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Grain-boundary structure
Abstract
Theoretical and experimental work on the atomic structure of grain boundaries in metals and ionic crystals is reviewed critically. The dislocation and O-lattice models are described and their usefulness is assessed with reference to a worked example. The models derived from computer simulations of the atomic structures of grain boundaries are described and critically assessed, particularly with regard to their predictive capacities. Key transmission electron microscope observations of lowenergy boundary planes and grain-boundary dislocations are discussed. The difficultles in interpreting high-resolution electron-microscope images of grain -boundary atomIC structures are described and some recent results are discussed in the light of these remarks and computer calculations of grainboundary atomic structures. Finally, an important result from X-ray diffraction studies of grain boundaries is analysed.
... Ces derniers se différentient des joints de grains dits « généraux », en anglais « random grain boundary » et sont définis comme des joints de grains avec un nombre élevé de sites de coïncidence entre les réseaux des deux grains. Ces sites définissent un réseau de coïncidence, « coïncidence site lattice » (CSL) en anglais [276,277]. Le degré de coïncidence est caractérisé par l'indice Σ, il est défini par le ratio entre le volume de maille du réseau de coïncidence sur le volume de la maille du cristal [276]. À titre d'exemple les joints de macles sont des joints spéciaux avec un degré de coïncidence Σ3. ...
... Ces sites définissent un réseau de coïncidence, « coïncidence site lattice » (CSL) en anglais [276,277]. Le degré de coïncidence est caractérisé par l'indice Σ, il est défini par le ratio entre le volume de maille du réseau de coïncidence sur le volume de la maille du cristal [276]. À titre d'exemple les joints de macles sont des joints spéciaux avec un degré de coïncidence Σ3. ...
La résistance à l’oxydation isotherme et cyclique de l’alliage 718 produit par le procédé de fusion sélective par faisceau laser (LBM) et par faisceau d’électrons (EBM) a été comparée à celle de l’alliage 718 forgé (AMS5662). Les essais d’oxydation isotherme à 850 °C sous air ont montré des tenues à l’oxydation similaires en termes de prise de masse et d’oxydation intergranulaire pour les trois alliages. L’effet de la rugosité sur les cinétiques d’oxydation a été quantifié et il a été démontré que la cinétique d’oxydation intergranulaire suit le modèle de Wagner de l’oxydation interne avec un contrôle partiel par la diffusion de Al en volume. Les essais d’oxydation cyclique à 900 °C ont montré une couche d’oxyde bien plus adhérente pour l’échantillon forgé que pour les échantillons LBM et EBM. Cela pourrait être dû à une quantité de soufre en solution plus importante dans les échantillons issus de la FA. La résistance à la corrosion chaude cyclique et à l’oxydation cyclique à 900 °C et 1100 °C de superalliages issus de la FA (Alliage A, IN738, C1023 et Hastelloy X) ont été comparées. Les essais réalisés sur le banc d’oxydation cyclique du CIRIMAT et sur le banc brûleur de Safran Helicopter Engine, ont montré des cinétiques de variation de masse similaires sur les deux bancs malgré les atmosphères très différentes, sauf pour les alliages fortement affectés par la corrosion chaude à 900 °C sur banc brûleur. Les alliages les plus sensibles à la corrosion chaude cyclique ont une plus faible teneur en Cr (Alliage A) et/ou une teneur élevée en Mo (C1023), et présentent de l’oxydation intergranulaire (Alliage A, C1023 et 738). [...]
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... These boundaries created during material processing act as barriers to impede the motion of dislocations, strengthening materials [18][19][20][21][22][23][24][25][26]. For example, grain boundaries commonly contain grain boundary dislocations or disconnections (GBDs) [27][28][29][30][31], the interaction force between GBDs and the incoming dislocations could be either attractive or repulsive depending on the character of the impinging dislocation [32]. The reaction products left in the boundary could lead to the rearrangement of atomic structure of the grain boundary in order to achieve a low energy state. ...
... The strengthening mechanisms of twin boundaries have been widely studied by using transmission electronic microscopy (TEM) and molecular dynamic (MD) simulation [35][36][37][38][39][40]. The transmission of a dislocation across a coherent twin boundary (CTB) can take place at high applied stresses [26][27][28]. The transmission mechanisms vary with the character of dislocations and the local stress states. ...
