Kinetics of non-equilibrium grain-boundary segregation

Abstract

I. During the isothermal holding at a constant temperature after a sample is cooled quickly enough from a higher temperature a critical time exists, at which a maximum level of NGS will occur. This is the most characteristic aspect of NGS isotherm. The formula of critical time was given in Section 2 to predict the time at which maximum level of NGS will occur during the isotherm. 2. A kinetic model of NGS was suggested from Section 3 to Section 5 of this paper, which is along the same thought structure as McLean's model of EGS. A thermodynamic equation for NGS was first established describing the maximum concentration of NGS that can occur due to cooling between any two temperatures, and then an isothermal kinetic equation was established by solving Fick's equation of diffusion based on the thermodynamic equation. Based on the isothermal kinetic equation the grain boundary segregation level during cooling was calculated using effective time method and correction factor method. 3. The NGS can occur during cooling. The different cooling rates can produce different levels of NGS. There is a certain cooling rate for a kind of material, at which when the material is cooled a maximum level of NGS will appear. This cooling rate is called the critical cooling rate and is another characteristic aspect of NGS. 4. In Section 6, we suggested such a new model to describe the interactions between different kinds of solute and solute atom with vacancy for NGS: In a binary solution of 2 in solvent 3, if solute 2 has a binding energy with a vacancy beyond a suitable range for NGS to occur, then little or no NGS of solute 2 would occur in the binary. If solute 1 has a binding energy with a vacancy in a suitable range for NGS to occur in solvent 3, and if a attraction between the solute pairs 1-2 is stronger than that between pairs 1-3 or 2-3 (α' > 0), then NGS of solute 2 would also occur along with NGS of solute 1 in the ternary alloy when solute 1 is added to the 2-3 binary alloy. This is called NGCS. 5. A model for the effects of applied stress on grain boundary segregation/dilution of solute has been suggested and a set of kinetic equations have been established in Section 7. The simulation using the equations is in good accordance with the observations of sulfur and phosphorus grain-boundary segregation in steels. It is based on the following assumptions: (1) grain boundaries work as free sources of vacancies when a compressive stress is exerted on them and as free sinks when a tension stress is exerted. (2) Oversaturated vacancies induced by applied stress will be combined with the solute atoms to form complexes. (3) A flux of complexes will produce a concomitant but reverse flux of solute atoms between the grain boundary and the center. (4) The effects of applied stress, NGS/NGD, are controlled all by the balance between these two diffusion fluxes. As a result of this balance, they have a most characteristic aspect, critical time, in a manner to be similar to the NGS induced by quenching. 6. For some solute elements, which have NGS characteristic when a sample is quenched from a quenching temperature with a medium cooling rate, the resultant segregation at grain boundaries will be the sum of EGS produced at the quenching temperature and NGS produced during the quenching. Such a resultant segregation level will vary with the holding temperature when quenching rate is constant.