Kinetics Of Grain Boundary Segregation Research Articles

Kinetics of grain boundary segregation in multicomponent systems – The example of a Mo-C-B-O system

A model for kinetics of segregation of several interstitial and substitutional components to different kinds of traps at grain boundaries is derived by applying the Thermodynamic Extremal Principle. Evolution equations for the site fractions of the segregating elements at the grain boundary, considered as independent variables, are presented and solved numerically. The kinetic model is applied to the case of Mo containing C, O, and B as impurities and a spectrum of trapping energies obtained from first principles simulations. This newly developed model offers an efficient tool for understanding segregation from several kinds of components at different types of traps.

Ultra-fast sulphur grain boundary segregation during hot deformation of nickel

Sulphur grain boundary segregation during hot-compression of nickel (5.4wt.ppmS) is monitored using Auger electron spectroscopy and wavelength dispersive X-ray spectroscopy. The deformation conditions (temperature/deformation rate) investigated are: 550°C/0, 550°C/3×10−5s−1, 550°C/3×10−4s−1 and 450°C/3×10−5s−1. It is shown that plastic deformation accelerates the kinetics of sulphur grain boundary segregation by a factor of ∼103 to a few 105, depending on the deformation conditions. Very high levels of segregation (∼0.8 monolayer of sulphur) are obtained after very low deformation (∼5%). In addition a linear dependence of the segregation level with time and deformation is demonstrated. The segregation kinetics during plastic deformation is proportional to the deformation rate and almost independent of temperature. Several metallurgical mechanisms are discussed and confronted with the experimental results: dislocations dragging, pipe diffusion, dislocation collection/diffusion and acceleration by excess vacancies. It appears that the models developed in this work on the basis of the two latter mechanisms (dislocation collection/diffusion and acceleration by excess vacancies) predict the experimental data correctly.

Publisher’s Note: “A unified model of grain-boundary segregation kinetics” [J. Appl. Phys. 110, 063531 (2011)

Publisher’s Note: “A unified model of grain-boundary segregation kinetics” [J. Appl. Phys. 110, 063531 (2011)

A unified model of grain-boundary segregation kinetics

A unified model of grain-boundary segregation kinetics is established, which can simulate the equilibrium and non-equilibrium grain-boundary segregation kinetics during isothermal ageing. The results of model fittings/predictions are in a good consistence with those of the experiments. Values of several important parameters, such as vacancy formation energy, vacancy migration energy, and complex migration energy derived by model fittings, show a reasonably good agreement with those in the references. Relationship between the equilibrium and non-equilibrium grain-boundary segregation mechanisms is discussed in detail. The segregation peak/depletion trough observed in the non-equilibrium segregation kinetics may be ascribed to the vacancy flux. The equilibrium segregation kinetics is considered as a special case in non-equilibrium segregation kinetics with the zero vacancy flux. Both the equilibrium and non-equilibrium segregation kinetics are believed to be dominated by vacancy-solute complex flux. The proposed unified model can be a significant progress in grain-boundary segregation theory, with applications in guiding the design of materials.

A STUDY ON THE BEHAVIOR OF BORON DISTRIBUTION IN LOW CARBON STEEL BY PARTICLE TRACKING AUTORADIOGRAPHY

The behavior of the non-equilibrium grain boundary segregation of boron in low carbon steel was studied through a particle tracking autoradiography. The behavior of the non-equilibrium grain boundary segregation of boron during continuous cooling was compared with the isothermal kinetics of the non-equilibrium grain boundary segregation of boron at the holding temperature using an effective time method. On the basis of the experiments, the cooling rate dependence of the non-equilibrium segregation of boron was explained using the time dependence of the non-equilibrium segregation of boron in low carbon steel. The experimental observations for the cooling rate dependence of the grain boundary segregation of boron are in good agreement with the time dependence of the grain boundary segregation of boron. The mechanisms of the non-equilibrium segregation of boron during cooling in low carbon steel are also discussed.