The deformation mechanism of CoCrNi alloy with high density of annealing twins was studied by in situ transmission electron microscopy. Dislocation transmission and reflection at the twin boundary were observed during in situ loading. We characterized these reaction processes by combining TEM, dislocation theory and crystallography of twin. Twin boundary not only strengthens the material by impeding the motion of dislocation, but also acts as dislocation source to produce large of slip bands. These processes generate large of slip bands to accommodate the plastic deformation or strengthening material.
... More specifically, these degradation incidents have been attributed to irradiation assisted stress corrosion cracking (IASCC) [1,2]. Over the operating lifetime, nuclear power plant reactor core internal components of a pressurized water reactor (PWR) can experience temperatures as high a 400°C, neutron flux at 5.1x10 13 neutrons per cm 2 per s, with energies of E>1.0 MeV, neutron fluence at 40 years of 6.44x10 22 n cm -2 (E>1.0 MeV) or on average ~90 displacements per atom (DPA) [3]. ...
... The concept of "grain boundary design and control" has been previously introduced, where the bulk properties of materials could be improved by controlling the grain boundary nature [12]. A method of describing the grain boundary structure is through the coincident site lattice (CSL) model [13]. According to the CSL model, the number of coincident sites of the lattices from adjacent grains in the boundary plane gives a measure of the degree of coincidence, which is related to excess free energy of the internal interface, i.e., the grain boundary energy. ...
Thermo-mechanical processing plays an important role in materials property optimization through microstructure modification, required by demanding modern materials applications. Due to the critical role of austenitic stainless steels, such as 316L, as structural components in harsh environments, e.g. in nuclear power plants, improved degradation resistance is desirable. A novel two-dimensional plane strain machining process has shown promise achieving significant grain size refinement through severe plastic deformation (SPD) and imparting large strains in the surface and subsurface regions of the substrate in various metals and alloys. The deformation process creates a heavily deformed 20 – 30 micron thick nanocrystalline surface layer with increased hardness and minimal martensite formation. Post-deformation processing annealing treatments have been applied to assess stability of the refined scale microstructures and the potential for obtaining grain boundary engineered microstructures with increased fraction of low-energy grain boundaries and altered grain boundary network structure. Varying the deformation and heat treatment process parameters, allows for development of a full understanding of the nanocrystalline layer and cross-section of the surface substrate created. Micro-characterization was performed using hardness measurements, magnetometry, x-ray diffraction, scanning and transmission electron microscopy to assess property and microstructural changes. This study provides a fundamental understanding of two-dimensional plane strain machining as a thermo-mechanical processing technique, which may in the future deliver capabilities for creating grain boundary engineered surface modified components, typified by a combination of grain refinement with improved grain boundary network interconnectivity attributes suitable for use in harsh environments, such as those in commercial nuclear power plants where improved resistance to irradiation stress corrosion cracking is desirable.
... It can be seen in Fig. 13 that the wrought sample presented a high proportion of special grain boundaries. Special grain boundaries are defined as boundaries with a high number of coincident sites in the coincident sites lattice (CSL) characterized by a low Σ factor [50]. In the wrought sample, around 30 % of the grain boundaries detected are special boundaries, against 3 % and 9 % found in LBM and EBM samples respectively. ...
The intergranular oxidation in air at 850 °C of alloy 718 produced by laser beam melting and electron beam melting was compared to that of the wrought alloy. Quantitative analyses revealed that the amount of grain boundary oxidation was similar for these alloys. However, the additively manufactured ones presented deeper and thicker oxides at grain boundaries, due to grain size heterogeneity and to a smaller number of special boundaries. Results show that intergranular oxidation kinetics follows Wagner’s theory on internal oxidation considering not only O diffusion at the intergranular oxide/metal interfaces but also Al and Ti diffusion in the bulk.
... For example, high-resolution transmission electron microscopy and diffractometry have been used to analyze the local structure and orientation relationships of grain boundaries and interfaces in experimental bicrystal or polycrystal samples [5,6]. Similarly, atomistic simulations of grain boundaries and interfaces have enabled researchers to extract important thermodynamic data [7][8][9][10][11][12], analyze grain boundary structure [13][14][15], and identify mechanisms underlying grain boundary motion [16][17][18]. Virtual diffraction is a computational technique that enables a synergistic coupling between experiments and simulations, which can help shed light on the internal atomic structure of materials with nanoscale resolution. ...
