Quadruple Junctions Research Articles

Grain Distribution for Optimal Strength in Homogeneous and Gradient Nano‐Grained Coppers

The distribution of grains plays a crucial role in determining the strength of polycrystalline copper when the grain size is constant. Herein, the mechanical properties of homogeneous nano‐grained (HNG) and gradient nano‐grained (GNG) coppers with different grain distributions are examined using molecular dynamics (MD) simulations. The HNG‐ordered structure has all triple junctions (TJs), whereas the random structure contains many quadruple and quintuple junctions. When grain size is below the critical size in the inverse Hall–Petch relationship, the high‐density TJs in the HNG‐ordered structure effectively inhibit grain boundary (GB) softening compared with the random structure, leading to higher strength. However, when grain size is above the critical size, subgrains are produced inside the large grains due to dislocation slip. In addition, disordered atoms in HNG‐random structure are stacked in the quadruple and quintuple junctions, resulting in thicker GBs. This triggers grain boundary migration, and forms more subgrains at GBs. Subsequently, grain boundary sliding and grain rotation of subgrains induce partial recrystallization in the structure. This consecutively triggered deformation mechanism leads to extra strengthening in the random structure. Further research indicates that combining small‐grained ordered and large‐grained random structures can be a new approach to effectively strengthen GNG materials.

Reaction‐Induced Mantle Weakening at High‐Pressure Conditions: An Example From Garnet Pyroxenites of Ulten Zone (Eastern Alps, N Italy)

AbstractPeridotites of Ulten Zone (Eastern Alps, N Italy) show a transition from coarse protogranular spinel lherzolites to fine‐grained amphibole + garnet peridotites, recorded by the crystallization of garnet coronas around spinel. Pyroxenite veins, transposed along the peridotite foliation, show a similar metamorphic evolution from coarse‐grained (garnet‐free) websterites to fine‐grained garnet websterites. In both peridotites and websterites, garnet previously exsolved from porphyroclastic high‐temperature pyroxenes and later crystallized along the foliation. This evolution has been interpreted to reflect cooling and pressure increase of websterites and host peridotites from spinel‐ to garnet‐facies conditions. Microstructures and crystallographic orientation data indicate that the re‐equilibration of garnet websterites in the garnet stability field occurred during deformation. Porphyroclastic pyroxenes have been interpreted to deform by dislocation glide and creep. In particular, TEM observations indicate the activation of the (100)[010] slip system in orthopyroxene. Core‐and‐mantle microstructures also suggest that dislocation creep was aided by subgrain rotation recrystallization, leading to the formation of neoblastic pyroxenes. These recrystallized grains deformed by diffusion‐accommodated grain boundary sliding, as indicated by the occurrence of quadruple junctions and straight, aligned grain boundaries. The transition from dislocation creep to diffusion creep in websterites was accompanied by the crystallization of garnet along foliation, which triggered the pinning of the recrystallized matrix and stabilized the fine‐grained microtexture for diffusion creep, promoting rheological weakening. Garnet websterites of Ulten Zone thus offer a unique opportunity to investigate the effects of reaction softening during the corner flow in the supra‐subduction lithospheric mantle induced by the descending slab.

Roles of triple and quadruple junctions on plasticity by phase-field crystal approach

Roles of non-/symmetric triple and quadruple junctions on plasticity of ploycrystals are examined using phase-filed crystal model combined with an isovolumetric deformation technique. We designed four polycrystalline samples containing the four types of junctions respectively to simulate the deformation process under a strain rate comparable to practical situations. Our results uncover relationships between the ability of resistances to external deformations and the deformation mechanisms. For the ploycrystals containing quadruple junctions, the symmetric junction is beneficial to maintain the stability of the junctions during deformations, while asymmetric ones would be disjointed and result in formation and growth of sub-grains. For the polycrystals containing triple junctions, the stability of the junction is strongly related to the misorientation angles of the associated grains. The triple junction composed with high-angle GBs exhibits excellent stability under successive deformations and the deformation is dominated by GB migrations. Low-angle GBs migrate more easily than the high-angle ones.

