Grain Growth Stagnation Research Articles

Microstructure evolution and strengthening mechanism of FeCo-1.5V0.5Nb0.4 W soft magnetic alloy rolled strip with high yield strength and low coercivity

The low strength of soft magnetic alloy limits the ability to operate high speed rotors in aero-generators. Strengthening of soft magnetic alloys remains a challenge, as most methods that enhance strength lead to the deterioration of magnetic properties. In this work, a rolled strip of FeCo-1.5V0.5Nb0.4W (wt.%) alloy with high yield strength and low coercivity was developed. We demonstrated that minor additions of Nb and W has a little effect on the magnetic properties. Due to the microalloying has a negligible effect on magnetocrystalline anisotropy, and low content of the secondary phase. Additionally, solute atoms are enriched at the grain boundaries, which reduces the grain boundary energy and promotes the nucleation and growth of Laves-Co2Nb phase at the grain boundary by grain boundary diffusion. These lead to almost stagnation of grain growth during isothermal annealing at 1123 K for 3 h and stabilization at ∼6 μm. Therefore, based on the reduction of dislocation density by high-temperature annealing to restore the magnetic properties of the alloy, fine-grain strengthening coupled with solid solution strengthening, and a certain amount of Orowan bypass effect and dislocation strengthening contribution, provide for the high strength of the alloy. The yield strength of the rolled strip reached 742 MPa under the conditions of no significant decrease in the saturation magnetization of 2.39 T and an extremely low coercivity of 152 A/m. These results are of great significance for understanding the relationship between the strengthening mechanisms of metallic materials and further developing high-performance FeCo-based soft magnetic alloys.

Grain growth stagnation in solid state thin films: A phase-field study

Grain boundary grooving significantly affects the grain growth behavior in a polycrystalline thin film with columnar grain structure by partial or complete pinning of moving grain boundaries. Theoretically, it can be shown that the stagnation of grain growth can occur for certain combinations of grain size and film thickness, for which grain boundaries cannot escape from the groove root. However, in real systems, grooves attached with the grain boundaries can migrate along with the moving grain boundaries. The possibility for stagnation arises when a groove behaves like a notch fixed at the surface. Such a condition can arise if the surface diffusivity is sufficiently reduced after stable groove formation using surface treatment. In the present study, grain growth in a solid-state thin film is investigated using a three-dimensional phase-field method that allows grains of a solid phase to be in equilibrium with a vapor phase at a constant temperature. The model captures the essential physics of surface diffusion-controlled thermal grooving and its interaction with a moving grain boundary. From the phase-field simulations, three possible interactions between the grain boundary and the groove are identified: stagnation of grain boundary, grain boundary-groove detachment, and coupled movement of the groove and the grain boundary.

Grain growth stagnation in thin films due to shear-coupled grain boundary migration

Normal grain growth in thin films attached to a substrate has been considered. It has been shown that shear-coupled grain boundary migration results in the build-up of elastic stresses in the film. A semi-quantitative model of grain growth combining the elements of disclinations theory with the Burke-Turnbull model of normal grain growth has been proposed. It has been shown that shear-coupled grain boundary migration may lead to stagnation of normal grain growth, whereas for high coupling factor values, the grains in the film do not grow at all. Finally, the mechanisms of stress relaxation enabling some grain growth are discussed.

Grain Growth Stagnation in Thin Films Due to Shear-Coupled Grain Boundary Migration

We have considered normal grain growth in thin films attached to a substrate and shown that shear-coupled grain boundary migration results in the build-up of elastic stresses in the film. We proposed a semi-quantitative model of grain growth, combining the elements of disclinations theory with the Burke-Turnbull model of normal grain growth. We have shown that shear-coupled grain boundary migration may lead to stagnation of normal grain growth, whereas for high coupling factor values, the grains in the film do not grow at all. Finally, we discussed the possible mechanisms of stress relaxation and resulting activation energies of grain growth.