Measuring grain boundary segregation using Wavelength Dispersive X-ray Spectroscopy: Further developments

A technique for the quantification of surface and grain boundary segregation using Wavelength Dispersive X-ray Spectroscopy (WDS) in the Scanning Electron Microscope (SEM) is proposed. As an example, the case of sulphur segregation in nickel is considered. The sulphur segregation can be quantified using a single voltage measurement (20 kV) of the sulphur Kα line intensity. The quantification is made from a simple proportionality equation derived from the XPP microanalysis model of correction. The result of segregation quantification by WDS is a surface concentration expressed in g.cm -2. Special attention was paid to the quantification of grain boundary segregation on fracture surfaces, taking into account the off-normal incidence of the electron beam on the analyzed surface. A simple technique that allows determination of the tilt angle from the specimen absorbed current is proposed. The influence of the azimuth angle of the analyzed surface with respect to WDS spectrometer is also discussed. The results of the WDS technique are shown to be repeatable within 5% with reasonable counting times (a few minutes per facet). As an example, the kinetics of sulphur grain boundary segregation in nickel at 750 °C was measured using WDS to document the quantitative capabilities of the technique. As already pointed out in a previous paper, it is confirmed that WDS is insensitive to surface contamination, which allows the analysis of ex-situ fractured samples.

Non-equilibrium grain boundary segregation of phosphorous during high temperature plastic deformation

The quasi-thermodynamics and the kinetics of deformation-induced non-equilibrium grain boundary segregation are described. This model is used to predict non-equilibrium segregation of P during high temperature plastic deformation in an austenite microstructure. There is a segregation concentration peak of P near 800 ℃ for a strain rate of 1×10-3 s-1 and the deformation magnitude is 20%. When the deformation reaches 20% in magnitude at 1000 ℃ the segregation of P at grain boundaries increases with increasing strain rate. The predictions are generally consistent with some available experimental observations.

Computational Program for Non-Equilibrium Grain Boundary Segregation Kinetics

The solute segregation to grain boundaries may be classified into equilibrium and non-equilibrium segregation. The models and kinetics calculation equations were proved in previous work. However, the computational task for grain-boundary segregation kinetics process is complex and cumbersome as it can involve a vast amount of numerical data. It is therefore necessary to develop an easily usable computational program which can provide the researchers with a powerful tool in grain-boundary segregation kinetics process analysis in addition to having a sound theory. A computational program of non-equilibrium grain-boundary segregation (NGS) kinetics of solute is therefore developed in this paper. It includes programs for critical time calculation, effective time calculation and diffusion coefficients calculation, the program of Auger Electron Spectroscopy test data disposal, the program of curve fitting and the program of NGS kinetics simulation. A simulation example by using the computation program of NGS kinetic equations is in good accordance with the experimental observation of phosphorus in steel 12Cr1MoV. The computational program of NGS is therefore proved to be appropriate and helpful.

Effect of Isothermal Holding Temperature on NGS Kinetics of Phosphorus and Temper Embrittlement

When failure occurs in material, it is often occurs by fracture along some grain boundaries and often by the micro-segregation of embrittling impurity to the grain boundaries. In the present work, the non-equilibrium grain-boundary segregation (NGS) kinetics of phosphorus and the temper embrittlement at the same solution treatment and different isothermal holding temperature in steel 2.25Cr1Mo are studied. The NGS kinetics curves of phosphorus at the same solution temperature （1050 oC ）and different isothermal holding temperature (540 oC and 600 oC) are given. Experimental results provide a direct evidence of NGS kinetic model and show that the grain boundary segregation concentrations of phosphorus for specimen isothermal holding at 540 oC are higher than those at 600 oC. The peak values of AES patterns of solute atoms for specimen isothermal holding at 540 oC are also higher than those at 600 oC. It is therefore concluded that the lower the isothermal holding temperature, the higher the segregation concentration of phosphorus at the grain-boundaries, and also the higher the degree of embrittlement.

