arXiv subjects

Saswata Bhattacharyya

Publications and source records attributed to Saswata Bhattacharyya.

11 recordsLinked to original sources

arXiv2026

Experimental and computational diffusion analysis in Ni-X binary and Ni-Al-X (X = Cr, Mo, Ta, W, Re) ternary systems

An extensive diffusion analysis is presented for binary Ni-X and ternary Ni-Al-X (X = Cr, Mo, Ta, W, Re) systems, which play a crucial role in microstructural evolution and phase stability in Ni-Al-based superalloys. Specifically, we highlight changes in the diffusion coefficients of X in the presence of Al and compare diffusional interactions across systems considered. First-principles calculations, combined with activation energies derived from temperature-dependent experiments, reveal consistent trends in Ni-X systems, with variations in activation energies largely attributed to differences in migration energies. In ternary systems, diffusion coefficients estimated from intersecting diffusion profiles show that the main interdiffusion coefficient of X is comparable to its binary counterpart, with similar activation energies. However, cross-diffusion coefficients are shown to significantly influence fluxes, either enhancing or reducing diffusion lengths depending on the relative directions of diffusing elements. For Ni-Al-Re, a single-profile method is employed to overcome uncertainties in estimating composition gradients at the near-end-member intersecting composition. The diffusion coefficients obtained correlate well with the nature of diffusion paths when represented on Gibbs triangles. To extend these findings, a physics-informed neural network (PINN) optimization method is applied to extract composition-dependent diffusion coefficients across the full composition range. The analysis demonstrates the necessity of incorporating experimentally estimated diffusion coefficients as equality constraints, without which optimization reliability is compromised. Overall, the results establish a robust framework for diffusion studies in Ni-Al-X systems, highlighting the critical role of cross-diffusion effects and constraint-enhanced numerical methods.

cond-mat.mtrl-sci↗

arXiv2025

Comprehensive Mapping of Tracer Diffusivities Across Composition Space in Ternary NiAlTi and Quinary NiCoFeAlTi High-Entropy Alloy Using Diffusion Couple Experiments and Physics Informed Neural Network Inversion

A comprehensive experimental and physics informed neural network numerical inverse diffusion analysis is conducted in technologically important NiAlTi ternary and NiCoFeAlTi quinary solid solutions for estimating and extracting composition dependent diffusion coefficients. A systematic variation of tracer, intrinsic and interdiffusion coefficients with composition could be estimated in the ternary solid solution. Following, the possibility of producing Al Ti constant PB diffusion profiles keeping constant Ni, Co, Fe in the quinary system is demonstrated. The estimation of diffusion coefficients of all the elements at the Kirkendall marker plane of a single diffusion couple profile is elaborated. PINN optimisation parameters are established using self and impurity diffusion coefficients in Ni and tracer diffusion coefficients at the Kirkendall marker plane. The reliability of optimized parameters is validated by comparing with the interdiffusion coefficients estimated from binary NiTi, NiAl and PB diffusion profiles, indicating extendibility to even lower order systems.

cond-mat.mtrl-sci↗

arXiv2025

Learning coupled Allen-Cahn and Cahn-Hilliard phase-field equations using Physics-informed neural operator(PINO)

Phase-field equations, mostly solved numerically, are known for capturing the mesoscale microstructural evolution of a material. However, such numerical solvers are computationally expensive as it needs to generate fine mesh systems to solve the complex Partial Differential Equations(PDEs) with good accuracy. Therefore, we propose an alternative approach of predicting the microstructural evolution subjected to periodic boundary conditions using Physics informed Neural Operators (PINOs). In this study, we have demonstrated the capability of PINO to predict the growth of $θ^{\prime}$ precipitates in Al-Cu alloys by learning the operator as well as by solving three coupled physics equations simultaneously. The coupling is of two second-order Allen-Cahn equation and one fourth-order Cahn-Hilliard equation. We also found that using Fourier derivatives(pseudo-spectral method and Fourier extension) instead of Finite Difference Method improved the Cahn-Hilliard equation loss by twelve orders of magnitude. Moreover, since differentiation is equivalent to multiplication in the Fourier domain, unlike Physics informed Neural Networks(PINNs), we can easily compute the fourth derivative of Cahn-Hilliard equation without converting it to coupled second order derivative.