Virtual diffraction is a computational technique that enables a synergistic coupling between experiments and atomistic simulations, which can help to elucidate nanoscale structure–property relationships. The research objective herein is to highlight recent advances in the use of virtual diffraction as a method to study the geometry and structure of homophase grain boundaries and heterophase interfaces with direct experimental validation. Virtual selected area diffraction patterns for two types of boundaries—homophase Al twist grain boundaries and heterophase Al2O3/Al interfaces—are created without a priori assumption of the periodic interface structure by computing diffraction intensities across high-resolution, 3-D reciprocal space meshes. In this work, computed diffraction patterns clearly identify Al grain boundary misorientation angles, reveal subsidiary peaks created by the dislocation arrays within select Al grain boundaries, and allow experimental validation of the minimum energy orientation relationship for the Al2O3/Al interface. Due to its advanced implementation, virtual diffraction characterization used throughout this work can be easily extended providing routes for similar analysis and experimental validation of atomistic simulations.
... The atomic structure of the ∑5 (310) [001] symmetric tilt grain boundary in Fe 3 Al is obtained using geometrical rules of the Coincidence Site Lattice model (CSL) [11]. The cell size was chosen in order to preserve a large amount of bulk crystal between two interfaces and thereby reasonable energy convergence. ...
The formation energies of the T.M impurities Ti and Zr were calculated using DFT calculations at absolute zero and ab initio MD simulations at 300 K. We found that, with increasing temperature, Zr impurities become more stable and prefer to segregate at the interface of ∑5 (310)[001] grain boundary. In the case of Ti, the results show that it remains a stable defect when temperature increases.
... The atomic structure of the ∑5 (310) [001] symmetric tilt grain boundary in Fe 3 Al is obtained using geometrical rules of the Coincidence Site Lattice model (CSL) [12]. The cell size was chosen in order to preserve a large amount of bulk crystal between two interfaces and thereby reasonable energy convergence. ...
The effect of the Ti and Zr transition metals on the D03-Fe3Al intermetallic compounds has been investigated by means of ab initio Pseudo Potentials numerical simulations based on Density Functional Theory. Two main issues will be addressed the understanding of the role of these two transition metals in terms of stability of the bulk at the light of their site preference in the D03-Fe3Al structure the behaviour of Ti and Zr transition metals in the sigma 5 (310) [001] grain boundary and their effect on the structural stability of this interface. An important issue when studying these aspects is to take into accounts the effect of temperature. This requires a molecular dynamics treatment of the atoms in the supercell. The technique known as ab initio molecular dynamics (AIMD) solves these problems by combining ‘on the fly’ electronic structure calculations with finite temperature dynamics. Thus, our study was conducted both using the conventional static ab initio calculations (0K) as well as by taking into account the effect of temperature (Ab Initio Molecular Dynamics).
... The atomic structure of the P 5 (310) [001] symmetric tilt grain boundary in Fe 3 Al is obtained using geometrical rules of the Coincidence Site Lattice model (CSL) [18]. The cell size was chosen in order to preserve a large amount of bulk crystal between two interfaces and thereby reasonable energy convergence. ...
The substitution of Ti and Zr transition metals in the bulk volume as well as at the interface of a ∑5 (310)[001] grain boundary of an ordered (D03-Fe3Al) intermetallic were studied by means of ab-initio calculations. The results show that both Ti and Zr prefer to segregate at the grain boundary for Fe types of site. It is demonstrated that the major difference between these two types of atoms is the solubility of Ti in the bulk while Zr substitution in the bulk is not energetically favoured. The preferred site for Ti substitution is confirmed to be FeI. Emphasis is also given on the importance of using relaxation when determining energy formation calculation for site preference configurations.
