Rajdip Mukherjee

Composition pathway in Fe–Cu–Ni alloy during coarsening

In this work the microstructure evolution for a two phase Fe–Cu–Ni ternary alloy is studied in order to understand the kinetic composition paths during coarsening of precipitates. We have employed a quantitative phase-field model utilizing the CALPHAD database to simulate the temporal evolution of a multi-particle system in a two-dimensional domain. The paths for the far-field matrix and for precipitate average compositions obtained from simulation are found to be rectilinear. The trends are compared with the corresponding sharp interface theory, in the context of an additional degree of freedom for determining the interface compositions due to the Gibbs–Thomson effect in a ternary alloy.

Phase-Field Modeling of Grain-Boundary Grooving Under Electromigration

In the present work, we study the phenomenon of grain-boundary grooving under electromigration using a phase-field method. The specific focus of the work is to explore the role of grain boundaries as potential electromigration pathways. We consider the evolution of grooves under the combined influence of capillary and electromigration-mediated surface diffusion and electromigration-induced grain-boundary diffusion. Mechanisms of grooving are elucidated using flux density maps that indicate various regimes depending upon the direction of net material transport. When grain-boundary atomic mobility is lower than the surface mobility, the groove depth is found to be lower than that evolving solely under surface diffusion (no electromigration). At comparable or larger values of grain-boundary atomic mobility, grooving is initially expedited but shows groove replenishment at later stages. A detailed investigation using the phase-field method reveals the influence of an incumbent healing mechanism on grain-boundary grooving which is electrically induced. The drift characteristics such as edge and root displacement and velocity are examined in light of this assuaging effect.

Influence of substrate interaction and confinement on electric field induced transition in symmetric block copolymer thin films

In the present work, we study morphologies arising due to competing substrate interaction, electric field, and confinement effects on a symmetric diblock copolymer. We employ a coarse-grained nonlocal Cahn-Hilliard phenomenological model taking into account the appropriate contributions of substrate interaction and electrostatic field. The proposed model couples the Ohta-Kawasaki functional with Maxwell equation of electrostatics, thus alleviating the need for any approximate solution used in previous studies. We calculate the phase diagram in electric-field-substrate strength space for different film thicknesses. In addition to identifying the presence of parallel, perpendicular, and mixed lamellae phases similar to analytical calculations, we also find a region in the phase diagram where hybrid morphologies (combination of two phases) coexist. These hybrid morphologies arise either solely due to substrate affinity and confinement or are induced due to the applied electric field. The dependence of the critical fields for transition between the various phases on substrate strength, film thickness, and dielectric contrast is discussed. Some preliminary 3D results are also presented to corroborate the presence of hybrid morphologies.

Numerical study on solutal Marangoni instability in finite systems with a miscibility gap

Solutal Marangoni instability (SMI) is investigated both in 2D and 3D using a combined Cahn-Hilliard and Navier-Stokes model in a finite system. Fe-Sn is chosen as a representative alloy system since the phase diagram reveals a region with a miscibility gap, where two liquid phases, namely, the Fe-rich phase L1 and the Sn-rich phase L2, are in chemical equilibrium. In 3D, considering a perturbed liquid cylinder (L2 phase) with a length of λ and a radius of R0 embedded in the middle of a simulation box of λ × H × H (length × width × height) surrounded by the phase L1, we find that the perturbation induced Marangoni flow is either clockwise or anti-clockwise depending on the mean curvature difference between the convex and concave regions which is affected by the ratio of λ/R0. The critical ratio of λ/R0 for SMI is shown to be invariant for different Marangoni numbers as well as independent of the geometrical properties of the L1 phase. In 2D, a perturbed liquid pipe with a length of λ and a radius of R0 em...

Phase Field Models as Computer Experiments: Growth Kinetics of Anisotropic Precipitates

Phase field models are widely used for the study of microstructures and their evolution. They can also be used as computer experiments. As computer experiments, they serve two important roles: (a) theoretical results which are hard to verify/validate experimentally can be verified/validated on the computer using phase field models; and, (b) when severe assumptions are made in a theory, they can be relaxed in the phase field model, and hence, results with wider reach can be obtained. In this paper, we discuss some such computer experiments in general, and the growth kinetics of precipitates in systems with tetragonal and cubic interfacial anisotropies in particular.

Experimental and Numerical Investigation on the Phase Separation Affected by Cooling Rates and Marangoni Convection in Cu-Cr Alloys

In this work, we study the microstructures upon rapid solidification from the melt which occurs in Cu-Cr electrical contacts after switching operations. As the local cooling rates are difficult to be determined experimentally, we numerically compute the mean radius of Cr-particles from phase separation as a function of the cooling rate by utilizing a convective Cahn–Hilliard model. Based on the computationally derived correlation and on the metallographically observed microstructure, we are able to extract back the local cooling rates during heat treatment. We further examine the effect of Marangoni convection on the phase separation structure in a particularly composed simulation study. We obtain the cooling rate for a given particle size affected by the solutal Marangoni convection.