Model Of Grain Boundary Segregation Research Articles

Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach

Recent works have proposed the treatment of alloy defect states with thermodynamics analogous to phase thermodynamics, so they can be analyzed in a manner that is comparable to bulk phase diagrams. We refer to such diagrams containing both bulk phase and defect state information as “phase-and-defect diagrams.” Segregated grain boundaries (GBs) are an example of one such defect state, which enable, for example, the stabilization of nanocrystalline alloys. The recent development of spectral thermodynamic isotherms has demonstrated that a fully spectral description, which captures the complete distribution of local atomic environments in the grain boundary network, is necessary for accurate modeling of segregation behavior. To our knowledge, there is currently no spectral free energy formulation from which a phase-and-defect diagram of the segregated polycrystalline state can be produced. In this work, we present a spectral regular solution model of grain boundary segregation, from which we derive an analytical free energy function for the segregated polycrystalline state. We then use this free energy representation to construct a phase-and-defect diagram for a hypothetical alloy system, providing a framework for future efforts in developing spectral phase-and-defect diagrams.

Improved Al-Mg alloy surface segregation predictions with a machine learning atomistic potential

Various industrial/commercial applications use Al-Mg alloys, yet the Mg added to Al materials, to improve strength, is susceptible to surface segregation and oxidation, leaving behind a softer and Al-enriched bulk alloy. To better understand this process and provide a systematic methodology for investigating dopants that can mitigate corrosion, we have developed a robust atomistic deep neural net potential (DNP) using a dataset generated with first-principles density-functional theory (DFT). The potential, validated systematically against DFT values, has been shown to have a high fidelity in calculating different elemental and intermetallic Al-Mg systems' properties. Our calculations predict a linear trend in the formation energy of the Al-Mg alloy and its density as a function of temperature, consistent with experimental literature. Employing the DNP within a hybrid Monte Carlo and molecular dynamics (MC/MD) approach, we predict anisotropic surface segregation for Al-Mg alloys such that (111)(100)(110), with (111) surfaces displaying the lowest segregation enthalpies and Mg enrichment. Furthermore, we model the segregation tendencies by adapting a recently introduced isotherm model for grain boundary segregation. Our results show that this model describes the MC/MD segregation profiles with higher fidelity than the McLean and Fowler-Guggenheim isotherm models.

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.

Solute segregation at 46.8°(111) twist grain boundary of a phosphorus doped Fe–2.3%V alloy

The Auger electron spectroscopy study on chemistry of the 46.8°(111) twist grain boundary of an Fe–2.3%V alloy showed an extended phosphorus enrichment at temperatures in range of 500°C and 800°C. Simultaneously, slight but nearly independent segregation of vanadium was also detected. The standard enthalpy and entropy of grain boundary segregation of phosphorus and vanadium were determined according to the Guttmann model of multicomponent interfacial segregation. Obtained data clearly show that this Σ=19 coincidence boundary is special (i.e. low energy interface). The data also fit well with the predictive model of grain boundary segregation and confirm that phosphorus segregates interstitially at the grain boundary while vanadium substitutes iron atoms in the interface structure.

Comparison between Kinetic and Thermodynamic Effects on Grain Growth in Nano-Scale Materials

A detailed comparison between kinetic and thermodynamic effects on grain growth in nanocrystalline Gd doped ceria ceramics was given. From the thermodynamic standpoint, the evolution of grain size with annealing time can be described using an analytical model for grain boundary segregation upon isothermal grain growth. From the kinetic standpoint, the single isothermal grain growth can be understood in terms of a single, thermally-activated rate process with constant grain boundary energy, σb. The solute excess in grain boundaries increases with grain growth and tends to its saturated value, therefore, the inhibition of grain growth can be attributed to the reduction of grain boundary energy σb through solute segregation.

Effects of Soluble Ti and Zr Content and Austenite Grain Size on Microstructure of the Simulated Heat Affected Zone in Fe–C–Mn–Si Alloy

The effect of soluble Ti and Zr contents on the microstructure in a simulated heat affected zone of a Fe-0.05mass%C-1.5mass%Mn-0.20mass%Si alloy was studied. This was done as a function of the austenite grain size as well as the number and size of TiN, Ti2O3, MgO(+Ti2O3), TiN(+MgO) and ZrO2(+Ti2O3) particles under different peak temperature (1300 and 1400°C), peak holding time (0, 60 and 600 s) and a constant time of cooling (70 s) from 800 to 500°C. The effectiveness of inclusion phases for intragranular ferrite (IGF) formation was studied from the area fraction of IGF for a given austenite grain size and soluble Ti content. For a given austenite grain size, the primary ferrite decreases and the IGF increases with an increased soluble Ti content up to about 100 ppm. After going through a maximum the replacement of IGF by lath bainitic ferrite occurs with an increased soluble Ti content. It is found that the effect of soluble Zr content on the microstructure is much stronger than that of a soluble Ti content. The area fraction of IGF decreases gradually with an increase in the austenite grain size (50–1000 μm) for a given soluble Ti content (50–400 ppm). By using the hardenability parameter based on the non-equilibrium grain-boundary segregation model, it is observed that the IGF formation is encouraged in the following order: TiN>{Ti2O3, MgO(+Ti2O3)}>ZrO2(+Ti2O3).