Constant of motion for ideal grain growth in three dimensions

Most metallic and ceramic materials are comprised of a space-filling collection of crystalline grains separated by grain boundaries. While this grain structure has been studied for more than a century, there few rigorous results regarding its global properties available in the literature. We present a new, rigorous result for three-dimensional grain structures that relates the integral of the Gaussian curvature over the grain boundaries to the numbers of grains and quadruple junctions. The result is numerically verified for a grain structure consisting of periodic truncated octahedra.

Arrangements of three to six cubes with maximum disorientation angles

ABSTRACTThe well-known problem of determining the maximum possible disorientation angle of two cubes is extended to groups of three to six cubes. This problem is considered here to allow identification of specific arrangements of grains with a cubic structure at triple-line or quadruple junctions in polycrystals. The minimum disorientation angle between cubes in the group is defined as the characteristic disorientation angle of the group. The maximum values of and the arrangements of cubes giving the maximum are determined for groups of three to six cubes.

Analytical Modeling and Computer Simulation of the Transformation of Ellipsoids Nucleated on Random Parallel Planes

A considerable number of engineering materials is polycrystalline. Cahn proposed analytical expressions for transformations nucleated at the grain faces, triple junctions, and quadruple junctions. Those places are usually the places in which a new phase takes place. Cahn assumed that the new grain boundary nucleated phase grew as spheres. Nonetheless, the austenite grain boundary nucleated ferrite does not always grow as spheres. Bradley et al. demonstrated in a series of papers that a grain boundary nucleated ferrite allotriomorph is best described by an oblate ellipsoid. The reason for ellipsoidal growth is that the growth along the grain boundary plane is faster than the thickening into the austenite. Because of this, it is of interest to have analytical solutions and computer simulations of grain boundary nucleated transformations not only for spherical growth but also for ellipsoidal growth. In this work, we present a computer simulation of grain boundary nucleated transformations that grow as ellipsoids. The computer simulation results were compared with a new exact analytical expression obtained by Villa and Rios.

On the Hardness and Strain Rate Sensitivity of Electrodeposited Nanocrystalline Ni–18 wt% Co Alloy Studied by Nanoindentation

Ni–18wt% Co foils made by electrodeposition possesses an average grain size, computed using diffraction contrast in TEM, of about 30 nm. Vickers microindentation and depth-sensing nanoindentation have been adapted to assess the deformation parameters such as hardness, strain rate sensitivity (SRS) and activation volume. These foils with single-phase fcc-structured solid solution exhibit the hardness values of 4.5 ± 0.1 GPa and 6.2 ± 0.2 GPa measured by microindentation and nanoindentation, respectively. The dependence between hardness and applied load in the present solid solution cannot be attributed to the indentation size effect, but to the changes in internal friction and/or reduction in stacking fault energy that may have resulted from the Co additions. An elastic modulus of 193 ± 3 has been realized in these foils. Performing nanoindentation at various loading rates and subsequent analysis has resulted in a SRS of 0.017 and an activation volume of 7.6 b3. These values suggest that in these nanocrystalline Ni–18Co foils made by electrodeposition, interfaces such as grain boundaries, triple junctions and quadruple junctions play a governing role in dictating the deformation kinetics. A model reported in the literature has been successfully modified to reasonably explain the dependence of SRS on grain size for various Ni-based alloys including the one reported in the present study. However, the model fails to follow the established dependence for the materials with grain size below 10 nm as the deformation mechanisms at these extremely finer length scales (below 10 nm) are expected to be totally different from considerations applicable for the present alloy with a grain size of 30 nm.

