TY - JOUR A1 - Ikeda, Yuki A1 - Wallis, Theophilus A1 - Maaß, Robert A1 - Darvishi Kamachali, Reza T1 - Thermodynamics of grain boundary segregation transition and their relevance for liquid metal embrittlement in Fe-Zn system N2 - Grain boundaries (GBs) are common sites of failure in polycrystalline materials. Recently, a massive Zn segregation transition at Fe GBs was discovered and shown to act as a potent precursor of liquid metal embrittlement (LME) in the Fe-Zn system (Kamachali et al., Scripta Materialia 238 (2024) 115758). In this study, we elaborate on how temperature, GB type and the chemo-structurally coupled phase decomposition at the GB impact this segregation transition. CALPHAD and atomistic simulation data were utilized as inputs to conduct quantitative density-based thermodynamic modeling and phase-field simulations across various GBs, alloy compositions, and temperatures. We reveal that once the segregation transition becomes possible, the GB structural variation stabilizes spinodally formed Zn-rich phases within the GB region, with a higher tendency in disordered GBs. GB phase diagrams were constructed to identify and analyze the range of critical temperatures and alloy compositions associated with the segregation transition. The phase diagrams reveal that the miscibility gap for more disordered GB expands and, although the segregation transition is inevitable and occurs for all GBs, the barrier to triggering it is lower for more disordered GBs. Based on our thermodynamic analyses, potential processing modifications and GB engineering strategies for mitigating segregation-induced LME are thoroughly discussed. KW - Thermodynamics KW - Phase-Field Modelling KW - Steels PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-634145 DO - https://doi.org/10.1016/j.actamat.2025.121134 SN - 1359-6454 VL - 296 SP - 1 EP - 11 PB - Elsevier BV AN - OPUS4-63414 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Ikeda, Yuki A1 - Han, Seungchang A1 - Wallis, Theophilus A1 - Darvishi Kamachali, Reza A1 - Maaß, Robert T1 - On the preference of liquid-metal embrittlement along high-angle grain-boundaries in galvanized steels N2 - Focusing on the early stages of liquid-metal embrittlement (LME) of Zinc (Zn) coated advanced high-strength steels, we show that the Zn infiltration path prior to grain-boundary decohesion and therefore cracking distinctly follows high-angle grain boundaries (HAGBs). This selective transport prior to LME-induced microcracking rationalizes the experimentally observed post-mortem cracking along martensitic HAGBs. We discuss the selective Zn transport and GB-weakening in terms of an misorientation-angle dependent atomic density and diffusivity, and its effect on GB-segregation. KW - Liquid-metal embrittlement KW - Advanced high-strength steels KW - Grain boundaries PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-631103 DO - https://doi.org/10.1016/j.scriptamat.2025.116723 SN - 1359-6462 VL - 265 SP - 1 EP - 5 PB - Elsevier Inc. AN - OPUS4-63110 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wallis, Theophilus A1 - Darvishi Kamachali, Reza T1 - Linking atomistic and phase-field modeling of grain boundaries II: Incorporating atomistic potentials into free energy functional N2 - The density-based phase-field model for grain boundary (GB) thermodynamics and kinetics has offered a broad range of applications in alloy and microstructure design. Originally, this model is based on a potential energy terms that is connected to the cohesive energy of a given substance. A more rigorous approach, however, is a full consideration of an interatomic potential over the possible range of distance and therefore density. In Manuscript I of this series, we developed and thoroughly analyzed the coarse-graining of atomistic GB structures. In this work (Manuscript II), we complete the coupling between atomic and mesoscale modeling of GBs by incorporating the full interatomic potentials into the density-based free energy functional. Using GB energies calculated from atomistic simulations, the coarse-graining approach and the atomistic-integrated density-based Gibbs free energy, we effectively evaluate the density gradient energy coefficient. We found that coupling the density-based model with atomistic potentials reveal physically-sound trends in the GB equilibrium properties. A universal equation was derived to describe the potential energy contribution to the GB energy and the gradient energy coefficient for BCC-Fe and -Mo GBs, similar to the universal equation for GB excess free volume presented in Manuscript I. The proposed approach provides a mesoscale density-based model rooted in atomic-scale characteristics for reliable predictions of GB properties. KW - Density-based model KW - Phase-field KW - Grain boundary structure KW - Grain boundary thermodynamics PY - 2026 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-654904 DO - https://doi.org/10.1016/j.actamat.2025.121787 SN - 1359-6454 VL - 305 SP - 1 EP - 17 PB - Elsevier AN - OPUS4-65490 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wallis, Theophilus A1 - Ratanaphan, Sutatch A1 - Darvishi Kamachali, Reza T1 - Linking atomistic and phase-field modeling of grain boundaries I: Coarse-graining atomistic structures N2 - The longstanding gap