The design of polycrystalline alloys hinges on a predictive understanding of the interaction between the diffusing solutes and the motion of the constituent crystalline interfaces. Existing frameworks ignore the dynamic multiplicity of and transitions between the interfacial structures and phases. Here, we develop a computationally-accessible theoretical framework based on short-time equilibrium fluctuations to extract the drag force exerted by the segregating solute cloud. Using three distinct classes of computational techniques, we show that the random walk of a solute-loaded interface is necessarily non-classical at short time-scales as it occurs within a confining solute cloud. The much slower stochastic evolution of the cloud allows us to approximate the short-time behavior as an exponentially sub-diffusive Brownian motion in an external trapping potential with a stiffness set by the average drag force. At longer time-scales, the interfacial and bulk forces lead to a gradual recovery of classical random walk of the interface with a diffusivity set by the extrinsic mobility. The short-time response is accessible via {\it ab-initio} computations, offering a firm foundation for high throughput, rational design of alloys for controlling microstructural evolution in polycrystals, and in particular for nanocrystalline alloys-by-design.
We show that molecular dynamics (MD) simulations are capable of reproducing the drag of solute segregation atmospheres by moving grain boundaries (GBs). Although lattice diffusion is frozen out on the MD timescale, the accelerated GB diffusion provides enough atomic mobility to allow the segregated atoms to follow the moving GB. This finding opens the possibility of studying the solute drag effect with atomic precision using the MD approach. We demonstrate that a moving GB activates diffusion and alters the short-range order in the lattice regions swept during its motion. It is also shown that…
The long wavelength limit of a recent microscopic phase field crystal (PFC) theory of a binary alloy mix- ture is used to derive an analytical approximation for the segregation coefficient as a function of the interface velocity, and relate it to the two-point correlation function of the liquid and the thermodynamic properties of solid and liquid phases. Our results offer the first analytic derivation of solute segregation and solute drag de- rived from a microscopic model, and analytically support recent molecular dynamics and fully numerical PFC simulations. Our analytical result also provid…
We investigate the effect of solute drag on grain growth (GG) kinetics in olivine-rich rocks through full field and mean field modelling. Considering a drag force exerted by impurities on grain boundary migration allows reconciling laboratory and natural constraints on olivine GG kinetics. Solute drag is implemented in a full field level-set framework and on a mean field model, which explicitly accounts for a grain size distribution. After calibration of the mean field model on full field results, both models are able to both reproduce laboratory GG kinetics and to predict grain sizes consiste…
A three-dimensional atomistic Kinetic Monte Carlo model was developed and used to study the interaction between mobile solutes and a migrating interface. While the model was developed with a simplified energetic and topological description, it was also constructed to capture, in the absence of solute, the Burke-Turnbull model for interface migration and, in the presence of solutes, solute segregation to different types of interface sites. After parameterizing the model, simulations were performed to study the relationship between average interface velocity and imposed driving pressure for vary…
A discrete model and the regular solution approximation are applied to describe the effect of grain boundary motion on grain boundary phase transformations in a binary alloy. The model predicts all thermodynamic properties of the grain boundary and the solute drag force, and permits a broad exploration of the parameter space and different dynamic regimes. The grain boundary phases continue to exist in the moving grain boundary and show a dynamic hysteresis loop, a dynamic critical line, and other features that are similar to those for equilibrium phases. Grain boundary motion strongly affects …
Atomic-Scale Insights into Solute Drag Effects on Grain Boundary Motion in Mg-Al and Mg-Ca Alloys
College of Materials Science and Engineering, State Key Laboratory of Cemented Carbide, Hunan University（湖南大学材料科学与工程学院）；McGill University（麦吉尔大学）；Institute of Solid State Physics, Chinese Academy of Sciences（中国科学院固体物理研究所）；School of Physics and Electronics, Hunan University（湖南大学物理与电子学院）；Hunan University（湖南大学）
Stochastic model and kinetic Monte Carlo simulation of solute interactions with stationary and moving grain boundaries. I. Model formulation and application to one-dimensional systems
