Thermal Grooving Research Articles

Large-scale phase-field simulation of three-dimensional isotropic grain growth in polycrystalline thin films

In this study, assuming an ideal system free from thermal grooving and anisotropy in grain boundary properties, we analyze thin-film grain growth via three-dimensional (3D) phase-field simulations with approximately one million initial grains. The large-scale simulations accelerated by multiple graphics processing units allow for the reliable statistical investigation of grain growth behaviors in films with various thickness. Over the transition from 3D to two-dimensional (2D) growth modes, variations in the averages and distributions of grain sizes are quantified and compared for different regions of the films. Furthermore, we propose a comprehensive scaling law of thin-film grain growth, by which the 3D–2D transition behaviors and grain growth kinetics can be described in a unified manner independent of film thickness.

3D Analysis of Observed and Simulated Microstructure Evolution in SOFC Anodes

An important degradation mechanism in solid oxide fuel cells (SOFCs) is the microstructural evolution of Ni-YSZ anodes caused by diffusional transport of nickel under operating conditions. In this work, we carry out 3D analysis on several data sets from FIB-SEM reconstructions of a full-ceramic co-sintered SOFC as well as from large-scale phase-field simulations, in order to obtain a quantitative understanding of the different microstructure evolution effects and their impact on anode degradation. The experimental data stem from FIB-SEM reconstructions of both newly fabricated anodes and anodes aged for ca. 1000h under operating conditions. The simulated data stem from large-scale phase field simulations that have been initialized with a reconstructed microstructure. The underlying phase-field model incorporates both volume diffusion of nickel and interface diffusion along the Ni surfaces, grain boundaries, and Ni-YSZ interfaces. The required material parameters (interface energies and diffusivities) are determined partly by ab-initio simulations and partly by thermal grooving experiments on bicrystalline and polycrystalline nickel. For the 3D analysis, we calculate standard microstructural features such as volume fractions, active and inactive three-phase-boundary (3PB) length, and tortuosity, and we use the transmission line model to calculate the expected anode performance. Comparison with the measured anode performance shows that the observed decrease of 3PB length explains the measured degradation only partly, while the main degradation factor is loss of connectivity of the nickel phase. To understand the connectivity loss in more detail, we carry out a bottleneck analysis to quantify the gradual tightening of the bottlenecks. In addition, we statistically assess the spatial homogeneity, and we calculate several shape descriptors such as interface areas and local structure size, which allows us to show that nickel relocates over considerable distances from small pores to larger pores within the YSZ skeleton.

Combined Simulative and Experimental Multi-Scale Approach to Study the Microstructural Evolution of a Ni-Based SOFC Anode Under Operating Conditions

The degradation mechanism of Ni-based solid oxide fuel cell (SOFC) anodes under operating conditions is dominated by an unfavorable microstructural evolution that involves the coarsening of nickel grains. The resulting reduction of the active triple-phase boundary leads to a significant loss of performance. In this work, we present a combined simulative and experimental multi-scale approach to predict the microstructural evolution, and therefore degradation, of the anode while avoiding time-consuming long-term experiments. To generate a fundamental understanding of the relevant mechanisms, all applicable material parameters, such as interfacial energies and diffusion constants, are considered and exploited in large-scale 3D phase-field simulations. For their non-trivial determination, we are following a combined simulative and experimental approach using atomistic simulation methods and thermal grooving experiments that is presented in this work. Our determined material parameters are discussed in a comparative way with a focus on the accuracy and capabilities of the used method. Their applicability and relevance to the phase field simulations is elaborated based on a sensitivity analysis.

