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.     

Strong pinning of triple junction migration for robust high strain nanostructures

The universality of a key recovery mechanism: triple junction migration in high strain nanostructures is revealed herein. This migration is the only means to uniformly coarsen deformed lamellar microstructures. Migration of medium to high angle geometrically necessary boundaries at triple junctions is resisted by strong pinning phenomena. Pinning by low angle dislocation boundaries is the novel mechanism that greatly adds to the solute drag of these higher angle boundaries during migration at triple junctions. Solutes furthermore cause a significant increase in the dislocation density of the low angle boundaries formed during deformation and thus greatly enhance the observed pinning. Boundary pinning by dislocation boundaries and solute drag is analysed for deformed Ni of different purities via in and ex situ electron microscopy. A kinetic model is utilised to obtain activation energies that quantitatively demonstrate the strength of this pinning. A new strategy for achieving robust nanostructured metals is developed based on solute and dislocation pinning of triple junction migration – a universal recovery mechanism in deformed lamellar microstructures.     

Triple Junction Mobility: A Molecular Dynamics Study

We present a molecular dynamics simulation study of the migration of individual grain boundary triple junctions. The simulation cell was designed to achieve steady state migration. Observations of the triple junction angle and grain boundary profiles confirm that steady state was achieved. The static, equilibrium grain boundary triple junction angles and the dynamic triple junction angles were measured as a function of grain size and grain boundary misorientation. In most cases, the static and dynamic triple junction angles are nearly identical, while substantial deviations were observed for low boundary misorientations. The intrinsic, steady-state triple junction mobilities were extracted from measurements of the rate of change of grain boundary area in simulations with and without triple junctions. The triple junction velocity is found to be inversely proportional to the grain size width. The normalized triple junction mobility exhibits strong variations with boundary misorientation, with strong minima at misorientations corresponding to orientations corresponding to low values of . The triple junctions create substantial drag on grain boundary migration at these low mobility misorientations.     

Compensation Effect for the Kinetic Properties of Triple Junctions

The compensation effect or Meyer-Neldel rule has been observed in a wide range of phenomena. It seems to be a fundamental property of the many families of activated processes following an Arrhenius dependence on temperature. The kinetic properties of grain boundaries and triple junctions depend strongly on their crystallographic parameters and obey the Arrhenius law. The data on the Meyer-Neldel rule for grain boundaries and triple junctions in Al and Zn and the values of the compensation temperature for the migration of grain boundaries and triple junctions are presented in this paper.     

Study of the motion of individual triple junctions in aluminum

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.     

Molecular dynamics investigation of the diffusion permeability of triple junctions of tilt and mixed-type boundaries in nickel

The diffusion permeability of triple junctions of high-angle tilt boundaries 〈111〉 and 〈100〉 and mixed-type boundaries in nickel has been investigated using the molecular dynamics method. It has been shown that the diffusion permeability of equilibrium triple junctions does not exceed the permeability of the grain boundaries forming them. The effective diffusion radius of the considered triple junctions and the width of the grain boundaries are determined.     

Grain boundary sliding and lattice dislocation emission in nanocrystalline materials under plastic deformation

A theoretical model is proposed to describe the physical mechanisms of hardening and softening of nanocrystalline materials during superplastic deformation. According to this model, triple interface junctions are obstacles to glide motion of grain boundary dislocations, which are carriers of grain boundary glide deformation. Transformations of an ensemble of grain boundary dislocations that occur at triple interface junctions bring about the formation of partial dislocations and the local migration of triple junctions. The energy characteristics of these transformations are considered. Pileups of partial dislocations at triple junctions cause hardening and initiate intragrain lattice sliding. When the Burgers vectors of partial dislocations reach a critical value, lattice dislocations are emitted and glide into adjacent grains, thereby smoothing the hardening effect. The local migration of triple interface junctions (caused by grain boundary sliding) and the emission of lattice dislocations bring about softening of a nanocrystalline material. The flow stress is found as a function of the total plastic strain, and the result agrees well with experimental data.     

Mathematical Models of Triple Junctions

Including triple junctions in rigorous mathematical models had very limited success until about 25 years ago. This paper surveys the mathematical results on triple junctions since then. Anisotropic surface energies, zero triple line energy, positive triple line energy, and negative triple line energy are all considered, in both sharp and diffuse interfaces. In particular, the problems with negative line junction energies in sharp interface theory are presented. Both equilibrium and growth models are reviewed, in 2 and 3 dimensions.     

Effect of triple junctions of nanotubes on strengthening and fracture toughness of ceramic nanocomposites

A theoretical model has been proposed for describing the influence of triple junctions of nanotubes on the strengthening of a nanocomposite. It has been assumed that the slip of nanotubes along the boundary with the matrix takes place via the nucleation and glide of prismatic dislocation loops enveloping the nanotubes. These loops are retarded by the triple junctions of nanotubes, which leads to a strengthening and increase in the fracture toughness (crack resistance) of the nanocomposite. It has been shown that, in order for the dislocation loop to overcome the triple junction, the shear stress acting on the loop should exceed a certain critical level. This critical stress increases as the radius and wall thickness of the nanotube decrease. The inference has been made that the triple junctions of thinnest nanotubes, such as single-walled carbon nanotubes, should lead to the greatest strengthening and to an increase in the crack resistance of these nanocomposites.     

