The importance of grain boundary complexions in affecting physical properties of polycrystals

In recent decades researchers have revealed a rich variety of grain boundary segregation phenomena, including interfacial phase, or complexion, transitions. Grain boundary complexion transitions have been shown to induce discontinuous changes in materials properties as a function of temperature and chemical potential, and have been used to explain phenomena that had previously evaded satisfactory explanation. This review article discusses how grain boundary complexions relate to mass transport and mechanical properties, by highlighting both what is understood and emphasizing topics requiring additional study.     

The role of grain boundary energy in grain boundary complexion transitions

Recent findings about the role of the grain boundary energy in complexion transitions are reviewed. Grain boundary energy distributions are most commonly evaluated using measurements of grain boundary thermal grooves. The measurements demonstrate that when a stable high temperature complexion co-exists with a metastable low temperature complexion, the stable complexion has a lower energy. It has also been found that the changes in the grain boundary energy lead to changes in the grain boundary character distribution. Finally, recent experimental observations are consistent with the theoretical prediction that higher energy grain boundaries transform at lower temperatures than relatively lower energy grain boundaries. To better control microstructures developed through grain growth, it is necessary to learn more about the mechanism and kinetics of complexion transitions.     

Simultaneous grain boundary motion,grain rotation,and sliding in a tricrystal

Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.     

Comparative study of two phase-field models for grain growth

There exist different phase-field models for the simulation of grain growth in polycrystalline structures. In this paper, the model formulation, application and simulation results are compared for two of these approaches. First, we derive relations between the parameters in both models that represent the same set of grain boundary energies and mobilities. Then, simulation results obtained with both models, using equivalent model parameters, are compared for grain structures in 2D and 3D. The evolution of the individual grains, grain boundaries and triple junction angles is followed in detail. Moreover, the simulation results obtained with both approaches are compared using analytical theories and previous simulation results as benchmarks. We find that both models give essentially the same results, except for differences in the structure near small shrinking grains which are most often locally and temporary for large grain structures.     

Phase field simulations of elastic deformation-driven grain growth in 2D copper polycrystals

In this work, a phase field grain growth model coupled with a spectral stress calculation method is used to investigate the effect of applied elastic deformation on grain growth in 2D copper polycrystals with isotropic grain boundary properties. The applied deformation accelerates the grain growth compared to a relaxed polycrystal, though the effect of the deformation decreases rapidly with time. The softest grain orientations with respect to the applied deformation grow at the expense of other orientations, though they have higher elastic energy density. Due to a rapid decrease in the elastic energy stored in the system, the GB energy eventually dominates the growth leading to a linear change in the average grain area with time. Increasing the magnitude of the applied deformation accelerates the growth, while increasing the temperature accelerates the growth but decreases the effect of the applied deformation.     

Towards the diffusion source cost reduction for NdFeB grain boundary diffusion process

Aiming at improving the performance/cost ratio in grain boundary diffusion process(GBDP),the critical RE containing Pr-Al-Cu alloy,less expensive RE containing La-Al-Cu alloy and non-RE Al-Cu alloy were employed as the diffusion sources.The preliminary results show that the coercivity was successfully enhanced from 1000 kA/m to 1695,1156 and 1125 kA/m by Pr70Al20Cu10,La70Al20Cu10 and Al75Cu25(at.%) alloys diffusion,respectively,due to the formation of(Nd,Pr)-Fe-B,La2 O3 and c-Nd2 O3 phases respectively,after diffusion.It is also found that the corrosion resistance can be improved by Al-Cu diffusion due to the positive effects of Al and Cu elements in grain boundary.The present results demonstrated the various coercivity enhancement mechanisms for the GBDP based on different diffusion sources,and provided feasible solutions for cost reduction of GBDP and NdFeB production by saving RE resource.     