Topologically close packed (TCP) phases are often formed in nickel-base superalloys with high refractory elements during service, and they are detrimental for the high temperature performance of superalloys. The precipitation process of TCP phases is under scrutiny in particular for deformations that integrate strain and temperature but replicate the working conditions of superalloys. In this work, TCP phase precipitation is studied in nickel-base single crystal superalloys with or without Ru addition under thermomechanical fatigue deformation. Deformation twins on different {111} planes are observed intersecting with each other and forming large number of high angle boundaries. The structure of these high angle boundaries has high similarity to topologically close packed σ phase, and the boundaries are enriched in Re, Ru, Co and Cr, thus it provides both structural origins and constituent elements for the formation of σ phase. Ru is revealed intensely segregating to semi-coherent and incoherent interfaces between TCP phase and the matrix, this reduces the interface energies and leads to a dramatic change of the morphology of TCP phase precipitates. These results provide insight to effects of lattice imperfections and coevolution chemistry on TCP phase formation in superalloys, and shed light on inhomogeneous precipitation in alloys in general.
Grain boundaries (GB) have a significant impact on mechanical, physical properties and microstructure of polycrystalline materials. Their studies are necessary for designing materials of improved properties. We present molecular dynamics based studies of grain boundary in nanocrystalline aluminum. A Voronoi tessellation based method (Voronoi analysis, VA) and order parameter approach were used for describing structure and topological features in nanocrystalline aluminum. We are portraying new functionality and usefulness of VA combined with order parameter (OP) to picturing structure nature of grain boundary (GB) and its order given in form of configuration entropy. Voronoi analysis unveiled sub-nanoscale topological features contributing to GB which correspond to lattice distortions and liquid-like GB behavior. Grouping of Voronoi cell indices to a crystal lattice distortion group was made together with corresponding to them OP values. Two complementary methods used in this work provide new information and open new possibilities for studying structure and properties of nanomaterials.
We compare two quantities to describe a microstructure: the length fraction of Σ3/Σ9‐grain boundaries and the number fraction of Σ3‐x‐x/Σ3‐Σ3‐Σ9‐triple junctions using Cu, Ni and four of their alloys in several microstructural states. The fractions of Σ3‐grain boundaries show similar tendencies as the respective fractions of Σ3‐x‐x‐triple junctions in relation to the grain size upon deformation and annealing. However, the fraction of Σ9‐grain boundaries stagnates at certain grain sizes, while there is still a considerable change of Σ3‐Σ3‐Σ9‐triple junctions during grain growth, meaning that the Σ3‐Σ3‐Σ9‐triple junction microstructure is still evolving. To analyze the evolution of the triple junction microstructure, a program, such as pythorient, is necessary.
Methods available for determining the crystallography of grain boundaries are surveyed. It is suggested that the reason why relatively few studies of the crystallography of large numbers of boundaries have been made is the intensity of labour involved in the data analysis. A scheme is described which allows a large sample population of grain boundaries to be handled with maximum efficiency, whilst maintaining high precision in the parameters which describe the boundary. It also permits a comparison of these parameters with those which describe special cases (e.g. high-density coincidence site lattice, etc). The method involves a combination of stereographic manipulation and matrix algebra.
Die in der Metallkunde behandelten Materialien sind zumeist kristallin. Schmelzen und Dampf werden nur als Grenzfälle betrachtet, neuerdings auch glasartige Materialien (unterkühlte Schmelzen). Wir setzen voraus, daß wir von jeder Substanz die (Kristall-)Struktur kennen. Sie wird nach den bekannten Röntgenmethoden ermittelt und in ihrem Aufbau nach Atomlagen, Symmetrien, Einheitszelle etc. kristallographisch beschrieben. (Auch für nichtkristalline Substanzen läßt sich eine strukturelle Beschreibung geben, die von den Atomen allerdings nicht so streng befolgt wird wie im Kristall.) Makroskopische Metallkörper bestehen, wie in der Übersicht gesagt wurde, nun aber i. allg. nicht aus einem einzigen Kristall, sondern aus vielen Kristall-„Körner“. Die Proben haben eine Mikrostruktur, ein Gefüge. Die Körner unterscheiden sich voneinander durch ihre Orientierung, u. U. aber auch in der (Kristall-) Struktur oder Zusammensetzung. Im ersten Fall spricht man von einem homogenen, im letzten von einem heterogenen System. Die in sich homogenen Bestandteile des letztgenannten heißen Phasen. Ihre Kristallstrukturen, Zusammensetzungen und auch Volumenanteile in der Probe stellen sich so ein, daß die Freie Enthalpie des Systems im Gleichgewicht ein Minimum ist. Phasen im hier definierten Sinne gehen durch Umwandlungen 1. Ordnung (thermodynamisch durch Unstetigkeiten in der 1. Ableitung der Enthalpie nach der Temperatur definiert) ineinander über, wie z. B. den Schmelzprozeß (s. Kap. 5).
