Kumar Ankit

Theoretical and numerical study of lamellar eutectoid growth influenced by volume diffusion.

We investigate the lamellar growth of pearlite at the expense of austenite during the eutectoid transformation in steel. To begin with, we extend the Jackson–Hunt-type calculation (previously used to analyze eutectic transformation) to eutectoid transformation by accounting for diffusion in all the phases. Our principal finding is that the growth rates in the presence of diffusion in all the phases are different compared to the case when diffusion in growing phases is absent. The difference in the dynamics is described by a factor ’ρ’ which comprises the ratio of the diffusivities of the bulk and the growing phases, along with the ratios of the slopes of the phase coexistence lines. Thereafter, we perform phase-field simulations, the results of which are in agreement with analytical predictions. The phase-field simulations also reveal that diffusion in austenite as well as ferrite leads to the formation of tapered cementite along with an overall increase in the transformation kinetics as compared to diffusion in austenite (only). Finally, it is worth noting that the aim of present work is not to consider the pearlitic transformation in totality; rather it is to isolate and thereby investigate the influence of diffusivity in the growing phases on the front velocity.

Phase-field study of grain boundary tracking behavior in crack-seal microstructures

In order to address the growth of crystals in veins, a multiphase-field model is used to capture the dynamics of crystals precipitating from a super-saturated solution. To gain a detailed understanding of the polycrystal growth phenomena in veins, we investigate the influence of various boundary conditions on crystal growth. In particular, we analyze the formation of vein microstructures resulting from the free growth of crystals as well as crack-sealing processes. We define the crystal symmetry by considering the anisotropy in surface energy to simulate crystals with flat facets and sharp corners. The resulting growth competition of crystals with different orientations is studied to deduce a consistent orientation selection rule in the free-growth regime. Using crack-sealing simulations, we correlate the grain boundary tracking behavior depending on the relative rate of crack opening, opening trajectory, initial grain size, and wall roughness. Further, we illustrate how these parameters induce the microstructural transition between blocky (crystals growing anisotropically) to fibrous morphology (isotropic) and formation of grain boundaries. The phase-field simulations of crystals in the free-growth regime (in 2D and 3D) indicate that the growth or consumption of a crystal is dependent on the orientation difference with neighboring crystals. The crack-sealing simulation results (in 2D and 3D) reveal that crystals grow isotropically and grain boundaries track the opening trajectory if the wall roughness is high, opening increments are small, and crystals touch the wall before the next crack increment starts. Further, we find that within the complete crack-seal regime, anisotropy in surface energy results in the formation of curved/oscillating grain boundaries (instead of straight) when the crack-opening velocity is increased and wall roughness is not sufficiently high. Additionally, the overall capability of phase-field method to simulate large-scale polycrystal growth in veins (in 3D) is demonstrated enumerating the main advantages of adopting the novel approach.

Microstructural evolution in bitaxial crack-seal veins: A phase-field study

Bitaxial crack sealing by epitaxial crystal growth is the most common vein-forming process in Earths crust, but the details of the microstructural processes in these are not well understood. Here we model the evolution of bitaxial crack-seal quartz veins in two and three dimensions, using the phase-field method. Our numerical simulations show the influence of different parameters, such as the obliquity of crack opening and crack location, grain size, and orientations on the evolving vein microstructure. We examine the underlying growth competition observed during epitaxial growth of quartz. Results show many similarities with natural microstructures such as stretched crystals and compare well with the previous numerical findings. As the ratio of crack aperture and matrix grain size for the present studies is chosen to be sufficiently large for growth competition to occur before complete sealing, it leads to the formation of crystal fragments along the crack-opening trajectory. We explain how such fragment trails act as potential indicators of the opening of crack-seal veins, if they are confirmed to be common in natural microstructures. Finally, we highlight the importance of accounting for the third dimension in the numerical simulations by analyzing the evolution of fluid connectivity in 2-D and 3-D during the sealing process.

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.

Three-dimensional phase-field study of crack-seal microstructures - insights from innovative post-processing techniques

Numerical simulations of vein evolution contribute to a better understanding of processes involved in their formation and possess the potential to provide invaluable insights into the rock deformation history and fluid flow pathways. The primary aim of the present article is to investigate the influence of a realistic boundary condition, i.e. an algorithmically generated fractal surface, on the vein evolution in 3-D using a thermodynamically consistent approach, while explaining the benefits of accounting for an extra dimensionality. The 3-D simulation results are supplemented by innovative numerical post-processing and advanced visualization techniques. The new methodologies to measure the tracking efficiency demonstrate the importance of accounting the temporal evolution; no such information is usually accessible in field studies and notoriously difficult to obtain from laboratory experiments as well. The grain growth statistics obtained by numerically post-processing the 3-D computational microstructures explain the pinning mechanism which leads to arrest of grain boundaries/multi-junctions by crack peaks, thereby, enhancing the tracking behavior.

Electric-field-induced lamellar to hexagonally perforated lamellar transition in diblock copolymer thin films: kinetic pathways

Symmetric block-copolymers, hitherto, are well known to evolve into parallel, perpendicular and mixed lamellar morphologies under the concomitant influence of an electric field and substrate affinity. In the present work, we show that an additional imposed confinement can effectuate a novel parallel lamellar to hexagonally perforated lamellar (HPL) transition in monolayer and bilayer films. Three dimensional numerical studies are performed using the Ohta-Kawasaki functional, complemented with an exact solution of Maxwells equation. HPL is shown to stabilize at large substrate affinity in a narrow region of the phase diagram between parallel and perpendicular lamellar transitions in ultra-thin films. Additionally, we also identify perforated lamellae as intermediate structures during parallel-to-perpendicular lamellar transition. A systematic analysis using Minkowski functionals yields deeper insights into the associated kinetic pathways.

Measuring solid–liquid interfacial energy fields: diffusion-limited patterns

The Leibniz–Reynolds transport theorem yields an omnimetric interface energy balance, i.e., one valid over all continuum length scales. The transport theorem, moreover, indicates that solid–liquid interfaces support capillary-mediated redistributions of energy capable of modulating an interface’s motion—a thermodynamic phenomenon not captured by Stefan balances that exclude capillarity. Capillary energy fields affect interfacial dynamics on scales from about 10 nm to several mm. These mesoscopic fields were studied using entropy density multiphase-field simulations. Energy rate distributions were exposed and measured by simulating equilibrated solid–liquid interfaces configured as stationary grain boundary grooves (GBGs). Negative rates of energy distributed over GBGs were measured as residuals, by subtracting the linear potential distribution contributed by applied thermal gradients constraining the GBGs from the nonlinear distributions actually developed along their solid–liquid interface. Rates of interfacial cooling revealed numerically confirm independent predictions based on sharp-interface thermodynamics, variational calculus, and field theory. This study helps answer a long-standing question: What creates patterns for diffusion-limited transformations in nature and in material microstructures?

Phase-field modeling of microstructural pattern formation in alloys and geological veins

With the advent of high performance computing, the application areas of the phase-field method, traditionally used to numerically model the phase transformation in metals and alloys, have now spanned into geoscience. A systematic investigation of the two distinct scientific problems in consideration suggest a strong influence of interfacial energy on the natural and induced pattern formation in diffusion-controlled regime.