriving the Gibbs free energy functional for PBs lying between heterogeneous bulk phases of different atomic densities. Here, we use phase-specific atomic densities to normalize the phase properties on either side of the PB such that the relative density fields are continuous across the interface. Using the model, the multi-phase interfacial thermodynamic data are obtained and related phase boundary diagrams are constructed. We study binary and ternary Fe-Mn-X alloy systems. In the Fe-Mn multi-phase boundary diagram, a shrinkage in the α-ferrite region is observed. Integrated with CALPHAD databases, the developed model may be used to calculate the segregation of solute to the PBs, paving way to manipulate segregation behaviour for microstructure design.
Phase stability in multi-components alloy systems is still largely unknown, especially at the internal interfaces. Grain boundary (co-)segregation is one of the main causes of instability and therefore safety issues in microstructures. In this work, the segregation in FCC Fe-Ni-Cr alloy system, which is the base for several steels, super-alloys and high entropy alloys, is studied. The density-based phase-field model is advanced to compute the segregation of Fe, Ni and Cr at the grain boundary corresponding to the bulk composition. Here the relative density of the grain boundary to the bulk is the mean-field parameter of the model. The necessary thermodynamic parameters of the bulk are obtained from the CALPHAD database. We performed high-throughput screening of the elemental segregation at the grain boundary across the stable bulk compositions at different temperatures (723 K, 1023 K and 1323 K). The results reveal complex enrichment/depletion of each element depending on the alloy composition and temperature. Opposite segregation of Ni and Cr and co-segregation of Ni and Fe is observed for almost all compositions at 723 K, but a changing trend is observed with increasing temperature. We discuss the origin and consequences of these segregation behaviours in the light of magnetic ordering effects.
Understanding phase stability in multicomponent alloy systems, particularly at internal interfaces, remains a major challenge in materials science. Grain boundary (co-)segregation is a critical factor influencing interfacial stability, often leading to microstructural degradation and safety concerns. In this study, we investigate segregation behavior in the face-centered cubic (FCC) Fe–Ni–Cr alloy system, a foundational system for many steels, superalloys, and high-entropy alloys. CALPHAD-integrated density-based phase-field model is extended to compute the segregation of Fe, Ni, and Cr at grain boundaries as a function of the bulk composition, with the relative GB density serving as a key parameter representing grain boundary character. A high-throughput computational screening is performed across the stable compositional space at 723 K, 1023 K, and 1323 K. The results reveal a rich and temperature-sensitive segregation landscape, with element-specific enrichment and depletion patterns that vary with alloy composition. Notably, opposite segregation trends between Ni and Cr, and frequent co-segregation of Fe and Ni, are observed at lower temperatures. The developed framework captures the coupled effects of temperature, chemical interactions, grain boundary structure, and enthalpy-entropy compensation on segregation and GB phase stability. The origin and implications of these phenomena are discussed in terms of the underlying thermodynamic driving forces.
Incorporating elasticity into the thermodynamics and phase diagrams of multi-component systems
(2025)
Elastic energy plays a critical role in determining phase stability in compositionally complex alloys. However, quantifying elastic contributions in multi-component systems and incorporating them into phase diagram construction remain challenging. In this study, we present a generalized elastic energy formalism tailored for multi-component alloys, which can be directly and efficiently integrated with CALPHAD thermodynamic databases and existing frameworks such as Thermo-Calc (Andersson et al., 2002), Pandat (Cao et al., 2009) or FactSage (Bale et al., 2016). This elasticity formalism can also be introduced as a post-processing layer in open-source software such as pyCALPHAD (Otis and Liu, 2017) and Kawin (Ury et al., 2023) , enabling elastic assessments in multi-component systems. We apply our framework for constructing the phase diagram of quinary Fe–Mn–Ni–Co–Cu alloy system, utilizing convex hull and Hessian matrix under elastic considerations. Our results reveal that incorporating elastic energy leads to an expansion of both the spinodal region and the miscibility gap. These are governed by the intricate interplay of chemical and elastic driving forces: We found that Mn and Ni contribute strongly to chemical stabilization, while Cu and Co tend to destabilize the alloy, especially at low Mn concentrations. The stabilizing effect of Fe is also pronounced in Mn-deficient regions. Acting as a destabilizing factor, the elastic energy is primarily driven by the presence of Mn, underscoring its multifaceted role in thermodynamic stability. In Mn-rich compositions, Cu markedly reduces the elastic energy contribution. Combined with CALPHAD infrastructures, the current framework offers a practical pathway to improve the predictive accuracy of phase stability and transformations in complex multi-component alloys.
Chemically complex materials (CCMats) including high-entropy alloys, oxides, and related multi-principal element systems offer a paradigm shift in materials design by leveraging chemical diversity to simultaneously optimize functional, structural, and sustainability criteria. The vastness of the compositional and structural space in CCMats propels the field into an expanding exploratory state. To reconcile functional and structural performance across this immense parameter space remains an open challenge. This Perspective evaluates the opportunities and challenges associated with harnessing chemical complexity across a broad spectrum of applications, such as hydrogen storage, ionic conductors, catalysis, magnetics, dielectrics, semiconductors, optical materials, and multifunctional structural systems. It is delineated how three central design strategies: targeted substitution (SUB), defect engineering (DEF), and diversity management (DIV) enable the reconciliation of high functional performance with long-term structural stability and environmental responsibility.
Advances in computational thermodynamics, microstructure simulations, machine learning, and multimodal characterization are accelerating the exploration and optimization of CCMats, while robust data infrastructures and automated synthesis workflows are emerging as essential tools for navigating their complex compositional space. By fostering cross-disciplinary knowledge transfer and embracing data-driven design, CCMats are poised to deliver next-generation materials solutions that address urgent technological, energy, and
environmental demands.
By evaluating the long-wavelength limit of Khachaturyan’s microelasticity theory, we show that it recovers the Kamachali–Wang continuum formulation for multi-component solid solutions [Scripta Mater 206 (2022) 114226]. A corresponding expression for the elastic energy of multi-component solid solutions under cubic anisotropy is also obtained and discussed in comparison with the isotropic case. The framework is demonstrated on the Fe–Mn–Ni–Co–Cu alloy system to perform phase stability analysis at 873 K, including spinodal and binodal part of the phase diagram. The resulting cubic-anisotropic (incoherent) phase diagrams show that the spinodal promotion is reduced compared to the isotropic case, consistent with the derivations. The limit transition is examined using a Gaussian window function, which allows the definition of a critical coarse-graining length above which the continuum description becomes valid. This study provides a rigorous microscopic foundation for continuum multi-component elastic energy formulations, with broad computational implications in thermodynamic and phase-field modeling of chemically complex alloys and microstructures.