Grain boundaries and dislocations are the most common extended defects in crystalline materials. The principal difference between them is that grain boundaries are planar imperfections which are not accompanied by long-range strain and stress fields, while dislocations are line defects that produce long-range elastic strains and stresses in the material. They both strongly affect, and to a great extent control, the physical and mechanical properties of materials. This is the reason why both dislocations and grain boundaries, and also more general types of interfaces, have been studied very extensively throughout the development of materials science. A common feature of both grain boundaries and dislocations is that their basic characteristics are of crystallographic, geometrical nature. Indeed, in earlier structural studies these characteristics were the main topic of experimental and theoretical investigations (Bollman, 1970; Hirth and Lothe, 1982; Sutton, 1984; Sutton and Balluffi, 1995). In the case of dislocations they were closely linked with studies of their elastic fields and associated long-range interactions (Nabarro, 1967; Hirth and Lothe, 1982). Since crystallographic attributes of dislocations and grain boundaries have to be defined prior to any study of their structures and properties we summarize these characteristics briefly in the following section.
The importance of understanding the atomic and chemical structure of grain boundaries in intermetallic compounds for a fundamental comprehension of their fracture behavior is the principal theme of this contribution. Since intermetallics are the prime examples of quasi-brittle materials, we first discuss general features of brittle fracture in ductile materials. Ll2 intermetallic compounds, in particular Ni3Al, have been studied most extensively; therefore, we review in detail the present state of our understanding of the atomic and chemical structure of grain boundaries in these alloys and discuss possible reasons for intrinsic brittleness of their grain boundaries. Results of recent atomistic studies of grain boundaries in Ll2 alloys are then described. First, we concentrate on comparison of the boundary structures in Ni3Al and Cu3Au, the two alloys with the same crystal structure but rather different propensities to ordering. Second, we discuss the effects of temperature and bulk nonstoichiometry on the structure and chemistry of grain boundaries in Ni3Al. At this point, the most important finding is that significantly different structures are invoked by segregation of nickel and aluminum, respectively, which may be related to the fact that only nickel-rich alloys may be ductilized by boron alloying. Finally, we discuss briefly the structure and properties of grain boundaries in NiAl and assess the possibilities and limits of further research on atomic level behavior of interfaces in intermetallic compounds.
A parametrized tight-binding (TB) method based on the TB-UMTO approach in the atomic sphere approximation (ASA) [26] has been developed. The Hamiltonian is written in terms of the canonical structure matrix and potential parameters. The former is for a given configuration of atoms evaluated using a Dyson-type equation and the latter are those found self-consistently for the ideal lattice. A warping correction has been added to the scheme to be able to account for the effects of local straining which can not be included in the ASA. This is essential for applications in defect studies. Using this method the structure and energy of the ∑ = 5 [001] twist boundary in copper has been calculated.
The structure and associated translational states of the Σ = 3(112) symmetrical tilt grain boundary in niobium and molybdenum are investigated theoretically by three distinct computational methods. The results are compared with those of previous theoretical studies as well as with transmission electron microscopy observations. It was found that for this grain boundary, when fully relaxed, two possible translation states - "reflection" and "sheared" - are energetically almost degenerate in the two transition metals studied and thus comparison with experiments is ambivalent. This prevents the Σ = 3(112) boundary from being a suitable benchmark for validations of semi-empirical theoretical models of interatomic interactions.
In recent years, the influence of the establishment of long-range order in cubic alloys on the structure of grain boundaries in L12 alloys has been considered. Thus, for example, for the ⅀=5 (310) tilt boundary the various possible structures have been investigated that are generated upon ordering, starting from plausible structures in the disordered state. However, apart from some rough energy estimates based upon nearest neighbour interactions, no reliable energy calculations have been performed of these different possible structures. In this paper, computer calculations based upon interatomic pair potentials constructed in such a way that the L12 structure is stable with respect to disordering, are reported for the ⅀=5 (310) boundary. The relative stability of various possible structures, with associated different boundary compositions, has been investigated.