A new model of grain-boundary segregation with the formation of atomic complexes in a grain boundary

The process of grain-boundary segregation (GBS) has been considered under an assumption that the formation of associates (atomic complexes with a composition that corresponds to the nearest chemical composition in the phase diagram) is possible in a grain boundary (GB). The grain boundary is considered as a two-component mixture of A and B atoms, which can exist both in free and bound states (bound in a complex). The formation of complexes with an arbitrary composition and complexes of an AB type have been considered. It has been shown that, even in the absence of segregation (b = 1), the interactions of atoms in a GB that induce the formation of complexes leads to an enrichment of GBs in impurity atoms. It has been demonstrated that under certain conditions, a GBS isotherm can exhibit saturation corresponding to the chemical composition of the complex.

Concentration phase transition associated with grain boundary segregation in systems with restricted solubility

Abstract A new model of grain boundary segregation in systems with restricted solubility is proposed. The model is based on the following assumption: As soon as the solute concentration in the grain boundary achieves the bulk solubility limit, embryos of compounds appear in the grain boundary. The composition of these embryos corresponds closely with the nearest phase in the grain according to the phase diagram. The appropriate segregation isotherm taking into account these embryos demonstrates the concentration phase transition which shows itself as a jump in grain boundary concentration. The location and the height of this jump are discussed.

Grain boundary segregation and thermodynamically stable binary nanocrystalline alloys

A free-energy function for binary polycrystalline solid solutions is developed based on pairwise nearest-neighbor interactions. The model permits intergranular regions to exhibit unique energetics and compositions from grain interiors, under the assumption of random site occupation in each region. For a given composition, there is an equilibrium grain size, and the alloy configuration in equilibrium generally involves solute segregation. The present approach reduces to a standard model of grain boundary segregation in the limit of infinite grain size, but substantially generalizes prior thermodynamic models for nanoscale alloy systems. In particular, the present model allows consideration of weakly segregating systems, systems away from the dilute limit, and is derived for structures of arbitrary dimensionality. A series of solutions for the equilibrium alloy configuration and grain size are also presented as a function of simple input parameters, including temperature, alloy interaction energies, and component grain boundary energies.

Grain-boundary segregation in binary alloys

Results of experimental studies of grain-boundary segregation in binary alloys have been considered and analyzed. The model of grain-boundary segregation and an isotherm that allows for the possibility of the formation of complexes in grain boundaries have been suggested.

An atom probe tomography study of grain boundary segregation in nanocrystalline Ni-W

AbstractAtom probe tomography is used to observe the solute distribution in electrodeposited nanocrystalline Ni-W alloys with three different grain sizes (3, 10, and 20 nm) and the results are compared with atomistic computer simulations. The presence of grain boundary segregation is confirmed by detailed analysis of composition fluctuations in both experimental and simulated structures, and its extent quantified by a frequency distribution analysis. In contrast to other nanocrystalline alloys, the present Ni-W alloys exhibit only a subtle amount of solute segregation to the intergranular regions. This finding is consistent with quantitative predictions for these alloys based upon a thermodynamic model of grain boundary segregation.

Solute segregation at grain boundaries of a partially ordered Fe3Al base alloy

AbstractThe equilibrium chemical composition of grain boundaries in a polycrystalline FeAlCr ordered alloy was studied using AES at intergranular fracture surfaces. It was found that the grain boundaries are slightly enriched in aluminium and chromium. The temperature dependence of grain boundary segregation was correlated according to a recently proposed model of grain boundary segregation in ordered alloys that provides the values of enthalpy and entropy of grain boundary segregation of aluminium (ΔHAl0 = −11.5 ± 0.5 kJ/mol, ΔSAl0 = −7.5 ± 0.5 J/mol.K) and chromium (ΔHCr0 = −8 ± 2 kJ/mol, ΔSCr0 = −4 ± 2 J/mol.K) in α‐iron. These values are in agreement with predictions of grain boundary segregation parameters. Copyright © 2004 John Wiley & Sons, Ltd.