Photoelectrochemical Water Splitting using Adapted Silicon Based Multi-Junction Solar Cell Structures: Development of Solar Cells and Catalysts, Upscaling of Combined Photovoltaic-Electrochemical Devices and Performance Stability

Abstract Thin film silicon based multi-junction solar cells were developed for application in combined photovoltaic electrochemical systems for hydrogen production from water splitting. Going from single, tandem, triple up to quadruple junctions, we cover a range of open circuit voltages from 0.5 V to 2.8 V at photovoltaic cell (PV) efficiencies above 13%. The solar cells were combined with electrochemical (EC) cells in integrated devices from 0.5 cm2 to 64 cm2. Various combinations of catalyst pairs for the oxygen and hydrogen evolution reaction side (OER and HER) were investigated with respect to electrochemical activity, stability, cost and – important for the integrated device – optical quality of the metal catalyst on the HER side as back reflector of the attached solar cell. The combined PV-EC systems were further investigated under varied operation temperatures and illumination conditions for estimation of outdoor performance and annual fuel production yield. For 0.5 cm2 size combined systems a maximum solar-to-hydrogen efficiency ηSTH = 9.5% was achieved under standard test conditions. For device upscaling to 64 cm2 various concepts of contact interconnects for reduced current and fill factor loss when using large size solar cells were investigated. To replace high performance noble metal based catalyst pairs (Pt/RuO2 or Pt/IrOx), more abundant and cheaper NiMo (HER) and NiFeOx (OER) compounds were prepared via electrodeposition. With the NiMo/NiFeOx catalyst pair we obtained ηSTH = 5.1% for a 64 cm2 size solar cell which was even better than the performance of the Pt/IrO2 system (ηSTH = 4.8%). In simulated day-night cycle operation the NiMo/NiFeOx catalyst pair showed excellent stability over several days. The experimental studies were successfully accompanied by simulation of the entire PV-EC device using a series connection model which allowed studies and pre-estimations of device performance by varying individual components such as catalysts, electrolytes, or solar cells. Based on these results we discuss the prospects and challenges of integrated PV-EC devices on large area for hydrogen and solar fuel production in general.

Thermodynamic model of porosity stabilization in polycrystalline solids

We demonstrate that a strong surface segregation of one of the components of the binary polycrystalline material can lead to barrier-less pore formation at the triple and quadruple junctions of the grain boundaries. These pores deplete the bulk of the polycrystal from the segregating component, which can lead to a local minimum in the dependence of the Gibbs free energy of the system on the pore size. We show that in some cases a porous polycrystal can be thermodynamically stabilized.

Microstructural and rheological evolution of calcite mylonites during shear zone thinning: Constraints from the Mount Irene shear zone, Fiordland, New Zealand

Layers of calc-mylonite in the Mount Irene shear zone, Fiordland, New Zealand, show substantial variations in thickness due to deflection of the shear zone boundaries around wall rock asperities. In relatively thick parts (c. 2.6 m) of the shear zone, calcite porphyroclasts are internally strained, contain abundant subgrain boundaries and have a strong shape preferred orientation (SPO) and crystallographic preferred orientation (CPO), suggesting that deformation occurred mainly by dislocation creep involving subgrain-rotation recrystallization. In relatively thin parts (c. 1.5 m) of the shear zone, aggregates of fine-grained recrystallized calcite surrounding flattened porphyroclasts have a weak SPO and CPO, and contain polygonal calcite grains with low degrees of internal misorientation. The recrystallized aggregates also contain microstructures (e.g. grain quadruple junctions, randomized misorientation axes) similar to those reported for neighbor-switching processes during grain-boundary sliding. Comparison of subgrain sizes in the porphyroclasts to published grain-size differential-stress relationships indicates that stresses and strain rates were substantially higher in relatively thin parts of the shear zone. The primary microstructural response to higher stresses and strain rates was an increase in the amount of recrystallization to produce aggregates that deformed by grain-boundary sliding. However, even after the development of interconnected networks of recrystallized grains, dislocation creep by subgrain-rotation recrystallization continued to occur within porphyroclasts. This behavior suggests that the bulk rheology of shear zones undergoing thinning and thickening can be controlled by concomitant grain-size insensitive and grain-size sensitive mechanisms. Overall, our observations show that shear zone thickness variations at constant P-T can result in highly variable stresses and strain rates, which in turn modifies microstructure, deformation mechanism and shear zone rheology.