The process of rapid solidification of a binary mixture is considered in the framework of local nonequilibrium model (LNM) based on the assumption that there is no local equilibrium in solute diffusion in the bulk liquid and at the solid-liquid interface. According to LNM the transition to complete solute trapping and diffusionless solidification occurs at a finite interface velocity $V=V_D$, where $V_D$ is the diffusion speed in bulk liquid. In the present work, the boundary conditions at the phase interface moving with the velocity $V$ close to $V_D$ ($V \lesssim V_D$) have been derived to f…
Solidification structures are determined by the interaction between the interfacial processes and transport processes of heat and solute. In this paper, we investigate planar instability in directional solidification. Firstly, the interfacial evolution at the initial growth stage is simulated, indicating the planar instability is represented by the transition from the planar to the cellular. Secondly, to represent the history-dependence of solidification, constant thermal gradient G and varying pulling speed VP are used in the simulations. The results indicate the cooling rate R ( = G*VP) domi…
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 …
The effect of nonequilibrium solute trapping by a growing solid under rapid solidification conditions is studied using a phase-field model. Considering a continuous steady-state concentration profile across the diffuse solid-liquid interface, a new definition of the nonequilibrium partition coefficient in the phase-field context is introduced. This definition leads, in particular for high growth velocities, to a better description of the available experimental data in comparison with other diffuse interface and sharp-interface predictions.
Mechanism of solute-enriched clusters formation in neutron-irradiated pressure vessel steels is proposed and developed in case of Fe-Cu model alloys. We show that the obtained results are in a good agreement with available experimental data on the parameters of clusters enriched with the alloying elements. The suggested solute-drag mechanism is analogous to the well-known zone-refining process. Our model explains why the formation of solute-enriched clusters does not happen in austenitic stainless steels with fcc lattice structure. It also allows to quantify the method of evaluation of neutron…
Numerous experimental data on the rapid solidification of binary systems exhibit the formation of metastable solid phases with the initial (nominal) chemical composition. This fact is explained by complete solute trapping leading to diffusionless (chemically partitionless) solidification at a finite growth velocity of crystals. Special attention is paid to developing a model of rapid solidification which describes a transition from chemically partitioned to diffusionless growth of crystals. Analytical treatments lead to the condition for complete solute trapping which directly follows from the…
Non-radiative decay channels in the L-edge fluorescence spectra from transition metal-aqueous solutions give rise to spectral dips in X-ray transmission spectra. Their origin is unraveled here using partial and inverse partial fluorescence yields on the micro-jet combined with multi-reference ab initio electronic structure calculations. Comparing Fe2+, Fe3+, and Co2+ systems we demonstrate unequivocally that spectral dips are due to a state-dependent electron delocalization within the manifold of d-orbitals.
DFT and MLIP study of solute segregation to coherent and semi-coherent α-Fe/Fe$_3$C interfaces
Christian Doppler Laboratory for Knowledge-based Design of Advanced Steels, Department of Materials Science, Montanuniversität Leoben（奥地利莱奥本矿业大学材料科学系先进钢知识基础设计基督教多普勒实验室）
A thorough understanding of pattern selection is necessary for the control of solidification structures, which are dissipative structures created by irreversible processes. In this paper, we simulate solidification evolution with different Preferred Crystallographic Orientations (PCOs) through the Phase-Field model. Then we study the effect of solute segregation on the interface energy, as well as the influence of the interface energy on the pattern selection. At the initial stage, the solute segregation influences the interface energy, determining the instability of the planar interface. Duri…
The control of solute segregation at grain boundaries (GBs) is essential in engineering alloy properties, however the structure-activity relationship of the key parameter-the segregation energies-still remains elusive. Here we propose the electronic and geometric descriptors of GB segregation based on the valence, electronegativity and size of solutes and the non-local coordination number of free surfaces, with which we build a predictive framework to determine the segregation energies across different solutes, matrices, GB structures and segregation sites. This framework uncovers not only the…
