Non-equilibrium Grain-boundary Segregation Kinetics Research Articles

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.

Graphical representation for isothermal kinetics of non-equilibrium grain-boundary segregation

Abstract A model of non-equilibrium grain-boundary segregation of solute is expressed with graphs for the isothermal aging at various temperatures after quenching from a solution temperature. It is found from the graphical representations that when the samples are aged for a certain time at various temperatures there is a maximum value in the segregation concentration at a certain temperature. The aging time is equal or close to the critical time of non-equilibrium segregation corresponding to this temperature. This finding is experimentally confirmed with sulfur in an Ni-base superalloy with the aid of Auger electron spectroscopy. As an application of the new finding, a mechanism for intermediate temperature embrittlement of alloys is suggested and identified experimentally with tension tests of the superalloy.

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.

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.

Non-equilibrium grain boundary segregation kinetics of phosphorus in 12Cr1MoV steel at different solution temperatures

The non-equilibrium grain boundary segregation (NGS) concentrations of phosphorus in an industrial steel, 12Cr1MoV, at different solution temperatures, 1050 and 1300°C, were measured. The NGS kinetics curves of phosphorus at the isothermal holding temperature of 540°C are given. These results provide direct support for a NGS kinetic model, and also show that the higher the solution temperature, the higher the segregation concentration of phosphorus at the grain-boundaries, and also the longer the critical time.

Comment on “Kinetics of non-equilibrium grain-boundary segregation induced by applied tensile stress and its computer simulation”

Non-equilibrium solute grain boundary segregation, a model for which was proposed by Xu, is discussed with particular focus on the influences of atomic diffusion and microstructure on grain boundary segregation.

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.

Kinetics of non-equilibrium grain-boundary segregation induced by applied tensile stress and its computer simulation

A set of kinetic equations is offered for non-equilibrium grain-boundary segregation induced by applied tensile stress. The simulation using the equations is in good accordance with the observation of sulfur grain-boundary segregation in steel.

A kinetic model of non-equilibrium grain-boundary segregation

An isothermal kinetics of non-equilibrium grain-boundary segregation was developed both for segregation processes and for desegregation processes within a phenomenological theory. An effective time concept of a cooling process was discussed. On these bases, a simple and accurate method for evaluation of the levels of non-equilibrium grain-boundary segregation during cooling was proposed. According to the method, we have calculated the levels of non-equilibrium segregation to austenite or prior austenite grain boundaries for boron in Fe-30%Ni alloy, aluminium in Inconel 600, chromium in 2.25%Cr1%Mo steel and tin in 2.25%Cr1%Mo0.08%Sn steel in different experimental conditions respectively. Results calculated from the kinetic model in this paper are in satisfactory agreement with the observed data of experimental measurements for all the above samples.

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.