Liquid assisted grain growth in solution processed Cu(In,Ga)(S,Se)2

Many solution based methods of fabricating thin film Cu(In,Ga)Se2 solar cell absorbers can be described as a two step process, consisting of initial precursor deposition followed by high temperature post processing. This post processing step is termed “selenization” when the sample is treated in a selenium-rich environment, and is responsible for transforming the nanocrystalline or amorphous precursor layer into the large crystal grains that are necessary for high efficiency solar cells. Here we study the selenization of nanoparticle Cu(In,Ga)S2 precursor layers by a rapid thermal processing method, and develop a liquid assisted growth model to explain how large grain Cu(In,Ga)(S,Se)2 crystals nucleate and grow. We find that processing with saturated selenium, achieved by maintaining a higher temperature for the selenium source than the sample, is a necessary but not sufficient condition for grain growth of a 1–2 μm thick Cu(In,Ga)(S,Se)2 film. An additional necessary condition is an external supply of Na, without which grain growth of films on soda-lime glass stagnates at about 400 nm thickness, with the remainder of the film consisting of a bottom layer of fine grains. This stagnation of grain growth is hypothesized to be caused by diffusion limitations of Cu, In and Ga containing species from the coarsened selenized particles in the fine grain layer as well as accumulation of carbon left behind by the solution processing method which is rejected during grain growth. We find that deposition of a NaF layer on the nanoparticle precursor film followed by selenization at temperatures greater than 534 °C under a saturated selenium atmosphere results in large surface grains that span the thickness of the film, with only a thin bottom small grain layer primarily composed of carbon and selenium. Grain growth prior to stagnation is well described by a normal grain growth model, and our kinetic study yielded an estimated rate constant activation energy of 126.1 kJ/mol. Attempting to grow grains beyond the stagnation point results in abnormal grain growth. We develop a liquid assisted grain growth model to explain these observations.

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms.

Rotation-induced grain growth and stagnation in phase-field crystal models

We consider grain growth and stagnation in polycrystalline microstructures. From the phase-field crystal modeling of the coarsening dynamics, we identify a transition from a grain-growth stagnation upon deep quenching below the melting temperature T(m) to a continuous coarsening at shallower quenching near T(m). The grain evolution is mediated by local grain rotations. In the deep quenching regime, the grain assembly typically reaches a metastable state where the kinetic barrier for recrystallization across boundaries is too large and grain rotation with subsequent coalescence or boundary motion is infeasible. For quenching near T(m), we find that the grain growth depends on the average rate of grain rotation, and follows a power-law behavior with time, with a scaling exponent that depends on the quenching depth.

Crystallization and grain growth characteristics of yttria-stabilized zirconia thin films grown by pulsed laser deposition

Knowledge about the crystallization and grain growth characteristics of metal oxide thin films is essential for effective microstructural engineering by thermal post-annealing and the integration to Si-based miniaturized electroceramic devices. Finite size and interface effects may cause fundamentally different behavior compared to three dimensional macroscopic systems. This work presents a comprehensive investigation of the crystallization kinetics and microstructural evolution upon thermal post-annealing of amorphous 200 nm and 1.2 μm thin films of 8 mol% yttria-stabilized zirconia grown by pulsed laser deposition (PLD) using ex- and in-situ X-ray diffraction, Raman spectroscopy, and electron microscopy techniques. The layers exhibit a remarkably low crystallization temperature of 200–250 °C while exposure to energetic electrons induces the formation of randomly dispersed ~ 20 nm sized crystallites already at ambient temperature. The isothermal amorphous to crystalline phase transformation kinetics can be described quantitatively by the Johnson–Mehl–Avrami–Kolmogorov model. They reveal characteristics of a three dimensional growth under cation bulk diffusion control with heterogeneous nucleation that changes from continuous to instantaneous initial seeding at temperatures above 300 °C. Large (> 100 nm) equiaxed grains are formed rapidly without a stabilization of transient nanocrystals during the thermally induced phase transformation. A stagnation of normal grain growth resulting in a logarithmic normal size distribution is observed once the average grain dimensions approach the film thickness. The results on the crystallization and grain growth of the PLD-grown YSZ films are evaluated with regards to the fabrication of YSZ solid electrolyte membranes for Si-supported micro solid oxide fuel cells and gas sensors.

How Grain Growth Stops: A Mechanism for Grain-Growth Stagnation in Pure Materials

The thermodynamic equilibrium state of crystalline materials is a single crystal; however, polycrystalline grain growth almost always stops before this state is reached. Although typically attributed to solute drag, grain-growth stagnation occurs, even in high-purity materials. Recent studies indicate that grain boundaries undergo thermal roughening associated with an abrupt mobility change, so that at typical annealing temperatures, polycrystals will contain both smooth (slow) and rough (fast) boundaries. Mesoscale grain-growth models, validated by large-scale polycrystalline molecular dynamics simulations, show that even small fractions of smooth, slow boundaries can stop grain growth. We conclude that grain-boundary roughening provides an alternate stagnation mechanism that applies even to high-purity materials.

On the stagnation of grain growth in nanocrystalline materials

The stagnation of grain growth with solute segregation in nanocrystalline materials is often analyzed by using two kinetic models [J.E. Burke, Trans. Metall. Soc. AIME 180 (1949) 73; A. Michels, C.E. Krill, H. Ehrhardt, R. Birringer, D.T. Wu, Acta Mater. 47 (1999) 2143], in which it is supposed that solute drag stops grain growth. However, we show that the drag force in these kinetic models is not equivalent to the solute drag force, but to the reduced driving force due to the decrease in grain boundary energy.

