Papers by Nikolas Provatas
arXiv (Cornell University), Oct 17, 2012
Phase field crystal methodology is applied, for the first time, to study the effect of alloy comp... more Phase field crystal methodology is applied, for the first time, to study the effect of alloy composition on the clustering behavior of a quenched/aged supersaturated ternary Al alloy system. An analysis of the work of formation is built upon the methodology developed in Fallah et al. to describe the dislocation-mediated formation mechanisms of early clusters in binary alloys [Phys. Rev. B.,
Physical Review B, Sep 2, 2014
This paper re-visits the weakly fourth order anisotropic Ginzburg-Landau (GL) theory of freezing ... more This paper re-visits the weakly fourth order anisotropic Ginzburg-Landau (GL) theory of freezing (also known as Landau-Brazowskii model or theory of weak crystallization) by comparing it to the recent density functional approach of the the Phase-Field Crystal (PFC) model. First we study the critical behavior of a generalized PFC model and show that (i) the so-called one-mode approximation for the Phase-Field Crystal model is exact, and (ii) the direct correlation function has no contribution to the phase diagram in the leading order. Next, we calculate the anisotropy of the crystal-liquid interfacial free energy in the Phase-Field Crystal (PFC) model analytically. For comparison, we also determine the anisotropy numerically and show that no range of parameters can be found for which the Phase-Field Crystal equation can quantitatively model anisotropy for metallic materials. Finally, we derive the leading order PFC amplitude model and show that it coincides with the weakly fourth order anisotropic GL theory, as a consequence of that the assumptions of the GL theory are inherent in the PFC model. We also propose a way to calibrate the anisotropy in the Ginzburg-Landau theory via a generalized gradient operator emerging from the direct correlation function appearing in the generating PFC free energy functional.
Physical Review Letters, Apr 15, 2015
A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of... more A new phase field crystal (PFC) type theory is presented, which accounts for the full spectrum of solid-liquidvapor phase transitions within the framework of a single density order parameter. Its equilibrium properties show the most quantitative features to date in PFC modelling of pure substances, and full consistency with thermodynamics in pressure-volume-temperature space is demonstrated. A method to control either the volume or the pressure of the system is also introduced. Non-equilibrium simulations show that 2 and 3-phase growth of solid, vapor and liquid can be achieved, while our formalism also allows for a full range of pressure-induced transformations. This model opens up a new window for the study of pressure driven interactions of condensed phases with vapor, an experimentally relevant paradigm previously missing from phase field crystal theories.
Physical Review E, Aug 19, 2010
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional t... more The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation functions in DDFT, and the lowest order approximation using scale analysis. The complete amplitude equation formalism for binary PFC is developed to describe the coupled dynamics of slowly varying complex amplitudes of structural profile, zerothmode average atomic density, and system concentration field. Effects of noise (corresponding to stochastic amplitude equations) and species-dependent atomic mobilities are also incorporated in this formalism. Results of a sample application to the study of surface segregation and interface intermixing in alloy heterostructures and strained layer growth are presented, showing the effects of different atomic sizes and mobilities of alloy components. A phenomenon of composition overshooting at the interface is found, which can be connected to the surface segregation and enrichment of one of the atomic components observed in recent experiments of alloying heterostructures.
arXiv (Cornell University), Jan 18, 2011
This paper studies how solute segregation and its relationship to grain boundary energy in binary... more This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elastoplastic effects on diffusional time scales. Grain boundaries are simulated using two binary alloy PFC models-the original binary model by Elder et al (2007) and the XPFC model by Greenwood et al (2011). In both cases, grain boundary energy versus misorientation data is shown to be well described by Read-Shockley theory. The Gibbs Adsorption Theorem is then used to derive a semi-analytic function describing solute segregation to grain boundaries. This is used to characterize grain boundary energy versus average alloy concentration and undercooling below the solidus. We also investigate how size mismatch between different species and their interaction strength affects segregation to the grain boundary. Finally, we interpret the implications of our simulations on material properties related to interface segregation.