Effect of grain orientations on the thermal grain boundary grooving in a three‐dimensional setting

AbstractThe objective of this work is to study the effect of grain orientation on the thermal grooving by surface diffusion. Hackl et al. [1] have presented a finite element model for thermal grooving in three‐dimensions. This variational model involves surface energy, grain boundary energy, external and internal triple line energy. In this study, We use an orientation dependent surface energy. For {1 0 0} grain orientation in the normal direction, we have self‐similar groove profiles for increasing extent of anisotropy of the surface energy. For {1 1 0} and {1 1 1} orientations, there are formation of facets for critical anisotropic cases. These formations are due to so‐called missing orientations concerning the shape of an unconstrained crystal in equilibrium. The rate of grooving varies with change in the extent of surface free energy anisotropy. Flux along the triple line is also important in determining the groove root shape. Triple line energy and its mobility lead to deviate from a typical t1/4 scaling law. For all theses simulations, grain boundary energies are constant, satisfying Herring's relation. Comparisons are made for different values of mobilities for groove shape and its growth rate, using different grain orientations.

Plastic strain-induced grain boundary migration (SIBM) in pure aluminum: SEM in-situ and AFM examinations

Plastic strain induced grain boundary migration (SIBM) is investigated by means of in-situ SEM experiments and AFM surface observations in the case of 4N pure aluminum. The study focuses on two polycrystalline samples obtained through different thermo-mechanical treatments that provide different initial (grain size and orientation) microstructures with different evolutions during heating. A total of 77 grain boundaries (GBs) were characterized from both samples. Evaluation of GB displacements was allowed by determining fixed points on initial and final EBSD maps and marks from thermal grooving along GB contours. Some sub-surface final examinations ensured the surface ones being pretty well representative of the bulk behaviour. The GB displacements were related to their geometry and to their initially available migration driving force P, the two main contributions of which were estimated. The boundary curvature contribution Pc is estimated from SEM observations and the so-called "stored energy" contribution PΔρ (that results from the differential of dislocation densities Δρ across the boundary) is estimated using a crystal plasticity modeling within a homogenization scheme for aggregates validated on slip trace identifications from AFM observations. The resulting driving force P, related to the GB velocity V through the widely used law V=MP is compared with the observed displacement during a finite annealing time. Additional effects as thermal grooving and triple junction pinning or pulling are also discussed from complementary SEM and AFM observations of some typical GBs. Some evidences of GB out-of-plane displacements possibly contributing to the migration process are also commented. The quite extensive set of data regarding grain orientation, GB misorientation and curvature, intracrystalline slip activity and evolution during heating constitutes references for future comparisons with mesoscale simulations.

Globularization using heat treatment in additively manufactured Ti-6Al-4V for high strength and toughness

A bimodal globularized microstructure in contrast to martensitic laths is known to impart high strength and toughness in Ti-6Al-4V. Heat treatment for the phase transformation of the laths to the globularized microstructure must be preceded by plastic deformation. This work reports an innovative strategy to obtain the bimodal microstructure consisting of globular α in additively manufactured Ti-6Al-4V alloy by heat treatment alone. The heat treatment schedule involves repeated thermal cycling close to but below the β transus temperature to form globular α eliminating the need for plastic deformation prior to heat treatment. A new mechanism of globularization other than known in literature is proposed to explain the formation of globular α. The inherent dislocation sub-structure of the martensitic laths initiates globularization by thermal grooving and boundary splitting but is unable to completely globularize the microstructure. Mechanisms such as cylinderization and edge spheroidization also do not lead to globularization. The purposefully designed thermal cycling causes oscillations in the volume fractions of α and β phases that in synergism with the slow cooling segments of the cycle globularize the α phase by epitaxial growth. The bimodal microstructure thus produced led to a significant improvement in the ductility by 80% and the toughness by 66%, which are desirable for structural applications. Furthermore, beneficial compressive stresses were generated in the alloy because of cyclic heat treatment. It is envisaged that the exceptional combination of mechanical properties observed here will lead to the fabrication of SLM printed Ti-6Al-4V parts that could leverage the advantages of additive manufacturing with material properties that are comparable to those obtained by conventional fabrication routes.

