Boundary Facets Research Articles

Faceting of Ʃ3 Grain Boundaries in Cu: Three-Dimensional Wulff Diagrams

Diffusional growth of the grain boundary (GB) groove permits one to measure the ratio between GB energy sGB and surface energy ssur. The faceting of twin tilt grain boundaries in Cu has been studied using the GB thermal groove method. No rough facet edges were observed. It means that melting temperature is lower than the roughening temperature for the observed facets in Cu. The influence of orientation and misorientation deviation Dq = ½q – qS½ from coincidence misorientation qS has been studied. By increase of Dq the energy of (100)CSL facet increases. The convenient method for construction 3D three-dimensional Wulff diagrams was found. The 3- dimensional Wulff diagrams were constructed using this method and measured sGB / ssur values.

Cross-Sectional Evolution and Its Mechanism during Selective Molecular Beam Epitaxy Growth of GaAs Quantum Wires on (111)B Substrates

The mechanism of the cross-sectional evolution during the selective growth of GaAs quantum wires (QWRs) on (111)B-patterned substrates was studied in detail both experimentally and theoretically. For this purpose, growth experiments were carried out on <-1-12>-oriented wires by systematically changing growth conditions and pattern sizes. A detailed investigation on cross sections of wires has shown that the lateral wire width is determined by facet boundaries (FBs) within AlGaAs layers separating growth regions on top facets from those on side facets of mesa structures. FBs were found to be planar or curved, depending on initial pattern sizes and growth conditions. Computer simulation based on a phenomenological growth model was attempted, taking account of the facet-angle-dependent lifetime of adatoms. The simulation well reproduced the experimentally observed growth features including the evolution of FBs, indicating that the cross sections of wires grown on (111)B-patterned substrates are kinetically controlled by the pattern sizes and growth conditions.

Effect of grain boundary faceting on kinetics of grain growth and microstructure evolution

The Von-Neumann-Mullins relationship for two-dimensional grain growth is modified for the case of grain boundary faceting. It is shown that the anisotropy of grain boundary energy alone slows down the rate of normal grain growth. For highly mobile facets, however, the acceleration of the growth process is possible, accompanied by development of anisotropic microstructure. It is shown that the mean-field approach to the problem of grain growth in highly anisotropic polycrystal results in parabolic growth law similar to that for isotropic systems, with the facet mobility and maximal torque substituting the grain boundary mobility and grain boundary energy in isotropic systems.

The influence of misorientation deviation on the faceting of Σ3 grain boundaries in aluminium

Abstract The faceting of two tilt grain boundaries (GBs) in 99.999 % wt. purity AMK1010231 bicrystals has been studied. The first GB is a coincidence twin Σ3 GB (Σ is the inverse density of c...

Faceting and migration of twin grain boundaries in zinc

Abstract Faceting and migration of twin tips in slightly deformed Zn [112¯0] flat single crystals have been investigated. The stationary shape of the slowly migrating tip of the twin plate has been studied, and the migration rate has been measured between 592 and 692 K in situ using polarized light. Below 632 and above 682 K, the twin tip contains only one facet which is parallel to the (1¯102¯)2 and (11¯00)1 plane of the matrix single crystal, respectively. The non-physically high values of the apparent migration activation enthalpy between 632 and 682 K are discussed using the model of simultaneous migration of co-existing grain boundary facets based on the concept of weighted mean curvature. The experimentally determined temperature dependence of the twin tip mobility can be rationalized under the assumption that the migration of individual facets is characterized by identical activation enthalpies of 46.6 kJ/mol, but different pre-exponential factors (1.1 × 10−11 and 7 × 10−9m2/s, respectively).

Control of Boundary Structure and Grain Growth for Microstructural Design

The design of microstructure in materials, ranging from ultrafine, moderately sized, duplex to single crystalline, has long been a challenging subject to material scientists. A basic means to achieve this goal is related to the control of grain growth. Taking BaTiO3 as a model system, this investigation shows that control of grain boundary structure between rough and faceted and control of initial grain size can allow us to achieve the goal. When the grain boundary is rough, normal grain growth occurs with a moderate rate. On the other hand, for faceted boundaries, either abnormal grain growth or grain growth inhibition occurs resulting in a duplex grain structure or fine-grained structure, respectively. Growth of single crystals is also possible when the boundary is faceted. During crystal growth amorphous films can form and thicken at dry grain boundaries above the eutectic temperature. As the film thickness increases, the growth rate of the crystals is reduced. This observed growth behavior of grains with boundary structure is explained in terms of the difference in mobility between the two types of boundaries. The results demonstrate the basic principles of obtaining various microstructures from the same material.

