Machiko Ode

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.

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.

A thermodynamic description of the Al-Ir system

The thermodynamic assessment of the Al-Ir binary system, one of the key sub-systems of the Ir-based alloys, was performed using the CALPHAD technique. The AlIr(B2) phase was described using the two sublattice model with the formula (Al,Ir)0.5(Ir,Va)0.5, while other intermetallic phases were treated as stoichiometric compounds. The calculated data of the phases in the Al-Ir system can be used to accurately reproduce experimental data, such as phase equilibria, invariant reactions, and formation enthalpies of the intermetallic phases.

Ternary Interdiffusion in L12-Ni3Al with Ir Alloying Addition

Average ternary interdiffusion coefficients in Ni3Al with Ir additions have been determined using solid-to-solid diffusion couples annealed at 1200°C for 5 hours. Disc shaped alloy specimens were prepared by the vacuum arc melting at compositions of Ni-24Al, Ni-25Al, Ni-26Al, Ni-23.5Al-1Ir, Ni-24.5Al-1Ir, Ni-23Al-2Ir, Ni-23Al-2Ir, Ni-24Al-2Ir, Ni-23Al-3Ir (at.%). Surfaces of alloys were polished down to 1200 grit and diffusion couples were assembled in Si3N4 jig for initial bonding heat treatment at 1200°C for 0.5 hours. Additional diffusion anneal was carried out at 1200°C for 4.5 hours outside of Si3N4 jig so that diffusion couples can be water quenched. Concentration profiles of individual components were measured by electron probe microanalysis using pure standard of Ni, Al and Ir. Interdiffusion flux of individual component was determined directly from the experimental concentration profiles, and the moments of interdiffusion flux were examined to calculate the average ternary interdiffusion coefficients, D˜ ij k either with Al or Ni as dependent component. Calculated interdiffusion coefficients suggest that Ir-alloyed Al2O3-forming oxidation resistant coatings would be beneficial to reduce the interdiffusion flux of Ni from superalloy substrates to the coating, and reduce the interdiffusion flux of Al from the coating to the superalloy substrate.

Simulation of reaction-diffusion phenomena occurring between Ir coating and Ni–Al alloy substrate using phase-field model

Abstract It is very important to understand the development of the microstructure in the interdiffusion zone between coatings and superalloy substrates for designing bond coat materials. In this study, the reaction-diffusion phenomena in the Ir-coating/Ni – Al binary substrate system are simulated using the phase-field model. The thermodynamic database developed based on the CALPHAD method is directly incorporated in the simulation. The effect of coating thickness on the growth of the secondary precipitated -phase is discussed. In the case of a semi-infinite system, the thickness of the -phase increases proportionally with the square root of time. In the case of a thin (1 thick) coating, inconstant -phase growth is observed. It is suggested that the phase growth is related to the change in the -phase fraction, which is derived from a thermodynamic line calculation from the substrate composition to pure Ir.

Phase-field simulation of microstructure evolution during the initial stage of rapid solidification of alloys

Microstructure evolution during the rapid solidification of Fe-C alloys is simulated using the phase-field model for binary alloys with thin interface limit parameters. The heat transfer equation is solved simultaneously to study the heat flow and the effect of latent heat generation on the microstructure. The calculations have been carried out using a double grid method and parallel computing technique. The competitive growth of growing cells was reproduced, and the cellular/dendritic transition was also observed. Since there is a negative thermal gradient in front of the leading tip, growth can be regarded as unidirectional free dendrite growth. The microstructure changes depending on the preferred growth orientation and the secondary arms start developing only on one side with the increase of the tilted angle. With the two-dimensional heat diffusion effect, negative thermal gradient appears on both the solid and liquid side of the leading tip.