Nucleation and evolution of ridge-ridge-ridge triple junctions: Thermomechanical model and geometrical theory

Ridge-ridge-ridge triple junctions are among the most remarkable features of global plate tectonics but their nucleation and evolution remains incompletely understood. Here, we employ 3D numerical models to study the processes of the nucleation and evolution of triple junctions induced by multi-directional lithospheric extension. The simulations show that two major classes of junctions develop: (i) transient quadruple and triple plate rifting junctions formed by the initial plate breakup that are gradually converted into (ii) stable triple oceanic spreading junctions formed by the accretion of new lithosphere. Quadruple junctions break into two diverging triple oceanic spreading junctions connected by a linear spreading center lengthening with time. This process gradually decreases the length of deforming boundaries between four diverging rigid plates and thus the integral mechanical resistance of these boundaries to the spreading. The geometry of triple oceanic spreading junctions varies from asymmetrical T-junctions to ideal 120° junctions. The structure of these junctions includes two crucial tectonic elements: oceanic ridges (spreading centers) and intra-plate ranges (triple junction traces) dividing crust accreted from different spreading centers. The geometrical steady state is achieved within several million years. We propose a new geometrical theory of a migrating steady state triple junction, which describes its structure as a function of the relative plate velocities in a moving triple junction reference frame. The relative plate velocities define the orientations and growth rates of respective intra-plate ranges. Orientations and lengthening rates of oceanic ridges are in turn given by the average relative velocity of two adjacent plates. The steady state triple junction migration velocity satisfies the condition of minimal cumulative ridge lengthening rate weighted by the square root of the spreading velocity. Our analytical theory agrees well with the results of the numerical simulations and natural data.

The topology of three-dimensional grain boundary network and its influence on stress corrosion crack propagation characteristics in austenitic stainless steel in a simulated BWR environment

The intergranular cracking and the grain boundary network along the cracks in an austenitic stainless steel 316L after stress corrosion cracking (SCC) test in simulated BWR water were investigated in terms of three-dimensional characterization. It was found that the twin boundaries not only show a strong resistance to cracking, but they could also prevent their neighboring boundaries from cracking, as the cracking probability is lower for boundaries that have higher fraction of neighboring twin boundaries. The propagation of intergranular SCC can be hindered by triple junctions or quadruple junctions in the presence of twin boundaries.

Three-dimensional characteristics of the grain boundary networks of conventional and grain boundary engineered 316L stainless steel

The three-dimensional microstructures of two conventional 316L stainless steel and a grain boundary (GB) engineered one of the same material have been characterized by serial sectioning and electron backscatter diffraction (EBSD) mapping. The twin boundaries arrangement in the grain boundary network were investigated and compared. Although the triple junction character distribution and quadruple junction character distribution were improved slightly by grain boundary engineering, considerably higher proportions of triple junctions with two twin boundaries and quadruple junctions with three twin boundaries were formed after GB engineering, which will be more beneficial to the resistance to intergranular degradation. Large grain-clusters formed in the GB engineered material, and the topology structures of them are complex tree-ring shape twin-chain. In comparison, the grain-clusters in conventional material are small, having simple tree shape twin-chain.