High-Pressure Influence on the Kinetics of Grain Boundary Segregation in the Cu–Bi System

The effect of pressure on the kinetics of grain boundary (GB) segregation in the Cu–50 at. ppm Bi alloy has been studied. It was found by means of Auger electron spectroscopy that at a temperature of 1173 K the segregation level decreases from 2 to 1.5 monolayer as the pressure increases from 0.01 to 1.2 GPa. This behavior was explained by considering the physical parameters controlling kinetics and thermodynamics of GB segregation. A simplified model based on dislocation pipe diffusion, proposed previously and discussed in more details in this work, was used to calculate the non-equilibrium GB segregation during cooling under high pressure. The pressure effect on bulk diffusion is responsible for the suppression of GB segregation, while the pressure effect on the phase stability in Cu–Bi alloys provides a negligible contribution on GB segregation in the pressure range studied.

Study on Temper Embrittlement of Phosphorus in Steel 12Cr1MoV

According to the non-equilibrium grain-boundary segregation (NGS) kinetics curve of phosphorus, a series of Charpy impact tests was performed in an industrial steel 12Cr1MoV, at solution temperature 1050oC, with isothermal holding temperature 540oC, on specimens of different holding time (at the segregation process, the critical time, and the desegregation process respectively). The DBTT values were measured and a temper embrittlement kinetics curve was given. The reverse temper embrittlement NGS mechanism for steel 12Cr1MoV was proposed.

Experimental observation and computer simulation on non-equilibrium grain-boundary segregation kinetics of phosphorus

An experimental study and computer simulation on non-equilibrium grain-boundary segregation kinetics and the critical time for phosphorus in 12 CrlMoV steel (which is used in steam pipeline of ships) are put forward in this paper. The segregation level of phosphorus with solution temperature 1050°C at the isothermal holding temperature of 540°C, have been measured at grain-boundaries. A non-equilibrium grain-boundary segregation kinetics curve of phosphorus is given. The critical time for phosphorus non-equilibrium grain-boundary segregation is about 500 h at 540°C for the experimental steel. When the holding time is longer than 1500 h, non-equilibrium segregation disappears and the level of segregation reaches full equilibrium. The simulation using the kinetic equations of non-equilibrium grain-boundary segregation is in good accordance with the experimental observation for phosphorus in steel 12Cr1MoV. The non-equilibrium grain-boundary segregation kinetic model is therefore proved.

Kinetics of grain boundary segregation during recrystallisation annealing

In batch annealing and continuous annealing processes, both recrystallisation and grain boundary segregation can occur. In this paper, a simple model is derived which explores the interaction of the boundary migration and segregation processes and considers the application to phosphorus segregation during the annealing of interstitial free steels. The model considers both segregation to a migrating boundary and the segregation which occurs during continuous cooling after the holding period during the anneal cycle.

Precipitation related anomalies in kinetics of phosphorus grain boundary segregation in low alloy steels

It has been shown that particles of M 6C in Cr–Mo–V low alloy steels can influence phosphorus grain boundary segregation in a similar manner to Laves phase particles in 12CrMoV steel. The influence of these particles arises from their ability to dissolve non- metallic elements such as phosphorus and silicon. As phosphorus is progressively segregated to the grain boundaries during prolonged ageing, the precipitation of M 6C particles leads to an anomalous decrease in the phosphorus grain boundary concentration as the ageing time is extended. This phenomenon originally observed for the Laves phase in long-term aged 12CrMoV steel at temperatures of 753, 773, and 803 K has now been observed for M 6C carbide in a 2.5Cr–0.4Mo–0.25V low alloy steel aged at 853 K.

Experimental study on non-equilibrium grain-boundary segregation kinetics of phosphorus in an industrial steel

The non-equilibrium grain-boundary segregation level of phosphorus in an industrial steel, 12Cr1MoV, was measured. A non-equilibrium grain-boundary segregation kinetics curve of phosphorus is given, which provides direct evidence of the non-equilibrium grain-boundary segregation kinetic model proposed by Xu Tingdong.