A large number of different lattice clusters has been analyzed according to the occurrence of low index atomic planes in the clusters. A relationship of this analysis to the classification of symmetrical grain boundaries is discussed. The classification is based on the combinations of structural units that describe the structure of different grain boundaries. The order of plane types following from the analysis can be considered as a measure of exceptionality of grain boundary types.
The methods for computer simulation of grain boundaries and hetero-interfaces in ceramics have long been available. We review developments in the field in two areas; the study of general grain boundaries and the simulation of hetero-interfaces. In both cases we discuss extrapolation from the symmetric case. We will also consider the validity of the continued use of classical potential models in an age of large-scale quantum calculations.
Cracks nucleated at nonequilibrium grain boundaries (GBs) under dislocation pile-ups and remote stresses are analyzed. The analysis takes into account the dissimilar anisotropic elastic constants of the grains sharing the boundaries. The results are represented as statistical crack length distributions. It is shown that the mean and variance of the distributions depend significantly on the structure of the nonequilibrium GBs, the grain elastic anisotropies and the grain orientations.
When considering the mechanical behaviour of materials an important property is the tensor of elastic moduli. Recently, local elastic moduli of interfaces have been defined and studied for metallic materials [1 to 3]. In these works grain boundaries are regarded as heterogeneous continua composed of ‘phases’ associated with individual atoms which possess elastic moduli identified with the atomic-level moduli evaluated at corresponding atomic positions. From this representation it is possible to define the ‘effective’ moduli of the grain boundary region. In this paper this concept is developed for materials with covalent character of bonding, specifically silicon. Using the Tersoff's potential [4, 5], the atomic-level and effective elastic moduli of the interfacial region have been evaluated for three alternate structures of the Σ = 3 (112-)/[11-0] tilt boundary. These calculations are then compared with the continuum bounds on the effective moduli evaluated using the classical minimum-energy principles of elasticity. The effective moduli calculated in the atomistic framework are generally within the continuum bounds and thus the present study demonstrates that the heterogeneous continuum model of the interfaces is appropriate for the description of the elastic properties of grain boundaries in silicon. An important aspect addressed in this study is the uniqueness of interfacial elastic moduli since their evaluation involves the energy associated with an atom which cannot be defined uniquely. The calculations have been made for two different partitions of the total energy into energies associated with individual atoms. These two partitions lead to almost identical results for the effective moduli and continuum bounds when the tensor of the atomic-level moduli is positive definite. When some atomic-level moduli are not positive definite the results may depend on the chosen energy partition.
Electron backscatter diffraction has been used in conjunction with a scanning electron microscope to obtain orientation measurements of individual grains in an interstitial-free steel. The microstructure of the material reveals the presence of “raised” grains with respect to the surface. Electron backscatter diffraction reveals that the majority of these grains are {100} 〈011〉 oriented in the normal direction to the surface. Furthermore, the electron backscatter diffraction patterns associated with this grain type are of poor quality, indicating that they retain a high degree of deformation that may ultimately detract from the properties of the materials. Grain-boundary analysis revealed that low-angle boundaries are unlikely to exist between “raised” grains and other grain types, which may play a role in adhesion characteristics of zinc coatings. The electron backscatter diffraction technique was additionally used to demonstrate that a texture gradient exists between the surface and the midplane of the material.
Susceptibility to intergranular stress corrosion cracking in Ni–16Cr–9Fe–xC alloys in 360°C primary water is reduced with increasing fraction of special grain boundaries, i.e. coincident site lattice boundaries (CSLB) and low angle boundaries, and grain boundary carbides. Intergranular stress corrosion cracking (IGSCC) was investigated using interrupted constant extension rate tensile tests in a primary water environment at 360°C. Thermal–mechanical treatments were used to increase the fraction of special boundaries from approximately 20–25% to between 30 and 40%. In a carbon-doped heat, further heat treating was used to precipitate grain boundary carbides preferentially on high-angle boundaries (HAB). Orientation imaging microscopy was used to determine the relative grain misorientations and scanning electron microscopy (SEM) was used to identify specific grain boundaries after each interruption. After each strain increment, the same regions in each sample were examined for cracking. Results showed that irrespective of the microstructure condition, CSLBs always cracked less than HABs. Results also showed that IGSCC is reduced with increasing solution carbon content, and for the same amount of carbon in solution, the addition of grain boundary carbides reduced IGSCC still further. The best microstructure was the one consisting of an enhanced CSLB fraction and chromium carbides precipitated preferentially on high-angle boundaries.