Effects of ledge density on the morphology and growth kinetics of precipitates in a Ni–Cr Alloy

Aging a quenched, face-centered cubic, Ni–45wt%Cr alloy at intermediate temperatures produces Cr-rich body-centered cubic precipitates with a lath morphology and two prominent boundary facets. Both the faceted boundaries migrate by a ledge mechanism. The density of ledges in these boundaries were measured as a function of time and related to the precipitate’s shape and growth kinetics. A tendency of ledges to coalesce on one of the facets contributes to differences in the migration behavior of the two boundaries. One boundary has a distinct crystallographic habit, the other does not, and while both boundaries migrate with parabolic kinetics, they have different rate constants. The rate constants are influenced by the formation rate of ledges on the respective boundaries. Growth models are used in conjunction with the experimental measurements to show that the boundaries and ledges move at rates controlled by solute diffusion in the matrix.

Faceting of Σ3 and Σ9 grain boundaries in Cu–Bi alloys

The faceting of Σ3 and Σ9 tilt grain boundaries (GBs) has been studied in bicrystals of pure Cu and Cu–Bi alloys containing 2.5 × 10 −3, 10 × 10 −3 and 16 × 10 −3 at.% Bi. The Σ3(1 0 0), Σ9(1 0 0), Σ9(−1 1 0), and Σ9(−1 2 0) facets and non-CSL Σ3 82° 9R facet were observed, where Σ is the inverse density of coincidence sites. The ratio between GB energy, σ GB, and surface energy, σ sur, was measured by atomic force microscopy using the GB thermal-groove method. The GB energy and thermal-groove deepening rate increased slightly between 0 and 10 × 10 −3 at.% Bi for all facets studied. However, between 10 × 10 −3 and 16 × 10 −3 at.% Bi the GB energy increased dramatically [from a factor 2 for the Σ9(1 1 0) facet to 15 times larger for the Σ3(1 0 0) facet]. The thermal-groove deepening rate also increased by a factor of 10 in this concentration range. This change corresponds well with the GB solidus line (i.e., the formation of a stable layer of a liquid-like GB phase called GB prewetting) observed previously. Wulff diagrams were constructed using measured σ GB/ σ sur values.

Analysis of faceting of grain boundaries in GaN

Faceting of coincidence grain boundaries was experimentally observed in an MBE GaN layer. The energy of a few configurations including special facets as the first and the second shortest periods of the CSL unit cell was calculated with the empirical potential of Stillinger and Weber adapted to GaN. It is shown that the experimental configuration presents the lowest increase of energy by comparison to the two individual periods.

Grain Boundary Phosphorous Segregation and Its Influence on the Ductile Brittle Transition Temperature in Reactor Pressure Vessel Steels

Abstract The materials used for this work were two sorts of reactor pressure vessel (RPV) steels, which contain different amounts of phosphorous (P), namely 0.011 and 0.002 wt%. The specimens for Charpy V-notch (CVN) impact test, Auger electron spectroscopy (AES), and tensile test were thermally aged at 400, 450, and 500°C for 1000, 3000, and 5000 h. After the thermal aging, the AES specimens were broken in the AES chamber to measure the P concentration at grain boundaries. The AES measurements for as-received specimens were carried out following hydrogen charging so that grain boundary facets were available even without P segregation. The AES measurements revealed that the peak height ratio (PHR) of P/Fe at the grain boundaries of the high-P steel were 0.066, 0.141, and 0.120 in the specimens aged at 400°C for 3000 h, 450°C for 3000 h, and 500°C for 1000 h, respectively. The ductile-brittle transition temperature (DBTT) was measured for the aged specimens, and the ΔDBTT of 15K was observed only for the specimen aged at 450°C for 3000 h, although no changes in the hardness and tensile properties were observed. The grain boundary fracture ratio (GBFR) increased with increasing the PHR of P/Fe. Grain boundary fracture mode was located at the area close to the V-notch root. There was a good relationship among PHR, GBFR, and DBTT, indicating directly that the shift in the DBTT was due to grain boundary embrittlement caused by P segregation.

Grain boundary faceting close to the Σ3 coincidence misorientation in copper

The faceting of a cylindric tilt grain boundary (GB) in Cu bicrystal has been studied. The crystal lattices of both grains give rise to a superlattice called coincidence site lattice (CSL) with inverse density of coincidence sites Σ = 3. The (100) C S L , (210) C S L, (130) C S L facets and the non-CSL 82°9R facet develop upon annealing at 0.95 T m , where T m is the melting temperature. The ratio of GB energy σ G B and surface energy σ s u r of the specimen was measured applying atomic force microscopy from the profile of the GB thermal groove formed upon additional annealing. The influence of deviation from the exact coincidence misorientation θ Σ , Δθ = ‖θ - θ Σ ‖, has been studied on the basis of electron backscattering diffraction patterns. The Wulff-Herring diagrams were constructed using measured σ G B / σ s u r values, revealing stable and metastable GB facets. T m is lower than the roughening temperature for the (100) C S L and 9R facets facets in Cu.