An Overview of Accomplishments and Challenges in Recrystallization and Grain Growth

The study of microstructural evolution in polycrystalline materials has been active for many decades so it is interesting to illustrate the progress that has been made and to point out some remaining challenges. Grain boundaries are important because their long-range motion controls evolution in many cases. We have some understanding of the essential features of grain boundary properties over the five macroscopic degrees of freedom. Excess free energy, for example, is dominated by the two surfaces that comprise the boundary although the twist component also has a non-negligible influence. Mobility is less well defined although there are some clear trends for certain classes of materials such as fcc metals. Computer simulation has made a critical contribution by showing, for example, that mobility exhibits an intrinsic crystallographic anisotropy even in the absence of impurities. At the mesoscopic level, we now have rigorous relationships between geometry and growth rates for individual grains in three dimensions. We are in the process of validating computer models of grain growth against 3D non-destructive measurements. Quantitative modeling of recrystallization that includes texture development has been accomplished in several groups. Other properties such as corrosion resistance are being related quantitatively to microstructure. There remain, however, numerous challenges. Despite decades of study, we still do not have complete cause-and-effect descriptions of most cases of abnormal grain growth. The response of nanostructured materials to annealing can lead to either unexpected resistance to coarsening, or, coarsening at unexpectedly low temperatures. General process models for recrystallization that can be applied to industrial alloys remain elusive although significant progress has been made for the specific case of aluminum alloy processing. Thin films often exhibit stagnation of grain growth that we do not fully understand, as well as abnormal grain growth. Grain boundaries respond to driving forces in more complicated ways than we understood. Clearly many exciting challenges remain in grain growth and recrystallization.

Advection-diffusion model for the stagnation of normal grain growth in thin films

This paper presents an advection-diffusion model to describe the stagnation of normal grain growth in thin films. The underlying advection-diffusion model describes grain growth in a two-dimensional topological-class/size space. Grain boundary grooving and the correlation between neighbouring grains are introduced into the model to represent stagnation. Grain boundary grooving causes the stagnation of grain growth, and the correlation between neighbouring grains accelerates the effects of stagnation. Numerical solution of continuity equations gives a grain size distribution that is close to log-normal, and fits experiments well. The time development of average grain size also shows the stagnation of grain growth.

Microstucture evolution and interfacial properties in the Fe–Pb system

Fe-rich Fe-Pb alloys were synthesized from elemental powders for studying the grain boundary wetting by the liquid phase and for studying the effect of dispersed insoluble inclusions of a liquid phase on microstructure evolution. From the atomic force microscopy analyses of the grain boundary grooves formed at the sample surface, the grooving mechanisms in pure Fe, Fe in contact with Pb vapor, and Fe in contact with liquid Pb were identified, and the interface diffusion coefficients were determined. It was demonstrated that the wetting of grain boundaries in Fe by liquid Pb is imperfect. For the first time, an anomaly of the surface self-diffusion coefficient of Fe below the Curie temperature was observed (magnetic effect for the surface diffusion). Based on the diffusion coefficients measured, the interaction of moving grain boundaries with the liquid Pb particles was quantitatively analyzed. The theoretically predicted limiting grain size in the Fe-Pb alloy after stagnation of the normal grain growth was in a good agreement with the experimental observations.

Consideration of Zener drag effect by introducing a limiting radius for neighbourhood in grain growth simulation

A model for grain growth simulation, in the presence of preferential particle distribution, is presented. The model predicts two grain size limits due to second-phase particles. Less than the maximal critical radius the grains will shrink. Greater than the minimal critical radius the grains will grow. Between the two limiting radii no grain growth takes place. These critical radii permit us to introduce the effect of the precipitates directly in the simulation procedure, without their assigning sites in the base matrix. In this case, all sites of the matrix are only occupied by grains. The conditions necessary for the development of secondary recrystallization in textured materials such as Fe–3%Si are, first, the stagnation of normal grain growth, second, the presence of special boundaries around the secondary grains. The grain growth simulation is performed until the grain structure was pinned, i.e. when boundaries become pinned.

Annealing time dependence of structural and magnetotransport properties of Ni 81Fe 19 (2 nm)/Ag (4 nm) multilayers

Granular films of Ni 81Fe 19 nanoparticles embedded in a non-magnetic Ag matrix were prepared, after annealing the as cast multilayers, and the evolution of the structural and magnetotransport properties as a function of annealing time were investigated. The as cast films exhibit negligible isotropic magnetoresistance and upon annealing grain boundary diffusion occurs resulting in the appearance of giant magnetoresistance (GMR) effect. Stagnation of grain growth and significant residual values of GMR for prolonged annealing times occur due to retarding forces on grain boundary movement. X-ray refinement analysis indicates incoherent growth of Ni 81Fe 19 and Ag. A phenomenological model was use to fit the GMR curve as a function of the reduced magnetization.

