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Papers by Abhik Choudhury

Research paper thumbnail of Theoretical and numerical determination of phase concentrations during growth in ternary alloys

arXiv: Materials Science, 2016

Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of... more Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of a second phase in ternary and higher multicomponent two phase alloys is an important problem due to the strong dependence of mechanical properties on compositions. In this paper, we derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar and cylindrical precipitates with the assumption of diagonal diffusivity matrices. We confirm our calculations by sharp-interface and phase-field simulations. The numerical techniques are in turn utilized for investigating the role of off-diagonal entries in the diffusivity matrix. In addition, the sharp-interface methods allow for the tracking of the tie-line compositions during growth of 2D precipitates which contribute to an understanding of the change in equilibrium tie-lines chosen by the system during growth

Research paper thumbnail of Phase-field modeling of stress evolution in heterogen structures

Daniel Schneider, Oleg Tschukin, Abhik Choudhury, Michael Selzer, Britta Nestler 1 Institute of M... more Daniel Schneider, Oleg Tschukin, Abhik Choudhury, Michael Selzer, Britta Nestler 1 Institute of Materials and Processes, Karlsruhe University of Applied Science, Moltkestrasse 30, D-76133 Karlsruhe, Germany, daniel.schneider@kit.edu, oleg.tschukin@hs-karlsruhe.de, www.imp.hs-karlsruhe.de 2 Institute of Materials and Processes, Karlsruhe University of Applied Science, Moltkestrasse 30, D-76133 Karlsruhe, Germany, oleg.tschukin@hs-karlsruhe.de, www.imp.hs-karlsruhe.de 3 The Department of Materials Engineering, Indian Institute of Science Bangalore, abhiknc@materials.iisc.ernet.in, http://materials.iisc.ernet.in 4 IAM-ZBS, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, michael.selzer@kit.edu, britta.nestler@kit.edu, http://www.iam.kit.edu/zbs 5 IAM-ZBS, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, britta.nestler@kit.edu, http://www.iam.kit.edu/zbs

Research paper thumbnail of Phase-Field Methods for Pattern-Formation

Research paper thumbnail of Elasto-plastic phase-field model accounting for mechanical jump conditions during solid-state phase transformations

Research paper thumbnail of Anwendung thermodynamischer Datensätze in der Phasenfeldsimulation

Research paper thumbnail of Crystallographic and Morphological Evidence of Solid–Solid Interfacial Energy Anisotropy in the Sn-Zn Eutectic System

Metallurgical and Materials Transactions A, 2020

In this paper, we explore the morphological evolution during two-phase growth in the Sn-Zn eutect... more In this paper, we explore the morphological evolution during two-phase growth in the Sn-Zn eutectic system, which has a particularly low volume fraction of the minority Zn phase. The reason for this choice is its exotic nature, as even with such a low volume fraction, the reported morphology is ''broken-lamellar,'' in contrast to the usually expected hexagonal arrangement of Zn rods in the Sn matrix. Thus, the main objective of the study is to investigate the reasons behind this phenomenon. We begin by presenting experimental results detailing the morphology and crystallography of the eutectic microstructures under various combinations of thermal gradients and velocities in directional solidification conditions. Based on the crystallography and further specially designed experiments we find that the solid-solid interface between the Sn and Zn crystal is anisotropic. On the basis of the results, we propose a hypothesis that the presence of solid-solid interfacial energy anisotropy leads to the formation of predominantly broken-lamellar structures, even when the minority fraction is significantly low.

Research paper thumbnail of Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems

Metallurgical and Materials Transactions A, 2020

Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morpho... more Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morphology is the periodic arrangement of lamellar plates with well-defined orientations of the solid–solid interface in a given eutectic grain. It is typically believed that this form of morphology develops due to the presence of solid–solid interfacial energy anisotropy. In this paper, we provide evidence using phase-field simulations where our focus is on alloys where the minority phase fraction is low. Our aim is to establish the role of solid–solid interfacial energy anisotropy in the stabilization of broken lamellar structures in such systems in contrast to the formation of a rod microstructure. In this regard, we conduct phase-field simulations for different strengths of anisotropy in both constrained and extended settings, using which we clarify the mechanisms by which a lamellar arrangement gets stabilized in the presence of anisotropy in the solid–solid interfacial energy.