Growth kinetics and modeling of selective molecular beam epitaxial growth of GaAs ridge quantum wires on pre-patterned nonplanar substrates

The growth kinetics involved in the selective molecular beam epitaxial growth of GaAs ridge QWRs is investigated in detail experimentally and an attempt is made to model the growth theoretically. For this purpose, detailed experiments were carried out on the growth of 〈1̄10〉-oriented AlGaAs–GaAs ridge quantum wires on mesa-patterned (001) GaAs substrates. A phenomenological modeling was done based on the continuum approximation including parameters such as group III adatom lifetime, diffusion constant and migration length. Computer simulation using the resultant model well reproduces the experimentally observed growth features such as the cross-sectional structure of the ridge wire and its temporal evolution, its temperature dependence and evolution of facet boundary planes. The simple phenomenological model developed here seems to be very useful for design and precise control of the growth process.

Modeling and visualization of polycrystalline thin film growth

A novel polycrystalline thin film growth simulator, FACET, has been developed. FACET is a multi-scale model with two major components: an atomic level one-dimensional kinetic lattice Monte Carlo (1D KLMC) model and a real time feature scale two-dimensional facet nucleation and growth model. The 1D KLMC model has been developed to calculate inter-facet diffusion rates. By inputting the diffusion activation energies, the model will calculate the inter-facet atomic flux between {1 0 0}, {1 1 0}, and {1 1 1} facets of FCC materials at any temperature. The results of the 1D KLMC model have been verified by comparison with a full three-dimensional kinetic lattice Monte Carlo (3D KLMC) model. The feature scale polycrystalline thin film nucleation and growth model is based on describing grains in terms of two-dimensional faceted surfaces and grain boundaries. The profile of the nuclei are described by crystallographically appropriate facets. The position and orientation of the nuclei can be randomly selected or preferred textures can be created. Growth rates are determined from different deposition fluxes and surface diffusion effects. Quantitative microstructural characterization tools, including roughness analysis, average grain size analysis, and orientation distribution analysis, were incorporated into the model, which allows the users to design, conduct and analyze the virtual experiments within one integrated graphical user interface. Users can also visualize the nucleation and growth process of the film and obtain the final film microstructure. The effects of thickness, temperature, and deposition flux on thin film microstructures have been studied by FACET.

Analysis of step-based silicon surfaces at facet boundaries during wet anisotropic etching

A step-based model describing the anisotropic etching of silicon by the advancement of steps on flat {111} planes is supported by under-etch experiments on {100} and {110} silicon wafers. However, such a model does not explain etch rate variations of surfaces having the same families of Miller Indices exposed to the same etchant. This work analyzes crystal features at intersections between facets composed of two different types of steps, one called “rows of kinks,” and the other called “periodic bond chains,” intersecting at an angle of 120°. This important configuration, called K-P-120°, is analyzed with a view to whether step movement would propagate across a boundary between facets. An under-etched surface, composed of three facets and a cavity bottom, having alternating K-P-K-P combinations, (where all of the facet boundary step interactions are K-P-120°), is analyzed. Facet roughness patterns, comparative etch rates, and analysis of boundary atom positions support the conclusion that that across-facet-boundary zipping of steps is favored from P steps to K steps, more than from K steps to P steps.

Maillage simplicial d'un polyèdre arbitraire

Issues related to the existence of a triangulation of an arbitrary polyhedron are addressed. Given a boundary surface mesh (a set of triangular facets), the problem to decide whether or not a triangulation (with no internal points apart from the Steiner points) exists is reported to be NP-hard. In this paper, an algorithm to triangulate a general polyhedron is used which makes use of a classical Delaunay triangulation algorithm, a phase for recovering the missing boundary facets by means of facet partitioning and a final phase that makes it possible to remove the additional (non-Steiner) points previously defined so as to recover the initial boundary mesh thus resulting in a mesh of the given polyhedron. To cite this article: P.-L. George, H. Borouchaki, C. R. Acad. Sci. Paris, Ser. I 338 (2004).