between atomistic and mesoscale simulations partly lies in the absence of a direct, physically grounded connection between atomic structure and mesoscale fields. In this work, we present a robust coarse-graining approach to systematically investigate the connection between phase-field and atomistic simulations of grain boundaries (GBs). The atomistic structures of 408 GBs in BCC-Fe and -Mo were studies to compute and analyze a continuous atomic density field. We discover a fundamental relationship between the GB density---defined as the average atomic density at the GB plane---and the GB excess free volume, an integral property of the boundary. An almost perfect linear correlation between the GB atomic density and GB excess free volume is identified. We also show that the width of BCC GBs, when scaled by the lattice constant, approaches a universal constant value. The relationships among GB density, width, and energy are systematically examined for various GB planes, and the GB energy--density correlations are classified with respect to GB types. It turns out that the atomic planes forming the GB strongly influence both the GB density and excess volume. The current results establish a dependable framework to bridge across scales, enabling density-based phase-field modeling of GBs with atomistic fidelity and enhancing the predictive reliability of mesoscale simulations. KW - Density-based model KW - Grain boundary structure KW - Grain boundary thermodynamic KW - Atomistic simulations PY - 2026 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-654872 DO - https://doi.org/10.1016/j.actamat.2025.121786 SN - 1359-6454 VL - 305 SP - 1 EP - 14 PB - Elsevier Inc. AN - OPUS4-65487 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Wallis, Theophilus A1 - Darvishi Kamachali, Reza T1 - Grain boundary structural variations amplify segregation transition and stabilize co-existing spinodal interfacial phases N2 - Grain boundaries (GBs)’s role in determining the functional and mechanical properties of polycrystalline materials is inscribed in both their structure and chemistry. Upon solute segregation, the structure and composition of a GB can change concurrently. We study the co-evolution of GB’s structure and segregation by enhancing the density-based phase-field model to account for the in-plane structural variations in the GB. Significant mutual coupling is revealed between the GB’s chemical and structural states during Mn segregation in Fe-Mn alloys. We found that the structural degrees of freedom in a GB (the ability of the GB structure to respond to the chemical variation) amplifies Mn segregation transition, even when the GB structure stays unchanged. When the GB structure is not uniform, that is the usual case, the coupling between GB structure and segregation evolution also enables the spinodally formed low- and high-Mn phases (upon segregation transition) to co-exist within the GB region. These findings explain the stabilizing mechanism of pronounced interfacial segregation fluctuations, experimentally evidenced in Fe-Mn GBs, and give new insights on the structural sensitivity of GBs’ segregation phenomena and the mutual chemo-structural interplay. KW - Grain boundary engineering KW - Segregation engineering KW - Grain boundary structure KW - Fe-Mn steels PY - 2022 DO - https://doi.org/10.1016/j.actamat.2022.118446 SN - 1359-6454 VL - 242 PB - Elsevier Ltd. AN - OPUS4-56160 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Darvishi Kamachali, Reza A1 - Wallis, Theophilus A1 - Ikeda, Yuki A1 - Saikia, U. A1 - Ahmadian, A. A1 - Liebscher, C. A1 - Hickel, Tilmann A1 - Maaß, Robert T1 - Giant segregation transition as origin of liquid metal embrittlement in the Fe-Zn system N2 - A giant Zn segregation transition is revealed using CALPHAD-integrated density-based modeling of segregation into Fe grain boundaries (GBs). The results show that above a threshold of only a few atomic percent Zn in the alloy, a substantial amount of up to 60 at.% Zn can segregate to the GB. We found that the amount of segregation abruptly increases with decreasing temperature, while the Zn content in the alloy required for triggering the segregation transition decreases. Direct evidence of the Zn segregation transition is obtained using high-resolution scanning transmission electron microscopy. Base on the model, we trace the origin of the segregation transition back to the low cohesive energy of Zn and a miscibility gap in Fe-Zn GB, arising from the magnetic ordering effect, which is confirmed by ab-initio calculations. We also show that the massive Zn segregation resulting from the segregation transition greatly assists with liquid wetting and reduces the work of separation along the GB. The current predictions suggest that control over Zn segregation, by both alloy design and optimizing the galvanization and welding processes, may offer preventive strategies against liquid metal embrittlement. KW - CALPHAD KW - Microstructure Design KW - Grain boundary engineering KW - Steels KW - Density-based Model KW - Segregation Engineering PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-584292 DO - https://doi.org/10.1016/j.scriptamat.2023.115758 SN - 1359-6462 SN - 1872-8456 VL - 238 SP - 1 EP - 5 PB - Elsevier CY - Amsterdam AN - OPUS4-58429 