Grain Boundary Solute Research Articles

Solute segregation in a moving grain boundary: a phase-field approach

We present a phase-field approach for investigating monolayer and multilayer type solute segregation in a moving Grain boundary (GB). In this model, we introduce an expression for the GB solute interaction potential which allows for easy modification of the shape of the solute segregation profile at the GB. As a consequence, our phase-field simulations capture various segregation profiles in both stationary and migrating GB that agree with Cahn’s solute drag theory. Furthermore, we explore how different segregation profiles evolve at varying GB velocities owing to the inequality of the atomic flux of solute between the front and back faces of the moving GB. At a low-velocity regime, we observe that multilayer segregation results in significantly increased drag force compared to monolayer segregation. At a high-velocity regime, the opposite holds. Our simulation results also provide valuable insights for predicting grain growth in polycrystalline materials in the presence of solute segregation.

Understanding grain boundary segregation and solute drag using computational and machine learning studies

Grain boundary (GB) solute segregation has been used as a strategy to tailor the properties and processing pathways of a wide range of metallic alloys. GB solute drag results when segregated alloying elements exert a resistive force on migrating GBs hindering their motion. While GB segregation has been the subject of active research, a detailed understanding of solute drag and the migration kinetics of doped boundaries is still lacking, especially in technologically-relevant alloys. Through theoretical analysis, mesoscale modeling, and machine learning studies, we investigate GB segregation and solute drag and establish design maps relating drag effects to relevant alloy and GB properties, i.e., the complete alloy design space. We find that solute drag is dominant in immiscible alloys with far-from-dilute compositions in agreement with experimental observations of GB segregation in metallic alloys. Our analysis reveals that solute–solute interactions within the GB and the degree of segregation asymmetry greatly influence solute drag values. In broad terms, our work provides future avenues to employ GB segregation to control boundary dynamics during materials processing or under service conditions.

Correlation between stabilizing and strengthening effects due to grain boundary segregation in iron-based alloys: Theoretical models and first-principles calculations

Grain boundary (GB) segregation can drastically affect both the thermal stability and fracture strength of nanocrystalline metals. Underlying physics of the correlation between the above two aspects, however, remains unclear, since a comprehensive study addressing a variety of properties and involving a wide range of solute types seems not available. In this work, we theoretically modeled the GB segregation and strengthening energies considering both the chemical and elastic contributions of segregated solutes. Then using first-principles method, the GB segregation behaviors of twenty-six 3d, 4d and 5d transition metal atoms at three typically symmetrical tilt GBs (∑3(112), ∑5(210) and ∑5(310)), with iron as representative, were studied, where the GB segregation and strengthening energies of solutes were calculated, thus revealing their dependence on GB structures, group number and solute parameters (such as atomic radius and electronegativity). Arising from the competition between the chemical (related to the electronegativity) and the elastic (related to the atomic radius) contributions from solutes, a concave-down (concave-up) parabolic-like dependency of the GB segregation (strengthening) energy on the group number has been discovered. Furthermore, the stabilizing and the strengthening mechanisms of the segregants were revealed by analyses of bond length and charge density. The strengthening energy generally decreases with increasing the GB segregation energy, as reflected by a so-called trade-off relationship between the strengthening effect and the stabilizing effect. This work could be beneficial for understanding the GB segregation and the strengthening behaviors of the segregants in iron-based alloys and designing the iron-based alloys with comprehensively desired performances.

