TY - JOUR A1 - Wang, Lei A1 - Darvishi Kamachali, Reza T1 - Incorporating elasticity into CALPHAD-informed density-based grain boundary phase diagrams reveals segregation transition in Al-Cu and Al-Cu-Mg alloys N2 - The phase-like behavior of grain boundaries (GBs), recently evidenced in several materials, is opening up new possibilities in the design of alloy microstructures. In this context, GB phase diagrams are contributing to a predictive description of GB segregation and (interfacial) phase changes. The influence of chemo-mechanical solute-GB interactions on the GB phase diagram remains elusive so far. This is particularly important for multi-component alloys where the elastic interactions among solute atoms, of various sizes and bonding energies, can prevail, governing a complex co-segregation phenomenon. Recently, we developed a density-based model for GB thermodynamics that intrinsically accounts for GB elasticity in pure elements. In this work, we incorporate the homogeneous and heterogeneous elastic energies associated with the solutes into the density-based framework. We derive the multi-component homogeneous elastic energy by generalizing the continuum misfitting sphere model and extend it for GBs. The density-based free energy functional directly uses bulk CALPHAD thermodynamic data. The model is applied to binary and ternary Al alloys. We reveal that the elastic energy can profoundly affect the GB solubility and segregation behavior, leading to Cu segregation in otherwise Cu-depleted Al GBs. Consequently, GB segregation transition, i.e., a jump in the GB segregation as a function of alloy composition, is revealed in Al-Cu and Al-Cu-Mg alloy systems with implications for subsequent GB precipitation in these alloys. CALPHAD-informed elasticity-incorporated GB phase diagrams enable addressing a broader range of GB phenomena in engineering multi-component alloys. KW - Grain boundary thermodynamics KW - Density-based model KW - Al alloys KW - Grain boundary phase diagram KW - CALPHAD KW - Elastic energy PY - 2021 DO - https://doi.org/10.1016/j.commatsci.2021.110717 VL - 199 SP - 110717 PB - Elsevier B.V. AN - OPUS4-53058 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wang, Lei A1 - Darvishi Kamachali, Reza T1 - CALPHAD integrated grain boundary co-segregation design: Towards safe high-entropy alloys N2 - Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys. KW - High-Entropy Materials KW - Density-based Phase-Field Modelling KW - CALPHAD KW - Alloys' Safety PY - 2023 DO - https://doi.org/10.1016/j.jallcom.2022.167717 SN - 0925-8388 VL - 933 SP - 1 EP - 12 PB - Elsevier CY - Lausanne AN - OPUS4-56274 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Suárez Ocano, Patricia A1 - Fries, S. G. A1 - Agudo Jácome, Leonardo T1 - Thermodynamic study of a refractory complex concentrated alloy (rCCA) using the CALPHAD method N2 - Multi-principal-element alloys (MPEAs), have recently come to the attention of the scientific community due to their potential for improving properties such as, e.g. mechanical strength and oxidation resistance in high temperature structural applications. The AlMo0.5NbTa0.5TiZr refractory (r)CCA is one such candidate, showing a two-phase microstructure after a two-stage heat treatment under argon atmosphere at a controlled cooling rate. Since the application conditions intended for this alloy require a long-term high temperature (> 700 °C) mechanical and oxidation resistance, it becomes necessary to assess the possible phase development in this regime. The diagrams reveal that two BCC-based phases could form during alloy solidification, where one phase would be enriched with Mo, Nb and Ta while the other phase, with Al, Ti and Zr. Activity oxides diagrams show that a stable form of aluminum oxide (α-Al2O3, Pearson symbol: hR10, corundum) can be formed. T2 - EUROMAT 2019 CY - Stockholm, Sweden DA - 01.09.2019 KW - Chemically Complex Alloy KW - CALPHAD KW - Electromicroscopy PY - 2019 AN - OPUS4-50730 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Rizzo, F. T1 - Evaluation of nano-sized internal oxidation in a Fe-13Cr alloy exposed to water vapor atmosphere N2 - The topotactic formation of nano-sized precipitates immediately under the internal oxide layer in a Fe-13Cr alloy exposed to oxidizing water vapor atmosphere was recently reported. The precipitates were identified as lath-shaped Fe-Cr spinel exhibiting a crystallographic orientation relationship with the ferritic matrix. The authors proposed that these precipitates could act as a precursor to the formation of the spinel layer observed in the adjacent part of the oxide scale.The occurrence of internal oxidation in Fe–Cr alloys subjected to similar conditions had been previously identified and directly correlated to the presence of water vapor. In the present work, we attempt to rationalize the processes occurring during the oxidation of this alloy through thermodynamic and kinetic analyses based on the CALPHAD approach, using the geometrical representation of phase equilibria and concepts developed to describe internal oxidation. The influence of water vapor on the mechanism and kinetics of formation of the