Evolution of Near-Surface Internal and External Oxide Morphology During High-Temperature Selective Oxidation of Steels

In this work we examine some observations made using high-temperature confocal scanning laser microscopy (HT-CSLM) during selective oxidation experiments. A plain carbon steel and advanced high-strength steel (AHSS) were selectively oxidized at high temperature (850–900°C) in either low oxygen or water vapor atmospheres. Surface evolution, including thermal grooving along grain boundaries and oxide growth, was viewed in situ during heating. Experiments investigated the influence of the microstructure and oxidizing atmosphere on selective oxidation behavior. Sequences of CSLM still frames collected during the experiment were processed with ImageJ to obtain histograms that showed a general darkening trend indicative of oxidation over time with all samples. Additional ex situ scanning electron microscopy and energy dispersive spectroscopy analysis supported in situ observations. Distinct oxidation behavior was observed for each case. Segregation, grain orientation, and extent of internal oxidation were all found to strongly influence surface evolution.

Effect of predeformation on globularization of Ti–5Al–2Sn–2Zr–4Mo–4Cr during annealing

Abstract The microstructure evolution during annealing of Ti–5Al–2Sn–2Zr–4Mo–4Cr alloy was investigated. The results show that for the alloy compressed at 810 °C and 1.0 s−1 deformation amount (height reduction) 20% and 50% and annealed at 810 °C, thermal grooving by penetration of β phase is sufficient during the first 20 min annealing, resulting in a sharp increase in globularization fraction. The globularization fraction continuously increases with the increase of annealing time, and a height reduction of 50% leads to a near globular microstructure after annealing for 4 h. For the alloy with deformation amount of 50% by compressing at 810 °C, 0.01 s−1 and then annealed at 810 °C, thermal grooving is limited during the first 20 min of annealing and large quantities of high-angle grain boundaries (HABs) remain. With long time annealing, the chain-like α grains are developed due to the HABs, termination migration and Ostwald ripening. The present results suggest that a higher strain rate and a larger height reduction are necessary before annealing to achieve a globular microstructure of Ti–5Al–2Sn–2Zr–4Mo–4Cr.

Mullins' Self-Similar Grooving Solution Revisited

In W.W. Mullins' classical 1957 paper on thermal grooving, motion by surface diffusion was proposed to describe the development of a thermal groove separating two grains in a simple semi-infinite planar geometry. After making a small slope approximation which is often realistic, Mullins' sought self-similar solutions, and obtained an explicit time series solution for the groove depth. In the years since, Mullins' grooving solution has become a standard tool; however it has yet to be rigorously demonstrated that self-similar solutions exist when the small slope approximation is not applicable. Here we demonstrate that reformulation of Mullins' nonlinear problem in arc-length variables yields a particularly simple fully nonlinear formulation, which is useful for verifying large slope grooving properties and which should aid in proving existence.

Anti-thermal grain growth in SrTiO3: Coupled reduction of the grain boundary energy and grain growth rate constant

The dihedral angles at grain boundary thermal grooves in SrTiO3 were measured and used to determine the relative grain boundary energy at several temperatures where the grain growth rate constant displays anti-thermal properties (it decreases with increasing temperature). The measurements indicate that at temperatures in the anti-thermal region (1390 °C–1400 °C), the average grain boundary energy is less than at a lower temperature (1350 °C) where grain boundaries move more rapidly. Three-dimensional electron backscatter diffraction was used to measure the geometries of internal triple junctions in a sample where the slow and fast grain boundaries co-exist. Based on the dihedral angles at triple junctions, the ratio of the energies of slow boundaries to fast boundaries is 0.86. The results indicate that at temperatures between 1350 °C and 1425 °C, the higher and lower energy boundaries coexist. The coexistence of the two boundary types in this temperature range is likely because there is a range of grain boundary energies and the temperature at which a boundary transforms from the slow type to the fast type depends on its grain boundary energy.

Abnormal growth of {100} grains and strong Cube texture in strip cast Fe-Si electrical steel

High-grade non-oriented electrical steel was successfully processed by controlling texture using strip casting technology. Remarkable abnormal grain growth of {100} grains occurred in the as-cast strip after isothermal annealing. This phenomenon is considered to be the synergistic effect involving the size advantage of coarse columnar grains and surface energy, where the normal grain growth was inhibited by thermal grooving in the surface layer. Special rotation path was identified during the cold rolling process and metastable {118} 〈110〉–{113} 〈110〉 texture dominated the deformation texture. The final annealed sheet exhibited strong Cube texture together with significantly superior magnetic properties.

Fourth-order fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the Mullins model

A multiple integration technique of the integral-balance method allowing solving high-order subdiffusion diffusion equations is presented in this article. The new method termed multiple-integral balance method (MIM) is based on multiple integration procedures with respect to the space coordinate. MIM is a generalization of the widely applied Heat-balance integral method of Goodman and the double integration method of Volkov. The method is demonstrated by a solution of the linear subdiffusion model of Mullins for thermal grooving by surface diffusion.

Multi-phase-field model for surface and phase-boundary diffusion.

The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase boundaries, i.e., the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nanoclusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic craterlike structure with an elevated perimeter, observed in recent experiments, is a transient nonequilibrium state during the annealing process.

Interactions at the planar Ag3Sn/liquid Sn interface under ultrasonic irradiation

The interactions at the interface between planar Ag3Sn and liquid Sn under ultrasonic irradiation were investigated. An intensive thermal grooving process occurred at Ag3Sn grain boundaries due to ultrasonic effects. Without ultrasonic application, planar shape of Ag3Sn layer gradually evolved into scalloped morphology after the solid-state Sn melting, due to a preferential dissolution of the intermetallic compounds from the regions at grain boundaries, which left behind the grooves embedding in the Ag3Sn layer. Under the effect of ultrasonic, stable grooves could be rapidly generated within an extremely short time (<10s) that was far less than the traditional soldering process (>10min). In addition, the deepened grooves leaded to the formation of necks at the roots of Ag3Sn grains, and further resulted in the strong detachment of intermetallic grains from the substrate. The intensive thermal grooving could promote the growth of Ag3Sn grains in the vertical direction but restrain their coarsening in the horizontal direction, consequently, an elongated morphology was presented. All these phenomena could be attributed to the acoustic cavitation and streaming effects of ultrasonic vibration.

Orientation dependent spheroidization response and macro-zone formation during sub β-transus processing of Ti-6Al-4V alloy

In the present study, sub β-transus static annealing was carried out on a (α+β)-warm-rolled (700 °C, 90% thickness reduction) Ti-6Al-4V alloy at 900 °C for various durations (15, 30, 45, 60, 75 and 90 min). The key observation was that the spheroidization response of the constituent α-colonies from the starting warm-rolled material differs significantly during subsequent (α+β)-annealing treatment. While some of the α-colonies underwent an early morphological conversion from lamellar to equiaxed, some others stayed stable for prolonged durations. This unique phenomenon has been examined, for the first time, from an orientation perspective by coupling slip activation, boundary formation, and interfacial energy anisotropy of individual α-colonies with their response to static spheroidization. Orientation of the α-colonies in reference to the loading directions dictate the nature of slip activation (single versus multiple slip; basal or prism <a> slip plus pyramidal 〈c+a〉 slip) during prior (α+β)-rolling. During subsequent static (α+β)-annealing, this factor translates into the relative ease of boundary splitting and thermal grooving for them. Formation of longitudinal boundaries, then set the order of spheroidization for diffusion based coarsening processes during long term annealing. Anisotropy in interfacial energy, owing to the loss of coherency during prior deformation (warm-rolling), creates further orientation dependency in the spheroidization sequence. An immediate consequence of this orientation dependent spheroidization response is realized in the formation of the macro-zones for two-phase Titanium alloys after secondary thermomechanical processing. Some remedial processing strategies are highlighted therein.

