Multi-scale Study Of Thermodynamics And Kinetics Of The Phase Transformations In Metallic Materials

During the processing of metallic materials,various phase transformations occur depending on the external condition.Owing to the different transformations and atomic scale mechanisms,the products of phase transformations usually have various phases constitutions and microstructures,resulting in a variety of mechanical,physical and chemical properties.Therefore,developing the theories for phase transformations to relate the composition and processing conditions to the phases constitutions and microstructures is not only of scientific significances but also of engineering interest.Although great achievement has been made in the last few decades,the previous theories are usually based on several major assumptions and approximations,which,to a large extent,limits the applicability of the theories to engineering practice.For example,the local equilibrium at the interface or in the bulk phases are assumed,which cannot account the non-equilibrium effects in the rapid solidification;classical theories focus on dilute binary system and usually adopted ideal mixing assumption,which cannot be applied to concentrated multi-component alloys;the previous theories usually focus on a specific scale(atomic scale or mesoscopic scale)and cannot account the evolution evolving multiple length and time scale.In the current work,departing from the irreversible thermodynamics and non-equilibrium statistical mechanics,various processes in solidification and solid state transformations are modeled and first-principles calculation based density functional theory are performed,aiming to elucidate the thermodynamics and kinetics of transformations.The main conclusions are the follows,(1)A sharp interface model for rapid solidification of multi-component concentrated alloys was developed based on the thermodynamic extremal principle and the extended irreversible thermodynamics.The evolution path of the system,including diffusion in the bulk phases and the contact conditions at the interface,was determined in which local non-equilibrium effect both in the bulk phases and at the interface were considered.Applying the present model,a comparative study with the model of Ludwig was performed to show the kinetics of the steady state interface.Due to correlations among different components in the concentrated solutions,the partition coefficients of certain alloys are predicted to change non-monotonically with interface velocity,accompanied with a significant lowering of the interface temperature.Combining the non-steady state interface conditions with the present model and the model of Ludwig,the non-equilibrium transients after temperature perturbation were studied to show the evolution of the interface conditions,where the quasi-steady states are reached after a very short time span.(2)Based on the interface kinetic model for concentrated multi-component alloys,an extended morphological stability analysis was performed for a planar interface upon rapid solidification of concentrated multi-component alloys.Taken the Al-Mg-Zn alloy as an example,the stability mechanisms for the neutral Zn concentration subjected to different Mg concentrations and off-diagonal diffusion effect were clarified.Particularly for high Mg concentrations,a stage of absolute instability dependent on the Mg diffusion effect but independent of the Zn concentration happens.With this stability criterion,a model was developed for dendrite growth in undercooled concentrated multi-component alloys.An experimental study of the dendrite growth in undercooled Ni-18 at.%Cu-18 at.%Co melts was carried out and the measured interface velocities(V)were predicted well by the present model throughout the whole undercooling range(ΔT=30~313K).During dendrite growth,the partition coefficients change non-monotonically due to the interaction among the species and the change of the dendrite tip radius.The controlling mechanisms during dendrite growth were discussed according to the calculation results.(3)From the non-equilibrium solidification,solid state transformation and grain growth processes in processing of metallic materials,the effective thermodynamic driving force and the corresponding energy barrier as function of the processing conditions are analyzed empirically.All the experiments and calculations show that,for a spontaneously evolving process,the increase(decrease)of thermodynamic driving force is accompanied with the decrease(increase)of energy barrier.To quantitatively analyze the correlation between thermodynamics and kinetics,the Bain path of Fe at finite temperatures are analyzed with the ground state input from density functional calculation.The Helmholtz free energy at each c/a and volumes are calculated by the quasi-harmonic Debye-Grüneisen model and partition function approach.With the free energy surface,the minimum energy path is searched by the string method and the thermodynamics and kinetics of the Bain path is analyzed,where a correlation between the thermodynamic driving force and kinetic barrier is observed.(4)In order to develop a self-consistent theory to elucidate the physics at multiple length/time scales for first-order phase transformations,a multi-scale framework based on the probability density functional of grains is proposed to bridge the microscopic transition at the surface of the grains and the evolution of the mesoscopic system,which is governed by a Fokker-Planck equation developed using the maximal entropy production principle with the kinetic rate constants from the variational transition state theory.Applied to the precipitation of θ’ in Al-Cu alloy,free of adjustable parameters,the present model yields reasonable descriptions for the surface fluctuations at micro-scales and the coarsening behavior at meso-scales.