Segregation Kinetics Research Articles

Universal finite-size scaling function for coarsening in the Potts model with conserved dynamics

We study kinetics of phase segregation in multicomponent mixtures via Monte Carlo simulations of the q-state Potts model, in two spatial dimensions, for 2 ≤ q ≤ 20. The associated growth of domains in finite boxes, irrespective of q and temperature, can be described by a single universal finite-size scaling function, with only the introduction of a nonuniversal metric factor in the scaling variable. Our results show that although the scaling function is independent of the type of transition, the q-dependence of the metric factor hints to a crossover at q = 5 where the type of transition in the model changes from second to first order.

Quantitative dependence of ductile-to-brittle transition on phosphorus grain boundary segregation for a novel Ni–Cr–Mo RPV steel

SA508-4 N steel is considered a novel Ni–Cr–Mo low-alloy steel for reactor pressure vessels. The low-temperature embrittlement in the steel is an important issue that needs to be addressed. Herein, the main aim of this work is to investigate the non-hardening embrittlement caused by grain boundary segregation (GBS) of P in a P-doped SA508-4 N steel with the use of impact testing in conjunction with Auger electron spectroscopy (AES) and microstructural characterization. The steel samples are quenched from 1000 °C, followed by tempering at 650 °C and subsequent ageing at different lower temperatures. The ductile-to-brittle transition temperatures (DBTTs) of the aged specimens are determined by mini-Charpy impact testing (specimen: 2.5 mm × 2.5 mm in cross section), and the GBS of P is evaluated using AES. The results show that there is a linear dependence of DBTT (oC) on the boundary concentration of P (Cp/at.%), when the steel hardness is fixed after the 650 °C-tempering (∼260 HV10), being expressed as DBTT=13.31Cp−339.28. Employing this relation, one can forecast the DBTT once the boundary level of P is known. With the DBTT−segregation relation in combination with segregation thermodynamics and kinetics, a time–temperature embrittlement diagram is also developed. This may be employed to predict the tendency of embrittlement in the steel, caused by GBS of P after serving at a temperature. It is believed that this study is helpful in monitoring the safe operation of devices manufactured with this novel low-alloy steel.

Precipitate Shearing, Fault Energies, and Solute Segregation to Planar Faults in Ni-, CoNi-, and Co-Base Superalloys

The mechanical properties of superalloys are strongly governed by the resistance to shearing of ordered precipitates by dislocations. In the operating environments of superalloys, the stresses and temperatures present during thermomechanical loading influence the dislocation shearing dynamics, which involve diffusion and segregation processes that result in a diverse array of planar defects in the ordered L12γ′ precipitate phase. This review discusses the current understanding of high-temperature deformation mechanisms of γ′ precipitates in two-phase Ni-, Co-, and CoNi-base superalloys. The sensitivity of planar fault energies to chemical composition results in a variety of unique deformation mechanisms, and methods to determine fault energies are therefore reviewed. The degree of chemical segregation in the vicinity of planar defects reveals an apparent phase transformation within the parent γ′ phase. The kinetics of segregation to linear and planar defects play a significant role in high-temperature properties. Understanding and controlling fault energies and the associated dislocation dynamics provide a new pathway for the design of superalloys with exceptional properties.

Photochemically-Induced Phase Segregation of Mixed Halide Perovskite Solar Cells

The emerging low cost perovskite solar cell quickly reached power conversion efficiency (PCE) parity with crystalline Si solar cells [1]. Optional bandgap tuning of the perovskites by partial substitution of I- with Br- expand their application to tandem solar cells and LEDs. The only critical issue remaining to solve is their poor long term stability under operational conditions, specifically photochemical degradation by splitting into I- and Br- rich phases. Sufficient suppression of this process requires a thorough understanding of the underlying phenomena. Here we report the detailed investigation of the photoinduced phase transformation in stoichiometric and non-stoichiometric mixed halide CsPbI3-xBrx. Using in-situ Atomic Force Microscopy, we visualized real-time kinetics of halide phase segregation under illumination. The I-rich phase segregated predominantly along grain boundaries while the grain bulk remained enriched with Br. It was proposed that photogenerated Pb0 and I3 - species are selectively expelled from grain bulk into grain boundary resulting in the phase splitting. This work supports our focus in understanding degradation mechanisms in perovskite materials for next generation solar cells [2-3].[1] Best Research-Cell Efficiency Chart | Photovoltaic Research | NREL, (n.d.). https://www.nrel.gov/pv/cell-efficiency.html (accessed October 12, 2019).[2] Akbulatov, A.; Frolova, L.; Dremova, N.; Zhidkov, I.; Martynenko, V.; Tsarev, S.; Luchkin, S.; Kurmaev, E.; Aldoshin, S.; Stevenson, K. J.; Troshin, P. “Light or Heat: What Is Killing Lead Halide Perovskites Under Solar Cell Operation Conditions?," J. Phys. Chem. Lett. 2020, 11(1), 333-339.[3] Frolova, L. A.; Luchkin, S. Yu; Akbulatov, A. F.; Dremova, N. N.; Stevenson, K. J.; Troshin, P. A. “Efficient and Stable All-Inorganic Perovskite Solar Cells Based on Nonstoichiometric CsxPbI2Brx (x>1) Alloy,” J. Mater. Chem. A 2019 , 7(18), 5314-5323.