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - THES A1 - Wallis, Theophilus T1 - Density-Based Phase-Field Modeling of Grain Boundary Segregation and Structural Transitions N2 - Polycrystalline materials are central to everyday engineering applications and technological advancements. The mechanical and functional properties of these materials can be influenced either negatively or positively by the presence of grain boundaries (GBs). These properties are interconnected with the structure, chemistry, or a combination of both (referred to as chemo-structure) at the GB. Therefore, an in-depth understanding of GBs, and their associated phenomena is key to tuning these materials properties for desired applications. Nevertheless, the intricate and unique characteristics of GBs impose constraints on their general descriptions in existing models designed for studying and understanding them. In this dissertation, a comprehensive tool, the CALPHAD-integrated density-based phase-field (DPF) model \cite{darvishikamachali2020model}, that harnesses atomic-scale GB characteristics, is employed and extended to reveal a deeper understanding of the GB structure, chemistry, chemo-structural coupling and their potential contributions to GB phenomena such as GB structural (and/or chemo-structural) transitions and liquid metal embrittlement. Although GBs possess distinctive crystallographic properties that render them unique and individualistic, it is important to note that they cannot exist independently; rather, they are made of the same constituents as the corresponding bulk material. To this end, the DPF model uses a continuous atomic density field ($\rho$), derived from atomistic simulations, to characterize the GB with reference to its corresponding homogeneous bulk (grain interior). This perspective allows the DPF model to approximate the GB free energy functional based on available bulk thermodynamic data. The DPF model has been utilized to investigate a variety of systems, form unary to multi-component systems \cite{kamachali2024giant,darvishikamachali2020model,darvishikamachali2020segregation,wang2021density,li2020grain,wang2021incorporating,zhou2021spinodal}. Among several novelties in the elucidation of the thermodynamics and kinetics of GBs, the DPF model has shown that GBs can have their own miscibility gap. It further reveals a temporal co-evolution of low and high segregation levels at the GB, which can act as precursor states for the formation of new phases \cite{kwiatkowskidasilva2018phase, kwiatkowskidasilva2019thermodynamics}. In the recent publication on Fe-Mn \cite{darvishikamachali2020segregation} and in various other works \cite{kamachali2024giant,darvishikamachali2020model,darvishikamachali2020segregation,wang2021density,li2020grain,wang2021incorporating,zhou2021spinodal, ikeda2023segregation, ahmadian2023interstitial} of the DPF model, the variation of atomic density field was allowed normal to the GB plane. At the GB plane, the in-plane GB density $\rho^{GB}$ was treated as a constant average value, representing its intrinsic dependence on the GB nature and misorientation. Although this assumption provides a useful simplification in studying GB phenomena, it does have the drawback of overlooking the significance of the in-plane structure variation. This seems to be particularly central in the view of experimental observations that confirm relatively stable grain boundary composition fluctuation \cite{darvishikamachali2020segregation}. In this thesis, the significance and impact of the atomic structure of GBs on their thermodynamics is investigated. This is achieved in two ways: On one hand, by extending the CALPHAD-integrated density-based free energy functional to account for structural degrees of freedom of GBs, and on the other hand, by deducing and linking density-related GB properties to the GB structure through the results of atomistic simulation of the GBs. Naturally, the structure (atomic density) within the GB plane fluctuates. This variation may also be linked to changes in composition due to solute segregation at the GB. While the fact that the GB structure can undergo transitions (referred to as complexions) \cite{frolov2015segregation, cantwell2020grain, cantwell2014grain} is not entirely new, the quantitative measurements of co-existing GB phases are scarce. Recently, instances were reported where the coexistence of two in-plane GB phases was revealed through the application of high-resolution transmission electron microscopy and atomistic simulation \cite{frommeyer2022dual, meiners2020observations}. To this end, the potential of GB structural variation within the DPF model is introduced in this thesis, where the GB in-plane density $\rho^{GB}$ is described as a field, that can vary both in time and space. This extension enables the in-plane GB density $\rho^{GB}$ to evolve and exhibit two distinct low-energy states, denoted as $\rho^{GB} = \rho_1$ and $\rho^{GB} = \rho_2$, where $\rho_2 > \rho_1$. Separating these two structural states is an in-plane line defect. This way, the model allows the studies of the co-evolution between the chemical and structural states of the GB. As a proof of concept and benchmark study, the extended-DPF model is implemented for studying Fe-Mn system. The results