Density-based phase-field modeling of grain boundary segregation and structural transitions

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, 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 (ρ), 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, from unary to multi-component systems.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.In the recent publication on Fe-Mn and in various other works 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 ρGB 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 fluctuations.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) 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.To this end, the potential of GB structural variation within the DPF model is introduced in this thesis, where the GB in-plane density ρGB is described as a field, that can vary both in time and space.This extension enables the in-plane GB density ρGB to evolve and exhibit two distinct low-energy states, denoted as ρGB = ρ₁ and ρGB = ρ₂, where ρ₂ > ρ₁.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 the 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 undergoes 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 provide insight into the range of alloy compositions where these GB phases remain stabilized. 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. 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 model's reliability, but also provides 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 ρ is established. This is achieved by a systematic coarse-graining approach wherein an atomistically-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 ρGB.The investigation revealed a linear proportional relationship between the GB excess free volume and ρGB.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 ρGB for certain classifications of GB types, therefore enhancing the model's predictive accuracy. Concurrently, the atomic-scale characteristics of GBs can be further harnessed in the DPF model 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 ρ) from molecular dynamics simulations. This way, a reliable prediction of the atomic density gradient energy coefficient for mesoscale simulations can be obtained.