Formation of the Excess Free Volume in Triple Junctions during Nickel Crystallization

The formation of an excess free volume in triple junctions during crystallization has been studied by the molecular dynamics model using nickel as an example. It is shown that an excess free volume that forms during nickel crystallization in triple junctions predominantly forms as a result of the fixation of the liquid phase volume when contacting three crystallization fronts that contains, after crystallization, a high fraction of the free volume. In some cases, as the free volume is concentrated in triple junctions, a comparatively small crystalline subgrain (from one to several nanometers in diameter) forms, and the subgrain has the orientation different from those of contacting grains and exists in the extended state.     

Twin Junctions in Monoclinic Zirconia

Analysis of high-resolution transmission electron microscopy images of the microstructure of monoclinic zirconia film has revealed that some areas are built entirely of twins. Twin boundaries form triple and quadruple junctions. While the misorientations of the constituent boundaries are completely balanced at quadruple junctions, there is a small rotational mismatch at the junctions of three twin boundaries. This mismatch is compensated by wedge disclinations. Crystallography of the triple junctions is considered and factors stabilizing intrinsic junction disclinations are discussed.     

The Geometric and Thermodynamic Properties of Grain Boundary Junctions

We provide an overview of the properties of triple junctions and quadruple points. It is shown that these junctions may exhibit distinct behaviors that imply that they have and thermodynamically distinct properties in the same way that grain boundaries can be considered as thermodynamically distinct phases, separate from the material that they inhabit. It is shown that the treatment of triple junctions as thermodynamically distinct defects is a natural extension of the treatment of grain boundaries, and that it can be further extended to other junctions such as quadruple nodes. Equilibrium dihedral angles under conditions of anisotropic interfacial energy are explored, and it is found that the dihedral angles may be variable under a range of different conditions.     

On the Origin and Energy of Triple Junction Defects Due to the Finite Length of Grain Boundaries

King [1] established that due to the discrete nature of their dislocation structure, finite length grain boundaries (GBs) in polycrystalline materials possess discrete values of misorientation angle. For a GB with a length that is not a multiple of the GB period, this leads to the formation of specific disclinations at their junctions with neighboring GBs, which compensate the difference between the misorientations of finite and infinite boundaries. In the present paper the origin of these compensating disclinations within GB triple junctions is elucidated and their strength is calculated using the disclination-structural unit model. It is shown that for a GB with length of about 10 nm the junction disclinations can have a strength value not more than 1°, in contrast to King's calculations that indicate much larger values. Elastic energies of triple junctions due to compensating disclinations are calculated for both equilibrium and non-equilibrium structures of a finite length GB, which differ by the position of the grain boundary dislocation network with respect to the junctions. The calculations show that triple junction energies are comparable to dislocation energies, and that compensating disclinations can play a significant role in the properties of nanocrystalline metals with grain sizes less than about 10 nm.     

Nanocrack nucleation in polycrystalline silicon during grain-boundary sliding

A theoretical model is proposed to describe nanocrack nucleation in polycrystalline silicon. In terms of this model, nanocrack nucleation is stimulated by grain-boundary sliding, which creates sources of local stresses in triple junctions of grain boundaries. The relaxation of these local stresses is the main driving force of nanocrack nucleation near triple junctions in polycrystalline silicon, in which grain-boundary sliding contributes substantially to plastic deformation under cyclic loading at room temperature. The model is used to calculate the critical external stress required for nanocrack nucleation in polycrystalline silicon.     

Effect of atomic ordering on the role of grain boundaries in the plastic deformation of Ni<Subscript>3</Subscript>Fe alloy

The structure of dislocations and the defect structure of grain boundaries and their parameters in Ni₃Fe alloy with short-range order (SRO) and long–range order (LRO) at different stages of plastic deformation are studied by means of transmission diffraction electron microscopy using thin foils and replicas. It is found that atomic ordering reduces the Σ3 twins plasticizing effect, increases the density of grain boundary defects, slows their annihilation during deformation, and intensifies the microstrains at the triple junctions of grain boundaries.     

Effect of finite boundary junction mobility on the growth rate of grains in 3D polycrystals

With decreasing grain size, grain boundary junctions become increasingly important for microstructure evolution. We show that the effect of a limited mobility of triple junctions on the growth rate of polycrystals can be implemented in theories of three-dimensional (3D) grain growth. Respective analytical relations are derived on the basis of the average n-hedra approach introduced by Glicksman to describe the volume rate of change of 3D grains in a polycrystalline aggregate under the impact of a limited triple junction mobility. The theoretical predictions were compared to network-model computer simulations, and good agreement was obtained.     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

Normal distribution profile for doping concentration in multilayer tunnel junction

In this paper, the effect of doping concentration and layer thickness on the performance of tunnel junctions (TJs) is studied. We investigate the behavior of single, double and triple layer structures of TJs. Triple layer structure shows better performance in comparison with the other structures and can reach the higher tunneling current besides lower voltage drop. Also, the behavior of the triple layer TJ with different doping concentration profiles is studied. We propose a new normal distribution profile for doping concentration in multilayer TJs which shows better performance in comparison with the linear and graded doping concentration profiles. The higher $\upalpha $ parameters in normal distribution enhance the device performance with increasing the smoothness of doping variations in the center and edge of the TJ. Finally, we examine different thicknesses of triple layer TJ in order to achieve the optimum structure.     

Determination of the Radius of Triple Junctions of Tilt Boundaries: A Molecular Dynamics Simulation

Russian Physics Journal - Using the method of molecular dynamics, an investigation of the free volume and energy distribution is performed in the region of triple junctions of high-angle tilt...