Seong Gyoon Kim

Phase-field model for solidification of ternary alloys coupled with thermodynamic database

Abstract A phase-field model coupled to real thermodynamic data in which the vanishing kinetic coefficient condition is proposed. The validity of the model is examined by comparing the calculated result of the equilibrium state with theoretical predictions for both one and two-dimensional simulations. Numerical simulations of micro-segregation and isothermal dendrite growth is presented to demonstrate the effectiveness of the model.

A phase field model for the solute drag on moving grain boundaries

Abstract We propose a model based on a phase-field approach to study the effect of the solute drag on moving grain boundaries in a binary alloy system. By considering the grain boundary as a distinguishable phase and adopting a “segregation potential” in the grain boundary region, the effect of solute drag is automatically incorporated into the model. It is shown at equilibrium that the model can reproduce the equilibrium solute segregation and Gibbs adsorption. It is also demonstrated at a one-dimensional steady state that the model includes both the solute drag proposed by Cahn and the free energy dissipation by Hillert and Sundman. In the dilute solution limit, the simple expressions for the concentration distribution around the interfacial region and the solute drag are obtained as functions of boundary velocity, diffusivity and segregation potential and they are found to be consistent with the previous theories for solute drag phenomenon. In two-dimensional quasi steady state, the phase field model reduces to the relationship between normal velocity and the curvature of the boundary and the relationship between phase field mobility and the grain boundary mobility is obtained.

Phase-field model of dendritic growth

Abstract The phase-field models for binary and ternary alloys are introduced, and the governing equations and phase-field parameters for dilute alloys are derived at a thin interface limit. The phase-field simulations on isothermal dendrite growth for Fe-C, Fe-P and Fe-C–P alloys are carried out and the effect of the ternary alloying element on dendrite growth is examined. The secondary arm spacing for Fe-C, Fe-P and Al–Cu alloys is numerically predicted using the phase-field model and compared to the experimental data. The change in the arm spacing, and the exponent of local solidification time depending on alloy is systematically examined by imposing artificial set of physical properties. The phase-field simulation for the microstructure evolution during rapid solidification is also successfully carried out. Through the numerical examples, the wide potentiality of the phase-field model to the applications on solidification has been demonstrated.

Phase-field model for solidification of Fe–C alloys

Abstract The phase–field model for binary alloys by Kim et al. is briefly introduced and the main difference in the definition of free energy density in interface region between the models by Kim et al. and by Wheeler et al. is di cussed. The governing equations for a dilute binary alloy are derived and the phase-field parameters are obtained at a thin interface limit. The examples of the phase–field simulation on Ostwald ripening, isothermal dendrite growth and particle/interface interaction for Fe–C alloys are demonstrated. In Ostwald ripening, it is shown that small solid particles preferably melt out and then large particles agglomerate. In isothermal dendrite growth, the kinetic coefficient dependence on growth rate is examined for both the phase-field model and the dendrite growth model by Lipton et al. The growth rate by the dendrite model shows strong kinetic coefficient dependence, though that by the phase–field model is not sensitive to it. The particle pushing and engulfment by interface are successfully reproduced and the critical velocity for the pushing/engulfment transition is estimated. Through the simulation, it is shown that the phase-field model correctly reproduces the local equilibrium condition and has the wide potentiality to the applications on solidification.

Phase-field modeling for facet dendrite growth of silicon

Abstract Dendrite growth of silicon from its undercooled melt was investigated by using the phase-field model for a faceted crystal with anisotropic interfacial energy. The phase-field parameters at the thin interface limit were derived and used in the simulation. The accuracy of the model was estimated from the calculated equilibrium interface shape. The errors in anisotropy and Gibbs-Thomson coefficient were within 1% and 10%, respectively. The growth of a silicon crystal from its undercooled melt has been analyzed and it is shown that the shape of growing crystal changes from square-like to dendritic with increase of undercooling. In a facet dendrite growth the tip grows keeping its shape and the shape is the same regardless of undercooling or growth velocity. It is also shown that there exists the scaling law between the characteristic length of the tip and growth velocity similar to that of a non-facet dendrite.

Phase-field modeling for 3D grain growth based on a grain boundary energy database

A 3D phase-field model for grain growth combined with a grain boundary (GB) energy database is proposed. The phase-field model is applied to a grain growth simulation of polycrystalline bcc Fe to investigate the effect of anisotropic GB energy on the microstructural evolution and its kinetics. It is found that the anisotropy in the GB energy results in different microstructures and slower kinetics, especially when the portion of low-angle, low-energy GBs is large. We discuss the applicability of the proposed phase-field simulation technique, based on the GB or interfacial energy database to simulations for microstructural evolution, including abnormal grain growth, phase transformations, etc., in a wider range of polycrystalline materials.

Abnormal Grain Growth Induced by Boundary Segregation of Solute Atoms

Abnormal grain growth (AGG) proceeds in case that normal grain growth is inhibited. It has long been known that the inhibition involves finely dispersed particles and/or the development of specific textures. There is another strong obstacle against the grain boundary (GB) motion; the solute atoms can reduce their energy by moving from the bulk into a GB. Resultant interaction between the solute atoms and a GB makes the GB motion more difficult. However the role of the GB segregation effect on AGG has not been clarified. In this study we simulate the 2D and 3D grain growth accompanying boundary segregation of solute atoms by using a phase-field model. It is shown that the segregation plays an important role on the occurrence of AGG. The boundary-segregation-induced AGG can take place when the average driving force of grain growth approaches a critical condition for pinning-depinning transition in solute-drag atmosphere.

Faceted dendrite growth of silicon from undercooled melt of Si–Ni alloy

Abstract Two-dimensional faceted dendrite growth of silicon from undercooled melt of Si–6 wt%Ni alloy was experimentally investigated, in which molten alloy film from 10 to 20 mm in thickness was undercooled up to 115 K and growing dendrites were observed in situ. Both the in situ observation of dendrite morphology and the EBSP crystallographic analysis for solidified samples showed that both a ‹211› twin dendrite and a ‹100› twin-free dendrite grew in the range of undercooling from50 to 115 K. Dendrite growth velocity was also measured for different undercooling conditions. The growth velocity of ‹211› dendrites was slightly larger than that of ‹100› dendrites. It is concluded that the upper envelope of the data provide the correct dendrite growth velocity and it is compared with that obtained by phase-field simulations. Growth velocity in both follows power relationships to undercooling and the linear kinetic coefficient is estimated to be 0.01 m/s K.

Phase-field modeling of rapid solidification

Abstract Rapid directional solidification under a constant thermal gradient was simulated by a new phase-field model. The banded structures in an Al–Cu alloy were successfully reproduced. Only a few cells or dendrites survive in every transition steps into the plane-front mode, which explains the large grain size of banded structure observed in experiments. The noise level in concentration plays a crucial role in the transition procedure of the cell/dendrite into the plane-front mode and so in the overall pattern formation of the banded structure.

Phase Field Study on the Austenite/Ferrite Transition in Low Carbon Steel

A phase field model for the austenite/ferrite transition, including the elastic effect caused by the volume mismatch between the austenite and the ferrite, has been presented and applied to the nucleation and growth of the ferrite in the austenite with various cooling rates. The ferrite particles nucleated at the triple junctions of the austenite grains initially grow fast along the grain boundaries. After the austenite grain boundaries are completely wetted by the ferrite, the ferrite starts to grow to the inside of the austenite grain. While it suppresses the growth of the ferrite at the early stage, the elastic field due to the austenite-ferrite volume difference enhances the growth of the ferrite particles at the late stage.