On the Surface Diffusion Flow with Triple Junctions in Higher Space Dimensions

Non-linear stability of double bubbles under surface diffusion

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.

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.

Generalized type III internal stress from interfaces, triple junctions and other microstructural components in nanocrystalline materials

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

Triple junction drag and grain growth in 2D polycrystals

Modelling the influence of microstructural morphology and triple junctions on hydrogen transport in nanopolycrystalline nickel

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.

Influence of triple junctions on grain boundary motion

The correlation between the atomic structures and the misorientation angles of [0001]-tilt grain boundaries at triple junctions in ZnO thin films grown on Si substrates was investigated by using high-resolution transmission electron microscopy (HRTEM) measurements. The HRTEM images showed three symmetric grain boundaries and one asymmetric grain boundary around the triple junction in the ZnO film. The correlation between the atomic structures and the misorientation angles of the grain boundaries at triple junctions in ZnO films is described on the basis of the HRTEM results.

The junction between oceanic crust generated, within the Antarctic plate, at the Southeast Indian Ridge and the Southwest Indian Ridge has been studied using a SEABEAM swathe bathymetry mapping system and other geophysical techniques between the Indian Ocean Triple Junction (approximately 25°S, 70° E), and a point some 500 km to the southwest (at 28°25′ S, 66°35′ E). The morphotectonic boundary which marks this trace of the ridge-ridge-ridge triple junction is complex and varies with age. Recent theories proposing a cyclicity of volcanic and tectonic processes at this mode of triple junctions appear to be supported by a series of regularly spaced, en echelon escarpments facing the slowly spreading (0.6 to 0.8 cm a-1, half rate) Southwest Indian Ridge axis. The en echelon escarpments intersect at approximately right angles with the regularly spaced oceanic spreading fabric formed on the Antarctic plate at the Southeast Indian Ridge and together locally flank uplifted northward-pointing ‘corner’ sections of ocean floor. The origins for the localised elevations are unclear, but may relate to intermittent and/or alternating rifting and volcanic episodes. Variations of degree of asymmetry and/or obliquity in spreading on the Central Indian Ridge and the Southwest Indian Ridge are suggested to explain detailed structural changes along the triple junction trace. It is suggested that discontinuities of the trace may be related to an intermittent development of new spreading centres beneath the most easterly part of the Southwest Indian Ridge, coupled with a more continuous process beneath the faster spreading Central Indian Ridge (2 to 2.5 cm a-1) and the Southeast Indian Ridge (2.5 to 3 cm a-1). A detailed history of triple junction evolution may be thus inferred from basic morphological and structural mapping along the three triple junction traces.

Rift‐Rift‐Rift triple junctions are key features of emergent plate boundary networks during fragmentation of a continent. A key example of such a setting is the Afar triple junction where the African, Arabian and Somalian plates interact. We performed analog and numerical models simulating continental break‐up in a Rift‐Rift‐Rift setting to investigate the resulting structural pattern and evolution. We modified the ratio between plate velocities, and we performed single‐stage (with all plates moving at the same time) and two‐stage (where one plate first moves alone and then all the plates move simultaneously) models. Additionally, the direction of extension was changed to induce orthogonal extension in one of the three rift branches. Our models suggest that differential extension velocities in the rift branches determine the localization of the structural triple junction, which is located closer to the rift branch experiencing slower extension velocities. Furthermore, imposed velocities affect the deformation resulting in end‐member fault patterns. The effect of applying similar velocities in all rift arms is to induce a symmetric fault pattern (generating a Y‐shaped geometry). In contrast, a faster plate generates structures trending orthogonal to dominant velocity vectors, while faults associated with the movement of the slower plates remain subordinate (generating a T‐shaped pattern). Two‐stage models reveal high‐angle faults interacting at the triple junction, confirming that differential extension velocities strongly affect fault patterns. These latter models show large‐scale similarities with fault patterns observed in the Afar triple junction, providing insights into the factors controlling the structural evolution of this area.

We investigate the role of grain constraint upon martensitic transformation through in situ scanning electron microscope tensile experiments on shape memory microwires with a small number of grains and grain junctions. The martensite transformation morphology becomes more complex with increasing grain constraint: In unconstrained monocrystalline regions, the transformation is simple, single variant, and complete; near grain boundaries, the transformation is only partial, containing regions of untransformed austenite; near a triple junction, the morphology is complex, the transformation is partial and also multi-variant. These observations speak of transformation-induced stress concentrations that are more severe around triple junctions than around grain boundaries. Finite element modeling also provides an estimate for constraint effects on martensitic transformation yielding higher stresses near triple junctions than near grain boundaries. Towards the goal of developing polycrystalline Cu-based shape memory alloys that avoid intergranular fracture, our results support three design objectives: (1) Removal of triple junctions, (2) reduction of the total grain boundary area, and (3) geometry design containing unconstrained regions where the transformation can be most easily accommodated.

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.