Research paper thumbnail of Formation of solid-state dendrites under the influence of coherency stresses: A diffuse interface approach

In this paper, we have formulated a phase-field model based on the grandpotential functional for ... more In this paper, we have formulated a phase-field model based on the grandpotential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns arising out of diffusive instabilities during the growth of a precipitate in a supersaturated matrix. Here, we characterize the role of elastic energy anisotropy and its strength on the selection of a dendrite tip radius and velocity. We find that there is no selection of a unique tip shape as observed in the case of solidification, and the selection constant σ∗ = 2d0D/R 2 tipVtip increases linearly with simulation time for all the simulation conditions (where Rtip and Vtip are the tip radius and velocity). Therefore, structures derived in solid-state in the presence of elastic anisotropy may only be referred to as dendrite-like.

Research paper thumbnail of Phase-field study of the fragmentation secondary arm in Al-Cu alloys

Research paper thumbnail of Microstructures in a ternary eutectic alloy

Research paper thumbnail of Interphase anisotropy effects on lamellar eutectics: A numerical study

Physical Review E, 2015

In directional solidification of binary eutectics, it is often observed that two-phase lamellar g... more In directional solidification of binary eutectics, it is often observed that two-phase lamellar growth patterns grow tilted with respect to the direction z of the imposed temperature gradient. This crystallographic effect depends on the orientation of the two crystal phases α and β with respect to z. Recently, an approximate theory was formulated that predicts the lamellar tilt angle as a function of the anisotropy of the free energy of the solid(α)-solid(β) interphase boundary. We use two different numerical methods-phase-field (PF) and dynamic boundary-integral (BI)-to simulate the growth of steady periodic patterns in two dimensions as a function of the angle θ R between z and a reference crystallographic axis for a fixed relative orientation of α and β crystals, that is, for a given anisotropy function (Wulff plot) of the interphase boundary. For Wulff plots without unstable interphase-boundary orientations, the two simulation methods are in excellent agreement with each other, and confirm the general validity of the previously proposed theory. In addition, a crystallographic "locking" of the lamellae onto a facet plane is well reproduced in the simulations. When unstable orientations are present in the Wulff plot, it is expected that two distinct values of the tilt angle can appear for the same crystal orientation over a finite θ R range. This bistable behavior, which has been observed experimentally, is well reproduced by BI simulations, but not by the PF model. Possible reasons for this discrepancy are discussed.

Research paper thumbnail of Quantitative phase-field model for phase transformations in multi-component alloys

Phase-field modeling has spread to a variety of applications involving phase transformations. Whi... more Phase-field modeling has spread to a variety of applications involving phase transformations. While the method has wide applicability, derivation of quantitative predictions requires deeper understanding of the coupling between the system and model parameters. The book highlights a novel phase-field model based on a grand-potential formalism allowing for an elegant and efficient solution to problems in phase transformations.

Research paper thumbnail of Phase-Field Modeling as a Method Relevant for Modeling Phase Transformation During Interdiffusion

Handbook of Solid State Diffusion, Volume 1

Abstract Phase-field modeling has developed as an important tool in investigating microstructural... more Abstract Phase-field modeling has developed as an important tool in investigating microstructural evolution in a variety of phenomena such as solidification, solid-state phase transformations, electrochemical reactions, mechanical deformation and fracture processes, and also domain evolution in ferro-electric materials. Given the strong thermodynamic basis for the formulation of these models, they can be used to obtain strong predictions about structural pattern formation as a function of the material processing parameters. In this chapter, I will first give a brief history of the evolution in phase-field modeling, thereafter discuss the ingredients of a particular phase-field formulation, starting from the construction of the functional and the eventual derivation of the evolution equations of the order-parameters and the relevant state-variables. I will then utilize the formulation to highlight, how some of the phenomena regarding interdiffusion in a diffusion couple can be captured. Subsequently, I will place the model in the context of modeling real alloys with the incorporation of thermodynamic information from CALPHAD databases and mobilities from kinetic databases.