Revealing the structure-property relationships of amorphous carbon tribofilms on platinum-gold surfaces

Nanocrystalline metal alloys have shown great promise as electrical contact materials, given their mechanical and tribological properties. In particular, platinum-gold (Pt–Au) nanocrystalline alloys have demonstrated coefficients of friction as low as 0.01 and specific wear rates on the order of 10−9 mm3 N−1 m−1, largely due to the formation of carbon-based tribofilms at the sliding interfaces. In this study, we advance our understanding of the Pt–Au tribofilm structure-property relations and growth mechanisms via high-throughput and high-resolution measurements as a function of Pt–Au composition. As the solute content increased from 0 at. % to 10 at. % Au, cross-sectional and plan-view transmission electron microscopy demonstrated a decrease in average grain size d and an accompanied increase in grain boundary (GB) segregation. The decrease in d and increase in GB solute segregation translated to a decrease in modulus Er and an increase in hardness H as determined via nanoindentation; the Er trend was mainly described using a rule-of-mixtures approximation, whereas the H trend was ascribed to solid solution strengthening and GB stabilization. The steady state-friction μ and wear rate decreased with the addition of Au; low Au-content films showed substrate wear, while high Au-content films showed stable tribofilm growth in both macroscale and nanoscale friction tests. The carbon bonding configuration of the tribofilms was investigated by near-edge X-ray absorption fine structure spectroscopic analyses and found to be similar to that of hydrogenated amorphous carbon films. Altogether, the study provided insight into the mechanistic origins of the tribofilms, thus opening the door to tunable properties ranging from mitigation for electrical contacts to the creation of self-healing films for solid lubricants.

Universally characterizing atomistic strain via simulation, statistics, and machine learning: Low-angle grain boundaries

When applied to catalysis and related materials phenomena, grain boundary (GB) engineering optimizes over many currently disparately defined properties. Such properties include GB mobility, solute diffusivity, and catalytic footprints correlating current density with dislocation-induced strain. A recent universalizing framework has systematically classified low-Σ GBs in relation to analogous high-angle references, distinguishing them using footprints formed from the directional straining needed to reversibly yield bicrystals from their separated grains. Correlating the elastic work profiles derived from this thermodynamic process with matching changes in GB dislocations, strain footprints can comprehensively link formerly disparate catalytic properties and materials phenomena. This research investigates such structure-energy correlations to evaluate differences between low-angle (LAGBs) and high-angle (HAGBs) GBs, systematically delineating LAGB-HAGB transitions, explaining their origins, and connecting transitions to materials phenomena. A hierarchical statistical model, nesting GB degrees of freedom within one another, systematically detects such transitions via simplified strain footprints without failure of a single unique GB structure and material combination. A more comprehensive analysis of footprint directional components and discontinuities links transitions to catalytically relevant materials phenomena, describing thermal grooving, shear coupling, complexions, and defect migration under a single universal atomistic framework. With machine learning and spatially generalized strain footprints, this framework reconciles such phenomena via more comprehensive geometry-energy correlations.

CALPHAD-informed phase-field modeling of grain boundary microchemistry and precipitation in Al-Zn-Mg-Cu alloys

The grain boundary (GB) microchemistry and precipitation behaviour in high-strength Al-Zn-Mg-Cu alloys has an important influence on their mechanical and electrochemical properties. Simulation of the GB segregation, precipitation, and solute distribution in these alloys requires an accurate description of the thermodynamics and kinetics of this multi-component system. CALPHAD databases have been successfully developed for equilibrium thermodynamic calculations in complex multi-component systems, and in recent years have been combined with diffusion simulations. In this work, we have directly incorporated a CALPHAD database into a phase-field framework, to simulate, with high fidelity, the complex kinetics of the non-equilibrium GB microstructures that develop in these important commercial alloys during heat treatment. In particular, the influence of GB solute segregation, GB diffusion, precipitate number density, and far-field matrix composition, on the growth of a population of GB η-precipitates, was systematically investigated in a model Al-Zn-Mg-Cu alloy of near AA7050 composition. It is shown that the GB solute distribution in the early stages of ageing was highly heterogeneous and strongly affected by the distribution of GB η-precipitates. Significant Mg and Cu GB segregation was predicted to remain during overageing, while Zn was rapidly depleted. This non-trivial GB segregation behaviour markedly influenced the resulting precipitate morphologies, but the overall precipitate transformation kinetics on a GB were relatively unaffected. Furthermore, solute depletion adjacent to the GB was largely determined by Zn and Mg diffusion, which will affect the development of precipitate free zones during the early stages of ageing. The simulation results were compared with scanning transmission electron microscopy and atom probe tomography characterisation of alloys of the similar composition, with good agreement.

