Representative Grain Boundaries Research Articles

Atomistic simulations and machine learning of solute grain boundary segregation in Mg alloys at finite temperatures

Understanding solute segregation thermodynamics is the first step in investigating grain boundary (GB) properties, such as strong yttrium (Y) effects on grain growth and texture evolution in micro-scale polycrystalline magnesium (Mg) alloys. To estimate the average GB segregation behavior in low-solute-concentration Mg alloys (e.g., 2 at.% Y), a state-of-the-art spectral approach is applied based on a per-site segregation energy spectrum for Y solute atoms at zero K obtained from molecular statistics (MS) simulations of ∼104 GB sites in Mg symmetric tilt GBs (STGBs). Although selected MS simulation results are consistent with verification by density functional theory (DFT) calculations, estimates of average segregation tendency based on the zero-K energy spectrum deviate from experimental observations. To resolve this problem, thermodynamic integration (TI) methods based on molecular dynamics (MD) simulations are used to determine the per-site segregation free energies of Y at representative GB sites, which show contributions beyond harmonic approximations can be important for certain GB sites at high temperatures. A surrogate model of per-site segregation free energy is constructed from a small set of TI data points using stacking cross-validation regressors and physics-informed descriptors. This model is applied to predict the Y segregation free energy spectra for thousands of GB sites in Mg STGBs with uncertainty quantification. The average segregation tendency predicted by the spectral approach based on the free energy spectra agrees well (within the uncertainty range) with experimental observations for micro-scale polycrystalline Mg alloys at typical thermomechanical processing temperatures (500 ∼ 800 K), where thermodynamic equilibrium states are likely to be achieved due to fast diffusion.

Atomistically informed phase field study of austenite grain growth

Atomistically-informed phase field simulations have been performed to investigate the effect of five common alloying elements (Nb, Ti, Mo, V, Mn) on austenite grain growth. The anisotropic simulations based on the segregation energy profiles of the solutes to four different grain boundary (GB) types from density functional theory calculations suggest a secondary role of solute drag anisotropy on grain growth. Hence, the solute trends are determined to be the same for all investigated GBs, and as a result, the Σ5(310)[001] GB can be considered as a representative GB for solute trend predictions. The decrease in grain growth rates due to solute additions is quantitatively described using a solute trend parameter. The following hierarchy of the solute’s effectiveness to retard austenite grain growth has been determined based on the results of the presented model calculations in agreement with the experimental observations: Nb>Ti>Mo>V≈Mn. The limitations and the strengths of the proposed approach are discussed in detail, and a potential application of this approach to steel design is suggested.

Representative grain boundaries during anisotropic grain growth

Conventional grain growth models do not account for the variability in grain boundary (GB) mobility, GB energy, and solute segregation energy that depend in detail on the GB structure. Instead, these parameters are typically determined empirically from experimental measurements. In this study, we present a systematic quantitative analysis that accounts for anisotropic GB properties, i.e., GB mobility and solute drag pressure to rationalize the average grain size evolution using representative GB properties under normal grain growth conditions in a non–textured system. We perform two–dimensional phase field simulations to analyze the role of (1) anisotropic mobility, (2) anisotropic segregation, and (3) combined anisotropic mobility and segregation on the average grain size evolution. A corresponding “representative GB” is introduced for each case considering a phenomenological grain growth model that fits the simulated average grain size evolution. A relationship is proposed to determine the representative GB properties for an arbitrary distribution of anisotropic GB properties in the initial microstructure. Simulations with the combined variation of GB mobility and segregation energy suggest that the representative GB mobility and segregation energy determined from independent simulations with varying either GB mobility or segregation energy can be superimposed to determine the average grain size evolution in agreement with the phase field simulations. The limits of validity, i.e., the range of moderate anisotropies, are identified where the phenomenological model with representative GB properties may be applicable, i.e., as long as a mean grain size is an appropriate descriptor of the grain structure.

