18th MIE Graduate Student Conference April 6, 2019

ATOMISTICALLY INFORMED PHASE FIELD SIMULATION OF SOLIDIFICATION IN NI-TI ALLOY

Sepideh Kavousi Ph.D. Candidate

Faculty Advisor: Dr. Dorel Moldovan

ABSTRACT Solid-liquid interface properties and their anisotropies

play an important role in dendritic solidification of alloys affecting both the shape and the growth rate of dendrites. Accurate phase-field simulation models of dendritic solidification require as input liquid-solid interface energy and energy anisotropy as well as interface kinetic coefficient (mobility) and kinetic coefficient anisotropy. In this study, we link phase-field and molecular dynamics (MD) simulation approaches to study the solidification of Ni-Ti alloy. Specifically, first a new MEAM potential is developed which can predict solid-liquid phase equilibrium at high temperatures. Then doing MD simulations with our developed interatomic potential and using capillary fluctuation method we calculated the solid-liquid interface energy and its anisotropy and by using the free-solidification MD simulations we extract the interface kinetic coefficient and anisotropy. Finally, the atomistic-informed phase field model was used to investigate the role of anisotropy on the morphology of dendrites and the segregation coefficient.

The interatomic potential dictates the quality of MD simulation results. Several interatomic potentials have been developed for the Ti-Ni binary systems, but all of these potentials were mainly developed to reproduce the main characteristics of the martensitic transformation close to the equiatomic composition. In order for the results of the MD simulations to be predictive, the interatomic potential used should be able to reproduce the experimental CM phase equilibrium conditions, such as solute partitioning as well as the slopes of solidus and liquidus lines

A new 2NN-MEAM potential has been developed Ni-Ti alloys. The goal of this potential is in prediction of the crystal-melt phase equilibrium for Ni-Ti alloys. For this means, starting from an existing potential developed by Ko et al. [1] for the Ni-Ti system, we fine-tuned potential parameters to fit the melting point and latent heat of Ni and Ti to the experimental values. The transferability of the unary potentials were also tested by calculating physical, mechanical, defect, thermodynamic and transport properties. Using Table 1 one can compare the experimental and MD-calculated thermal properties for pure Ni and Ti. The results of MD potential is close to the experimental data.

Table 1 Calculated thermal properties of pure Ni and Ti at their melting point using the present 2NN MEAM potential, in comparison with the experimental data Ti Ni Property Exp. MD Exp. MD

(K) 1941 1941 1728 1728

(kJ/mol) 14.15 11.45 17.48 17.41

2.817 1.62 4.5 6.1

(g/cm3) 4.14 4.23 7.93 7.821

(mPa.s) 3.25 3.73 4.7 6.3

(10-5cm2/s) 4.922 4.733 3.27 2.83

(kJ/mol) 399.8 400.6 - 364.9

In the fitting process of the binary potential, we focused on fitting the temperature dependent equilibrium solidus and liquidus concentrations of the Ni-rich and Ti-rich compositions to the experimental phase diagram, and enthalpy of mixing. Then the transferability of the potential was also tested by comparing the physical properties and formation energy of different compounds, and the temperature dependent liquid densities for multiple compositions with the experimental data.

Figure 1 Comparison of Ni-Ti phase diagram calculated using the present MEAM potential with the thermo-calc data

Now this potential can be used to calculate anisotropic solid-liquid interface free energy. We will also use the

capillary fluctuation method to calculate the temperature dependent solid-liquid interfacial and its anisotropy. In this method the fluctuations of interface around its mean position can be written as summation of Fourier modes. Based on the equipartition of energy on the degrees of freedom applied to individual capillary fluctuation modes, they can be related to the stiffness of the solid-liquid interface. In figure 2 a snapshot from the MD simulation is illustrated for different alloy compositions and different temperatures.

Figure 2 snapshot from the MD simulation for solid-liquid coexistence for different compositions and different temperatures

Figure 3 shows how the average interface energy changes with temperature. Increasing the temperature, which comes along with reducing the solute concentration in the alloy, leads to an increase in the interface energy.

Figure 3 Temperature dependence of solid-liquid interface free energy γ0(mJ/m2)

Now that we have calculated anisotropic solid-liquid kinetic and interface properties, we are ready to do the atomsitically-induced phase field method. Thin interface analysis was used to map the phase-field equations to the classical sharp-interface moving boundary equations for solidification; the mapping is applicable in the limit where the interface thickness is small compared to the characteristics length-scales of the microstructure which is the case for metals[2]. Using this method, the parameters present in the phase field equations are calculated by using the MD calculated solid-liquid interfacial free energy and its kinetic coefficient.

In figure 4 the effect of different anisotropy parameters on the shape of the dendrites is shown. For small anisotropies, the dendrite grows in see-weed shape and it

does not have any preferred directions. Also the secondary arms are not perpendicular to the primary dendrite. As the anisotropy values increases from left to right, the dendrite preferred growth direction becomes (100) direction. And the generated secondary arms are perpendicular to the preferred growth direction.

Figure 4 Anisotropy effect on dendrite shape of Ti-8%Ni

In figure 5 the effect of change in solute concentration and solidification velocity on the shape of dendrites, and the the distribution of solute particles is illustrated. One can find for smaller solute concentrations, the solidificaton velocity effects the shape of the dendrites more dramatic than the larger concentrations. Also for higher solidifcation velocities the dendrite shapes is not being effected by the solute concentration.

Figure 5 The effect of solute concentration and solidification velocity on the dendrite shapes

ACKNOWLEDGMENTS This authors gratefully acknowledge the support from

the U.S. National Science Foundation (CIMM Project OIA-1541079). The computer resources were provided by LONI and HPC at LSU.

REFERENCES 1. W.-S. Ko, B. Grabowski, J. Neugebauer, Physical

Review B 92(13) (2015) 134107. 2. A. Karma, W.-J. Rappel, Physical Review E 57(4)

(1998) 4323-4349.