Effects of precipitates versus solute atoms on the deformation-induced grain refinement in an Al–Cu–Mg alloy

With prior knowledge of alloying additions beneficial to grain boundary (GB) stability of nanostructured metals, here we demonstrate that an artificially aged Al–Cu–Mg alloy exhibits superior grain refinement capability compared to its solution-treated counterpart after surface severe plastic deformation processing. The concurrent precipitate dissolution and GB solute segregation, together with the strong precipitate-dislocation interaction enhanced dislocation multiplication but reduced dislocation mobility, is the fundamental reason for improved grain refinement. This result offers a novel insight into the role of precipitate in deformation-induced grain refinement and a new design pathway towards nanostructured materials with smaller grains and higher hardness.

Achieving Ultrahigh Hardness in Electrodeposited Nanograined Ni-Based Binary Alloys.

Annealing hardening has recently been found in nanograined (ng) metals and alloys, which is ascribed to the promotion of grain boundary (GB) stability through GB relaxation and solute atom GB segregation. Annealing hardening is of great significance in extremely fine ng metals since it allows the hardness to keep increasing with a decreasing grain size which would otherwise be softened. Consequently, to synthesize extremely fine ng metals with a stable structure is crucial in achieving an ultrahigh hardness in ng metals. In the present work, direct current electrodeposition was employed to synthesize extremely fine ng Ni-Mo and Ni-P alloys with a grain size of down to a few nanometers. It is demonstrated that the grain size of the as-synthesized extremely fine ng Ni-Mo and Ni-P alloys can be as small as about 3 nm with a homogeneous structure and chemical composition. Grain size strongly depends upon the content of solute atoms (Mo and P). Most importantly, appropriate annealing induces significant hardening as high as 11 GPa in both ng Ni-Mo and Ni-P alloys, while the peak hardening temperature achieved in ng Ni-Mo is much higher than that in ng Ni-P. Electrodeposition is efficient in the synthesis of ultrahard bulk metals or coatings.

On the thermal stability and grain boundary segregation in nanocrystalline PtAu alloys

Grain boundary (GB) solute segregation has been proposed as a new mechanism to stabilize nanocrystalline (NC) metals. In this study, we investigate the thermal stability and GB solute segregation in a noble metal alloy system (Pt–Au). Thermal stability of the Pt.90Au.10 alloy system was evaluated by annealing a thin film (∼20 nm in thickness) at 500 °C and 700 °C as well as a thick film (∼2 µm in thickness) at a temperature range from 200 °C to 700 °C. The remarkable stability of the Pt.90Au.10 alloy system was demonstrated by comparing its thermal stability to that of pure Pt films processed under identical conditions. Although presence of voids in the GBs may contribute to thermal stability, the enhanced thermal stability of the Pt.90Au.10 alloy is mainly attributed to preferential Au segregation to GBs in the alloy film, which is revealed by aberration-corrected scanning transmission electron microscopy. Our results show that Au segregation to GBs is heterogeneous, with variation in solute content between different GBs as well as non-uniformity along individual GBs. The heterogeneity is dependent on the annealing temperature and is less pronounced at a higher processing temperatures (e.g., 700 °C). By using the noble Pt–Au system, which avoids oxidation and impurities, this study validates the mechanism of GB solute segregation and provides further understanding of the thermodynamics and kinetics underlying NC stabilization.