Selective Molecular Beam Epitaxy Growth of GaAs Hexagonal Nanowire Networks on (111)B Patterned Substrates

In view of applications to hexagonal binary decision diagram (BDD) quantum circuits, the growth of hexagonal GaAs nanowire networks was attempted by selective molecular beam epitaxy (MBE) on (111)B prepatterned substrates. The basic feasibility of <112>-oriented straight nanowires was first investigated. GaAs nanowires were selectively formed on the top (111)B plane of AlGaAs mesa structures with high uniformity. The lateral width of the wires was determined by two facet boundary planes separating the growth regions on the top and the side facets of the mesa structures. The angle of the boundary planes remained constant during growth, resulting in the wire width being precisely controlled by the thickness of the AlGaAs barrier layer. Then, GaAs/AlGaAs hexagonal nanowire networks were grown on the patterned substrates consisting of three equivalent <112>-oriented wires for a (111)B plane. The results of detailed structural and optical studies showed that highly uniform and smoothly connected hexagonal nanowire networks having threefold symmetry were successfully fabricated by the present selective MBE growth technique.

Sintering kinetics by structural transition at grain boundaries in barium titanate

For its analysis and understanding, sintering has been conventionally assumed to occur in proportion to driving force [J. Appl. Phys. 36 (1955) 1205; Acta Metall. 13 (1965) 227; Mater. Sci. Eng. 48 (1981) 53; Ceramic Processing and Sintering, Marcel Dekker, New York, 2003, p. 470]. This investigation, however, shows for the first time that the conventional assumption does not apply to faceted boundaries and that the microstructure can be frozen for faceted boundaries. A structural transition from rough to faceted was induced in BaTiO 3, by changing oxygen partial pressure. As long as the boundary was rough, continuous grain growth and densification occurred with sintering time, in agreement with the conventional assumption. With the onset of the structural transition from rough to faceted, however, grain growth and densification rates were reduced and became zero at the completion of the transition. This result demonstrates that critical driving forces are present for grain growth and densification for faceted boundaries, unlike the conventional understanding. The result also suggests that the formation or maintenance of faceted boundaries is crucial to inhibit grain growth and thus to produce ultrafine-structured materials.

Formation of high-density GaAs hexagonal nano-wire networks by selective MBE growth on pre-patterned [formula omitted] substrates

Attempts were made to grow high-density GaAs hexagonal nano-wire networks on (0 0 1) patterned substrates by selective molecular beam epitaxy. To form a hexagon, 〈 1 ̄ 1 0〉 - and 〈5 1 0〉 -directions were combined. By the growth of straight wire arrays in each direction, the growth mode, conditions and mechanism were investigated. The wire width was shown to be determined for both directions by the facet boundary planes resulting from the growth rate difference on different facets. By optimizing growth conditions, highly uniform and smoothly connected hexagonal nano-wire networks with a density of 3×10 8 cm −2 were successfully formed.

Characterization of Gallium-induced Intergranular Fracture Surface and the Auger Electron Spectroscopic Analysis for Mg Grain Boundary Segregation in AA6061 T4 Al-Mg-Si Alloy

This investigation examines the grain boundary segregation of Mg and Si in AA6061-T4 alloy, using Auger electron spectroscopy technology. Liquid metal embrittlement by gallium was conducted to fracture the AA6061-T4 alloyintergranularly to obtain compositional information directly from the grain boundary facets. The amount of liquid gallium applied is controlled to break the alloy intergranularly at room temperature, importantly without Ga-bearing particles or a film covering the fracture surface. The method of generating a fully intergranular fracture surface for AA6061 is elucidated. The AES analysis reveals that Mg in 6061 T4 alloy is segregated at grain boundaries, but Si does not. The segregation of Mg depends on the rolling direction. The mean peak-to-peak ratio I M g /I A l of the specimen whose longitudinal axis is perpendicular to the rolling direction is about three times that of the specimen whose axis parallel thereto. The grain boundary segregation is not result oxidation-induced; surface segregation also makes no contribution.

Dependence of Grain Growth and Grain‐Boundary Structure on the Ba/Ti Ratio in BaTiO3

The grain‐growth behavior and grain‐boundary structure in titanium‐excess BaTiO3 depend on the amount of excess titanium at 1250° and 1300°3C. With excess titanium, abnormal grain growth (AGG) occurs and the grain boundaries are mostly flat or faceted with hill‐and‐valley shapes. With 0.5 at.% excess titanium, the large grains have flat {111} faces forming singular grain boundaries parallel to {111} double twins. With excess‐titanium content between 0.1 and 0.3 at.%, the abnormal grains appear to have polyhedral shapes with {100} faces. These flat or faceted grain boundaries are expected to have singular structures, and hence AGG can occur by the step growth mechanism. When the excess‐titanium content is decreased to 0, the grain boundaries become curved, indicating a rough atomic structure, and normal grain growth occurs.