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Rajdip Mukherjee

Publications and source records attributed to Rajdip Mukherjee.

14 recordsLinked to original sources

Influence of Interface Energy Anisotropy on the Solid-state Instability in Ni-based Superalloy: A Multiscale Study

The microstructural stability of nickel-based superalloys critically depends on the morphology and evolution of $\gamma'$-precipitates, which is governed by elastic and interfacial anisotropies at the atomic scale. Here, we present a novel quantitative multiscale framework that, for the first time, directly incorporates atomistically computed interface energy anisotropy into mesoscale phase-field simulations to elucidate morphological selection and instability in the Ni--Al system. We employ density functional theory (DFT) to accurately predict the orientation-dependent $\gamma/\gamma'$ interface energies for key crystallographic planes. A rigorous analytic mapping is then developed to systematically reduce the three-dimensional (3D) interface anisotropy landscape to the two-dimensional (2D) simulation plane. This enables quantitative transfer of DFT-informed anisotropy parameters into a continuum phase-field model that also accounts for elastic inhomogeneity and eigenstrain. Our simulations demonstrate that the explicit inclusion of DFT-based interface energy anisotropy fundamentally alters precipitate morphological evolution, robustly suppressing instability and faceting phenomena otherwise promoted by supersaturation and elastic effects. The framework bridges atomic- to mesoscale modeling, enabling predictive control of precipitate shapes and providing new insights into the interplay of elastic and interfacial contributions in Ni-based superalloys. This approach paves the way for quantitative microstructural design in advanced high-temperature alloys via first-principles-guided multiscale simulation.

cond-mat.mtrl-sci

Bridging Phase-Field Model and Deep Learning for Predicting 2D and 3D Microstructure Evolution in Ternary Alloys

We develop a hybrid framework that integrates a phase-field model (PFM) with an attention-enhanced deep learning (DL) architecture to study ternary spinodal dealloying, a sophisticated self-organization approach used to fabricate three-dimensional bicontinuous, hierarchical nanoporous materials. The study captures three distinct phase-separation mechanisms that emerge during the early stages of spinodal decomposition in both two and three dimensions. The DL workflow consists of three key components: (i) a dimensionality-reducing autoencoder that provides compact representations of high-resolution microstructure images (256x256x3), (ii) an attention-augmented convolutional long short-term memory (ConvLSTM) network that learns complex spatiotemporal correlations governing microstructure evolution, and (iii) a novel slice-by-slice strategy that enables extension of the model to three-dimensional systems (128x128x128x3). We further demonstrate a hybrid simulation strategy in which PFM accurately captures rapid early-stage microstructure evolution, while the DL model efficiently predicts late-stage coarsening dynamics. The trained DL model achieves remarkable predictive accuracy, maintaining fidelity up to 400 timesteps ahead and generalizing to compositions outside the training distribution. By bridging the physical fidelity of PFM with the computational efficiency of DL, this framework establishes a robust platform for predictive modeling of microstructure evolution in complex multicomponent systems.

cond-mat.mtrl-sci

Multiscale Modeling of Abnormal Grain Growth: Role of Solute Segregation and Grain Boundary Character

Abnormal grain growth (AGG) influences the properties of polycrystalline materials; however, the underlying mechanisms, particularly the role of solute segregation at the grain boundary (GB), are difficult to quantify precisely. This study demonstrates a multiscale framework that integrates atomic-scale segregation energetics (using density functional theory) with mesoscale grain growth dynamics (using phase-field model) to investigate AGG, using $\alpha$-Fe as an example system. Multisite segregation energies are calculated for symmetric tilt grain boundaries (STGBs) along the $\langle 110 \rangle$ axis for nine different solutes (Co, Cr, Mn, Mo, Nb, Ni, Ti, W, and V), encompassing three different types of coincident site lattice (CSL) boundaries: $\sum 3 (11\bar{2})$, $\sum 9 (\bar{2}21)$, and $\sum 3 (\bar{1}11)$. The model takes into account the effect of solute drag on GB mobility, estimated using a bulk solute concentration of 0.1 at\%. The results demonstrate that AGG originates due to GB anisotropy, the extent of which largely depends on the type of solute atom present. Such a complex dependence necessitates using a multiscale model to understand AGG comprehensively. In general, low-energy $\Sigma 3$ boundaries are found to have higher mobility and show preferential growth for most of the solutes, other than Co. The study reveals how the distribution of GB types significantly influences AGG. When 10-30\% of the GBs are high-mobility type, crown-like morphologies are observed, leading to AGG. These findings underscore the critical role of GB chemistry and crystallography in governing AGG, and the model can be generalized to provide a predictive framework for controlling grain growth through strategic solute design in advanced alloys.

cond-mat.mtrl-sci

Deep Learning-Driven Prediction of Microstructure Evolution via Latent Space Interpolation