Tuning the microstructure and mechanical properties of magnetron sputtered Cu-Cr thin films: The optimal Cr addition

Grain boundary (GB) engineering via alloying opens a pathway to design the interfaces in alloys for tuning their mechanical properties, thus it is quite critical to determine the optimum addition of alloying element. Here, we prepared immiscible Cu-Cr alloyed thin films by non-equilibrium magnetron sputtering deposition to study Cr alloying effects on the microstructure and mechanical properties of Cu thin films. It is found that Cr doping can notably refine the grains and promote the formation of fully nanotwinned columnar grains at low Cr volume concentrations (≤∼3.7 at.%) associated with the average GB Cr concentrations ≤ ∼15 at.%, beyond which the formation of nanotwins is significantly suppressed. The role of Cr atoms/clusters played in the twinning process is rationalized in terms of dislocation rebound-promotion mechanism. Importantly, a maximum hardness is discovered at the optimum Cr addition of ∼2.0 at.%. The Cr concentration-dependent hardness of Cu-Cr alloyed films was quantified by a combined strengthening model. The achievement of the maximum hardness was related to the greatest GB solute segregation-induced strength contribution. It is further uncovered that the Cu-Cr system exhibits strain rate sensitivity (SRS, m) monotonically reduced with increasing the Cr concentration, ranging from a positive m of 0.0314 (for pure Cu) to a negative m of −0.0245, which is attributed to a competition between the dislocation-boundary interactions (increasing m) and the dislocation-solute atoms interactions (decreasing m). These findings provide valuable insights into tuning the composition of alloyed thin films to achieve optimized mechanical performance.

Grain boundary segregation in immiscible nanocrystalline alloys

Grain boundary (GB) solute segregation has been proposed as a route to mitigate grain growth in nanocrystalline (NC) metals and stabilize their grain structures. An interesting effect emerges in immiscible NC alloys due to the intertwined roles of GB segregation and bulk alloy phase separation. Based on a diffuse interface model, we examine grain growth dynamics in immiscible NC alloys, where both GB solute segregation and bulk phase separation act in conjunction. Analytical treatments identify regimes, where the reduction in GB energy due to segregation is significant. Simulation results reveal that microstructural evolution and enhanced stability are a manifestation of the competing effects of GB heat of segregation and that of bulk heat of mixing. More specifically, in systems with low GB segregation precipitation of solute-rich domains and associated GB (Zener) pinning effects lead to sluggish grain growth rates. In contrast, GB solute segregation plays a more dominant role as the heat of segregation increases in comparison with the bulk heat of mixing. On the whole, this modeling framework provides an avenue to explore the role of bulk alloy and interfacial effects on the microstructural evolution of NC metals.

Modeling solute segregation in grain boundaries of binary substitutional alloys: Effect of excess volume

The effect of excess volume in grain boundary (GB) on GB solute segregation was quantitatively evaluated by means of thermodynamic modeling. Helmholtz free energies of bulk (grain interior) and GBs in binary substitutional systems with fcc (face centered cubic) and bcc (body centered cubic) crystal structures were derived as functions of composition, temperature and atomic volume by applying Embedded-atom-method (EAM) to standard thermodynamic relations under random site occupation assumption. The equilibrium solute distribution between GBs and bulk was then obtained in terms of the parallel tangent construction between bulk and GB phases’ Helmholtz free energy curves. By modeling the CuAg (fcc) and WNb (bcc) systems, an enhanced GB segregation with increased GB excess volume was predicted. The segregation enthalpy and the solute enrichment ratio were further calculated, showing good agreements with the experimental and simulated results.