Research paper thumbnail of Role of anisotropy in the formation of broken-lamellar morphology in the Sn-Zn eutectic system

Research paper thumbnail of Three-Phase Eutectic Microstructures: Influence of Interfacial Energy Anisotropy and Solute Diffusivities

Metallurgical and Materials Transactions A, 2021

In this paper, we study three dimensional microstructural evolution in a symmetric ternary three-... more In this paper, we study three dimensional microstructural evolution in a symmetric ternary three-phase eutectic alloy using phase-field simulations under directional solidification conditions. While previous studies have explored the influence of volume fractions, difference in solid-liquid interfacial energies, velocity changes, etc. on the microstructural evolution, in this paper we deal with two unexplored fundamental aspects, namely the influence of solid-solid interfacial energy anisotropy as well as the disparity in the solute diffusivities in the liquid phase on three-phase microstructure formation. We begin by comparing the undercooling vs spacing variations for different steady state microstructures like the three-fibrous (hexagonal), brick-type and lamellar morphology under symmetric conditions and estimate the stability limits for each of the patterns for spacing variations. Thereafter, we investigate the transformation of the three-fibrous (hexagonal) arrangement to lowe...

Research paper thumbnail of Investigation of process–structure–property relationship in ternary organic photovoltaics

Organic photovoltaics (OPVs) have held on to the race for providing a sustainable source of energ... more Organic photovoltaics (OPVs) have held on to the race for providing a sustainable source of energy for more than two decades, and ternary OPVs have emerged as a promising candidate for harnessing solar energy. While the ternary OPVs have potential, optimization of the process parameters, particularly for deriving active-layer morphologies with high efficiencies, is non-trivial as the parameter space is large and a theoretical framework is necessary. This is specifically important for determining the appropriate compositions of the ternary blend which, upon phase-separation, lead to the formation of the heterogenous active layer with a distribution of three phases. In this paper, we present an approach for deriving both the process–structure and structure–property correlations based on the diffuse-interface approach. Herein, we derive process–structure correlations using phase-field simulations based on the Cahn–Hilliard formalism for modeling phase-separation in ternary systems wher...

Research paper thumbnail of Growth in multi-component alloys: Theoretical and numerical determination of phase concentrations

Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of... more Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of a second phase in ternary and higher multicomponent two phase alloys is an important problem due to the strong dependence of mechanical properties on compositions. In this paper, we derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar and cylindrical precipitates with the assumption of diagonal diffusivity matrices. We confirm our calculations by sharp interface and phase field simulations. The numerical techniques are in turn utilized for investigating the role of off-diagonal entries in the diffusivity matrix. In addition, the sharp interface methods allow for the tracking of the tie-line compositions during growth of 2D precipitates which contribute to an understanding of the change in equilibrium tie-lines chosen by the system during growth.

Research paper thumbnail of Untersuchung der Diffusionsabhängigkeit des Schmelzverhaltens nadelförmiger Kristallstrukturen

Research paper thumbnail of Exotic three-phase microstructures in the ternary Ag-Cu-Sb eutectic system

Research paper thumbnail of Microstructures in a ternary eutectic alloy: devising metrics based on neighbourhood relationships

IOP Conference Series: Materials Science and Engineering

Ternary eutectics, where three phases form simultaneously from the melt, present an opportunity t... more Ternary eutectics, where three phases form simultaneously from the melt, present an opportunity to study the fundamental science of microstructural pattern formation during the process of solidification. In this paper we investigate these phenomena, both experimentally and by phase-field simulations. The aim is to develop necessary characterisation tools which can be applied to both experimentally determined and simulated microstructures for a quantitative comparison between simulations and experiments. In SEM images of experimental cross sections of directionally solidified Ag-Al-Cu ternary eutectic alloy at least six different types of microstructures are observed. Corresponding 3D phase-field simulations for different solidification conditions and compositions allow us to span and isolate the material parameters which influence the formation of three-phase patterns. Both experimental and simulated microstructures were analysed regarding interface lengths, triple points and number of neighbours. As a result of this integrated experimental and computational effort we conclude that neighbourhood relationships as described herein, turn out to be an appropriate basis to characterise order in patterns.