Solute segregation transition and drag force on grain boundaries

We investigate solute segregation and transition at grain boundaries and the corresponding drag effect on grain boundary migration. A continuum model of grain boundary segregation based on gradient thermodynamics and its discrete counterpart (discrete lattice model) are formulated. The model differs from much previous work because it takes into account several physically distinctive terms, including concentration gradient, spatial variation of gradient-energy coefficient and concentration dependence of solute–grain boundary interactions. Their effects on the equilibrium and steady-state solute concentration profiles across the grain boundary, the segregation transition temperature and the corresponding drag forces are characterized for a prototype planar grain boundary in a regular solution. It is found that omission of these terms could result in a significant overestimate or underestimate (depending on the boundary velocity) of the enhancement of solute segregation and drag force for systems of a positive mixing energy. Without considering these terms, much higher transition temperatures are predicted and the critical point is displaced towards much higher bulk solute concentration and temperature. The model predicts a sharp transition of grain boundary mobility as a function of temperature, which is related to the sharp transition of solute concentration of grain boundary as a function of temperature. The transition temperatures obtained during heating and cooling are different from each other, leading to a hysteresis loop in both the concentration–temperature plot and the mobility–temperature plot. These predictions agree well with experimental observations.

Characterization of phosphorus segregation in neutron-irradiated Russian pressure vessel steel weld

An atom probe field ion microscopy characterization of three Russian pressure vessel steels has been performed. Field ion micrographs of several lath boundaries have indicated that they are decorated with a semicontinuous film of discrete brightly-imaging precipitates that were identified as molybdenum carbonitrides. In addition, extremely high phosphorus levels were measured at the lath boundaries. The phosphorus was found to be confined to an extremely narrow region indicative of monolayer type segregation. The phosphorus coverage determined from the atom probe results of the unirradiated materials agree with predictions based on McLean's equilibrium model of grain boundary segregation. The boundary phosphorus coverage of a neutron-irradiated weld material was significantly higher than in the unirradiated material. Ultrafine darkly-imaging copper- and phosphorus-enriched precipitates were also observed in the matrix of the neutron-irradiated material.

Atom probe analysis of interfacial segregation

A discussion of the application of the atom probe technique to the characterization of the solute segregation to interfaces is presented. Methods based on simple geometrical models for all boundary orientations in the field ion specimen and on the Gibbsian interfacial excess are presented. Atom probe results for phosphorus segregation in two Russian pressure vessel steels were found to be in good agreement with the predictions based on McLean's model of grain boundary segregation.

Alloy thermodynamics in nanostructures

The importance of the interactions between alloy atoms and topological defects for the thermodynamic properties of nanostructured alloys is pointed out. The McLean model for grain boundary segregation is extended to yield an expression for the total Gibbs free energy of an alloy polycrystal. This provides a simple conceptual basis for a qualitative discussion of the thermodynamic properties of nanocrystalline alloys. It is demonstrated that certain alloy poly- or nanocrystals may reach a metastable state, where the alloy is stable with respect to variation of its total grain boundary area.

Characterization of Phosphorus Segregation in Neutron-Irradiated Pressure Vessel Steels by Atom Probe Field Ion Microscopy

AbstractAn atom probe field ion microscopy characterization of A533B and Russian VVER 440 and 1000 pressure vessel steels has been performed to determine the phosphorus coverage of grain and lath boundaries. Field ion micrographs of grain and lath boundaries have revealed that they are decorated with a semi-continuous film of discrete brightly-imaging precipitates that were identified as molybdenum carbonitride precipitates. In addition, extremely high phosphorus levels were measured at the boundaries. The phosphorus segregation was found to be confined to an extremely narrow region indicative of monolayer-type segregation. The phosphorus coverages determined from the atom probe results of the unirradiated materials were in excellent agreement with predictions based on McLean's equilibrium model of grain boundary segregation. The boundary phosphorus coverage of a neutron-irradiated weld material was significantly higher than that observed in the unirradiated material.

A new computer model of grain boundary segregation

Improvements have been made to an earlier model of grain boundary segregation. The new model includes an influx of vacancies into the region of the material considered by the model, and accounts for the effect of a grain boundary on defect-binding energies. The model predictions for boron segregation in steel are compared with the original model.

Thermomagnetic analysis, annealing effects, and Cr distribution in CoCr sputtered films

Thermomagnetic analyses (TMA) of rf-sputtered CoCr films have shown unusual magnetization versus temperature behavior. On heating, magnetization persists to around 700 °C. After cooling from 800 °C, however, magnetization does not appear again until around 300 °C. On all subsequent heatings and coolings, such films retain a Curie temperature of around 300 °C. At the same time, room-temperature Ms values decrease considerably. TMA of bulk samples of the same composition show a Curie temperature around 300 °C and no subsequent change of Curie temperature upon heating and cooling. These data cannot be explained on the basis of Cr-rich oxide formation. Additional experiments have ruled out Cr segregation in a planar transition layer. X-ray and electron diffraction measurements have shown no evidence of long-range order-disorder phenomenon. However, the data are consistent with explanations involving either Cr grain-boundary segregation or atomic-scale redistribution of the Cr. A simple model of grain-boundary segregation has been developed which predicts the expected relationship of average composition and Cr-rich grain boundary width. Minimum widths and minimum composition differences can be calculated.