cs.CE↗

arXiv2025

Extracting Composition-Dependent Diffusion Coefficients Over a Very Large Composition Range in NiCoFeCrMn High Entropy Alloy Following Strategic Design of Diffusion Couples and Physics Informed Neural Network Numerical Method

Estimating composition dependent diffusion coefficients in multicomponent alloys was a longstanding challenge due to limitations in experimental methods. In this study, we have first demonstrated a strategic design of producing only three diffusion couples to estimate all types, that is tracer, intrinsic, and interdiffusion coefficients at the Kirkendall marker planes. This establishes a systematic variation of diffusion coefficients with composition in a very wide composition range of the NiCoFeCrMn system in comparison to the data available on impurity diffusion coefficients in pure elements and tracer diffusion coefficients at the equiatomic composition estimated by the radiotracer method. Following, a physics-informed Neural Network based numerical inverse method is developed to extract composition-dependent diffusivities over the whole composition range of the diffusion couples.

cond-mat.mtrl-sci↗

arXiv2024

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↗

arXiv2024

MICROSIM: A high performance phase-field solver based on CPU and GPU implementations

The phase-field method has become a useful tool for the simulation of classical metallurgical phase transformations as well as other phenomena related to materials science. The thermodynamic consistency that forms the basis of these formulations lends to its strong predictive capabilities and utility. However, a strong impediment to the usage of the method for typical applied problems of industrial and academic relevance is the significant overhead with regard to the code development and know-how required for quantitative model formulations. In this paper, we report the development of an open-source phase-field software stack that contains generic formulations for the simulation of multi-phase and multi-component phase transformations. The solvers incorporate thermodynamic coupling that allows the realization of simulations with real alloys in scenarios directly relevant to the materials industry. Further, the solvers utilize parallelization strategies using either multiple CPUs or GPUs to provide cross-platform portability and usability on available supercomputing machines. Finally, the solver stack also contains a graphical user interface to gradually introduce the usage of the software. The user interface also provides a collection of post-processing tools that allow the estimation of useful metrics related to microstructural evolution.

cond-mat.mtrl-sci↗

arXiv2024

Splitting Instability in Superalloys: A Phase-Field Study

Precipitation-strengthened alloys, such as Ni-base, Co-base and Fe-base superalloys, show the development of dendrite-like precipitates in the solid state during aging at near-$γ^{\prime}$ solvus temperatures. These features arise out of a diffusive instability wherein, due to the point effect of diffusion, morphological perturbations over a growing sphere/cylinder are unstable. These dendrite-like perturbations exhibit anisotropic growth resulting from anisotropy in interfacial/elastic energies. Further, microstructures in these alloys also exhibit "split" morphologies wherein dendritic precipitates fragment beyond a critical size, giving rise to a regular octet or quartet pattern of near-equal-sized precipitates separated by thin matrix channels. The mechanism of formation of such morphologies has remained a subject of intense investigation, and multiple theories have been proposed to explain their occurrence. Here, we developed a phase-field model incorporating anisotropy in elastic and interfacial energies to investigate the evolution of these split microstructures during growth and coarsening of dendritic $γ^{\prime}$ precipitates. Our principal finding is that the reduction in elastic energy density drives the development of split morphology, albeit a concomitant increase in the surface energy density. We also find that factors such as supersaturation, elastic misfit, degree of elastic anisotropy and interfacial energy strongly modulate the formation of these microstructures. We analyze our simulation results in the light of classical theories of elastic stress effects on coarsening and prove that negative elastic interaction energy leads to the stability of split precipitates.