Grain boundary corrosion of oriented niobium bicrystals with symmetrical tilt boundaries has been investigated using interference microscopy. It is shown that the depth d of penetration increases with misorientation angle θ except near some coincidence-site-lattice boundaries where minimum cusps appear. For small-angle boundaries, d depends on θ following a ReadShockley-type relationship. The structure dependence of grain boundary corrosion is explained in terms of variations in free volume. The local expansion at large-angle grain boundaries was calculated using a soft-sphere model.
Analytical electron microscopy (AEM) has been used to examine the relationship between grain boundary structure and the segregation of chromium in a sensitised AISI 316 stainless steel. Fifty grain boundaries have been analysed. Among the boundaries there was a threefold difference in full width half maximum (FWHM) of the chromium concentration profiles. This variation is interpreted in terms of the different long-range stress fields created by different combinations of structural units in each boundary. From the narrowness of their profiles, it is deduced that the SIGMA = 3, 11, 13a, 13b and 29a boundaries are favoured while the SIGMA = 9 boundary is non-favoured. There was no correlation between FWHM and grain boundary chromium concentration. Additionally, we observe that it is not pre-requisite for the boundary plane to be close to {111} for a chromium carbide to nucleae. There is also no correlation between the boundary normal and either the FWHM of the chromium concentration profile or the grain boundary chromium concentration.
The distribution of grain boundary types along intergranular cracks in Ni3Al was measured, by Σ value, and compared to the distribution in the bulk, using statistically significant sample sizes. It was found that low angle (Σ1) and symmetrical Σ3 boundaries (twins) are particularly strong, and all high angle boundaries, independent of their Σ values are weak. In particular, low Σ, high angle boundaries, as a group, are also weak. These results are in qualitative agreement with predictions based on the structural unit model and imply that the fracture strength of an intergranularly brittle polycrystalline aggregate can be increased only by increasing the fraction of low angle and symmetrical Σ3 boundaries.
A modified hard sphere model and coincident site lattice theory were used to analyze the possible configurations of symmetrical tilt boundaries with the L1â structure. The minimum allowed interatomic distances used in the model were estimated from the structures of stable intermetallic phases in the corresponding binary system. Two different compounds were analyzed, CuâAu and NiâAl. For CuâAu, the grain boundary structures obtained were similar to those reported by other investigators for pure f.c.c. metals. Several boundaries were found to present two possible structures, differing in composition and ordering state. The contribution of disordering to the grain boundary energy was calculated in a point approximation based on the first coordination shell. For compounds of the NiâAl type the grain boundary structures that are most dense were found to be generally different from configuration of boundaries in pure f.c.c. metals and CuâAu. These configurations preserve order, but are less dense. The possibility of grain boundary ''phases'' that are not present in other f.c.c. materials may constitute an explanation for the extreme g.b. weakness observed in NiâAl and other L1â compounds with high ordering energy.
A TEM study was conducted of the interphase boundary structure of the two types of h.c.p. proeutectoid α plate formed in the b.c.c. β matrix of a hypoeutectoid Ti-7.15% Cr alloy. Ill-formed normal α plates were found to be partially coherent at their edges as well as along their broad faces. Misfit dislocations observed on the broad faces are of a-type, with Burgers vector a 3〈11 2 ̄0〉α spaced 20 nm apart, and on the edges are of c + a-type with b = a 3〈11 2 ̄3〉α and 89 nm apart. Very well formed black plates, developed at lower reaction temperatures, exhibit an interdislocation spacing of ca 35 nm on their broad faces. 0-lattice analysis indicates that the broad faces of neither morphology correspond to the b.c.c.:h.c.p. boundary with the smallest structural component of interfacial energy. This analysis also suggests that second arrays of misfit dislocations were absent because they are either too closely spaced or lie at too small an angle to the first arrays. The average spacing between the growth ledges on the broad faces of black plates is markedly greater than that on the broad faces of normal α plates, consistently with their smaller thickness/length ratio and higher lengthening rate.