Kinetics of surface and interface segregation in stressed nano-films on inert substrate

A general model is developed for describing the kinetic segregation in stressed ultrathin alloy films deposited on inert substrates. The essential role of the diffusion-induced stress and the intrinsic stress in ultrathin films upon the kinetic surface and interface segregation is addressed. By the developed model, it is demonstrated that the equilibrium segregation is the natural consequence of the kinetic segregation. The influences of temperature, film thickness, and average concentration on the surface and interface segregation are evaluated. As an example, the model is applied to simulate the kinetic surface/interface segregation in ultrathin Ni(111)(Au) alloy films deposited on the sapphire substrate and the simulation results are in agreement with the experimental observations.

Механизм обусловленного динамической примесной подсистемой аномального поведения пластического течения материалов с высоким кристаллическим рельефом

A model of dynamic interaction of dislocations with an impurity subsystem of crystals with a high potential relief of the crystal lattice (Peierls barriers) is developed. Such materials include metals with body-centered cubic structure, semiconductors, ceramics, and many others. It is shown that the modification of impurity migration barriers near the dislocation core significantly affects the segregation of impurities on the moving dislocation. The presence of a substantially nonequilibrium initial stage of segregation kinetics leading to anomalies of dislocation dynamics and yield strength of materials is substantiated.

Kinetics of Arsenic Surface Segregation in Scrap-Based Silicon Electrical Steel

The segregation kinetics of surface-active, residual elements are investigated in an in situ study of annealing scrap-based silicon electrical steel sheet where the arsenic (As) surface segregation is highlighted. During annealing in the temperature range of 300–950 °C, different kinds of interactions between the segregated residual elements were observed. Attractive interactions between the segregands produced co-segregation, e.g., between Sn and Sb, whereas repulsive interactions resulted in site competition, e.g., between Sn and As. These competing interactions are strongly time dependent. In spite of there being twice as much Sn compared to As in the bulk material, the As prevailed in the surface enrichments of the polycrystalline silicon steel at 950 °C. The intensity of the As surface segregation in the temperature range 800–950 °C is proportional to the calculated amount of γ-austenite phase in the (α + γ) steel matrix. The detected phenomenon of the As versus Sn site competition could be valuable for the texture design and surface engineering of silicon steels with a thermodynamically stable two-phase (α + γ) region.

Segregation-assisted spinodal and transient spinodal phase separation at grain boundaries

Segregation to grain boundaries affects their cohesion, corrosion, and embrittlement and plays a critical role in heterogeneous nucleation. In order to quantitatively study segregation and low-dimensional phase separation at grain boundaries, here, we apply a density-based phase-field model. The current model describes the grain-boundary thermodynamic properties based on available bulk thermodynamic data, while the grain-boundary-density profile is obtained using atomistic simulations. To benchmark the performance of the model, Mn grain-boundary segregation in the Fe–Mn system is studied. 3D simulation results are compared against atom probe tomography measurements conducted for three alloy compositions. We show that a continuous increase in the alloy composition results in a discontinuous jump in the segregation isotherm. The jump corresponds to a spinodal phase separation at grain boundary. For alloy compositions above the jump, we reveal an interfacial transient spinodal phase separation. The transient spinodal phenomenon opens opportunities for knowledge-based microstructure design through the chemical manipulation of grain boundaries. The proposed density-based model provides a powerful tool to study thermodynamics and kinetics of segregation and phase changes at grain boundaries.