arXiv (Cornell University), Mar 21, 2020
In this work, the effect of building direction on the microstructure evolution of laser-powder be... more In this work, the effect of building direction on the microstructure evolution of laser-powder bed fusion (LPBF) processed AlSi10Mg alloy was investigated. The building direction, as shown in experimentally fabricated parts, can influence the solidification behavior and promote morphological transitions in cellular dendritic microstructures. We develop a thermal model to systemically address the impact of laser processing conditions, and building direction on the thermal characteristics of the molten pool during laser processing of AlSi10Mg alloy. We then employ a multi-order parameter phase field model to study the microstructure evolution of LPBF-AlSi10Mg in the dilute limit, using the underlying thermal conditions for horizontal and vertical building directions as input. The phase field model employed here is designed to simulate solidification using heterogeneous nucleation from inoculant particles allowing to take into account morphological phenomena including the columnar-to-equiaxed transition (CET). The phase field model is first validated against the predictions of the previously developed steady-state CET theory of Hunt [1]. It is then used under transient conditions to study microstructure evolution, revealing that the nucleation rate is noticeably higher in the horizontally built samples due to larger constitutional undercooling, which is consistent with experimental observations. We further quantify the effect of building direction on the local cooling conditions, and consequently on the grain morphology.
arXiv (Cornell University), Sep 13, 2018
Solute trapping is an important phenomenon in rapid solidification of alloys, for which the conti... more Solute trapping is an important phenomenon in rapid solidification of alloys, for which the continuous growth model (CGM) is a popular sharp interface theory. Using matched asymptotic analysis, we show how to quantitatively map the sharp interface behavior of a binary alloy phase field model onto the CGM kinetics of Aziz et al. [1], with a controllable partition coefficient k(V). We demonstrate the parameterizations that allow the phase field model to map onto the corresponding CGM or classical sharp interface models. We also demonstrate that the mapping is convergent for different interface widths. Finally we present the effect that solute trapping can have on cellular growth in a directional solidification simulation. The treatment presented for solute trapping can be easily implemented in different phase field models, and is expected to be an important feature in future studies of quantitative phase field modeling in rapid solidification regimes, such as those relevant to additive manufacturing.
arXiv (Cornell University), Mar 3, 2014
Material properties controlled by evolving defect structures, such as mechanical response, often ... more Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and nonconservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-type glide mechanisms involving closed dislocation loops or grain boundaries as well as Bardeen-Herring-type climb mechanisms involving precipitates, inclusions, and/or voids. Both source classes are naturally and simultaneously captured at the atomistic level by PFC descriptions, with arbitrarily complex defect configurations, types, and environments. An unexpected dipole-to-quadrupole source transformation is identified, as well as various new and complex geometrical features of loop nucleation via climb from spherical particles. Results for the strain required to nucleate a dislocation loop from such a particle are in agreement with analytic continuum theories. Other basic features of FCC and BCC dislocation structure and dynamics are also outlined, and initial results for dislocation-stacking fault tetrahedron interactions are presented. These findings together highlight various capabilities of the PFC approach as a coarse-grained atomistic tool for the study of three-dimensional crystal plasticity.
Bulletin of the American Physical Society, Mar 15, 2017
arXiv (Cornell University), Jan 18, 2011
This paper studies how solute segregation and its relationship to grain boundary energy in binary... more This paper studies how solute segregation and its relationship to grain boundary energy in binary alloys is captured in the phase field crystal (PFC) formalism, a continuum method that incorporates atomic scale elastoplastic effects on diffusional time scales. Grain boundaries are simulated using two binary alloy PFC models-the original binary model by Elder et al (2007) and the XPFC model by Greenwood et al (2011). In both cases, grain boundary energy versus misorientation data is shown to be well described by Read-Shockley theory. The Gibbs Adsorption Theorem is then used to derive a semi-analytic function describing solute segregation to grain boundaries. This is used to characterize grain boundary energy versus average alloy concentration and undercooling below the solidus. We also investigate how size mismatch between different species and their interaction strength affects segregation to the grain boundary. Finally, we interpret the implications of our simulations on material properties related to interface segregation.
arXiv (Cornell University), Oct 4, 2012
A phase field crystal model is used to investigate the mechanisms of formation and growth of earl... more A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that formation of early sub-critical clusters is triggered by the stress relaxation effect of quenched-in defects, such as dislocations, on the energy barrier and the critical size for nucleation. In particular, through analysis of system energetics, we demonstrate that the growth of sub-critical clusters into overcritical sizes occurs due to the fact that highly strained areas in the lattice locally reduce or even eliminate the free energy barrier for a first-order transition.
