Kinetics And Thermodynamics For Diffusional Phase Transformations In The Solid State

Kinetics and thermodynamics of diffusional phase transformations in the solidstate are becoming the most basic theories in the fields of materials science andprocessing, since the nucleation and growth involved in these transformations candirectly adjust the microstructure and thus tune the properties of materials. In today’scomplex transformation processes, application of traditionally classical theories willcause many contradictions and deviations. Thus, the exact theoretical descriptions, forthe interactions during the thermodynamics, kinetics and even mechanics uponsolid-state transformations, not only mean the accurate insight into the formationmechanisms of microstructure, but also mean the development of new materials withnew microstructure and properties. Therefore, this issue has crucial researchsignificance.On this basis, in the present work, the following three types of diffusionaltransformations: crystallization of amorphous alloys, precipitation of Si fromsupersaturated Al-Si and γ/α transformation of pure Fe or Fe-based alloys are selectedas research objects. This research is performed as the following principles: startingwith purely kinetic process under extreme non-equilibrium ignoring thermodynamiceffect; then switching to purely diffusion-controlled process under local-equilibrium;and finally turning to general kinetic process under near-equilibrium withconsideration of thermodynamic factors. Through the gradual relaxation of theoreticalassumptions made by traditional kinetic model, and further coupled the chemical andmechanical driving forces, this thesis will develop a series of relevant models,including the recipes to determine the kinetic mechanisms and parameters oftransformations from evaluation of the transformed fraction and the maximumtransformation rate, analytical model for anisotropic growth and its interaction withsoft-impingement, generalization of additivity rule and isokinetics indiffusion-controlled transformation and analysis for the elastic-plastic accommodationof inherent misfit strain and/or diffusion-induced strain upon interface-andmixed-controlled transformations, aimed at achieving a more profound theoreticallevel on diffusional phase transformations in solid state. The main conclusions of thepresent studies can be drawn as follows,(1) Based on an analytical transformation model, the transformed fraction andthe maximum transformation rate have been evaluated for isothermal and isochronal solid-state transformations. From the evolution of Avrami exponent n and effective activation energy Q with temperature T or transformed fraction f,the prevailing modes of nucleation, growth and impingement as well as the relevant kinetic parameters can be determined. Moreover, some recipes concerned with the conversion from non-isothermal to isothermal transformations using additivity rule and the determination of the separate activation energies for nucleation and growth are presented. The proposed recipes have been applied successfully to the crystallization kinetics of amorphous Mg-Cu-Y and Pd-Ni-P-Cu as measured by differential scanning calorimetry.(2) Following the statistical description of Johnson-Mehl-Avrami-Kolmogorov kinetics, a stochastic treatment accounting for the blocking effect arising from anisotropic growth was proposed, and analytical models for solid-state transformations where a particle undergoes1-scale blocking,κ-scale blocking and infinite-scale blocking were developed. On this basis, it was analytically proved for the first time that the classical phenomenological equation accounting for the anisotropic effect (f=1-[1+(ξ-1)xe]-1/ξ-1orresponds to an extreme case where a particle encounters infinite-scale blocking. From the model analysis, the anisotropic effect on the transformation depends on not only the non-blocking factor y but also the blocking scale k. These models were successfully applied to isothermal crystallization of amorphous Fe33Zr67ribbons.(3) Assuming pre-existing nuclei, one-dimensional growth, and linear approximation of concentration gradient, an analytic approach to describe the kinetics of diffusion-controlled transformation subjected to anisotropic effect and soft-impingement effect was presented. The anisotropic effect and soft-impingement effect are evaluated from the varying Avrami exponent. This approach is successfully applied to predict the isothermal thickening of ferrite layer in Fe-0.17wt.%C alloy at973K and isothermal transformation of austenite to allotriomorphic ferrite in0.37C-1.45Mn-0.11V microalloyed steel at913K.(4) Validity of traditional additivity rule in diffusion-controlled growth is discussed, taking the precipitation of pure Si in supersaturated Al-Si binary alloy as an example. This process has a memory of thermal history due to temperature-dependent interface concentrations. When the thermodynamics is involved, the application of additivity rule should be carefully considered. By introducing a thermal history related function, generalized isokinetic hypothesis and additivity rule involving the thermal history-dependent instantaneous reaction rate are proposed. According to the exactsolutions of diffusion-controlled growth, the generalized additivity rule is analyzed,discussed, and applied well.(5) Based on spherical inclusion, infinitesimal deformation theory anddisplacement continuous at the interphase, the corresponding stress, strain anddisplacement state in different elastic-plastic zones at different stages oftransformation were constructed, and the interaction between the misfitaccommodation and transformation was analyzed, and then solid-state transformationkinetic model coupled with chemical and mechanical driving forces was presented.Misfit strain energy van be relaxed by plastic accommodation. The mechanicaldriving force varies monotonously with f, which counteracts transformation at initialstage but favors transformation at later stage. This model was well applied to thecontinuous cooling γ→α transformation of pure iron, and the effect of misfitaccommodation on the metastable equilibrium temperature was demonstrated.(6) Concerned with mixed-mode γ→α transformation of Fe-C alloys under near-equilibrium, taking the inherent misfit strain and the diffusion-induced strain, basedon transformed fraction-dependent misfit accommodation, the diffusion equationunder stress and thermodynamic calculation, an interaction model during interfacemigration, solute diffusion and misfit accommodation was presented. The misfitaccommodation not only affects kinetic process, but also affects thermodynamics.Misfit strain energy can be relaxed further by the coupled fields of stress/strain andsolute diffusion.