Entropic and enthalpic factors determining the thermodynamics and kinetics of carbon segregation from transition metal nanoparticles

The free energy surface (FES) for carbon segregation from nickel nanoparticles is obtained from advanced molecular dynamics simulations. A suitable reaction coordinate is developed that can distinguish dissolved carbon atoms from segregated dimers, chains and junctions on the nanoparticle surface. Because of the typically long segregation time scale (up to μs), metadynamics simulations along the developed reaction coordinate are used to construct FES over a wide range of temperatures and carbon concentrations. The FES revealed the relative stability of different stages in the segregation process, and free energy barriers and rates of the individual steps could then be calculated and decomposed into enthalpic and entropic contributions. As the carbon concentration in the nickel nanoparticle increases, segregated carbon becomes more stable in terms of both enthalpy and entropy. The activation free energy of the reaction also decreases with the increase of carbon concentration, which can be mainly attributed to entropic effects. These insights and the methodology developed to obtain them improve our understanding of carbon segregation process across materials science in general, and the nucleation and growth of carbon nanotube in particular.

Application of equilibrium phase diagrams for calculation of segregation kinetics during two-component melt cooling

According to the equilibrium state diagrams, when the melt is cooled to a certain temperature below liquidus, compositions of liquid and solid phases are uniquely determined by corresponding curves in the diagram. However, it does not happen in reality. For equilibrium (which the diagram describes), it is necessary that the melt is maintained indefinitely at each temperature, or thermal conductivity of liquid and solid phases, and the diffusion coefficients of their components, are infinitely large. We made an attempt to find out how these processes occur in reality. In this work, we consider the growth of individual crystal during cooling of a two-component melt. Mathematical model is constructed based on the following. 1. The melt area with volume corresponding to one grain, the periphery of which is cooled according to a certain law, is considered. 2. At the initial instant of time, a crystal nucleus of a certain minimum size is in the liquid. 3. At the surface of crystal, compositions of liquid and solid phases correspond to equilibrium state diagram at a given temperature on its surface. 4. Changes in temperature and composition in liquid and solid phases occur according to the laws of heat conduction and diffusion, respectively. As the melt gets cold and the crystal grows, the liquid phase is enriched in one component and depleted in another, the solid phase – on the contrary. Since the diffusion coefficients of the components in the solid phase are small, the composition of the crystal does not have time to completely equalize its cross section. The model proposed in the work allows us to study this phenomenon, to calculate for each cooling mode how the composition of the crystal will vary over its cross section. The calculations have shown that the temperature equalization occurs almost instantly, and composition of the liquid phase equalizes much slower. Equalization of the solid phase composition does not occur in the foreseeable time. The results of the work will help to improve technology of generation of alloys with an optimal structure.

Routes toward Long-Term Stability of Mixed-Halide Perovskites

In the recent anniversary issue of Trends in Chemistry, Brennan et al. review halide segregation in mixed-halide perovskites, discussing multiple perspectives on the underlying origins and reported routes to retard halide segregation. Here, we argue that only slowing down the segregation may be insufficient to achieve long-term stability.

Metallurgical modeling of intergranular HAZ liquation cracking during laser welding newly developed crystallography-dependent aerospace materials. Part II: Grain boundary alloying segregation of microstructure modification

Metallurgical modeling of the nonequilibrium grain boundary segregation was coupled with a nonequilibrium weld pool solidification to numerically analyze the contributing factors to liquation cracking resistance. The effect of the welding conditions, material composition, and average grain size on the kinetics of the grain boundary segregation in the Inconel 718-type nickel-based superalloy during laser welding were optimized. The grain boundary segregation of boron near the fusion boundary is of particular interest, and is closely correlated to the intergranular heat-affected zone (HAZ) liquation cracking. It is indicated that the low heat input, fine-grained material and full penetration contribute to the reversible desegregation of boron and suppress the grain boundary segregation of boron to significantly minimize the segregation-induced grain boundary liquation and improve the weldablity. The subsolidus temperature due to nonequilibrium weld pool solidification is capable of ameliorating the segregation kinetics to reduce the HAZ grain boundary segregation. Intergranular HAZ liquation cracking is evitable with a crack-free weld without using filler wire. The grain boundary segregation decreases and the threshold tensile stress of solid-liquid interfacial decohesion across the intergranular liquid film simultaneously increases in the recrystallized HAZ during the weld shape change from partial penetration to full keyhole penetration. Furthermore, the numerical analysis results are verified indirectly by the experiment results of the total crack length. In addition, this metallurgical modeling is also applicable for the alloying segregation behavior prediction of other nickel-based superalloys with similar metallurgical properties.