Phase-field models accurately simulate microstructure evolution, but their dependence on solving complex differential equations makes them computationally expensive. This work achieves a significant acceleration via a novel deep learning-based framework, utilizing a Conditional Variational Autoencoder (CVAE) coupled with Cubic Spline Interpolation and Spherical Linear Interpolation (SLERP). We demonstrate the method for binary spinodal decomposition by predicting microstructure evolution for intermediate alloy compositions from a limited set of training compositions. First, using microstructures from phase-field simulations of binary spinodal decomposition, we train the CVAE, which learns compact latent representations that encode essential morphological features. Next, we use cubic spline interpolation in the latent space to predict microstructures for any unknown composition. Finally, SLERP ensures smooth morphological evolution with time that closely resembles coarsening. The predicted microstructures exhibit high visual and statistical similarity to phase-field simulations. This framework offers a scalable and efficient surrogate model for microstructure evolution, enabling accelerated materials design and composition optimization.

cond-mat.mtrl-sci

Microstructural Studies Using Generative Adversarial Network (GAN): a Case Study

The generative adversarial network (GAN) is one of the most widely used deep generative models for synthesizing high-quality images with the same statistics as the training set. Finite element method (FEM) based property prediction often relies on synthetically generated microstructures. The phase-field model is a computational method of generating realistic microstructures considering the underlying thermodynamics and kinetics of the material. Due to the expensive nature of the simulations, it is not always feasible to use phase-field for synthetic microstructure generation. In this work, we train a GAN with microstructures generated from the phase-field simulations. Mechanical properties calculated using the finite element method on synthetic and actual phase field microstructures show excellent agreement. Since the GAN model generates thousands of images within seconds, it has the potential to improve the quality of synthetic microstructures needed for FEM calculations or any other applications requiring a large number of realistic synthetic images at minimal computational cost.

cond-mat.mtrl-sci

Grain boundary grooving in thin film under the influence of an external magnetic field: A phase-field study

Using a phase-field model, we study the surface diffusion-controlled grooving of a moving grain boundary under the influence of an external magnetic field in thin films of a nonmagnetic material. The driving force for the grain boundary motion comes from the anisotropic magnetic susceptibility of the material, leading to the free energy difference between differently oriented grains. We find that above a critical magnetic field the grain boundary motion is in a steady state, and under this condition, the mobile thermal groove exhibits a universal behavior scaled surface profiles are timeinvariant and independent of thermodynamic parameters. The simulated universal curve agrees well with Mullins theory of mobile grooves for any groove shape. We extend our study to a three-dimensional polycrystalline thin film with equalsized hexagonal grains. We observe a preferential grain growth depending on the applied magnetic field direction, which can be leveraged for field-assisted texture control of polycrystalline thin films. Our study reveals that keeping other conditions the same, the rate of pitting at the vertices of the hexagonal grains substantially decreases in the presence of the external magnetic field.

cond-mat.mes-hall

Effect of Cr Segregation on Grain Growth in Nanocrystalline α-Fe Alloy: A Multiscale Modelling Approach

We present a multiscale modelling framework that integrates density functional theory (DFT) with a phase-field model (PFM) to explore the intricate dynamics of grain growth in nanocrystalline α-Fe single-phase alloy in the presence of chromium (Cr) segregation. We begin our study by validating our simulation results for equilibrium segregation in stationary GB with Mclean isotherm. Polycrystal simulations featuring nanocrystalline grains at different temperatures reveal that the grain growth kinetics depends on the ratio of Cr diffusivity to intrinsic GB mobility. In the absence of segregation, the relationship between the square of average grain size (d 2 ) and time (t) demonstrates a linear correlation. We observe that the d 2 vs. t plot exhibits a consistent linear trend up to a threshold grain size, independent of Cr segregation at GB. However, when Cr is segregated at GB, a deviation from this linear trend with a decreasing slope is evident within the temperature range of 700K to 900K beyond the threshold size. This threshold grain size decreases with increasing temperature. Notably, at 1000K, the deviation from the linear trend is observed from the initial stages of grain growth with segregation, albeit with a linear trend exhibiting a smaller slope. We also present an analytical formulation based on Cahn solute drag theory to predict grain growth behaviour in the presence of solute segregation and our simulation results well aligned this analytical formulation.

cond-mat.mtrl-sci

Interplay between thermal and compositional gradients decides the microstructure during thermomigration: a phase-field study