Acta Materialia, 2015
Strengthening in age-hardenable alloys is mainly achieved through nano-scale precipitates whose f... more Strengthening in age-hardenable alloys is mainly achieved through nano-scale precipitates whose formation paths from the atomic-scale, solute-enriched entities are rarely analyzed and understood in a directly-verifiable way. Here, we discover a pathway for the earliest-stage precipitation in Al-Mg-Si alloys: solute clustering leading to three successive variants of FCC clusters, followed by the formation of non-FCC GP-zones. The clusters, which originally assume a spherical morphology (C1), evolve into elongated clusters and orient themselves on {111} Al (C2) and subsequently on {100} Al planes and <100> Al directions (C3). We also analyze the association of quenched-in dislocations with clustering phenomena. The results of this work can open a new frontier in advancing alloy-process-property design for commercially-important age-hardenable Al alloys.
Modelling
The prediction of the equilibrium and metastable morphologies during the solidification of Ni-bas... more The prediction of the equilibrium and metastable morphologies during the solidification of Ni-based superalloys on the mesoscopic scale can be performed using phase-field modeling. In the present paper, we apply the phase-field model to simulate the evolution of solidification microstructures depending on undercooling in a quasi-binary approximation. The results of modeling are compared with experimental data obtained on samples of the alloy Inconel 718 (IN718) processed using the electromagnetic leviatation (EML) technique. The final microstructure, concentration profiles of niobium, and the interface-velocity–undercooling relationship predicted by the phase field modeling are in good agreement with the experimental findings. The simulated microstructures and concentration fields can be used as inputs for the simulation of the precipitation of secondary phases.
Bulletin of the American Physical Society, 2017
ACS Applied Nano Materials, 2021
Mechanochemistry is becoming an established method for the sustainable, solidphase synthesis of s... more Mechanochemistry is becoming an established method for the sustainable, solidphase synthesis of scores of nano-materials and molecules, ranging from active pharma-1
Physical Review Letters, 2016
We propose an atomistic model of electromigration (EM) in metals based on a recently developed ph... more We propose an atomistic model of electromigration (EM) in metals based on a recently developed phasefield-crystal (PFC) technique. By coupling the PFC model's atomic density field with an applied electric field through the EM effective charge parameter, EM is successfully captured on diffusive time scales. Our framework reproduces the well-established EM phenomena known as Black's equation and the Blech effect, and also naturally captures commonly observed phenomena such as void nucleation and migration in bulk crystals. A resistivity dipole field arising from electron scattering on void surfaces is shown to contribute significantly to void migration velocity. With an intrinsic time scale set by atomic diffusion rather than atomic oscillations or hopping events, as in conventional atomistic methods, our theoretical approach makes it possible to investigate EM-induced circuit failure at atomic spatial resolution and experimentally relevant time scales.
Physical Review E, 2017
We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion... more We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers thanks to a dynamic adaptive mesh refinement technique that reduces finite size effects, which can affect or even preclude the emergence of these patterns. This technique also allows achieving very large computational domains, enabling the study of system-size effects. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip-splitting and cell-merging, are well described within the framework of thermo-diffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as "quasi-linear" and characterized by low amplitude cells and may follow the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly non-linear effects become prominent and large amplitude, complex cellular and seaweed dendritic morphologies emerge.
A phase field crystal model is used to investigate the mechanisms of formation and growth of earl... more A phase field crystal model is used to investigate the mechanisms of formation and growth of early clusters in quenched/aged dilute binary alloys, a phenomenon typically outside the scope of molecular dynamics time scales. We show that formation of early sub-critical clusters is triggered by the stress relaxation effect of quenched-in defects, such as dislocations, on the energy barrier and the critical size for nucleation. In particular, through analysis of system energetics, we demonstrate that the growth of sub-critical clusters into overcritical sizes occurs due to the fact that highly strained areas in the lattice locally reduce or even eliminate the free energy barrier for a first-order transition.
The prediction of microstructure selection in solidification will play a vital role in the optimi... more The prediction of microstructure selection in solidification will play a vital role in the optimization of next-generation alloys. In this work we examine the fundamental nature of microstructure formation in directional solidification of binary alloys. We begin by re-visiting pattern selection in cellular growth in directional solidification experiments of binary alloys of pivalic acid (PVA) and succinonitrile (SCE). Various studies have characterized cell spacing versus pulling speed by fitting the cell wavelength to power laws of velocity over different growth ranges. We show that through suitable scaling, microstructure selection can be described in terms of a universal scaling function generic to the cellular growth regime. These results are confirmed by phase-field simulations of directional solidification, performed at experimentally relevant parameters through the use of a recent multi-scale adaptive-mesh refinement technique. We characterize the details of the cellular scal...
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Papers by Nikolas Provatas