Kinetic aspects of the grain boundary segregation in Cu(Bi) alloys

The kinetics of grain boundary segregation in Cu(Bi) alloys has been studied at temperatures of 600 and 850°C by Auger electron spectroscopy. A substantial acceleration of the grain boundary segregation kinetics in the two-phase area of the Cu–Bi phase diagram is observed. To explain this acceleration, a model of dislocation diffusion is proposed. In the framework of the model, the accelerated kinetics of grain boundary segregation in the two-phase area of the Cu–Bi phase diagram results from the microscopic pipe-like precipitation of a Bi-rich liquid phase along the dislocation cores. The dislocation diffusivities are estimated and two kinds of diagrams of the segregation kinetics are constructed.

Kinetics of grain-boundary segregation and desegregation of sulfur and phosphorus during post-irradiation annealing

A study on dynamic impurity–defect interaction in Cu-doped, P-doped and Cu–P-doped ferritic alloys all containing residual S has been made in terms of the influence of post-irradiation annealing (PIA: at 573–958 K for 0.1–1000 h) on the intergranular S and P segregation and the microhardness. In a Cu-doped alloy, which shows no P segregation, PIA produced a greater rate and magnitude of S segregation than thermal annealing (TA). Grain-boundary P enrichment was achieved during an early stage of lower-temperature PIA but not during that of TA in P-containing alloys. A Cu–P-doped alloy showed a stronger effect of the PIA on the P segregation rate than a P-doped alloy. Intergranular P desegregation and S segregation concurrently occurred at higher PIA temperatures. There was a tendency for the microhardness to increase with increasing amount of segregated P. The kinetics of the impurity segregation was analyzed using a modified McLean theory. Based on the estimated activation energies, it is shown that the S segregation in the post-irradiation-annealed Cu-doped alloy is controlled by vacancy-enhanced diffusion while the P segregation in P-containing alloys subjected to lower-temperature PIA proceeds via mobile P–interstitial complexes. By applying a Gaussian relaxation model, the P desegregation during prolonged PIA at higher temperatures was found to be assisted by the formation and migration of vacancies.

A Monte Carlo approach for the kinetics of grain boundary segregation and grain growth in binary alloys

A two-dimensional Monte Carlo approach for both impurity segregation on grain boundaries and grain growth in binary alloys is proposed. The Ising-type swamp of atom-atom pairs is imposed in a Potts lattice where the interaction of two differently oriented species is thermodynamically derived. Impurity segregation on grain boundaries and its effects on grain growth in a simplified system are simulated and discussed.

Non-equilibrium grain-boundary segregation kinetics

A new model is proposed in this article concerning non-equilibrium grain-boundary segregation kinetics. The model not only includes the isothermal non-equilibrium grain-boundary segregation kinetics but also provides a formula for calculating the non-equilibrium segregation level under continuous cooling. Results calculated from the non-equilibrium grain-boundary segregation model for boron in steel grade Type 316 and chromium in steel grade $$2\tfrac{1}{4}$$ % Cr-1 % Mo are in satisfactory agreement with the observed data for experimental measurements.

The kinetics of surface and grain boundary segregation in binary and ternary systems

Abstract A theory for the kinetics of surface segregation is proposed that takes specific account of the driving force for segregation, the different surface binding energy at the surface, and also includes the effect of saturation in the surface layer. A general solution is found and applied to the experimental results of Sn segregation in Fe obtained by Lea and Seah (1977). The theory provides a good fit to these data in contrast to the earlier equations proposed by McLean (1957). The theory is then developed for more complex situations including the segregation of two species to a grain boundary when the heat of segregation of each species is related to the surface concentration of the other. Calculations basod on the results are Bhown to display the main features of the temperature-time dependence of temper brittleness in the system Fe–Ni–P.