Research paper thumbnail of Theoretical and numerical determination of phase concentrations during growth in ternary alloys

arXiv: Materials Science, 2016

Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of... more Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of a second phase in ternary and higher multicomponent two phase alloys is an important problem due to the strong dependence of mechanical properties on compositions. In this paper, we derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar and cylindrical precipitates with the assumption of diagonal diffusivity matrices. We confirm our calculations by sharp-interface and phase-field simulations. The numerical techniques are in turn utilized for investigating the role of off-diagonal entries in the diffusivity matrix. In addition, the sharp-interface methods allow for the tracking of the tie-line compositions during growth of 2D precipitates which contribute to an understanding of the change in equilibrium tie-lines chosen by the system during growth

Research paper thumbnail of Phase-field modeling of stress evolution in heterogen structures

Daniel Schneider, Oleg Tschukin, Abhik Choudhury, Michael Selzer, Britta Nestler 1 Institute of M... more Daniel Schneider, Oleg Tschukin, Abhik Choudhury, Michael Selzer, Britta Nestler 1 Institute of Materials and Processes, Karlsruhe University of Applied Science, Moltkestrasse 30, D-76133 Karlsruhe, Germany, daniel.schneider@kit.edu, oleg.tschukin@hs-karlsruhe.de, www.imp.hs-karlsruhe.de 2 Institute of Materials and Processes, Karlsruhe University of Applied Science, Moltkestrasse 30, D-76133 Karlsruhe, Germany, oleg.tschukin@hs-karlsruhe.de, www.imp.hs-karlsruhe.de 3 The Department of Materials Engineering, Indian Institute of Science Bangalore, abhiknc@materials.iisc.ernet.in, http://materials.iisc.ernet.in 4 IAM-ZBS, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, michael.selzer@kit.edu, britta.nestler@kit.edu, http://www.iam.kit.edu/zbs 5 IAM-ZBS, Karlsruhe Institute of Technology, Kaiserstrasse 12, 76131 Karlsruhe, Germany, britta.nestler@kit.edu, http://www.iam.kit.edu/zbs

Research paper thumbnail of Phase-Field Methods for Pattern-Formation

Research paper thumbnail of Elasto-plastic phase-field model accounting for mechanical jump conditions during solid-state phase transformations

Research paper thumbnail of Anwendung thermodynamischer Datensätze in der Phasenfeldsimulation

Research paper thumbnail of Crystallographic and Morphological Evidence of Solid–Solid Interfacial Energy Anisotropy in the Sn-Zn Eutectic System

Metallurgical and Materials Transactions A, 2020

In this paper, we explore the morphological evolution during two-phase growth in the Sn-Zn eutect... more In this paper, we explore the morphological evolution during two-phase growth in the Sn-Zn eutectic system, which has a particularly low volume fraction of the minority Zn phase. The reason for this choice is its exotic nature, as even with such a low volume fraction, the reported morphology is ''broken-lamellar,'' in contrast to the usually expected hexagonal arrangement of Zn rods in the Sn matrix. Thus, the main objective of the study is to investigate the reasons behind this phenomenon. We begin by presenting experimental results detailing the morphology and crystallography of the eutectic microstructures under various combinations of thermal gradients and velocities in directional solidification conditions. Based on the crystallography and further specially designed experiments we find that the solid-solid interface between the Sn and Zn crystal is anisotropic. On the basis of the results, we propose a hypothesis that the presence of solid-solid interfacial energy anisotropy leads to the formation of predominantly broken-lamellar structures, even when the minority fraction is significantly low.

Research paper thumbnail of Role of Solid–Solid Interfacial Energy Anisotropy in the Formation of Broken Lamellar Structures in Eutectic Systems

Metallurgical and Materials Transactions A, 2020

Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morpho... more Eutectic solidification gives rise to a wide range of microstructures. A commonly observed morphology is the periodic arrangement of lamellar plates with well-defined orientations of the solid–solid interface in a given eutectic grain. It is typically believed that this form of morphology develops due to the presence of solid–solid interfacial energy anisotropy. In this paper, we provide evidence using phase-field simulations where our focus is on alloys where the minority phase fraction is low. Our aim is to establish the role of solid–solid interfacial energy anisotropy in the stabilization of broken lamellar structures in such systems in contrast to the formation of a rod microstructure. In this regard, we conduct phase-field simulations for different strengths of anisotropy in both constrained and extended settings, using which we clarify the mechanisms by which a lamellar arrangement gets stabilized in the presence of anisotropy in the solid–solid interfacial energy.