Application of Equilibrium State Diagrams for Calculating Segregation Kinetics during Cooling of a Two-Component Melt

According to equilibrium state diagrams, compositions of liquid and solid phases are determined by corresponding diagram curves at the melt cooling to below the liquidus temperature. For equilibrium to occur, the following is necessary: the melt is kept indefinitely at each temperature; or the thermal conductivity of the liquid and solid phases, as well as the diffusion coefficients of their components, are infinitely large. This study attempts to find out how these processes occur in reality. An individual crystal growth during cooling of a two-component melt is considered. A mathematical model is designed based on the following standings: (i) a melt region with a volume per one grain, the periphery of which is cooled according to a certain law, is selected; (ii) at the initial time, the crystal nucleus with a certain minimal size is in the liquid; (iii) near the crystal surface, the compositions of the liquid and solid phases correspond to a state diagram for the considered temperature on its surface; and (iv) changes in temperature and composition in the liquid and solid phases occur according to the heat conduction and diffusion laws, respectively. As the melt cools and the crystal grows, the liquid phase is enriched in one component and depleted in another, while the solid phase occurs in reverse. The component’s diffusion coefficient in the solid phase is small. Therefore, its composition does not completely equalize over the cross section. The model proposed here makes it easier to study this phenomenon and to calculate the crystal composition for each cooling mode as it moves away from its center. The calculations showed that the temperature equalizes almost instantly while the composition equalization of the liquid phase occurs much slower. The solid phase’s composition during observation practically does not equalize. The obtained results will be useful for improving the production technology for alloys with an optimal structure.

On solute depletion zones along grain boundaries during segregation

We propose a model for predicting the depletion zone arising next to grain boundaries during non-equilibrium segregation. The model directly links to distribution of segregation energies as provided by atomistic simulations. We expose the theoretical framework based on the thermodynamic extremal principle and propose an efficient algorithm to solve the underlying equations. The example of the W-25at%Re is discussed to illustrate the main features of the model. Multi-component segregation kinetics is discussed for segregation of B, C, and N in Mo to illustrate site-competition scenarios. Comparison with earlier results obtained without depletion illustrates the importance of this effects. Finally the depletion zones along GBs are investigated for many different compositions to asses for which material composition and heat treatments they may be observed experimentally. We find that extended depletion zones arise for very small solute concentrations.

The impact of swift electrons on the segregation of Ni-Au nanoalloys

We report on the electron beam-induced segregation of alloyed Ni-Au clusters into a Ni and Au rich phase at temperatures above the miscibility gap of a binary system. The nanoparticles, with diameters less than 10 nm, are grown fully inert in superfluid helium droplets with a Ni-Au core-shell morphology. Upon heating, the clusters are alloyed and subsequently transformed to a Janus-type morphology under irradiation with swift electrons. The underlying mechanisms are studied experimentally via in situ scanning transmission electron microscopy and theoretically via atomistic simulation techniques under consideration of elastic electron interactions. We find that the segregation kinetics is highly temperature-dependent and attribute this behavior to diffusive relaxation processes. The presented results shed light on radiation induced phenomena using clusters as a model system and suggest new routes for the synthesis of structures in nonequilibrium configurations.

Study of Nb non-equilibrium segregation at prior austenite grain boundary in welding using atom probe tomography and modeling

The non-equilibrium segregation of Nb at prior austenite grain boundary (PAGB) induced by welding is experimentally investigated by means of atom probe tomography (APT). The Nb concentration at PAGB appeared to be 0.115 at.% for experimental steel containing 0.06 at.% Nb at the simulated welding thermal cycle for 10 s from 1320 to 950 °C. The critical time tc for achieving maximum segregation is calculated to be 565 s for the experimental steel. For the first time, the diffusion coefficient of Nb in desegregation process is calculated for the temperature of Ti = 950 °C using non-equilibrium segregation model and APT experimental result and is confirmed to be 9.23 × 10−11 m2/s. Based on it, the kinetics of Nb non-equilibrium segregation at the PAGBs in welding process is outlined, and the segregation process and desegregation process are discussed. The Nb segregation at PAGB is also predicted over the t8/5 range of 3–600 s. The critical t8/5, at which the highest Nb concentration of 0.144 at.% at PAGB is predicted to be achieved, is ~ 29 s.

