Triple Junction Drag Research Articles

A unified explanation for variation of the grain growth exponent based on grain boundary migration kinetics

Based on molecular dynamics simulation on grain boundary migration, the large grain growth exponent extensively observed in high-purity nanocrystalline materials is proved to be ascribed to specific boundary migration kinetics determined. It is also found that temperature, topology of polycrystal and grain boundary type all affect the migration kinetics, which therefore causes the exponent to vary. The findings obtained in this work are capable of rationalizing various grain growth phenomena. In addition, triple junction drag against boundary migration has been evaluated and discussed.

3D grain growth in nanocrystalline Al via molecular dynamics: Influence of size, topology and integral mean curvature on grain kinetics

Grain growth in nanosized polycrystalline Al was studied via molecular dynamics. In particular, the volumetric growth rate of grains as a function of size, topology and mean curvature was analyzed. To this aim, an algorithm for the identification of the topological features and calculation of the mean curvature was developed. It was found that in average grains with ≈15 faces have zero integral mean curvature and show no change in volume implying that the critical number of face (Fcr) is ≈15. Furthermore, integral mean curvature of grains was found to be linearly correlated with the difference between the number of faces grains have and the average number of faces of their neighbors, F−<FNN>. That is, a grain with F−<FNN>=0 tends to have zero integral mean curvature and neither shrinks nor grows whereas grains with F−<FNN> greater than 0 grow and those with F−<FNN> less than 0 shrink. This agrees with the theoretical expectations from MacPherson–Srolovitz relationship and topology based descriptions of grain growth. Nonetheless, considering individual grain kinetics, the comparison of theoretical predictions (MacPherson–Srolovitz relationship, F−<FNN> and topological class) with measured growth rates showed more scatter. In addition, the deviation between the models and the measure values occurred for grains having a substantial relative size difference with the average grain size (|Rgrain−<R>|) and grains with relatively high |F−Fcr|. These grains also had average turning angles at triple lines (βTJ), which differed from the average equilibrium value expected in isotropic metals, π/3, but were consistent with grain growth under finite triple line mobility. This seems to confirm the existence of triple junction drag at the nanocrystalline length scale, which is not accounted for in classical theoretical models.

The influence of triple junction kinetics on the evolution of polycrystalline materials during normal grain growth: New evidence from in-situ experiments using columnar Al foil

Abstract During grain growth in 2D systems triple junction kinetics may significantly influence not only the rate of grain growth but also the geometric evolution of the grain boundary network. In this contribution we analyse results from in-situ heating experiments coupled with electron backscatter diffraction analysis using a columnar Al foil. It is shown that (a) the von Neumann– Mullins relation is not always satisfied, (b) there is a marked discontinuity and heterogeneity in TJ motion in space and time and (c) grain boundaries evolve from predominately curved to straight boundaries. To interpret these results we introduce 3 main types of triple junctions Tc, Tp, and Ts, which are made up by at least 2 concave, 2 convex, and 3 straight boundaries, respectively. Analyses show that triple junction drag plays a significant role during grain growth. Data suggest that the drag effect of Tp is higher than that of Tc. In addition, triple junctions with 3 low-angle boundaries are exceptionally stable, while those with at least 2 high-angle boundaries are unstable and tend to disappear during grain growth. Only ~ 20% of grain boundaries exhibit steady state triple junction motion.

Normal and abnormal grain growth in magnesium: Experimental observations and simulations

Commercial purity as-cast magnesium was hot rolled and subsequently annealed at different temperatures in order to investigate its grain growth behavior and link it to the texture evolution. Annealing at an intermediate temperature of 220 °C gave rise to abnormal grain growth with a few grains reaching a grain diameter 10 times larger than the mean. Increasing the annealing temperature to 350 °C yielded normal grain growth. Both types of grain growth revealed a strengthening of the (0001) 112-0 texture component. It is hypothesized that a dislocation density gradient after recrystallization grants (0001) 112-0 grains a size advantage during early stages of growth. The type of growth will be, however, determined by the mobility of the present grain boundaries and triple junction drag, which are strongly dependent on the annealing temperature. The above hypothesis of the interplay between these parameters was explored through curvature- and residual dislocation-density-gradient-driven grain growth simulations using a formerly developed level-set approach. The simulation outcome suggests that application of such a modeling approach in microstructure studies of magnesium can provide valuable new insights into the problem of grain growth and associated texture evolution.

Triple junction drag effects during topological changes in the evolution of polycrystalline microstructures

Experiments, theory and atomistic simulations show that finite triple junction mobility results in non-equilibrium triple junction angles in evolving polycrystalline systems. These angles have been predicted and verified for cases where grain boundary migration is steady-state. Yet, steady-state never occurs during the evolution of polycrystalline microstructures as a result of changing grain size and topological events (e.g., grain face/edge switching - “T1” process, or grain disappearance “T2” or “T3” processes). We examine the non-steady evolution of the triple junction angle in the vicinity of topological events and show that large deviations from equilibrium and/or steady-state angles occur. We analyze $∖tau$ the characteristic relaxation time of triple junction angles τ by consideration of a pair of topological events, beginning from steady-state migration. Using numerical results and theoretical analysis we predict how the triple junction angle varies with time and how τ varies with triple junction mobility. We argue that it is precisely those cases where grain boundaries are moving quickly (e.g., topological process in nanocrystalline materials), that the classical steady-state prediction of the triple junction angle about finite triple junction mobility is inapplicable and may only be applied qualitatively.

An advanced level set approach to grain growth – Accounting for grain boundary anisotropy and finite triple junction mobility

The novelty of the proposed level-set approach to grain growth resides in the explicit consideration of structural interfacial elements of the microstructure. The extensions allow to consider anisotropic grain boundary energies and triple junction drag in polycrystalline materials. The simulated predictions were compared to analytical expressions for the growth rate of grains under the influence of a finite triple junction mobility with excellent agreement.

Grain Growth and the Puzzle of its Stagnation in Thin Films a Detailed Comparison of Experiments and Simulations

We revisit grain growth and the puzzle of its stagnation in thin metallic films. We bring together a large body of experimental data that includes the size of more than 30,000 grains obtained from 23 thin film samples of Al and Cu with thicknesses in the range of 25 to 158 nm. In addition to grain size, a broad range of other metrics such as the number of sides and the average side class of nearest neighbors is used to compare the experimental results with the results of two dimensional simulations of grain growth with isotropic boundary energy. In order to identify the underlying cause of the differences between these simulations and experiments, five factors are examined. These are (i) surface energy and elastic strain energy reduction, (ii) anisotropy of grain boundary energy, and retarding and pinning forces such as (iii) solute drag, (iv) grain boundary grooving and (v) triple junction drag. No single factor provides an explanation for the observed experimental behavior.

Stabilizing nanostructured materials by coherent nanotwins and their grain boundary triple junction drag

The role of nanotwin lamellae in enhancing thermal stability of nanostructured materials is examined. Nanostructured copper with varying densities of twins was generated by controlling the deformation strain rate during severe plastic deformation at cryogenic temperatures. While the nanostructured materials produced under cryogenic conditions are characteristically unstable even at room temperatures, their stability is markedly improved when a dense dispersion of nanotwins is introduced. Observations of the role of nanotwins in pinning grain and subgrain structures suggest an interfacial engineering approach to enhancing the stability of nanostructured alloys.

Study of Grain Growth Kinetics in Submicrocrystalline Armco-Iron

The paper is devoted to the problem of thermal stability of ultra-fine grained (submicrocrystalline) materials prepared by severe plastic deformation. A basis of the paper lies in a fact that there is practically no grain growth in submicrocrystalline materials when annealing temperature is less than 0.35Tm. Reasons of high thermal stability of submicrocrystalline materials at low temperatures are widely discussed in literature. One of them is the affect of triple junction drag on grain boundaries motion. During annealing at a low temperature triple junction drag controls microstructure evolution in submicrocrystalline materials, and this phenomenon can be used to improve their thermal stability at high temperatures. The aim of this paper is to investigate grain growth kinetics in a two-step regime, low temperature and high temperature annealing. The experiments on grain growth were performed in submicrocrystalline Armco-iron fabricated by high pressure torsion. It is established that long-time low temperature pre-annealing reduces the grain growth rate in following high temperature annealing by a factor greater than two.

The influence of triple junction kinetics on the evolution of polycrystalline materials during normal grain growth: New evidence from in-situ experiments using columnar Al foil

Abstract During grain growth in 2D systems triple junction kinetics may significantly influence not only the rate of grain growth but also the geometric evolution of the grain boundary network. In this contribution we analyse results from in-situ heating experiments coupled with electron backscatter diffraction analysis using a columnar Al foil. It is shown that (a) the von Neumann–Mullins relation is not always satisfied, (b) there is a marked discontinuity and heterogeneity in TJ motion in space and time and (c) grain boundaries evolve from predominately curved to straight boundaries. To interpret these results we introduce 3 main types of triple junctions Tc, Tp, and Ts, which are made up by at least 2 concave, 2 convex, and 3 straight boundaries, respectively. Analyses show that triple junction drag plays a significant role during grain growth. Data suggest that the drag effect of Tp is higher than that of Tc. In addition, triple junctions with 3 low-angle boundaries are exceptionally stable, while th...

Drag effect of triple junctions on grain boundary and grain growth kinetics in aluminium

The motion and geometry of connected 2D grain boundary systems with triple junctions in aluminium was investigated in situ in an SEM with a specially designed heating stage. The results show that triple junctions can have a marked influence on grain boundary motion and grain growth kinetics. The grain area change with annealing time was recorded in situ in the SEM. An analysis of the experimental data reveals that there is no unique relationship between growth rate and the number n of grain sides (von Neumann–Mullins relation). This is attributed to the effect of triple junction drag on grain growth.

On the influence of triple junctions on grain growth kinetics and microstructure evolution in 2D polycrystals

Grain growth in 2D microstructure is modelled under the supposition that triple junctions possess a limited mobility. The impact of the triple junctions on the grain growth kinetics is shown to depend on a dimensionless parameter Λ¯ equal to the product of the triple junction mobility and the average grain size divided by the grain boundary mobility; it was varied in the range from 0.03 to 100. With low initial Λ¯, the growth kinetics is at first linear and becomes parabolic at the later stages only. The value of the triple junction mobility estimated from the available experimental data is used to prove that an initial Λ¯ as low as 0.005 can be observed in nano-crystalline materials. Thus, the triple junction drag could explain some features of the growth kinetics in these materials.

Effect of Triple Junctions on Grain Boundary and Grain Growth Kinetics in Aluminium - 10 ppm Magnesium Sheet

The motion and geometry of connected grain boundary systems with triple junctions in aluminium -10 ppm magnesium was investigated in-situ with a special designed SEM heating stage. The results show that triple junctions can have a marked influence on grain boundary motion. The grain area change with annealing time was from a hot stage in the SEM. An analysis of the experimental data reveals that there is no unique relationship between growth rate and the number n of grain sides (Von Neumann-Mullins relation). This is attributed to the effect of triple junction drag on grain growth.

Kinematics of connected grain boundaries in 2D

The motion of connected boundary systems was investigated in Al and Zn tricrystals. It was found that triple junctions can exert a drag force on the adjoining boundaries owing to a lower mobility. This drag manifests itself by a deviation of the dihedral angles at the triple junction from the equilibrium angles due to grain boundary surface tensions. The strength of triple junction drag can be expressed in terms of a criterion Λ = (m tj . a/m b ), where m tj is the triple junction mobility, m b the boundary mobility, and a is the grain size. Therefore, the effect should be particularly pronounced in fine-grained and nanocrystalline materials. It is shown that the von Neumann-Mullins relation of 2D grain growth is modified by triple junction drag such that there is no unique relationship between growth rate and the number of sides anymore. For very small Λ, the triple junctions control grain structure evolution during grain growth, which leads to polyhedral grain shapes with flat boundaries. The theoretical concept is supported by computer simulations of grain growth and in-situ annealing experiments in the SEM.

Efficiency of drag mechanisms for inhibition of grain growth in nanocrystalline materials

Abstract An attempt is made to assess the efficiency of drag effects by different structural elements of a polycrystal on grain growth. The rate of grain area change is chosen as a measure of stability of a grain structure, and the inhibition of grain growth is pairwise evaluated among all drag effects considered. In aluminium, at temperatures of about 200 °C, triple junction drag was found to be most effective. The derived hierarchy of drag efficiency can be used as an effective engineering tool to assess and compare the role of chemistry and crystal defects on the microstructural stability of nanocrystalline and fine-grained materials.

Molecular dynamics simulation of triple junction migration

We present a molecular dynamics simulation study of the migration of grain boundaries with triple junctions. We have monitored the grain boundary profile, triple junction angles and rate of grain boundary migration with and without triple junctions as a function of grain size, grain misorientation, direction of migration and temperature in a series of configurations designed to ensure steady-state migration. The present results demonstrate that triple junction mobility is finite and can be sufficiently small to limit the rate of grain boundary migration. The drag on grain boundaries due to limited triple junction mobility is important at small grain sizes, low temperature and near high symmetry grain misorientations. This drag limits the rate of grain boundary migration and leads to triple junction angles that differ substantially from their equilibrium value. Simulation data suggest that triple junction drag is much more a factor at low temperature than at high temperature. The triple junction mobility is shown to depend upon the direction of triple junction migration. The present results are in excellent qualitative agreement with experimental observations.

Triple junction drag and grain growth in 2D polycrystals

The process of grain growth in 2D systems is analyzed with respect to the controlling kinetics: from solely boundary kinetics, when grain growth in a polycrystal is determined by the Von Neumann–Mullins relation, to exclusively triple junction kinetics, when grain growth is governed by the mobility of triple junctions. It is shown that in the “intermediate” case, when the driving force for grain boundary motion and the characteristic mobility are grain boundary curvature and grain boundary mobility, respectively, a limited mobility of triple junctions essentially influences grain boundary motion. The Von Neumann–Mullins relation does not hold anymore, and this is the more pronounced the smaller the triple junction mobility. In the case where grain growth is determined by the mobility of grain boundary triple junctions (triple junction kinetics) all grains are transformed into polygons in the course of grain growth. Grain growth would cease if all grains assumed the shape of regular polygons, not only hexagons like in the Von Neumann–Mullins case. The only exceptions are triangles: they collapse without transforming into a polygon. The respective relation for the rate of a change of grain area under triple junction kinetics is obtained and discussed with regard to microstructure evolution.

The Effect of Triple Junctions on Grain Boundary Motion and Grain Microstructure Evolution

The theory of steady state motion of grain boundary sytems with triple junctions and the main features of such systems are considered. A special technique of in-situ observations and recording of triple junction motion is introduced, and the results of experimental measurements on Zn tricrystals are discussed. It is shown, in particular, that the described method makes it possible to measure the triple junction mobility. It was found that the measured shape of a moving half-loop with a triple junction agrees with theoretical predictions. A transition from triple junction kinetics to grain boundary kinetics was observed. This means that triple junctions can drag boundary motion. It is demonstrated that the microstructural (granular) evolution is slowed down by triple junction drag for any n-sided grain. The second consequence pertains to six-sided grains. For a boundary system with dragging triple junctions there is no unique dividing line between vanishing and growing grains with respect to their topological class anymore, like n = 6 in the Von Neumann-Mullins relation.