Research paper thumbnail of Formation of solid-state dendrites under the influence of coherency stresses: A diffuse interface approach

In this paper, we have formulated a phase-field model based on the grandpotential functional for ... more In this paper, we have formulated a phase-field model based on the grandpotential functional for the simulation of precipitate growth in the presence of coherency stresses. In particular, we study the development of dendrite-like patterns arising out of diffusive instabilities during the growth of a precipitate in a supersaturated matrix. Here, we characterize the role of elastic energy anisotropy and its strength on the selection of a dendrite tip radius and velocity. We find that there is no selection of a unique tip shape as observed in the case of solidification, and the selection constant σ∗ = 2d0D/R 2 tipVtip increases linearly with simulation time for all the simulation conditions (where Rtip and Vtip are the tip radius and velocity). Therefore, structures derived in solid-state in the presence of elastic anisotropy may only be referred to as dendrite-like.

Research paper thumbnail of Phase-field study of the fragmentation secondary arm in Al-Cu alloys

Research paper thumbnail of Microstructures in a ternary eutectic alloy

Research paper thumbnail of Interphase anisotropy effects on lamellar eutectics: A numerical study

Physical Review E, 2015

In directional solidification of binary eutectics, it is often observed that two-phase lamellar g... more In directional solidification of binary eutectics, it is often observed that two-phase lamellar growth patterns grow tilted with respect to the direction z of the imposed temperature gradient. This crystallographic effect depends on the orientation of the two crystal phases α and β with respect to z. Recently, an approximate theory was formulated that predicts the lamellar tilt angle as a function of the anisotropy of the free energy of the solid(α)-solid(β) interphase boundary. We use two different numerical methods-phase-field (PF) and dynamic boundary-integral (BI)-to simulate the growth of steady periodic patterns in two dimensions as a function of the angle θ R between z and a reference crystallographic axis for a fixed relative orientation of α and β crystals, that is, for a given anisotropy function (Wulff plot) of the interphase boundary. For Wulff plots without unstable interphase-boundary orientations, the two simulation methods are in excellent agreement with each other, and confirm the general validity of the previously proposed theory. In addition, a crystallographic "locking" of the lamellae onto a facet plane is well reproduced in the simulations. When unstable orientations are present in the Wulff plot, it is expected that two distinct values of the tilt angle can appear for the same crystal orientation over a finite θ R range. This bistable behavior, which has been observed experimentally, is well reproduced by BI simulations, but not by the PF model. Possible reasons for this discrepancy are discussed.

Research paper thumbnail of Quantitative phase-field model for phase transformations in multi-component alloys

Phase-field modeling has spread to a variety of applications involving phase transformations. Whi... more Phase-field modeling has spread to a variety of applications involving phase transformations. While the method has wide applicability, derivation of quantitative predictions requires deeper understanding of the coupling between the system and model parameters. The book highlights a novel phase-field model based on a grand-potential formalism allowing for an elegant and efficient solution to problems in phase transformations.

Research paper thumbnail of Phase-Field Modeling as a Method Relevant for Modeling Phase Transformation During Interdiffusion

Handbook of Solid State Diffusion, Volume 1

Abstract Phase-field modeling has developed as an important tool in investigating microstructural... more Abstract Phase-field modeling has developed as an important tool in investigating microstructural evolution in a variety of phenomena such as solidification, solid-state phase transformations, electrochemical reactions, mechanical deformation and fracture processes, and also domain evolution in ferro-electric materials. Given the strong thermodynamic basis for the formulation of these models, they can be used to obtain strong predictions about structural pattern formation as a function of the material processing parameters. In this chapter, I will first give a brief history of the evolution in phase-field modeling, thereafter discuss the ingredients of a particular phase-field formulation, starting from the construction of the functional and the eventual derivation of the evolution equations of the order-parameters and the relevant state-variables. I will then utilize the formulation to highlight, how some of the phenomena regarding interdiffusion in a diffusion couple can be captured. Subsequently, I will place the model in the context of modeling real alloys with the incorporation of thermodynamic information from CALPHAD databases and mobilities from kinetic databases.