show that the GB structure's capacity to respond to chemical variations, as incorporated in the DPF model, enhances the Mn segregation transition at the GB, even in the absence of any alterations to the GB structure. When the GB structure undergo changes (or is non-uniform), the model reveals a coupling between the GB structure and chemical evolution. The ability of the GB structure to change allows the coexistence of spinodally formed low- and high-Mn phases within the GB during segregation transition. The acquired equilibrium segregation isotherms provides insight into the range of alloy compositions where these GB phases remain stabilised. Moreover, the observations indicate that the tendency of the GB to undergo a structural transition (change) is associated with the energy of the in-plane line defect, between low- and high-density domains within the GB plane. The extended-DPF model is further applied to Zn-coated advanced high strength steels (Fe-Zn systems), where Zn segregation to the GB is known to cause severe performance degradation due to liquid metal embrittlement \cite{razmpoosh2021pathway, ikeda2022early, bhattacharya2018liquid}. The effect of GB type and its chemo-structural coupling on Zn segregation is investigated. The results showed a sharp Zn segregation that is strongly influenced by the nature of the GB itself, as well as the coupling between its chemistry and structure. Additionally, GB phase diagrams were constructed across a wide range of alloy compositions and temperatures. The impact of the GB type and chemo-structural coupling on the miscibility gap of GBs is discussed. The DPF model's ability to incorporate atomic-scale characteristics into the construction of Gibbs free energies at the mesoscale ensures it retains key physical insights when predicting microstructure properties. To this end, a robust investigation of the model’s parameters and outputs in comparison to atomistic simulations of GBs is presented. This not only serves as a gauge for the models reliability, but also provide a new framework in establishing an atomistically-informed density-based description of GBs. First, by examining a large dataset of GBs in BCC-Fe and -Mo from atomistic simulations, a connection between their discrete atomic structure and the continuous atomic density function $\rho$ is established. This is achieved by a systematic coarse-graining approach wherein an atomsitically-obtained density function (delta function) is substituted with a normalised Gaussian function, so that, a smooth and continuous atomic density profile in real space can be obtained, where the minimum is the average atomic density at the GB plane $\rho^{GB}$. The investigation revealed a linear proportional relationship between the GB excess free volume and $\rho^{GB}$. This correlation simplifies the computation of the excess free volume as the integration over the portion of the density profile where the atomic density is less than one. Furthermore, the GB energies calculated by atomistic simulations revealed a correlation with $\rho^{GB}$ for certain classification of GB types, therefore enhancing the model's predictive accuracy. Concurrently, the atomic-scale characteristics of GBs can be further harnessed in the DPF models by replacing the simple functional form of the potential energy as given in the original DPF model formulation with a material specific interatomic potential (expressed as a function of the atomic density $\rho$) from molecular dynamic simulations. This way, a reliable prediction of the atomic density gradient energy coefficient for mesoscale simulations can be obtained. KW - Grain boundary structure KW - Grain boundary chemistry KW - Density-based phase-field modelling KW - Grain boundary thermodynamics KW - Grain boundary segregation transition PY - 2025 SP - 1 EP - 134 CY - Aachen AN - OPUS4-64455 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Wallis, Theophilus A1 - Darvishi Kamachali, Reza T1 - Density-based phase field modelling of the interplay between grain boundary segregation transition and structure N2 - Grain boundary (GB) chemical and structural variations can significantly influence materials performance. The former is generally ascribed to the structural gradient between the grain and GB. While GB segregation may be accompanied by chemical and structural variations, clear insights about the GB’s thermodynamic phase behaviour upon coupling between its chemistry and structure is lacking. Using the CALPHAD integrated density-based phase field model, we study the co-evolution of GB’s structure and segregation in Fe-Mn alloys. We found that the GB segregation transition is amplified if its structure can respond to chemical variation. Additionally, the coupling between GB structural and segregation evolution was found to enable co-existence of the spinodally formed low- and high-Mn phases within the GB. In the light of atomistic simulations, we expand on investigating the correlation between the parameters that characterise the GB density map with GB properties. T2 - TMS 2023 CY - San Diego, California, USA DA - 19.03.2023 KW - Grain boundary engineering KW - Density-based phase-field modelling KW - Microstructure design PY - 2023 AN - OPUS4-57970 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -