Boundary Facets Research Articles

The effect of reduction atmospheres on the sintering behaviors of inkjet-printed Cu interconnectors

In order to overcome the serious problems posed by Cu ink, which include the strong tendency to the oxidation of Cu nanopowders, various reduction atmospheres were investigated. As a result, a resistivity of ∼4 μΩ cm was achieved in the Cu interconnectors sintered at 200 °C with a gaseous mixture of formic acid (HCOOH) and alcohol. As regards this sample, micrographs show the facet boundaries and an average grain size of ∼300 nm. The use of formic acid was an effective way to decrease the sintering temperature to 150 °C, at which temperature the resistivity was ∼72 μΩ cm. This low temperature sintering and microstructural densification was due to the decomposition of capping molecules and the reduction in Cu oxide by formic acid.

Boundary faceting-dependent densification in a BaTiO 3 model system

The effect of boundary faceting on densification has been studied in a 5 mol.% TiO 2–excess BaTiO 3 model system. It was possible to inhibit grain growth during sintering in moderately reducing atmospheres after a hydrogen presintering treatment and, thus, to exclude the effect of grain growth on densification. For a given oxygen partial pressure ( P O 2 ) there was a saturated relative density which decreased with increasing P O 2 and boundary faceting. The fraction of small pores was also higher in the samples sintered under high P O 2 than in those sintered under low P O 2 . These experimental observations demonstrate the presence of a critical driving force for densification in systems with faceted boundaries and its dependence on boundary faceting, i.e. the critical driving force is larger for systems with greater faceting. The result further confirms that a faceted boundary, either fully or partially faceted, is an imperfect atom source for densification; this idea is in contrast to the conventional understanding.

Moiré Superstructures of Graphene on Faceted Nickel Islands

Using scanning tunneling microscopy and spectroscopy, in combination with density functional theory calculations, we investigated the morphology and electronic structure of monolayer graphene grown on the (111) and (110) facets of three-dimensional nickel islands on highly oriented pyrolytic graphite substrate. We observed graphene domains exhibiting hexagonal and striped moiré patterns with periodicities of 22 and 12 Å, respectively, on (111) and (110) facets of the Ni islands. Graphene domains are also observed to grow, as single crystals, across adjacent facets and over facet boundaries. Scanning tunneling spectroscopy data indicate that the graphene layers are metallic on both Ni(111) and Ni(110), in agreement with the calculations. We attribute this behavior to a strong hybridization between the d-bands on Ni and the π-bands of carbon. Our findings point to the possibility of preparing large-area epitaxial graphene layers even on polycrystalline Ni substrates.

Entropically stabilized growth of a two-dimensional random tiling

The assembly of molecular networks into structures such as random tilings and glasses has recently been demonstrated for a number of two-dimensional systems. These structures are dynamically arrested on experimental time scales, so the critical regime in their formation is that of initial growth. Here, we identify a transition from energetic to entropic stabilization in the nucleation and growth of a molecular rhombus tiling. Calculations based on a lattice-gas model show that clustering of topological defects and the formation of faceted boundaries followed by a slow relaxation to equilibrium occur under conditions of energetic stabilization. We also identify an entropically stabilized regime in which the system grows directly into an equilibrium configuration without the need for further relaxation. Our results provide a methodology for identifying equilibrium and nonequilibrium randomness in the growth of molecular tilings, and we demonstrate that equilibrium spatial statistics are compatible with exponentially slow dynamical behavior.

A grain-scale study of spall in brittle materials

The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.

Faceting of twin grain boundaries in polysilicon films

AbstractThe faceting of grain boundaries (GB) under annealing in phosphorus‐doped polysilicon films, produced by low‐pressure chemical vapor deposition, has been investigated by transmission electron microscopy. It has been shown that the facet types and facet density depend on annealing temperature. It has been found that GB facets are generally parallel with close‐packed planes in coincidence site lattice. A correlation between GB faceting and grain‐growth mechanisms has been considered. It has been shown that faceting takes place both under normal and abnormal grain growth. It is revealed that twinning plays the key role for GB faceting under normal grain growth.

The Dynamics of Weakly Reversible Population Processes near Facets

This paper concerns the dynamical behavior of weakly reversible, deterministically modeled population processes near the facets (codimension-one faces) of their invariant manifolds and proves that the facets of such systems are “repelling.” It has been conjectured that any population process whose network graph is weakly reversible (has strongly connected components) is persistent. We prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets, or siphons. An important application of this work pertains to chemical reaction systems that are complex-balancing. For these systems it is known that within the interior of each invariant manifold there is a unique equilibrium. The global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies. Our results pertaining to weakly reversible systems imply that this conjecture holds for all complex-balancing systems whose boundary equilibria lie in the relative interior of the boundary facets. As a corollary, we show that the global attractor conjecture holds for those systems for which the associated invariant manifolds are two-dimensional.

Formation Energies of Antiphase Boundaries in GaAs and GaP: An ab Initio Study

Electronic and structural properties of antiphase boundaries in group III-V semiconductor compounds have been receiving increased attention due to the potential to integration of optically-active III-V heterostructures on silicon or germanium substrates. The formation energies of {110}, {111}, {112}, and {113} antiphase boundaries in GaAs and GaP were studied theoretically using a full-potential linearized augmented plane-wave density-functional approach. Results of the study reveal that the stoichiometric {110} boundaries are the most energetically favorable in both compounds. The specific formation energy γ of the remaining antiphase boundaries increases in the order of γ{113} ≈ γ{112} < γ{111}, which suggests {113} and {112} as possible planes for faceting and annihilation of antiphase boundaries in GaAs and GaP.

Quantifying the effect of fracture surface topography on the scattering of grain boundary segregation measurement by Auger electron spectroscopy

The aim of this paper is to estimate the effect of the geometrical orientation of grain boundary facets on the quantification of grain boundary segregation by Auger electron spectroscopy (AES) on an in-situ fractured surface. Phosphorus grain boundary segregation (PGBS) was studied on 17 different samples (including 3 different steels and 12 different thermal treatments) using a MAC2 analyzer from Riber company. For each sample, 14 to 41 grain boundary facets were analyzed. It is demonstrated that there is proportionality between the PGBS mean value and the PGBS standard deviation obtained on one particular sample: for each sample, the PGBS standard deviation represents approximately 40% of the PGBS mean value. The topography of a typical purely intergranular fracture surface was determined by 3D stereographic observation in a SEM. The influence of surface topography on Auger quantification was then evaluated using the Auger quantification equations. The orientation of grain boundary facets with respect to the primary beam and the Auger analyzer was taken into account. The result is that, considering a homogeneous PGBS on all the grain boundary facets, a large scattering (~ 45%) of the PGBS quantification by AES can be accounted for by a purely geometrical effect (orientation of each facet with respect to the primary beam and to the Auger analyzer). This geometrical effect is nevertheless strongly dependant on the spectrometer geometry (respective position of primary beam, sample and Auger analyzer with respect to each other) and could be reduced by optimizing the relative positions of primary beam, sample and Auger analyzer. The topographical analysis was extended to the case of the well-known CMA (Cylindrical Mirror Analyzer). The scattering of the PGBS measurements with Auger spectrometers fitted with a CMA perpendicular to the fracture surface is expected to be much smaller.

Boundary recovery for Delaunay tetrahedral meshes using local topological transformations

Numerous high-quality, volume mesh-generation systems exist. However, no strategy can address all geometry situations without some element qualities being compromised. Many 3D mesh generation algorithms are based on Delaunay tetrahedralization which frequently fails to preserve the input boundary surface topology. For biomedical applications, this surface preservation can be critical as they usually contain multiple material regions of interest coherently connected. In this paper we present an algorithm as a post-processing method that optimizes local regions of compromised element quality and recovers the original boundary surface facets (triangles) regardless of the original mesh generation strategy. The algorithm carves out a small sub-volume in the vicinity of the missing boundary facet or compromised element, creating a cavity. If the task is to recover a surface boundary facet, a natural exit hole in the cavity will be present. This hole is patched with the missing boundary surface face first followed by other patches to seal the cavity. If the task was to improve a compromised region, then the cavity is already sealed. Every triangular facet of the cavity shell is classified as an active face and can be connected to another shell node creating a tetrahedron. In the process the base of the tetrahedron is removed from the active face list and potentially three new active faces are created. This methodology is the underpinnings of our LAST RESORT method. Each active face can be viewed as the trunk of a tree. An exhaustive breath and depth search will identify all possible tetrahedral combinations to uniquely fill the cavity. We have streamlined this recursive process reducing the time complexity by orders of magnitude. The original surfaces boundaries (internal and external) are fully restored and the quality of compromised regions improved.

Grain boundary finite length faceting

We study symmetrical and asymmetrical aluminium grain boundary faceting with molecular dynamics simulations employing two embedded atom method potentials. Facet formation, coarsening, and the reversible phase transition of ∑ 3 { 1 1 0 } boundary into ∑ 3 { 1 1 2 } twin, and vice versa, are demonstrated in the simulations and the results are consistent with earlier experimental studies and theoretical models. The ∑ 11 { 0 0 2 } 1 / { 6 6 7 } 2 boundary shows faceting into { 2 2 5 } 1 / { 4 4 1 } 2 and { 6 6 7 } 1 / { 0 0 1 } 2 boundaries and coarsens with a slower rate when compared to ∑ 3 { 1 1 2 } facets. However, facets formed by { 1 1 1 } 1 / { 1 1 2 } 2 and { 0 0 1 } 1 / { 1 1 0 } 2 boundaries from a { 1 1 6 } 1 / { 6 6 2 } 2 boundary are stable against finite temperature annealing. In the above faceted boundary, elastic strain energy induced by atomic mismatch across the boundary creates barriers to facet coarsening. Grain boundary tension is too small to stabilize the finite length faceting in both ∑ 3 { 1 1 2 } twin and asymmetrical { 1 1 1 } 1 / { 1 1 2 } 2 and { 0 0 1 } 1 / { 1 1 0 } 2 facets. The observed finite facet sizes are dictated by facet coarsening kinetics which can be strongly retarded by deep local energy minima associated with atomic matching across the boundary.

Second-order faceting–roughening of the tilt grain boundary in zinc

AbstractThe faceting of the almost stationary tilt grain boundary with a misorientation angle of 84° in the Zn bicrystal has been investigated. The shape of the very slow migrating grain boundary has been studied in situ between 350 and 400 °C using polarized light. Two intersecting facets lie in the closely-packed planes of the constrained coincidence sites lattice with coincidence parameter = 15. In the as-grown sample flat grain boundary facets form the sharp first-order ridge with the break of the first derivative y/x of the grain boundary shape similar to those observed in our previous works on GB faceting in Zn. However, above 350 °C the sharp first-order ridge is substituted by the smooth grain boundary portion without a ∂y/∂xderivative break similar to that observed in twin grain boundaries in Mo. The transformation of the as-grown first-order grain boundary ridge into continuous one has been observed for the first time. The critical parameter α has been calculated using the grain boundary shape in the transition region. α increases from α = 1.7 ± 0.07 for 350 °C to α = 1.9 ± 0.07 for 385 °C approaching the α = 2 value predicted in the mean-field Andreev model for the continuous surface roughening.

Empathy, Connectedness, and the Evolution of Boundaries in Self Psychological Treatment

This article discusses the evolution of nonlinear boundaries in the therapeutic dyad when we work from a self psychological, connectedness sensibility. Using verbatim material from a session with a borderline, fragmentation-prone and, at times, rageful patient, the article argues that boundaries should evolve so that they embrace a form and shape whose structure will provide the relationship with a depth and connectedness that is in the service of enhancing the patient's self-organization. The article emphasizes four important facets of boundaries: boundary challenges as an attempt to explore the potential intimacy of the therapeutic dyad, the difference between safety and boundaries, the wish for physical contact as a search for heightened affective moments, and how the mutual evolution of boundaries catalyzes affective regulatory structures. Este artículo discute la evolución de los límites no lineales en la díada terapéutica cuando trabajamos con una sensibilidad basada en la conectividad y en la psicología del self. A través de la trascripción de una sesión con un paciente borderline con tendencia a la fragmentación y a veces con brotes de rabia, este artículo argumenta que los límites deben evolucionar de manera que incluyan una forma cuya estructura suministre a la relación una profundidad y una conexión que esté al servicio de aumentar la auto-organización del paciente. El artículo enfatiza cuatro importantes facetas de los límites: desafíos a los límites como un intento de explorar la intimidad potencial de la díada terapéutica; la diferencia entre seguridad y límites; el deseo de contacto físico como una búsqueda de momentos afectivos intensificados; y cómo la evolución mutua de los límites cataliza las estructuras de regulación afectiva. Dans cet article, l'auteur discute de l'évolution des frontières non-linéaires dans la dyade thérapeutique lorsque nous travaillons à partir d'une sensibilité à la connectivité inspirée de la psychologie du soi. A travers l'utilisation d'un verbatim d'une séance avec une patiente à l'état limite, vulnérable à la fragmentation et parfois rageuse, l'auteur affirme que les frontières doivent évoluer de telle sorte qu'elles prennent forme dans une structure qui va donner une profondeur et une connectivité à la relation au service du rehaussement de l'organisation de l'expérience de soi de la patiente. Dans cet article, l'auteur met l'accent sur quatre aspects importants des frontières: la mise à l'épreuve des frontières en tant que tentative d'exploration des possibilités d'intimité dans la dyade thérapeutique; la différence entre la sécurité et les frontières; le désir de contact physique en tant que recherche de moments affectifs intensifiés; et comment l'évolution mutuelle des frontières catalyse les structures de régulation affective. Diese Arbeit behandelt die Entwicklung non-linearer Grenzen in der therapeutischen Dyade, wenn wir vor dem Hintergrund der Selbstpsychologie und dem Wissen um die Verbundenheit arbeiten. Indem verbatim Material aus einer Sitzung mit einem borderline, von psychischem Zerfall bedrohten und zeitweise wütenden Patienten verwendet wird, zeigt die Arbeit, wie Grenzen sich in der Therapie entwickeln sollen, nämlich so, dass deren Struktur gleichzeitig eine Beziehung von Tiefe und Verbundenheit anbietet. Das bedeutet: Sie sollen im Dienst der Stärkung der Selbstorganisation des Patienten stehen. Die Arbeit beschreibt vier verschiedene Facetten der Grenzen: das Infragestellen der Grenze als ein Versuch die mögliche Intimität der therapeutischen Dyade auszuloten; der Unterschied zwischen Sicherheit und Grenzen; der Wunsch nach körperlichem Kontakt als Suche nach Momenten erhöhter Affektivität (heightened affective moments); und zuletzt wie die beidseitige Entwicklung von Grenzen affektive Regulationsstruktur katalysiert.

Professional boundaries in a person-centred paradigm

Since Valuing People (Department of Health, 2001), there has been a marked change in landscape for housing support and service provision for people with a learning disability. Care and supported living options are now provided by a myriad of providers across the healthcare, social-care and independent sectors. Due to the complexity of such individualized care arrangements, and the non-traditional roles of such service professionals and providers, examination of professional role boundaries with service users is essential; traditional role boundaries are not easily transferable or considered within such professional supports and services. This article discusses important facets of professional boundaries that impact directly on such contemporary, learning disability, person-centred services.

Surface hydrology of low-relief landscapes: Assessing surface water flow impedance using LIDAR-derived digital elevation models

Conventional hydrologic analyses of digital elevation models (DEMs) perform well in areas of high topographic relief, where surface water flow is typically unidirectional, convergent, spatially static, and directed toward a single discharge point at the edge of a catchment. Such analyses do not perform well on landscapes with low topographic relief (e.g., floodplains, river deltas, coastal wetlands, and estuaries) where surface water flow is influenced by subtle topographic depressions and may be bidirectional, divergent, and spatially dynamic in response to hydrologic forcing such as tides or variation in river discharge. We developed a framework for hydrologic analysis of low-relief landscapes using a high-resolution (1 m) DEM derived from light detection and ranging (LIDAR) data collected over a ~ 8.8 km 2 section of the Umatilla River Floodplain, Oregon, USA. Our approach assessed the pattern and characteristics of “hydrologic facets” (landscape patches that have high internal surface water connectivity and therefore function as a single hydrologic unit), where facet boundaries were defined by subtle topographic divides across the floodplain. We initially identified nearly 6000 small (fine-scale) hydrologic facets using standard GIS processing algorithms. We located the divide between each pair of adjacent facets, and determined “hydrologic impedance” (i.e., the maximum change in river stage necessary to inundate the divide) for each divide ( n = ~ 17,000). Using hydrologic impedance values, we analyzed patterns of surface water connectivity among the fine-scale facets and aggregated groups of adjacent facets that had high connectivity. This process yielded a reduced number of larger facets useful for hydrologic analysis at coarser spatial scales. We compared results derived using several alternate rule sets for aggregating facets. With appropriate aggregation rules, the results are useful for generating optimal link-and-node flow networks to support hydrologic modeling of surface water flux across low-relief landscapes.

Inclination dependence of grain boundary energy and its impact on the faceting and kinetics of tilt grain boundaries in aluminum

The shape evolution and migration of <1 0 0> and <1 1 1> tilt grain boundaries with rotation angles θ in the range between 6° and 24° were investigated in situ in a scanning electron microscope at elevated temperatures. The results revealed that boundaries with misorientation θ < 15° did not attain a continuously curved shape in the entire temperature range up to the melting point and, thus, did not move under a capillary driving force. Instead, they remained straight or formed several facets which were inclined to the initial boundary orientation. Molecular statics simulations suggest that the observed behavior of low-angle boundaries is due to the anisotropy of grain boundary energy with respect to boundary inclination. This anisotropy diminishes with increasing misorientation angle, and high-angle boundaries assume a continuously curved shape and move steadily under the curvature driving force.

Migration of faceted high-angle grain boundaries in Zn

Abstract The migration of a faceted high angle tilt grain boundary 85° in Zn was investigated. The migration behavior complies with theoretical predictions of a recently proposed model on the joint motion of curved and faceted boundary segments. The results are compared to data published for a 30° boundary. It is shown that the observed dynamic facet length corresponds to a maximum dissipation rate of free energy.

Determination of Critical Microstructural Features in an Austenitic Stainless Steel Using Image-Based Finite Element Modeling

Two-dimensional (2-D) and three-dimensional (3-D) image-based finite element (FE) modeling and scientific visualization techniques were employed to determine the critical microstructural features that control mechanical behavior in a commercial austenitic stainless steel, AL-6XN. Two-dimensional FE meshes were generated using microstructural images obtained from electron backscatter diffraction (EBSD), and three-dimensional meshes were generated from microstructural reconstructions created using serial-sectioning techniques and EBSD. Image-based FE simulations were run using anisotropic elasticity. The 2-D simulations revealed that higher local elastic stresses are produced near grain boundaries than at grain interiors for various loading conditions. Under normal uniaxial loading conditions, higher stresses were observed at faceted grain boundaries, particularly those with a Σ = 3 coincident site lattice misorientation. Under simple shear loading conditions, however, the highest stresses were observed at general high-angle grain boundaries. In the 3-D simulations, similar relationships held, with the highest elastic stresses observed at the junction between two Σ3 boundaries under normal uniaxial loading and slightly lower elastic stresses at these junctions under simple shear loading. In the 3-D models, high elastic stresses were associated only with grain boundaries and triple junctions and showed little to no correlation with grain size or morphology.

Multi-laminate plastic-strain organization for non-uniform TFA modeling of poly-crystal regularized plastic flow

A recently presented single plastic-potential, microstructure-based model of poly-crystal plasticity by the authors considers a globally regularized Schmid law (RSL) as the slip flow criterion of a homogeneous equivalent super-crystal. The homogenization scheme that is taken of affine type is specialized to the transformation field analysis (TFA) framework. The relevancy of the TFA here results from a description of intra-crystalline slip in terms of hierarchical multi-laminate (HML) structures that ensure the request of piece-wise homogeneous plasticity. This RSL–TFA–HML modeling has been shown efficient for heterogeneous intra-crystalline plastic slip in terms of overall stiffness estimates when laminates are parallel to slip planes or normal to slip directions. It is also suitable for twinning modes of crystal plasticity as stressed in this paper. The performed superposition of all possible HML plastic strain modes makes the TFA of the non-uniform (NTFA) and coupled type proposed by Michel and Suquet [Michel, J.C., Suquet, P., 2003. Non-uniform transformation field analysis. International Journal of Solids and Structures 40, 6937–6955; Michel, J.C., Suquet, P., 2004. Computational analysis of nonlinear composite structures using the non-uniform transformation field analysis. Computer Methods in Applied Mechanics and Engineering 193, 5477–5502]. In this new contribution, we investigate further our extension of this modeling to poly-crystals. It is interpreted as based on a description of the aggregate morphology in terms of the distribution of the crystallographic orientations of the grain boundary and sub-boundary facets, rather than in terms of a mean grain or domain shape. In its initial form, our extension amounted to assuming all these facets oriented either parallel to slip planes or normal to slip directions, what is proved convenient for large enough grains. In order to extend the relevancy of the modeling down to ultra-fine grains, we introduce a graded form of the modeling that is made grain size dependent from specifying the conditions for which the TFA accommodation hardening is negligible according to the range of the physical one. Some numerical stiffness comparisons from this graded RSL–TFA–HML modeling are provided.

Failure Analyses of Six Cylinder Aircraft Engine Crankshafts

Results of failure analyses of two aircraft crankshafts are described. These crankshafts were forged from AMS 6414 (similar composition to AISI 4340) vacuum arc remelted steels with sulfur contents of 0.003% (low sulfur) and 0.0005% (ultra-low sulfur). A grain boundary sulfide precipitate was caused by overheat of the low sulfur steel, and an incipient melting of grain boundary junctions was caused by overheat of the ultra-low sulfur steel. The precipitates and incipient melting in these two failed crankshafts were observed during the examination. As expected, impact fractures from the low sulfur steel crankshaft contained planar dimpled facets (PDF) along separated grain boundaries with a small spherical manganese sulfide precipitates within each dimple. In contrast, PDFs along separated grain boundaries of impact fractures from the ultra-low sulfur crankshaft steel contained a majority of small spherical particles consisting of nitrogen, boron, iron, carbon, and a small amount of oxygen. Some other dimples contained manganese sulfide precipitates. Fatigue samples machined from the ultra-low sulfur steel crankshaft failed internally at planar grain boundary facets. Some of the facets were covered with nitrogen, boron, iron, and carbon film, while other facets were relatively free of such coverage. Results of experimental forging studies defined the times and temperatures required to produce incipient melting overheat and facets at grain boundary junctions of ultra-low sulfur AMS 6414 steels.