Research paper thumbnail of Role of anisotropy in the formation of broken-lamellar morphology in the Sn-Zn eutectic system

Research paper thumbnail of Three-Phase Eutectic Microstructures: Influence of Interfacial Energy Anisotropy and Solute Diffusivities

Metallurgical and Materials Transactions A, 2021

In this paper, we study three dimensional microstructural evolution in a symmetric ternary three-... more In this paper, we study three dimensional microstructural evolution in a symmetric ternary three-phase eutectic alloy using phase-field simulations under directional solidification conditions. While previous studies have explored the influence of volume fractions, difference in solid-liquid interfacial energies, velocity changes, etc. on the microstructural evolution, in this paper we deal with two unexplored fundamental aspects, namely the influence of solid-solid interfacial energy anisotropy as well as the disparity in the solute diffusivities in the liquid phase on three-phase microstructure formation. We begin by comparing the undercooling vs spacing variations for different steady state microstructures like the three-fibrous (hexagonal), brick-type and lamellar morphology under symmetric conditions and estimate the stability limits for each of the patterns for spacing variations. Thereafter, we investigate the transformation of the three-fibrous (hexagonal) arrangement to lowe...

Research paper thumbnail of Investigation of process–structure–property relationship in ternary organic photovoltaics

Organic photovoltaics (OPVs) have held on to the race for providing a sustainable source of energ... more Organic photovoltaics (OPVs) have held on to the race for providing a sustainable source of energy for more than two decades, and ternary OPVs have emerged as a promising candidate for harnessing solar energy. While the ternary OPVs have potential, optimization of the process parameters, particularly for deriving active-layer morphologies with high efficiencies, is non-trivial as the parameter space is large and a theoretical framework is necessary. This is specifically important for determining the appropriate compositions of the ternary blend which, upon phase-separation, lead to the formation of the heterogenous active layer with a distribution of three phases. In this paper, we present an approach for deriving both the process–structure and structure–property correlations based on the diffuse-interface approach. Herein, we derive process–structure correlations using phase-field simulations based on the Cahn–Hilliard formalism for modeling phase-separation in ternary systems wher...

Research paper thumbnail of Growth in multi-component alloys: Theoretical and numerical determination of phase concentrations

Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of... more Understanding the role of solute diffusivities in equilibrium tie-line selection during growth of a second phase in ternary and higher multicomponent two phase alloys is an important problem due to the strong dependence of mechanical properties on compositions. In this paper, we derive analytical expressions for predicting tie-lines and composition profiles in the matrix during growth of planar and cylindrical precipitates with the assumption of diagonal diffusivity matrices. We confirm our calculations by sharp interface and phase field simulations. The numerical techniques are in turn utilized for investigating the role of off-diagonal entries in the diffusivity matrix. In addition, the sharp interface methods allow for the tracking of the tie-line compositions during growth of 2D precipitates which contribute to an understanding of the change in equilibrium tie-lines chosen by the system during growth.

Research paper thumbnail of Untersuchung der Diffusionsabhängigkeit des Schmelzverhaltens nadelförmiger Kristallstrukturen

Research paper thumbnail of Exotic three-phase microstructures in the ternary Ag-Cu-Sb eutectic system

Research paper thumbnail of Microstructures in a ternary eutectic alloy: devising metrics based on neighbourhood relationships

IOP Conference Series: Materials Science and Engineering

Ternary eutectics, where three phases form simultaneously from the melt, present an opportunity t... more Ternary eutectics, where three phases form simultaneously from the melt, present an opportunity to study the fundamental science of microstructural pattern formation during the process of solidification. In this paper we investigate these phenomena, both experimentally and by phase-field simulations. The aim is to develop necessary characterisation tools which can be applied to both experimentally determined and simulated microstructures for a quantitative comparison between simulations and experiments. In SEM images of experimental cross sections of directionally solidified Ag-Al-Cu ternary eutectic alloy at least six different types of microstructures are observed. Corresponding 3D phase-field simulations for different solidification conditions and compositions allow us to span and isolate the material parameters which influence the formation of three-phase patterns. Both experimental and simulated microstructures were analysed regarding interface lengths, triple points and number of neighbours. As a result of this integrated experimental and computational effort we conclude that neighbourhood relationships as described herein, turn out to be an appropriate basis to characterise order in patterns.