Abnormal grain growth in Al of different purity

The transition from normal to abnormal grain growth has been studied in four Al alloys of various purity (2N, 3N, 4N and 5N). The temperature and time for the onset of abnormal grain growth depend strongly on the deformation and homogenization treatment. Generally, the formation of large grains before cold rolling makes easier the transition to abnormal grain growth during the subsequent annealing. The abnormal grain growth can take place only above a certain temperature which decreases with increasing alloy purity. The onset time of the abnormal grain growth decreases with increasing temperature. It can be qualitatively explained by the dissolution of submicron particles of a second phase.     

Grain size, grain boundary sliding, and grain boundary interaction effects on nanocrystalline behavior

A dislocation–density grain boundary (GB) interaction scheme, a GB misorientation dependent dislocation–density relation, and a grain boundary sliding (GBS) model are presented to account for the behavior of nanocrystalline aggregates with grain sizes ranging from 25 nm to 200 nm. These schemes are coupled to a dislocation–density multiple slip crystalline plasticity formulation and specialized finite element algorithms to predict the response of nanocrystalline aggregates. These schemes are based on slip system compatibility, local resolved shear stresses, and immobile and mobile dislocation–density evolution. A conservation law for dislocation–densities is used to balance dislocation–density absorption, transmission and emission from the GB. The relation between yield stresses and grain sizes is consistent with the Hall–Petch relation. The results also indicate that GB sliding and grain-size effects affect crack behavior by local dislocation–density and slip evolution at critical GBs. Furthermore, the predictions indicate that GBS increases with decreasing grain sizes, and results in lower normal stresses in critical locations. Hence, GBS may offset strength increases associated with decreases in grain size.     

Interaction of lattice dislocations with a grain boundary during nanoindentation simulation

Interaction of dislocations with a Σ = 5 (210) [001] grain boundary was investigated using molecular dynamics simulation with EAM potentials. The results showed that the dislocation transmitted across the grain boundary during nanoindentation and left a step in the boundary plane. Burgers vector analysis suggested that a partial dislocation in grain I merged into the grain boundary and it was dissociated into another partial dislocation in grain II and a grain boundary dislocation, introducing a step in the grain boundary. Simulation also indicated that, after the transmission, the leading partial dislocation in the grain across the boundary was not followed by the trailing partials, expanding the width of the stacking fault. The results suggested that the creation of the step that accompanied grain boundary motion and expansion of the stacking fault caused resistance to nanoindentation.     

The influence of grain boundary segregation on the rate of contact melting in metals

The contact melting of polycrystalline solid solutions with metals is studied. The linear correlations between the average rate of contact melting and (i) the energy of interaction between the impurity atoms and grain boundaries and (ii) differences in properties of constituents of solid solutions (namely differences in surface energies, electron work functions and generalized statistical V.K. Semenchenko moments) are revealed. Found relations demonstrate the importance of grain boundary segregation in the contact melting phenomenon.     

Uniaxial creep behavior of nanostructured, solution and dispersion hardened V-1.4Y-7W-9Mo-0.7TiC with different grain sizes

Nanostructured vanadium (V) alloys are expected to exhibit high performance under neutron irradiation environments. However, their ultra-fine or refined grains cause significant decrease in flow stress at high temperatures due to grain boundary sliding (GBS), which is the major concern for their high-temperature structural applications such as future fusion reactors. The contribution of GBS to plastic deformation is known to depend strongly on grain size (GS) and may give more significant influence on long-time creep test results than on short-time tensile test results. In order to improve the creep resistance through elucidation of the effect of GS on the uniaxial creep behavior of nanostructured V alloys, a solution and dispersion hardened V alloy, V-1.4Y-7W-9Mo-0.7TiC (in wt%), with GSs from 0.58 to 2.16 μm was developed by mechanical alloying and HIP processes, followed by annealing at 1473-1773 K, and creep tested at 1073 K and 250 MPa in vacuum. It is shown that the creep resistance of V-1.4Y-7W-9Mo-0.7TiC increases monotonically with GS: The creep life for the alloy with 2.16 μm in GS is as long as 114 h, which is longer by factors of 2-30 than those for the other finer grained alloys and by two orders than that for coarse-grained V-4Cr-4Ti (Nifs heat2, GS: 17.8 μm) that is a primary candidate material for fusion reactor structural applications. The minimum (steady state) creep rate decreases with increasing GS as ?_s ∝ (1/?)³, where ?_s is the steady state creep rate and ? is the grain diameter. The observed superior creep resistance of V-1.4Y-7W-9Mo-0.7TiC is discussed in terms of GS effects on dislocation glide/climb, GBS, and strain hardening capability enhanced by solution and dispersion hardening.     