Microstructural and micromechanical evolution during dynamic recrystallization

Dynamic recrystallization (DRX) can in principle serve as an alternative way of controlling grain structure via a single route of hot working instead of the traditional cold working followed by annealing at elevated temperatures; in reality, its widespread application is hindered by the lack of quantitative understanding and prediction of the process. Using a recently developed model (Zhao et al., 2016) that integrates a fast Fourier transform-based elasto-viscoplastic model and a phase-field recrystallization model, we investigate the evolution of both microstructural and micromechanical fields in polycrystal copper during uniaxial compression at various elevated temperatures. Quantitative analysis based on the simulation results confirms that stress redistribution upon the formation of a new grain can significantly lower the dislocation density of neighboring grains, leading the so-called “DRX-enhanced recovery”, while the new grain itself undergoes accelerated work hardening as compared to the matrix. Numerical analysis using current simulation data reveals a macroscopic kinetic equation describing the average dislocation density evolution during DRX softening. The critical strain for the onset of DRX and the Zener–Hollomon parameter are found to obey a power law, with the model predicted exponent being consistent with that found in experiments. Temperature-dependence of the Avrami exponents have also been predicted using the simulation data, which agrees with the experimental finding. The population of grain boundaries and triple and quadruple junctions are shown to evolve with deformation and be temperature-dependent.

Universal meshes for a branched crack

We introduce an efficient approach to obtain conforming meshes for evolving branched cracks immersed in a fixed background mesh. The proposed approach is built on universal meshes (UM) proposed in Rangarajan et al. [34] which is able to construct conforming triangulations for a propagating simple crack. The UM functions by projecting certain nodes of the background mesh onto the crack and simultaneously relaxing their neighboring nodes to improve the quality of the resulting triangular mesh. The essence of the generalization to a branched crack is to determine which side of each branch to select nodes to move to the crack path. The choice is based on the consideration of minimizing mesh distortion. For the case of multiple junctions, we take into account the constraint that the nodes to be moved to the same crack branch must be on the same side of that branch. The proposed method inherits the main advantages of UM, including small perturbation to a fixed background mesh for a family of evolving cracks with no a priori conformity requirements. This advantage saves computational time compared with a brute-force mesh generation step. Numerical examples with one or multiple triple or quadruple junctions are provided.

Effect of strong nonuniformity in grain boundary energy on 3-D grain growth behavior: A phase-field simulation study

Large-scale phase-field simulations were performed of the evolution of grain structures with nonuniform grain boundary energy. A novel approach is proposed to determine the average grain boundary dihedral angles between the grain faces along triple and quadruple line junctions from 3-D voxel-based microstructures. We examine the effect of grain boundary energy nonuniformity on the distributions of the grain size, number of faces per grain, and dihedral angles between grain faces. We study the effect of the initial grain size distribution on the evolution toward steady state for both nonuniform and uniform boundary energy systems. The steady-state grain size and number of faces distributions remain unimodal under all conditions investigated, whereas the dihedral angle distribution is found to become multi-modal when the ratio R=σH/σL between high and low grain boundary energies lies in the range of 1.39–1.81. In addition, when R≈2 a topological transition is observed from a structure with grain faces meeting at triple lines (which themselves terminate in quadruple points) toward one in which the grain faces meet primarily at quadruple line junctions (ending at compact regions of triple junctions or very short triple lines).

Extended higher-order multi-phase-field model for three-dimensional anisotropic-grain-growth simulations

Based on the multi-phase-field (MPF) model reported by Steinbach et al., we constructed a higher-order MPF model in a previous study that contains a higher-order term and an additional kinetic parameter to represent the properties of triple junctions (TJs); this model was observed to be suitable for the simulation of 2D grain growth with anisotropic grain-boundary (GB) energy and mobility, which are strongly dependent on the misorientation angle (Δθ). In the current study, we attempt to improve the accuracy of 3D MPF simulations of anisotropic grain growth by extending this higher-order MPF model such that it accounts for the properties of quadruple junctions as well as those of TJs. In addition, using the extended higher-order MPF model, a series of grain-growth simulations are performed for a 3D columnar structure while considering the anisotropic GB properties, through which the accuracy of the model is examined in detail. The results confirm that the extended higher-order MPF model enables the anisotropic GB properties to be handled accurately for wider-ranging Δθ than in previous models.