cond-mat.mtrl-sci↗

arXiv2024

An Experimental Estimation Method of Diffusion Coefficients in Ternary and Multicomponent Systems from a Single Diffusion Couple Profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple methods need two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members, which may be tricky depending on the complications of diffusion paths in certain systems. In this study, we have proposed a method for estimating all types of diffusion coefficients directly at the Kirkendall marker plane from a single diffusion couple. The estimation method and design strategy for producing diffusion couples are discussed in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and Ni-rich Ni-Co-Fe-Cr-Al quinary alloys. As demonstrated further, one can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method and design strategy of producing diffusion couples demonstrated in this study can be suitable for generating a mobility database in Ni-, Co-based (superalloys) and Fe-based (steel) multicomponent systems with relative ease, which was considered impossible until recently.

cond-mat.mtrl-sci↗

arXiv2022

Accelerated Solutions of Coupled Phase-Field Problems using Generative Adversarial Networks

Multiphysics problems such as multicomponent diffusion, phase transformations in multiphase systems and alloy solidification involve numerical solution of a coupled system of nonlinear partial differential equations (PDEs). Numerical solutions of these PDEs using mesh-based methods require spatiotemporal discretization of these equations. Hence, the numerical solutions are often sensitive to discretization parameters and may have inaccuracies (resulting from grid-based approximations). Moreover, choice of finer mesh for higher accuracy make these methods computationally expensive. Neural network-based PDE solvers are emerging as robust alternatives to conventional numerical methods because these use machine learnable structures that are grid-independent, fast and accurate. However, neural network based solvers require large amount of training data, thus affecting their generalizabilty and scalability. These concerns become more acute for coupled systems of time-dependent PDEs. To address these issues, we develop a new neural network based framework that uses encoder-decoder based conditional Generative Adversarial Networks with ConvLSTM layers to solve a system of Cahn-Hilliard equations. These equations govern microstructural evolution of a ternary alloy undergoing spinodal decomposition when quenched inside a three-phase miscibility gap. We show that the trained models are mesh and scale-independent, thereby warranting application as effective neural operators.

cond-mat.mtrl-sci↗

arXiv2022

Surface-directed and bulk spinodal decomposition compete to decide the morphology of bimetallic nanoparticles

An embedded-domain phase-field formalism is used for studying phase transformation pathways in bimetallic nanoparticles (BNPs). Competition of bulk and surface-directed spinodal decomposition processes and their interplay with capillarity are identified as the main determinants of BNP morphology. The former is characterized by an effective bulk driving force $Δ\tilde{f}$ which increases with decreasing temperature, while the latter manifests itself through a balance of interfacial energies captured by the contact angle $θ$. The simulated morphologies, namely, core-shell, Janus and inverse core-shell, cluster into distinct regions of the $Δ\tilde{f}$-$θ$ space. Variation of $θ$ with $Δ\tilde{f}$ in the Ag-Cu alloy system is computed as a function of temperature using a CALPHAD approach in which surface energies are estimated from a modified Butler equation. This $θ-Δ\tilde{f}$ trajectory for Ag-Cu, when superimposed on the morphology map, enables the prediction of different morphological transitions as a function of temperature. Therefore, the study establishes a unique thermodynamic framework coupled with phase-field simulations for predicting and tailoring nanoparticle morphology through a variation of processing temperature.

cond-mat.mtrl-sci↗

arXiv2013

Effect of Epitaxial Strain on Phase Separation in Thin Films

We examine the role of an imposed epitaxial strain e in enhancing or depressing the spinodal instability of an alloy thin film. Since the alloy film starts with an imposed strain, phase separation offers a mechanism to relieve it, but only when the film is elastically inhomogeneous. With composition-dependence of elastic modulus given by y, and that of lattice parameter by η, our simulations using the Cahn-Hilliard model show (and analytical results for early stages confirm) that, for (ey/η) > 0, the imposed strain adds to the driving force for phase separation, decreases the maximally growing wave length, and expands the coherent spinodal in the phase diagram. Further, when (ey/η) > 0.372, it expands to even outside of chemical spinodal. Phase separation produces islands of elastically softer (harder) phase with (without) a favorable imposed strain. These results are in agreement with experimental results in GeSi thin films on Si and Ge substrates, as well as in InGaAs films on GaAs substrates.

cond-mat.mtrl-sci↗