Coordinated grain boundary deformation governed nanograin annihilation in shear cycling

Grain growth and shrinkage are essential to the thermal and mechanical stability of nanocrystalline metals,which are assumed to be governed by the coordinated deformation between neighboring grain boundaries(GBs)in the nanosized grains.However,the dynamics of such coordination has rarely been reported,especially in experiments.In this work,we systematically investigate the atomistic mechanism of coordinated GB deformation during grain shrinkage in an Au nanocrystal film through combined state-of-the-art in situ shear testing and atomistic simulations.We demonstrate that an embedded nanograin experiences shrinkage and eventually annihilation during a typical shear loading cycle.The continu-ous grain shrinkage is accommodated by the coordinated evolution of the surrounding GB network via dislocation-mediated migration,while the final grain annihilation proceeds through the sequen-tial dislocation-annihilation-induced grain rotation and merging of opposite GBs.Both experiments and simulations show that stress distribution and GB structure play important roles in the coordinated defor-mation of different GBs and control the grain shrinkage/annihilation under shear loading.Our findings establish a mechanistic relation between coordinated GB deformation and grain shrinkage,which reveals a general deformation phenomenon in nanocrystalline metals and enriches our understanding on the atomistic origin of structural stability in nanocrystalline metals under mechanical loading.     

Nonuniform cleavage cracking across persistent grain boundary

The nonuniform characteristics of cleavage cracking across high-angle grain boundaries are analyzed in considerable detail. To break through a grain boundary, a cleavage front would first penetrate across the boundary at its central part, with the side sections being locally arrested. Such a front behavior causes a strong crack trapping effect and a large increase in required crack growth driving force. Eventually, as the persistent grain boundary areas are separated apart, the crack front bypasses the grain boundary. The critical condition of the unstable crack propagation is determined by both the local fracture resistance and its increase rate with respect to the expansion of the break-through window. The grain boundary toughness is dominated by the effective grain boundary ductility.     

Breaking the purity-stability dilemma in pure Cu with grain boundary relaxation

High purity metals are increasingly demanded in modern manufacturing industries, but their processing and applications are limited by a dilemma that purer metals are thermally and mechanically less stable. The reduced stability of pure metals originates from the weakened drag effect of impurity atoms on the mobility of grain boundaries (GBs) that are hard to stabilize without alloying. Following recent studies on stabilizing nanograined metals by tailoring structures of GBs, here we report that structural relaxation of GBs breaks the purity-stability dilemma in pure Cu. Contrary to the conventional impurity effect, thermal stability and hardness of nanograined Cu samples with relaxed GBs increase (rather than decrease) with higher purities. The discovered anomalous impurity effect, owing to suppression of GB relaxation process with impurity atoms, offers an alternative vector to stabilizing purer metals for advanced processing and applications.     

Grain boundary migration during abnormal grain growth in nanocrystalline Ni

The transformation mechanisms of abnormal grain growth in nanocrystalline Ni were studied extensively by transmission electron microscopy (TEM). A combination of in situ TEM annealing and ex situ annealing followed by TEM characterization was used. It was observed that grain boundary migration is both spatially and temporally non-uniform; migration occurs in a series of discrete steps, which are followed by periods of stagnation.     

Diffusion induced grain boundary migration in the Ag–Zn system

Diffusion induced grain boundary migration (DIGM) has been studied in the Ag–Zn system by exposing polycrystalline Ag to Zn vapor with a Ag-25 wt.% Zn alloy as the source of Zn. The time and temperature dependence of the migration distance has been studied in the temperature range 660 to 810 K. The composition profile was obtained on the sheet cross-section along a line perpendicular to the edge to determine D_bδ at each temperature. Similarly, the Zn concentration profile was obtained from the region swept by the migrating grain boundary. The coherency strain energy, the total chemical free energy change and the effective free energy change were calculated. The regular solution model was used for calculating the free energy change. It has been observed that a fraction of the total free energy has been used for volume diffusion in front of the migrating grain boundary. The instantaneous rate of migration has been observed to be directly proportional to the chemical free energy change and the coherency strain energy. The instantaneous rate of migration versus the composition graph has indicated that the driving force for DIGM in the Ag–Zn system is the coherency strain energy.The fine-grained layer formed at the surface follows a parabolic growth behavior. The diffusion coefficients calculated from the composition profile as well as from the rate of growth of the fine-grained layer are of the same order of magnitude. The diffusivity values are four to six orders of magnitude higher than the volume diffusion coefficients. From the activation energy and the diffusivities it is clear that DIGM in the Ag–Zn system occurs by the diffusion of Zn along the grain boundaries of polycrystalline Ag.     

Modelling of the grain size probability distribution in polycrystalline nanomaterials

Theoretical analyses have always resulted in nanomaterials’ grain size probability distribution being of varied form: approximately either lognormal, Rayleigh, normal, Weibull, etc. The isotropic Hillert’s model of grain growth which is more suitable for soap froth has been frequently used to establish these distributions with the hope of approximating experimental observations. Observed grain growth in nanomaterials shows departures from the Hillert’s model.In the present paper, the probability distribution of grain size in nanomaterials is dealt with. Use is made of a modified model of grain growth in polycrystalline nanomaterials developed recently by the authors. The modified model accounts for grain growth caused by curvature driven grain boundary migration and grain rotation-coalescence mechanisms. Since the grain size in the aggregate is random, the stochastic counterpart of the expression governing the incremental change in individual grain size is obtained by the addition of two fluctuation terms.The integro-differential equation governing the development of the probability density function of the grain size is obtained which is the generalised Fokker–Planck–Kolmogorov equation. Numerical solution to the integro-differential equation is obtained.Results from analytical modelling of grain size probability distribution in polycrystalline nanomaterials are different if the effect of grain rotation-coalescence mechanism on grain growth process is taken into account and, further, due to the addition of the fluctuation terms. Results also depend on the nature of the fluctuation term, which is a material property as the fluctuation in grain sizes varies from one material to another. It is shown that many of the major attributes of grain growth, such as self similarity (probability density approaching a stationary one), can be predicted by the solution of the Fokker–Planck–Kolmogorov equation.     

Resistance to cleavage cracking and subsequent shearing of high-angle grain boundary

In a previous experimental study, it was observed that the break-through process of a cleavage front across a high-angle grain boundary can be highly nonuniform. While the central part of the boundary can be cleaved quite smoothly, the rest parts must be sheared apart. In this paper, the trapping effect of grain boundary shearing is analyzed in considerable detail. Before the shearing is completed, the crack flanks are locally pinned together and a bridging stress must be provided. The bridging stress has a negative contribution to the local stress intensity at the cleavage front segment that penetrates across the grain boundary, and thus the crack growth driving force must be increased. A closed-form equation is derived to relate the overall fracture resistance to the fracture mode through an energy analysis.     

Influence of grain boundary inclination on the grain boundary and triple junction motion in Zn

The experimental results of an investigation of the steady‐state motion of individual grain boundaries (GBs) of natural deformation twin and individual twin GBs in bicrystals and tricrystals with triple junction (TJ) are obtained. For experimental observation of GB mobility from the dependence on GB inclination the Zn specimens with individual GBs and TJs were produced. The mobility of natural deformation twin GBs and twin GBs in bicrystals and tricrystals are compared in connection with the GB inclination.