Surface segregation modeling in the case of evaporation

A kinetic model is proposed to characterize surface segregation in the case of evaporation. The kinetics is formulated using the difference between the diffusion rate of solute atom in the bulk and the evaporation rate of solute atom from the surface layer. The first-order reaction equation is applied to quantify evaporation flux. A balanced state is quantified when the vapor and ambient pressure is equal and thus a complete quantification of the kinetics forms. The kinetic curve is convex prior to critical time and concave after. The maximum surface concentration decreases as evaporation parameter decreases. The kinetics of Mg surface segregation of Al-0.8 wt%Mg alloy is fitted. An enrichment ratio of 16.484 and evaporation parameter of 0.57 are the values that fit the experimental results the best. The balanced surface concentration of Mg is calculated and implies further evaporation with prolonged time. The proposed model can adequately describe surface segregation in the case of evaporation, and the formulated kinetics can satisfactorily quantify this phenomenon.

Beyond the TCR, Antigen Discrimination in T Cells Continues in the LAT:GRB2:SOS Protein Condensate

T cells activate in response to a stochastic series of single molecule binding events between T cell receptors (TCRs) and peptide ligands presented on major histocompatibility complexes (pMHCs) accumulated at a cell-cell interface. Discrimination between ligands with subtly different affinities ensures selective and robust immunological responses upon TCR triggering. Formation of protein condensates based on the scaffolding protein Linker for Activation of T cells (LAT) is a key intermediate step in TCR signaling. LAT is multi-phosphorylated on tyrosine residues by the kinase, ZAP70, which is activated by triggered TCRs. The phosphotyrosines recruit Grb2, which, via interactions with the multivalent GEF, SOS, forms an extended LAT:Grb2:SOS assembly that resembles a phase transition. We mapped single pMHC:TCR binding events in T cells expressing fluorescent protein-tagged LAT and show that LAT assemblies are discrete and have characteristic features that are independent of the originating binding event. Furthermore, LAT assemblies can become spatially uncoupled from the pMHC:TCR complex. These individual assemblies are capable of deforming the plasma membrane and creating local domains that may participate in protein segregation or control reaction kinetics. The probability of LAT assembly is a function of the pMHC affinity, suggesting a second layer of kinetic proofreading that exists beyond the triggered TCR. We recently introduced a molecular impulse-response assay which maps pMHC:TCR binding events to early T cell activation. Results here argue that LAT assemblies may confer a molecular memory that connects a series of spatiotemporally correlated binding events to cellular decision-making. By extending the impulse-response assay, we show that activating cells experience a characteristic, fast rate of LAT assembly. Taken together, we present new molecular dimensions to T cell activation that could provide actionable therapeutic insights.

Adaptive kinetic Monte Carlo simulations of surface segregation in PdAu nanoparticles.

Surface segregation in bimetallic nanoparticles (NPs) is critically important for their catalytic activity because the activity is largely determined by the surface composition. Little, however, is known about the atomic scale mechanisms and kinetics of surface segregation. One reason is that it is hard to resolve atomic rearrangements experimentally. It is also difficult to model surface segregation at the atomic scale because the atomic rearrangements can take place on time scales of seconds or minutes - much longer than can be modeled with molecular dynamics. Here we use the adaptive kinetic Monte Carlo (AKMC) method to model the segregation dynamics in PdAu NPs over experimentally relevant time scales, and reveal the origin of kinetic stability of the core@shell and random alloy NPs at the atomic level. Our focus on PdAu NPs is motivated by experimental work showing that both core@shell and random alloy PdAu NPs with diameters of less than 2 nm are stable, indicating that one of these structures must be metastable and kinetically trapped. Our simulations show that both the Au@Pd and the PdAu random alloy NPs are metastable and kinetically trapped below 400 K over time scales of hours. These AKMC simulations provide insight into the energy landscape of the two NP structures, and the diffusion mechanisms that lead to segregation. In the core-shell NP, surface segregation occurs primarily on the (100) facet through both a vacancy-mediated and a concerted mechanism. The system becomes kinetically trapped when all corner sites in the core of the NP are occupied by Pd atoms. Higher energy barriers are required for further segregation, so that the metastable NP has a partially alloyed shell. In contrast, surface segregation in the random alloy PdAu NP is suppressed because the random alloy NP has reduced strain as compared to the Au@Pd NP, and the segregation mechanisms in the alloy require more elastic energy for exchange of Pd and Au and between the surface and subsurface.

Kinetics and Energetics of Solute Segregation in Granular Block Copolymer Microstructures

The segregation kinetics of deuterated polystyrene (d-PS) within the grain boundary regions of a lamellar poly(styrene-b-isoprene) copolymer is analyzed using a combination of electron imaging and ...