Effects of local elemental ordering on defect-grain boundary interactions in high-entropy alloys

The way in which defects interact with grain boundaries (GBs) has profound influences on materials performance. In this work, we study defect-GBs interactions in a model CuNiCoFe high-entropy alloy (HEA) based on atomistic simulations. Five representative GBs are considered, namely Σ3 < 101 > {11−1} coherent twin GB, Σ5 < 103 > {010} twist GB, Σ11 < 1–10 > {113} symmetric tilt GB (STGB), Σ11 < 1–10 > {554} asymmetric tilt GB (ATGB), and Σ45 < 1–20 > {001} tilt GB. A particular focus is placed on the role of chemical disorder and local elemental segregation in influencing the defect-GBs interactions. Specifically, we compare the results obtained within an averaged atom model, the random HEA with randomly distributed elements, and the equilibrated HEA with Cu segregation after a combined Monte-Carlo/Molecular statics algorithm. For the pristine CuNiCoFe HEA without GBs, we find chemical occupancy fluctuations tend to lower the formation energies of defects, especially for interstitials because of the larger lattice distortion. For defect-GBs interactions, we find GBs strongly interact with interstitials over vacancies. We further reveal that elemental segregation can enhance the sink strength of GBs towards vacancies, but at the same time, reduce the sink strength toward interstitials. Therefore, the bias effects of GBs toward interstitials and vacancies are suppressed in HEAs due to local ordering, promoting efficient defect annihilation within the grain interiors. We highlight that the local ordering tendency and elemental segregation in HEAs play dominant roles in influencing the defect-GB interactions.

Direct Four-Probe Measurement of Grain-Boundary Resistivity and Mobility in Millimeter-Sized Graphene.

Grain boundaries (GBs) in polycrystalline graphene scatter charge carriers, which reduces carrier mobility and limits graphene applications in high-speed electronics. Here we report the extraction of the resistivity of GBs and the effect of GBs on carrier mobility by direct four-probe measurements on millimeter-sized graphene bicrystals grown by chemical vapor deposition (CVD). To extract the GB resistivity and carrier mobility from direct four-probe intragrain and intergrain measurements, an electronically equivalent extended 2D GB region is defined based on Ohm's law. Measurements on seven representative GBs find that the maximum resistivities are in the range of several kΩ·μm to more than 100 kΩ·μm. Furthermore, the mobility in these defective regions is reduced to 0.4-5.9‰ of the mobility of single-crystal, pristine graphene. Similarly, the effect of wrinkles on carrier transport can also be derived. The present approach provides a reliable way to directly probe charge-carrier scattering at GBs and can be further applied to evaluate the GB effect of other two-dimensional polycrystalline materials, such as transition-metal dichalcogenides (TMDCs).

A Predictive Framework for Dislocation-Density Pile-Ups in Crystalline Systems With Coincident Site Lattice and Random Grain Boundaries

Evolving dislocation-density pile-ups at grain-boundaries (GBs) spanning a wide range of coincident site lattice (CSL) and random GB misorientations in face-centered cubic (fcc) bicrystals and polycrystalline aggregates has been investigated. A dislocation-density GB interaction scheme coupled to a dislocation-density-based crystalline plasticity formulation was used in a nonlinear finite element (FE) framework to understand how different GB orientations and GB-dislocation-density interactions affect local and overall behavior. An effective Burger's vector of residual dislocations was obtained for fcc bicrystals and compared with molecular dynamics (MDs) predictions of static GB energy, as well as dislocation-density transmission at GB interfaces. Dislocation-density pile-ups and accumulations of residual dislocations at GBs and triple junctions (TJs) were analyzed for a polycrystalline copper aggregate with Σ1, Σ3, Σ7, Σ13, and Σ21 CSLs and random high-angle GBs to understand and predict the effects of GB misorientation on pile-up formation and evolution. The predictions indicate that dislocation-density pile-ups occur at GBs with significantly misoriented slip systems and large residual Burger's vectors, such as Σ7, Σ13, and Σ21 CSLs and random high-angle GBs, and this resulted in heterogeneous inelastic deformations across the GB and local stress accumulations. GBs with low misorientations of slip systems had high transmission, no dislocation-density pile-ups, and lower stresses than the high-angle GBs. This investigation provides a fundamental understanding of how different representative GB orientations affect GB behavior, slip transmission, and dislocation-density pile-ups at a relevant microstructural scale.