An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

Many time-dependent deformation processes at elevated temperatures produce significant concurrent microstructure changes that can alter the mechanical properties in a profound manner. Such microstructure evolution is usually absent in mesoscale deformation models and simulations. Here we present an integrated full-field modeling scheme that couples the mechanical response with the underlying microstructure evolution. As a first demonstration, we integrate a fast Fourier transform-based elasto-viscoplastic (FFT-EVP) model with a phase-field (PF) recrystallization model, and carry out three-dimensional simulations of dynamic recrystallization (DRX) in polycrystalline copper. A physics-based coupling between FFT-EVP and PF is achieved by (1) adopting a dislocation-based constitutive model in FFT-EVP, which allows the predicted dislocation density distribution to be converted to a stored energy distribution and passed to PF, and (2) implementing a stochastic nucleation model for DRX. Calibrated with the experimental DRX stress–strain curves, the integrated model is able to deliver full-field mechanical and microstructural information, from which quantitative description and analysis of DRX can be achieved. It is suggested that the initiation of DRX occurs significantly earlier than previous predictions, due to heterogeneous deformation. DRX grains are revealed to form at both grain boundaries and junctions (e.g., quadruple junctions) and tend to grow in a wedge-like fashion to maintain a triple line (not necessarily in equilibrium) with old grains. The resulting stress redistribution due to strain compatibility is found to have a profound influence on the subsequent dislocation evolution and softening.

Phase-field study of pore-grain boundary interaction

During final stage sintering, a complex interplay of densification and grain growth dominates microstructural evolution. Grain growth starts, when pore drag effects become less important due to pore shrinkage. This grain growth then decreases the driving force available for sintering. Accordingly, the interplay of pores and grain boundaries needs to be considered in detail. A phasefield model was extended to treat pore dynamics under consideration of pressure stability. To study pore attachment and detachment at moving interfaces, an idealized hexagonal microstructure with a constant driving force relationship for pore migration is constructed. Additionally, realistic polycrystalline microstructures were used. The model is in good agreement with experiments and analytic equations. Three different cases were observed in the realistic microstructure: pore attachment at the moving interface, partial and total pore detachment. However, in the partial case, the initial location of pores was found to be important: pores tend to migrate from quadruple junctions over triple junctions to grain boundary planes, where they eventually detach. This results in a variation of pore detachment, which is not captured in analytic equations. Therefore large simulation setups are required to reflect the impact of initial pore location on pore drag effects.

Ferrite-Martensite Band Formation During the Intercritical Annealing

Microstructural evolution during the intercritical annealing at 740 and 770 °C for 120-900 s in a low-carbon low-alloy steel from the initial martensitic matrix was studied by electron microscopy equipped with energy dispersive x-ray spectroscopy and x-ray diffraction. It was seen that during the intercritical annealing, the martensitic structure changes to the tempered martensite with carbides. The results depicted that the temperature and time of intercritical annealing influence significantly the distribution and amount of the formed carbides. Two types of austenite morphology were identified to grow simultaneously, i.e., globular and acicular. A longer annealing time led to the coarse globular and thick acicular austenite morphology. The austenite with globular morphology nucleated preferably at prior austenite grain boundary triple and quadruple junctions. The austenite with globular and acicular morphology was developed in Mn-rich and -poor regions, respectively. The globular austenite morphology intensified the banded microstructure of ferrite-martensite dual-phase steel, whereas the acicular austenite morphology led to a more isotropic microstructure. The experimental results illustrated that the intercritical temperature is a significant factor which can contribute to intensify the banded ferrite-martensite microstructure. The volume fractions of austenite with globular and acicular morphology were quantitatively measured. The volume fraction of globular to acicular morphology of austenite was high and low at 770 and 740 °C, respectively.