The presence of thermal gradients in alloys often leads to non-uniformity in concentration profiles, which can induce the thermomigration of microstructural features such as precipitates. To investigate such microstructural changes, we present a phase-field model that incorporates coupling between concentration and thermal gradients. First, we simulated the evolution of non-uniform concentration profiles in the single-phase regions of Fe-C and Fe-N alloy systems due to imposed thermal gradients. To validate our model with the classical experiments performed by Darken and Oriani, we studied the evolution of spatially varying concentration profiles where thermal gradients encompass single-phase and two-phase regions. We developed a parameterized thermodynamic description of the two-phase region of a binary alloy to systematically study the effect of interactions between chemically-driven and thermal gradient-driven diffusion of solute on the evolution of precipitates. Our simulations show how thermal gradient, precipitate size, and interparticle distance influence the migration and associated morphological changes of precipitates. The composition profiles and migration rates obtained from single-particle simulations show an exact match with our analytical model. We use twoparticle simulations to show conditions under which thermomigration induces the growth of the smaller particle and shrinkage of the larger one in contrast to the isothermal Ostwald ripening behavior. Our multiparticle simulations show similar behavior during coarsening. Moreover, in the presence of a thermal gradient, there is a shift in the center of mass of the precipitates towards the high-temperature region. Thus, our study offers new insights into the phenomena of microstructure evolution in the presence of thermal gradient.

cond-mat.mtrl-sci

Microstructure-property prediction of a Ni-based superalloy: A combined phase-field and finite element modelling approach

Multiscale modelling is a new paradigm that has emerged in recent times to study the well-known problem of the process-structure-property relationship in the area of materials science and engineering. For obtaining the desired performance for materials of strategic importance, such as superalloys, it is essential to bridge different length and time scales in order to navigate the entire design space. In the present study, we develop a physics-based model for a Ni-based superalloy where the microstructures simulated using a phase-field model serve as input to finite-element computations. We examine the alloy's microstructure evolution and effective elastic properties quantitatively via phase-field and finite element methods integrated with CALPHAD database, by varying composition and aging temperature. The phase-field simulations provide us with an insight into the different regimes of microstructure evolution. The finite element analysis uncovers the relation of effective elastic properties with several system parameters.

cond-mat.mtrl-sci

$μ$2mech: a Software Package Combining Microstructure Modeling and Mechanical Property Prediction

We have developed a graphical user interface (GUI) based package $μ$2mech to perform phase-field simulation for predicting microstructure evolution. The package can take inputs from ab initio calculations and CALPHAD (Calculation of Phase Diagrams) tools for quantitative microstructure prediction. The package also provides a seamless connection to transfer output from the mesoscale phase field method to the microscale finite element analysis for mechanical property prediction. Such a multiscale simulation package can facilitate microstructure-property correlation, one of the cornerstones in accelerated materials development within the integrated computational materials engineering (ICME) framework.

cond-mat.mtrl-sci

Solute Segregation in a Moving Grain Boundary: A Novel Phase-Field Approach

We present a novel phase-field approach for investigating solute segregation in a moving grain boundary. In our model, the correct choice of various parameters can control the solute-grain boundary interaction potential, resulting in various segregation profiles that agree with Cahn solute drag theory. Furthermore, we explore how different segregation profiles evolve at varying GB velocities owing to the inequality of the atomic flux of solute between the front and back faces of the moving grain boundary. We highlight velocity variations among segregation profiles in low and high-velocity regimes. This model reveals how grain boundary segregation affects grain growth, providing insights for future alloy design

cond-mat.mtrl-sci

Accelerating microstructure modelling via machine learning: a new method combining Autoencoder and ConvLSTM

Phase-field modeling is an elegant and versatile computation tool to predict microstructure evolution in materials in the mesoscale regime. However, these simulations require rigorous numerical solutions of differential equations, which are accurate but computationally expensive. To overcome this difficulty, we combine two popular machine learning techniques, autoencoder and convolutional long short-term memory (ConvLSTM), to accelerate the study of microstructural evolution without compromising the resolution of the microstructural representation. After training with phase-field generated microstructures of ten known compositions, the model can accurately predict the microstructure for the future nth frames based on previous m frames for an unknown composition. Replacing n phase-field steps with machine-learned microstructures can significantly accelerate the in silico study of microstructure evolution.

cond-mat.mtrl-sci

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 non-local 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.

cond-mat.mtrl-sci

Deviations from cooperative growth mode during eutectoid transformation: insights from phase-field approach

The non-cooperative eutectoid transformation relies on the presence of pre-existing cementite particles in the parent austenitic phase and yields a product, popularly known as the divorced eutectoid. In isothermal conditions, two of the important parameters, which influence the transformation mechanism and determine the final morphology are undercooling (below A1 temperature) and inter-particle spacing. Although, the criteria which governs the morphological transition from lamellar to divorced is experimentally well established, numerical studies that give a detailed exposition of the non-cooperative transformation mechanism, have not been reported extensively. In the present work, we employ a multiphase-field model, that uses the thermodynamic information from the CALPHAD database, to numerically simulate the pulling-away of the advancing ferrite-austenite interface from cementite, which results in a transition from lamellar to divorced eutectoid morphology in Fe-C alloy. We also identify the onset of a concurrent growth and coarsening regime at small inter-particle spacing and low undercooling. We analyze the simulation results to unravel the essential physics behind this complex spacial and temporal evolution pathway and amend the existing criteria by constructing a Lamellar-Divorced-Coarsening (LDC) map.

cond-mat.mtrl-sci