Thermodynamic properties of phase-field models for grain boundary segregation

Impurity atoms segregated in grain boundary (GB) regions can dramatically change the physical and chemical properties of the GBs. Such changes often appear to be attributed to the GB energy reduction and/or solute drag effect. Phase-field models have been utilized to clarify both the thermodynamic and kinetic effects of the GB segregation. In this study, we developed phase-field models for GB segregation that are diffuse interface versions of the classical two-phase model of GB segregation. The thermodynamic state at any point in the system is represented as a mixture of a GB phase and a matrix phase. There are two choices for the thermodynamic relation between the GB phase and the matrix phase that constitute the point: the equal composition condition in model I and the equal diffusion potential condition in model II. Most of the previous PFMs for GB segregation appear to be specific cases of model I. We examined the thermodynamic properties of models I and II, and compared them with each other and the classical two-phase model. Although all the models resulted in the same GB composition, the GB energy and its dependency on the composition at the equilibrium state are quite different from each other. In model I, there is a lower bound to the GB energy, which originates from the equal composition condition. The GB energy from model II shows no such lower bound, and it is represented as the vertical distance between the parallel tangent lines on the free energy diagram, as in the classical two-phase model. Nevertheless, the compositional dependence in the model II is quite different from that in the classical two-phase model. This originates from the different choices for the composition-independent parameter in the models: a constant gradient energy coefficient in model II and a constant GB width in the classical two-phase model. Model I is not suitable for simulations of alloys that show a reduction of the GB energy due to GB segregation below a certain limit (in dilute alloys, about half of the GB energy of pure solvents). Model II is a correct choice for such alloys.

Stabilization of nanocrystalline alloys via grain boundary segregation: A diffuse interface model

Recent experimental and theoretical findings suggest that nanocrystalline binary alloys can be stabilized against interface-driven homogenization processes via grain boundary (GB) solute segregation mechanism. However, a detailed understanding of this process requires detangling the thermodynamic aspect, GB energy, from the kinetic one, GB mobility. In this work, we present a diffuse-interface model of GB segregation in binary metallic alloys that is capable of accounting for bulk thermodynamics, interfacial energies, and the interaction of alloying elements with GBs. In addition, the model presented herein extends current treatments by independently treating solute–solute interactions within both the bulk grain and GB regions, allowing for deviations from dilute and ideal systems and the ability to account for phase separation processes occurring in conjunction with grain growth. Starting with the analytical treatment of one-dimensional (1D) systems, we investigate the dependence of the GB energy, and subsequently the driving force for grain growth, on the segregation model parameters. More specifically, classic GB segregation isotherms are recovered in the limit of 1D infinite grains. Simulation results of two-dimensional systems reveal regimes of increased thermal stability, and highlight the importance of the thermodynamic model parameters of both bulk grain and GBs on grain growth processes. In broader terms, our modeling approach provides further avenues to explore GB solute segregation and its role in stabilizing polycrystalline aggregates.

Grain Boundary Motion during Ag and Cu Grain Boundary Diffusion in Cu Polycrystals

Grain boundary (GB) motion in high-purity Cu material (5N8 and 5N Cu) is investigated using the results of radiotracer GB diffusion measurements with tracers exhibiting fundamental differences in the solute-matrix atom interactions. The results on GB solute diffusion of Ag (revealing a miscibility gap in the Ag-Cu phase diagram) and Au (forming intermetallic compounds with Cu) in Cu and on Cu self-diffusion are analyzed. The initial parts of the Ag and Cu penetration profiles turned out to be substantially curved. The profile curvature is explained via the effect of GB motion during 110m Ag and 64Cu GB penetration. The activation enthalpies of GB motion in these two independent measurements occurred to be very close, 95 and 103 kJ/mol, respectively. Moreover, these values turn out to be close, but still somewhat larger than the activation enthalpy of Cu GB self-diffusion in Cu material of the same very high purity, Q Cu gb = 72 kJ/mol. Although tracer diffusion measurements of Au GB diffusion in Cu yielded only limited information on GB motion, the absolute values of GB velocities are consistent with those calculated from the Ag and Cu GB diffusion data.

The Effect of S Segregation on the Grain Boundary Geometry of a Σ11 Nickel Bicrystal

Grain boundary (GB) solute segregation has long been associated with premature failure of engineering materials. Local changes in composition at the GBs can result in such phenomena as intergranular corrosion, temper embrittlement, intergranular fracture and fatigue as well as changes in electrical properties. The relationship between GB structure and solute segregation is not well understood.