The interface stability against small perturbations of the planar solid-liquid interface is considered analytically in linear approximation. Following the analytical procedure of Trivedi and Kurz (Trivedi R, Kurz W. Acta Metall 1986;34:1663), which is advancing the original treatment of morphological stability by Mullins and Sekerka (Mullins WW, Sekerka RF. J Appl Phys 1964;35:444) to the case of rapid solidification, we extend the model by introducing the local nonequilibrium in the solute diffusion field around the interface. A solution to the heat- and mass-transport problem around the pert…
We minimized the interface diffuseness in the phase-field models by introducing the parabolic double-well potential and localizing the solute redistribution (or latent heat release) into a narrow region within the phase-field interface. In spite of the parabolic potential with cusps, highly localized solute redistribution and discontinuous diffusivity function adopted in this model, it works remarkably well in numerical computations. The computations on dendritic solidification of an one-sided system yield quantitatively the same results with the anti-trapping model [A. Karma, Phys. Rev. Lett.…
A method based on the Gibbs' adsorption isotherm is developed to calculate the decrease in interfacial free energy resulting from solute segregation at an internal interface, built on measured concentration profiles. Utilizing atom-probe tomography (APT), we first measure a concentration profile of the relative interfacial excess of solute atoms across an interface. To accomplish this we utilize a new method based on J. W. Cahn's formalism for the calculation of the Gibbs interfacial excess. We also introduce a method to calculate the decrease in interfacial free energy that is caused by the s…
On the basis of local nonequilibrium approach, the one-dimensional model of the solute diffusion during rapid solidification of the binary alloy in the semi-infinite volume is considered. Within the scope of the model it is supposed that mass transport is described by the telegrapher equation. The basic assumption concerns the behavior of the diffusion flux and the solute concentration at the interface. Under the condition that these quantities are given by the superposition of the exponential functions the solutions of the telegrapher equation determining the flux and the solute distributions…
In this study we have incorporated two time scales into the phase field crystal model of a binary alloy to explore different solute trapping properties as a function of crystal-melt interface velocity. With only diffusive dynamics, we demonstrate that the segregation coefficient, K as a function of velocity for a binary alloy is consistent with the model of Kaplan and Aziz where K approaches unity in the limit of infinite velocity. However, with the introduction of wave like dynamics in both the density and concentration fields, the trapping follows the kinetics proposed by S. Sobolev[Phys. Re…
Impurity diffusion coefficients are entirely obtained from a low cost classical molecular statics technique (CMST). In particular, we show how the CMST is appropriate in order to describe the impurity diffusion behavior mediated by a vacancy mechanism. In the context of the five-frequency model, CMST allows to calculate all the microscopic parameters, namely: the free energy of vacancy formation, the vacancy-solute binding energy and the involved jump frequencies, from them, we obtain the macroscopic transport magnitudes such as: correlation factor, solvent-enhancement factor, Onsager and diff…
We examine substrate-to-film interfacial phonon drag on typical spin Seebeck heterostructures, in particular studying the effect of ferromagnetic magnons on the phonon-electron drag dynamics at the interface. We investigate with high precision the effect of magnons in the Pt|YIG heterostructure by designing a magnon drag thermocouple; a hybrid sample with both a Pt|YIG film and Pt|GGG interface accessible isothermally via a 6 nm Pt film patterned in a rectangular U shape with one arm on the 250 nm YIG film and the other on GGG. We measure the voltage between the isothermal ends of the U, while…
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 elasto-plastic 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 se…
Impurity diffusion coefficients are entirely obtained from a low cost classical molecular statics technique (CMST). In particular, we show how CMST is appropriate in order to describe the impurity diffusion behavior mediated by a vacancy mechanism. In the context of the five-frequency model, CMST allows to calculate all the microscopic parameters, namely: the free energy of vacancy formation, the vacancy-solute binding energy and the involved jump frequencies, from them, we obtain the macroscopic transport magnitudes such as: correlation factor, solvent-enhancement factor, Onsager and diffusio…
A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than previous formulations and permits to eliminate non-equilibrium effects at the interface. Dendrite growth simulations with vanishing solid diffusivity show that both the interface evolution and the solute profile in the solid are well resolved.
We characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multi-phase-field equations for stationary interfaces to a multi-dimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range…
The influence of coherent interface on dissipations of mechanical energy of driven dislocations near to a point of martensite type phase transition is considered. The expressions for dynamic braking of dislocations, owing to losses of energy on excitation of deformations-type phase transition are received.
We present a detailed derivation and thin interface analysis of a phase-field model that can accurately simulate microstructural pattern formation for low-speed directional solidification of a dilute binary alloy. This advance with respect to previous phase-field models is achieved by the addition of a phenomenological "antitrapping" solute current in the mass conservation relation [A. Karma, Phys. Rev. Lett 87, 115701 (2001)]. This antitrapping current counterbalances the physical, albeit artificially large, solute trapping effect generated when a mesoscopic interface thickness is used to sim…
Observing solute hydrogen (H) in matter is a formidable challenge, yet, enabling quantitative imaging of H at the atomic-scale is critical to understand its deleterious influence on the mechanical strength of many metallic alloys that has resulted in many catastrophic failures of engineering parts and structures. Here, we report on the APT analysis of hydrogen (H) and deuterium (D) within the nanostructure of an ultra-high strength steel with high resistance to hydrogen embrittlement. Cold drawn, severely deformed pearlitic steel wires (Fe-0.98C-0.31Mn-0.20Si-0.20Cr-0.01Cu-0.006P-0.007S wt.%, …
Understanding the composition evolution of grain boundaries and grain boundary precipitation at near-atomic scale in aluminum alloys is crucial to tailor mechanical properties and to increase resistance to corrosion and stress corrosion cracking. Here, we elucidate the sequence of precipitation on grain boundaries in comparison to the bulk in a model Al-Zn-Mg-Cu alloy. We investigate the material from the solution heat treated state (475{\textdegree}C), through the very early stages of aging to the peak aged state at 120{\textdegree}C and further into the overaged regime at 180{\textdegree}C. …
Planar solidification from an undercooled melt has been considered using the phase-field model. The solute and the phase fields have been found in the limit of small impurity concentration. These solutions in the limit of vanishing velocity of the interface motion give the equilibrium partition coefficient and the liquidus slope. Asymptotic expansions for the solute and for the phase fields, and the relation between the diffusive speed and the parameters of the phase field model have been found at high growth velocity. A comparison with numerical calculations is presented.
We introduce a new phase-field formulation of rapid alloy solidification that quantitatively incorporates nonequilibrium effects at the solid-liquid interface over a very wide range of interface velocities. Simulations identify a new dynamical instability of dendrite tip growth driven by solute trapping at velocities approaching the absolute stability limit. They also reproduce the formation of the widely observed banded microstructures, revealing how this instability triggers transitions between dendritic and microsegregation-free solidification. Predicted band spacings agree quantitatively w…
Solute decoration at grain boundaries (GB) leads to a number of phenomenon such as changes in interface structure,mobility,cohesion etc.Recent experimental investigations on interfacial segregation in steels are based on microstructural characterisation using two correlative methodologies, namely,Transmission Electron Microscopy-Atom Probe Tomography (APT) and Electron Backscatter Diffraction-APT.Considering the growing interest in this avenue,the present review is aimed at addressing the common adsorption isotherms used for quantifying interfacial segregation and providing an overview of the …
Freezing of polymer solutions has been extensively investigated from many aspects, especially the complex pattern formation. The cell/dendrite micro-structures are believed to be in the type of diffusion-induced M-S instability. However, the presence of polymer as an impurity in water is significantly different from that of small ions. The quantitative transient investigation on directional freezing of polymer solutions remains lack due to some challenges. For the first time, we observed the planar instability behaviors during unidirectional freezing of a polymer solution together with a typic…
We present a new phase-field formulation for the non-equilibrium interface kinetics. The diffuse interface is considered an integral of numerous representative volume elements (RVEs), in which there is a two-phase mixture with two conserved and two non-conserved concentration fields. This particular way of separating concentration fields leads to two distinct dissipative processes besides the phase boundary migration, i.e., trans-sharp-interface diffusion between different phases within a single RVE and trans-diffuse-interface diffusion between different RVEs within a single phase. A two-part …