nano-sized precipitates and its role in the overall oxidation process is also considered. T2 - CALPHAD XLV The forty-fifth International Conference on CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) CY - Awaji Island, Hyogo, Japan DA - 29.05.2016 KW - Precipitation KW - Internal oxidation KW - CALPHAD KW - Topotactic transformation KW - Microscopy PY - 2016 AN - OPUS4-42156 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Murugan, Jegatheesan A1 - Darvishi Kamachali, Reza T1 - High‑throughput investigation of grain boundary segregation landscape in the Fe–Ni–Cr system N2 - 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. KW - Segregation Engineering KW - Grain boundary segregation KW - Thermodynamics KW - CALPHAD KW - Fe--Ni--Cr alloys PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-646404 DO - https://doi.org/10.1007/s10853-025-11717-5 SN - 1573-4803 SP - 1 EP - 21 PB - Springer Science + Business Media CY - Dordrecht [u.a.] AN - OPUS4-64640 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Murugan, Jegatheesan T1 - Extending Grain Boundary Phase Diagrams to Multi-Phase Boundary Diagrams N2 - 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. T2 - FEMS 2025 EUROMAT CY - Granada, Spain DA - 14.09.2025 KW - Phase boundary diagrams KW - Interface thermodynamics KW - CALPHAD PY - 2025 AN - OPUS4-64425 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Murugan, Jegatheesan T1 - Thermodynamics of Grain Boundary Segregation in Fe-Ni-Cr Alloy Systems N2 - 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. T2 - Materials Science and Engineering (MSE) 2024 CY - Darmstadt, Germany DA - 24.09.2024 KW - Segregation KW - Grain boundaries KW - CALPHAD PY - 2024 AN - OPUS4-62343 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Marschall, Niklas A1 - Murugan, Jegatheesan A1 - Darvishi Kamachali, Reza T1 - Incorporating elasticity into the thermodynamics and phase diagrams of multi-component systems N2 - 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. KW - Elastic energy KW - HEA KW - CALPHAD KW - Elastic spinodal KW - Elastic miscibility gap KW - Elastic phase diagram PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-643339 DO - https://doi.org/10.1016/j.mtla.2025.102546 SN - 2589-1529 VL - 44 SP - 1 EP - 18 PB - Elsevier CY - Amsterdam, Niederlande AN - OPUS4-64333 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Jacobson, D. A1 - Darvishi Kamachali, Reza A1 - Thompson, G. B. T1 - Extending Density Phase-Field Simulations to Dynamic Regimes N2 - Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers. KW - CALPHAD KW - Phase-field modelling KW - Phase-Field Simulations PY - 2023 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-581365 DO - https://doi.org/10.3390/met13081497 VL - 13 SP - 1 EP - 16 AN - OPUS4-58136 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Hickel, Tilmann T1 - Application of Density Functional Theory in the Context of Phase Diagram Modelling N2 - An important pillar for the modelling of phase diagrams is the availability of accurate thermodynamic data for the individual phases. While experimental calorimetry is a powerful technique, a prediction of materials behavior solely on the computer, i.e. complementary to experimental investigations, has its own advantages. It allows one to resolve uncertainties in experimental data, to develop physical thermodynamic models and to determine free energies of phases that are not stable in reality. For this purpose, density functional theory (DFT), which does not require any experimental or empirical fit parameters, is the method of choice. Its advantage is to take the quantum-mechanical solution for the electronic wave functions as a starting point, when determining the chemical bonding of atoms. In the first part of the talk, I will speak about enthalpies of formation resulting from this approach, the underlying approximations, the achievable accuracies, as well as the typical incorporation into Calphad assessments. We note, however, that a disadvantage of DFT is the restriction of the method to T = 0 K in their original formulation. Phase stabilities of real materials, on the other hand, are often dominated by processes that are due to finite temperatures. To include temperature effects in DFT, a significant method development was necessary in the last decade. In the second part of this talk, I will therefore provide the basic concepts for the calculation of vibrational, electronic, and magnetic entropy contributions. I will also highlight some recent methodological achievements in this field and show how these methods opened new routes in understanding and characterizing materials. At the end a few examples of ab initio based phase diagrams will be discussed. The focus will be on phase stabilities and microstructure formation in Ni-based materials. The advantages of combining theoretical, experimental and Calphad concepts will be particularly emphasized. T2 - MSIT Winter School on Materials Chemistry CY - Tegernsee, Germany DA - 21.01.2024 KW - Ab initio simulations KW - CALPHAD KW - Thermodynamics KW - Free energies PY - 2024 AN - OPUS4-62729 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -