Triple junction motion and grain microstructure evolution

Triple junction drag and grain growth in 2D polycrystals

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.

The mobility of individual triple junctions in aluminum is studied. Triple junctions with 〈111〉, 〈100〉, and 〈110〉 tilt boundaries are studied. The data obtained show that, at low temperatures, the mobility of the system of grain boundaries with a triple junction is controlled by the mobility of the triple junction (the junction kinetics). At high temperatures, the system mobility is determined by the mobility of the grain boundaries (the boundary kinetics). There is a temperature at which the transition from the junction kinetics to the boundary kinetics occurs; this temperature is determined by the crystallographic parameters of the sample.

Grain boundary networks composed of equal microstructural elements were investigated in a recent paper. In this work a more complicated artificial grain topology consisting of one four-sided, two six-sided and one eight-sided grain is designed to further investigate the influence of grain boundary and triple junction mobilities on the kinetics of the system in more detail. Depending on the value of the equal mobility of all triple junctions, the initially square-shaped four-sided grain changes its shape to become more or less rectangular. This indicates that the grain morphology is influenced by the value of the mobility of the triple junctions. It is also demonstrated that a grain arrangement with low mobility triple junctions controlling the kinetics of grain growth enhances growth of the large eight-sided grains. In addition, grain growth is investigated for different values of mobilities of triple junctions and grain boundaries. A strong elongation of several grains is predicted by the modeling results for reduced mobilities of the microstructural grain boundary elements. The two-dimensional modeling results are compared to micrographs of a heat-treated titanium niobium microalloyed steel. This feature, namely the evolution of elongated grains, is observed in the micrograph due to the pinning effect of (Ti, Nb)C precipitates at elevated soaking temperatures of around 1100 °C. Furthermore, the experiments show that a broader distribution of the grain sizes occur at 1100 °C compared to soaking temperatures, where pinning due to precipitates plays a less prominent role. A widening of the distribution of the grain sizes for small triple junction mobilities is also predicted by the unit cell model.

Commercial purity aluminium at true strains ε=2∼5.5 was annealed in a wide temperature range (from room temperature to 220°C), and the evolution of microstructure was characterized using transmission electron microscopy (TEM) and electron backscattered diffraction (EBSD) techniques. Triple junctions in an ultrafine lamellar structure are classified into three categories based on the structural morphology, and a relationship is formulated between the density (length per unit volume) of triple junctions and the boundary spacing. The triple junction density increases with increasing strain during plastic deformation and decreases during isochronal and isothermal annealing. Based on TEM and EBSD observations, thermally activated triple junction motion is identified as the key process during the recovery of highly strained aluminium, leading to the removal of thin lamellae with small dihedral angles at the ends and structural coarsening. A mechanism for recovery by triple junction motion is proposed, which can underpin the general observation that a lamellar structure formed by plastic deformation during annealing can evolve into an equiaxed structure, preceding further structural coarsening and recrystallization. Within this framework, the grain boundary surface tension on triple junctions is discussed based on the structural parameters characterizing the deformed and annealed microstructure.

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.

Influence of triple junctions on grain boundary motion

When a bicrystal or polycrystal are subjected to a change in temperature, the individual responses of the two adjoining crystals may differ in a manner, which tends to produce a dilatational mismatch along grain boundaries. If compatibility is to be retained along the interface, an additional set of stresses must then be generated in order to conserve this compatibility. ‘Compatibility stresses’ will also be generated whenever a polycrystal is heated or cooled and the thermal expansion coefficients of the individual grains are different due to thermal expansion anisotropy. In such cases adjacent grains will attempt to change dimensions and develop mismatches by amounts controlled by the parameter Δa*ΔΤ, where Δa is the difference between the thermal expansion coefficients in the appropriate directions, and ΔΤ is the temperature change. These ‘compatibility stresses’ may be relieves if grain boundary motion, triple junction migration and grain growth are possible. These ‘compatibility stresses’ may play important role in the kinetic behavior of the microstructure ranging from influencing the behavior of lattice dislocations near the grain boundaries to promoting grain boundary and triple junction dragging or moving. The motion of the ‘special’ grain boundaries, triple junctions with ‘special’ grain boundaries and twins under the influence of internal mechanical stresses is the main subject of this paper.

We use geometrical arguments based on grain boundary symmetries to introduce crystalline interfacial energies for interfaces in polycrystalline thin films with a cubic lattice. These crystalline energies are incorporated into a multi-phase field model. Our aim is to apply the multi-phase field method to describe the evolution of faceted grain boundary triple junctions in epitaxially growing microstructures. In particular, we are interested in symmetry properties of triple junctions in tricrystalline thin films. Symmetries of triple junctions in tricrystalline films have been studied in experiments by Dahmen and Thangaraj.6,25 In accordance with their experiments, we find in numerical simulations that any two neighboring triple junctions belong to different symmetry classes. We introduce a local equilibrium condition at triple junctions which can be interpreted as a crystalline version of Young's law. The local equilibrium condition at triple junctions is purely determined by the grain boundary energies. In particular no triple junction energies are necessary to explain which triple junctions are possible. All triple junctions observed in the experiments as well as in the simulations fulfil the crystalline version of Young's law. Our approach is also capable of describing grain boundary motion in general polycrystalline thin films.

Reduction in stored free energy provides the thermodynamic driving force for grain and bubble growth in polycrystals and foams. Evolution of polycrystalline networks exhibit the additional complication that grain growth may be controlled by several kinetic mechanisms through which the decrease in network energy occurs. Polyhedral boundaries, triple junctions (TJs), and quadruple points (QPs) are the geometrically distinct elements of three dimensional networks that follow Plateau’s rules, provided that grain growth is limited by diffusion through, and motion of, cell boundaries. Shvindlerman and co-workers have long recognized the kinetic influences on polycrystalline grain growth of network TJs and QPs. Moreover, the emergence of interesting polycrystalline nanomaterials underscored that TJs can indeed influence grain growth kinetics. Currently there exist few detailed studies concerned either with network distributions of grain size, number of faces per grain, or with ‘grain trajectories’, when grain growth is limited by the motion of its TJs or QPs. By contrast there exist abundant studies of classical grain growth limited by boundary mobility. This study is focused on a topological/geometrical representation of polycrystals to obtain statistical predictions of the grain size and face number distributions, as well as growth ‘trajectories’ during steady-state grain growth. Three limits to grain growth are considered, with grain growth kinetics controlled by boundary, TJ, and QP mobilities.

In addition to driving forces due to curvature of grain boundaries there are driving forces acting on triple junctions which also contribute to grain growth. Equations are derived for the rate of change, due to the triple junction forces, of the average area or average volume of 2D and 3D grains, respectively, with a fixed number of topological elements (edges in 2D and faces in 3D). The equations derived are compared with the von Neumann-Mullins equation for 2D curvature driven grain growth and to the extension of that equation to 3D grain growth. In triple junction controlled grain growth, the effect ofn orF is qualitatively the same as in curvature driven growth, with a threshold atn or −F between shrinkage and growth. However, the rates are in general not linear onn orF, and there is a size effect which has a repercursion on the overall growth kinetics.

Given that polycrystalline triple junctions are significant contributors to material properties, they are frequently becoming the focus of emerging research. Despite this interest, the tools to quickly and quantitatively analyze triple junction textures remain severely limited. To enable characterization of triple junctions on a large scale, the parameters, space, and conventions of twin dependent triple junction distributions have been developed. In addition, by adopting grain boundary stereological techniques, triple junction distributions have been generated from a single section plane for triple junctions containing a coherent twin boundary. This methodology has been validated using simulated microstructures and, with further experimental development, will provide insight into actual triple junction structures. This technique also establishes the foundation for a generalized non-twin dependent approach in the future.

Direct experimental observation of accelerated Zn diffusion along triple junctions in Al

Investigating the von Neumann–Mullins relation under triple junction dragging

The paper is dedicated to the steady state motion of the grain boundary systems with the triple junctions. The main features of one of the systems where steady state motion is possible are considered. In the experimental part the results of the experiments on the tricrystals of Zn are described. In particular, it was demonstrated that the vertex angle θ at the triple junction can deviate distinctly from the equilibrium value, when a low mobility of the triple junction drags the grain boundary motion. A transition from triple junction kinetics to grain boundary kinetics was observed. There is experimental evidence that in TJ motion pre-exponential factor changes linearly with the activation enthalpy. This behaviour is referred to as compensation effect.