Mesoscale simulations of particle pinning

Abstract Despite much debate, there is still little consensus of opinion on the dependence of Zener pinning (the stagnation of grain growth caused by second-phase particles) on the volume fraction. The controversy surrounds attempts to relate the volume fraction of particles to the final pinned grain size. Analytical theories and 3D Monte Carlo simulations are in disagreement and the experimental evidence is inconclusive. In this paper we contribute to the debate by describing mesoscale 3D Monte Carlo simulations of a single boundary moving through an array of particles. It is found that the simulation temperature is a critical variable, and the simulated boundaries possess mobilities independent of driving force only when kT′ ≥ 2. This is explained in terms of a ledge mechanism of migration in which ledge repulsion becomes important when kT′ < 2. The effect of T′ is critical in determining the geometry of the boundary (and hence the pinning force) during particle bypass. When kT′ = 0, the expected dimple shape is not observed because the boundary is in a non-equilibrium state (due to ledge repulsion) and this is the origin of the strong pinning observed in the simulations. When kT′ ≥ 1. dimples are observed and the pinning force is in good agreement with analytical theory. The implications of this work on the volume fraction dependence of Zener pinning are discussed.

Microstructural evolution in thin films

This article reviews the topic of computer simulation of the various processes that determine evolution of grain structure in polycrystalline thin films. The evolution typically begins with the nucleation of individual crystals, which then grow until they impinge upon each other and form a continuous film. The microstructures created depend on both the nucleation conditions and the growth conditions. After impingement, the grain boundaries so formed may migrate, which leads to grain growth. If the grain size is small compared with the film thickness, then the grain structure and the grain growth process are three-dimensional. As the grains grow to become larger than the film thickness, so that most grains traverse the entire thickness of the film, the microstructure may approach the conditions for a two-dimensional description to apply. At this point, however, the surface energy associated with the two free surfaces of the film becomes comparable with the surface energy of the grain boundaries, and the free surface may profoundly affect the grain growth. One effect is that grooves may develop along the lines where the grain boundaries meet the free surface, pinning the boundaries against further migration and leading to grain-growth stagnation. Another possible effect is that differences in the free surface energy for grains with different crystallographic orientation may provide a driving force for the migration of the boundaries that is additional to that provided by grain boundary capillarity. Grains with favorable orientations will grow at the expense of grains in which a few grains grow very large by consuming the normal grains.

Simulation of thin film grain structures—II. Abnormal grain growth

A computer simulation of grain growth in two dimensions has been used to model microstructural evolution in thin films. In a companion paper we have simulated the stagnation of grain-growth due to grain-boundary grooving at the free surface of the film. In this paper we model the effect of driving force variations (due to variations of the free-surface energy among different crystals) on the origination and propagation of abnormal or secondary grain growth. The simulation produces an estimate for the magnitude of the driving force which is required to produce abnormal grain growth. The simulation also indicates that a key requirement for classic abnormal grain growth behavior is that a majority of the grains have free-surface energies which differ very little from each other.

Simulation of Microstructural Evolution in Polycrystalline Films

ABSTRACTThis paper will review the topic of computer simulation of the evolution of grain structure in polycrystalline thin films, with particular attention to the modelling of the grain growth process. If the grain size is small compared to the film thickness, then the grain structure is three-dimensional. As the grains grow to become larger than the film thickness, so that most grains traverse the entire thickness of the film, the microstructure may approach the conditions for a two-dimensional grain structure. Both two- and three-dimensional grain growth have been simulated by various authors.When the grains become large enough for the microstructure to be two-dimensional, the surface energy associated with the two free surfaces of the film becomes comparable to the surface energy of the grain boundaries. In this condition, the free surface may profoundly effect the grain growth. One effect is that grooves may develop along the lines where the grain boundaries meet the free surfaces. This grooving may pin the boundaries against further migration and lead to grain-growth stagnation. Another possible effect is that differences in the free surface energy for grains with different crystallographic orientation may provide a driving force for the migration of the boundaries which is additional to that provided by grain boundary capillarity. Grains with favorable orientations will grow at the expense of grains with unfavorable orientations. The coupling of grain-growth stagnation with an additional driving force can produce abnormal or secondary grain growth in which a few grains grow very large by consuming the normal grains.

On the stagnation of grain growth

The effect of Zener drag on the grain growth process has been studied within the framework of the Wagner-Zlyosov-Hillert model. We find, as expected, that stagnation takes place, and we have studied how the limiting radius varies with Zener drag. We also demonstrate that previous models for the kinetics of the stagnation are unable to give a satisfactory description of the kinetics. We calculate the shape of the distribution function at stagnation and discuss how this is affected by the shape of the initial distribution function.