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 - 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 -