Effect of temperature on graphene grown by chemical vapor deposition

Large-area single-crystal graphene films remain a challenge which settlement will permit to take full profit of the intrinsic properties of the material in electronic application. Toward this direction, in the present work we study the effect of temperature on the chemical vapor deposition growth of graphene over copper foil, in low pressure. Graphene growth commence with the crystallization of a supersaturated fraction of carbon-adatom species, while the nucleation density is the result of competition between the mobility of the carbon-adatom species and their desorption rate. We study the nuclei size and density distribution, growth rate and coverage rate to calculate the nucleation activation energy. In addition, we provide information considering the control of the intrinsic strain present in the graphene domains as a result of the ripple formation. We study the agreement, considering the ripple formation, between the theoretical model of thermal grooving and observation made by atomic force microscopy.

Rapid Ag/Sn/Ag transient liquid phase bonding for high-temperature power devices packaging by the assistance of ultrasound

Rapid transient liquid phase (TLP) bonding process on Ag/Sn/Ag system is achieved in air by the assistance of ultrasonic, which has great potential to be applied to high-temperature power devices packaging. In this study, the influence of ultrasonic effect on the morphology and growth kinetics of Ag3Sn grains, and the joint microstructure, mechanical property and thermal reliability were systematically investigated. Experimental results indicated that the rapid consumption of the “dynamic” transient liquid phase was attributed to the accelerated dissolution of Ag substrate and the extrusion of liquid Sn, which were entirely induced by the complex sonochemical effects on the liquid/solid intermetallic compounds (IMCs) interface. An elongated scallop-like morphology of Ag3Sn grains was developed during Ag/Sn interfacial reaction with ultrasonic, accompanied by widening of grooves between neighbored grains. This phenomenon is called as a strengthening thermal grooving, in which the grooves at grain boundaries provide stable molten channels for Ag atoms diffusion from the substrate. Consequently, the improved elemental diffusion was evaluated through the growth kinetics of Ag3Sn IMCs, with conservative estimation of 6–16.5 times faster than the traditional TLP process. In addition, both excellent mechanical property and thermal reliability of the Ag-Sn intermetallic joint were experimentally verified by shear test and high-temperature storage test, respectively.

A variational approach to the modelling of grooving in a three-dimensional setting

We present a theory of thermal grooving, i.e. surface motion due to surface diffusion, based solely on geometrical and energetic arguments and a variational approach involving a thermodynamic extremal principle. The theory is derived for a fully three-dimensional setting. All interface and contact conditions at junction lines and points of the material aggregate are derived rigorously and without ambiguity. A finite element implementation of the model is employed. Numerical examples are presented and compared with experimental results from the literature.

Multiple integral-balance method: Basic idea and an example with Mullin’s model of thermal grooving

A multiple integration technique of the integral-balance method allowing solving high-order diffusion equations is conceived in this note. The new method termed multiple-integral balance method is based on multiple integration procedures with respect to the space co-ordinate and is generalization of the widely applied heat-balance integral method of Goodman and the double integration method of Volkov. The method is demonstrated by a solution of the linear diffusion models of Mullins for thermal grooving.

The temperature dependence of the relative grain‐boundary energy of yttria‐doped alumina

AbstractAtomic force microscopy was used to measure the dimensions of grain‐boundary thermal grooves on the surfaces of Al2O3, 100 ppm Y‐doped Al2O3, and 500 ppm Y‐doped Al2O3 ceramics heated at temperatures between 1350°C and 1650°C. The measurements were used to estimate the relative grain‐boundary energies as a function of temperature. The relative grain‐boundary energies of Al2O3 decrease slightly with increased temperature. When the doped samples were heated, there was an overall increase in the grain‐boundary energy, attributed to a reduction in the grain boundary excess at higher temperature. The overall trend of increasing grain‐boundary energy was interrupted by abrupt reductions in grain‐boundary energy between 1450°C and 1550°C. In the same temperature range, there is an abrupt increase in the grain‐boundary mobility that is associated with a complexion transition. When the 100 ppm Y‐doped sample was cooled, there was a corresponding increase in the relative grain‐boundary energy at the same complexion transition temperature, indicating that the transition is reversible.