Triple Junction Line Research Articles

Geometric methods for microstructure rendition and atomic characterization of poly- and nano-crystalline materials

Polycrystalline materials of both coarse-grain and nanometer scales have complex topological structures with multi-dimensions, including vertices (zero dimension), triple junction lines (one dimension), interfaces or grain boundaries (two dimensions), and grain volumes (three dimensions). Collectively, they contribute to the properties that make these materials valuable for many applications. However, for both numerical modeling and theoretical analysis, connecting the microstructures quantitatively with the properties remains a challenge, due simply to their complexity and also limitations in direct probing of the microstructures at atomic scales in experiments. Without an accurate description of the microstructures, it is difficult, if not impossible, to determine quantitatively the factors and parameters of microstructures and their contributions to the properties. In this study, we present systematic methods, using a series of geometric constructions, to render microstructures in the polycrystalline materials and their characterization at atomic scales. We tested the methods in nanocrystalline (nc) copper using molecular dynamics simulation, as it is the only polycrystalline sample that could be handled at atomic scale. We present the first set of results of atomic scale characterization of the microstructure attributes, grain boundary profile, effects of misorientation, grain size and temperature on grain boundaries, and discuss further applications of the methods.

Nucleation of recrystallization observed in situ in the bulk of a deformed metal

Abstract Nucleation of recrystallization is studied in situ in the bulk by three-dimensional X-ray diffraction. Copper samples cold rolled 20% are investigated. The crystallographic orientations near triple junction lines are characterized before, during and after annealing. Three nuclei are identified and it is shown that two nuclei are twin related to their parent grain and one nucleus has an orientation, which is neither present in the deformed parent grains nor first order twin related to any of them. Data on the nucleation kinetics is also presented.

Effects of Triple Line Tension on the Surface Topography of Polycrystals

AbstractA balance of surface energies exists where grain boundaries meet the surface of a flat solid specimen. The energy balance leads to grain boundary grooving on the surface, and the establishment of the equilibrium dihedral angle. Triple junctions are defined at the intersections of three grain boundaries. Surface grooves are typically observed to be the deepest at the triple junctions. In this work, a simple model is constructed of a polycrystalline thin film using Surface Evolver numerical software. The equilibrium sur face groove depths at triple junctions are investigated as a function of triple junction line tension. Results show that line tension can affect grain boundary groove depths for grain sizes less than ∼1μm.

Mesoscopic stress field arising from the grain interaction in plastically deformed polycrystals

Under consideration is the stress field arising in a plastically deformed polycrystal since its misoriented grains are subjected to different plastic strains. To analyse that, a two-dimensional model has been taken that allows for intergranular stress sources and comprises a finite aggregate of the grains together with its continuous surroundings of mean polycrystal properties. Within the scope of this model the stress field is analytically evaluated for three adjoined grains, special attention being given to the singularity at the triple junction line. Related features of the shear and hydrostatic stress components are respectively considered to actuate the low-angle boundary emission and the conglomeration of point defects.

Three-dimensional stress singularities at the tip of a grain triple junction line intersecting the free surface

The stress singularity at the point of intersection of a grain triple junction line with the free surface has been numerically evaluated in single-phase polycrystals of cubic and hexagonal grains. The angle spanned by the grain boundaries, the orientation of the crystal axes within each grain and the position of the triple junction line with respect to the free surface were taken as variables, and their effect on the singularity exponent γ (defined by σ ∞ r γ−1 ) determined. In general, the configurations possessing geometrical and material symmetries were associated with stronger singularities and almost all triple junction geometries were characterized by two singularity exponents, each corresponding to the symmetric and the antisymmetric fields. Thus, such a singular point is associated with a fixed mixed mode. Interestingly, the values obtained were somewhat different and stronger when compared with those obtained for the corresponding two-dimensional plane stress and strain configurations.

Three-dimensional stress concentration at grain triple junctions in columnar ice

The magnitude of the elastic anisotropy-induced stress concentration at points where the grain triple-junction lines in freshwater columnar ice intersect the free surface is analysed. The concentration effect is shown to be much weaker than that at the crack tip but stronger than obtained at similar grain triple junctions under plain-strain conditions. If preferential thermal etching of the ice surface occurs at the triple junction, the grooving and the elastic anisotropy effects add and significantly stronger concentrations result. The conditions under which cracks are expected to nucleate from these stress concentration sites are discussed.

Mean stresses in microstructures due to interface stresses: A generalization of a capillary equation for solids

We derive a general expression for the mean stress in a solid induced by the stresses of areal and linear defects such as grain boundaries and triple junction lines. The mean stress is a function of measurable stereological quantities, weighted areas of interfaces and lengths of the linear defects, not their curvatures. Generally the stress is non-hydrostatic. For anisotropic and textured microstructures, the mean stress depends on stereological moments of the interface orientation distribution function, but otherwise it is independent of the geometry of the microstructure. In two limiting cases, isolated spherical particles (in a matrix or not) and layer structures, the solution for the stress reduces to results which have been derived previously. These solutions can be used to determine average interface stresses from experimental lattice constant data. Although the specific interface area is always the important quantity in this relation, for the spheres this area/volume reduces to the particle curvatures commonly used in the literature for many microstructures.

Destabilization of the tetrahedral point junction by positive triple junction line energy

Destabilization of the tetrahedral point junction by positive triple junction line energy

Explosion of carbonic acid in a coal mine

Stereological relations that can be routinely applied for the quantitative characterization of microstructures of heterogeneous single- and two-phase materials via global microstructural descriptors are reviewed. It is shown that in the case of dense, single-phase polycrystalline materials (e.g., transparent yttrium aluminum garnet ceramics) two quantities have to be determined, the interface density (or, equivalently, the mean chord length of the grains) and the mean curvature integral density (or, equivalently, the Jeffries grain size), while for two-phase materials (e.g., highly porous, cellular alumina ceramics), one additional quantity, the volume fraction (porosity), is required. The Delesse–Rosiwal law is recalled and size measures are discussed. It is shown that the Jeffries grain size is based on the triple junction line length density, while the mean chord length of grains is based on the interface density (grain boundary area density). In contrast to widespread belief, however, these two size measures are not alternative, but independent (and thus complementary), measures of grain size. Concomitant with this fact, a clear distinction between linear and planar grain size numbers is proposed. Finally, based on our concept of phase-specific quantities, it is shown that under certain conditions it is possible to define a Jeffries size also for two-phase materials and that the ratio of the mean chord length and the Jeffries size has to be considered as an invariant number for a certain type of microstructure, i.e., a characteristic value that is independent of the absolute size of the microstructural features (e.g., grains, inclusions or pores).