Using the rotating-sphere-on-a-plate method, the relatively low energy orientations of grain boundaries in Cu, Ni and two Cu-Ni alloys lying, on average, parallel to the (100) surface of the plate were measured. Pole figures were plotted by using an X-ray texture goniometer. The data were analysed to determine whether special Σ-value boundaries existed (up to Σ35b), and crystallographic parameters such as Σ-value, boundary plane, rotation axis and angle, twist and/or tilt components were tabulated. The measured low energy orientations were compared with previous measurements from other studies and with predictions from geometric criteria.
The fundamental difficulties of incorporating experimentally obtained boundary misorientation distributions (BMDs) into three-dimensional microstructural models are discussed. An algorithm is described which overcomes these difficulties. The boundary misorientations are treated as a statistical ensemble which is evolved toward the desired BMD using a Monte Carlo method. The application of this algorithm to a number of complex arbitrary BMDs shows that the approach is effective for both conserved and non-conserved textures. The algorithm is successfully used to create the BMDs observed in deformation microstructures containing both incidental dislocation boundaries (IDBs) and geometrically necessary boundaries (GNBs). The application of an algorithm to grain boundary engineering is discussed.
The subject of grain-boundary structures in Ll2 alloys, generated upon ordering, is reconsidered taking the Σ = 5 (130) tilt boundary as an example. The full set of boundary configurations is discussed which may be obtained from two basic structures in the disordered state. Two types of interfacial dislocations are considered which may separate domains possessing one of these configurations. These types of dislocations have Burgers vectors belonging to the DSCd or DSCo lattice (where the superscripts o and d stand for ordered and disordered, respectively), and their properties are discussed. Finally the possibilities of observing domains in TEM (α-fringes) or with convergent-beam electron diffraction are explored.Die Korngrenzenstrukturen in Ll2-Legierungen, die nach dem Ordnungsprozeß generiert werden, werden erneut mit der Σ = 5 (130) Kippgrenze als Beispiel untersucht. Der vollständige Satz von Grenzenkonfigurationen, der aus zwei Grundstrukturen im fehlgeordneten Zustand erhalten werden kann, wird diskutiert. Zwei Arten von Grenzflächenversetzungen werden betrachtet, die Domänen trennen, die eine dieser Konfigurationen besitzen. Diese Versetzungstypen besitzen Burgersvektoren, die zum DSCd- oder DSCo-Gitter gehören (wobei die Beifügungen o und d für geordnet bzw. fehlgeordnet stehen), und ihre Eigenschaften werden diskutiert. Schließlich werden die Möglichkeiten der Beobachtung von Domänen im TEM (α-Streifen) oder mit Elektronenbeugung bei kovergentem Strahl untersucht.
A transmission electron microscopy study and geometric analysis has been performed on a vicinal 78.7° high-angle grain boundary in pure Ti which has mixed tilt-twist character and exhibits a characteristic dislocation arrangement. There is no feasible constrained coincident site lattice which could be adopted as the reference structure by this boundary and an alternative structure is proposed which corresponds to a two-dimensional atomic arrangement inclined at about 18° to the boundary plane. The dislocation configuration required to accommodate the deviation from the reference structure orientation was predicted using an O-lattice algorithm for class 1 interfacial dislocations and this matched well the arrangement observed experimentally.
Using the embedded atom method interatomic potential, all Σ < 50 tilt boundaries for hcp Ti with [0001] orientation are calculated by the method of molecular statics. Based on the atomic positions analysis, the structural units of dislocation cores are indicated. It is found that the atoms at the interfaces tend to form perfect regions and special dislocation cores, which exist in the forms of a tetrahedron and three joined irregular tetrahedra. The larger the perfect regions in one period are, the lower the grain boundary energies should be. The atomic structures of high angle (Θ > 10°) tilt boundaries with Σ = 19 and 7 are similar to those of low angle (Σ = 37). In the relaxation procedure, the atomic positions are not changed along the [0001] for any of the boundaries discussed.
Using the approach of Finnis and Sinclair, N-body potentials for copper, silver, gold and nickel have been constructed. The total energy is regarded as consisting of a pair-potential part and a many body cohesive part. Both these parts are functions of the atomic separations only and are represented by cubic splines, fitted to various bulk properties. For the noble metals, the pair-potentials were fitted at short range to pressure-volume relationships calculated by Christensen and Heine so that interactions at separations smaller than that of the first-nearest neighbours can be treated in this scheme. Using these potentials, point defects, surfaces (including the surface reconstructions) and grain boundaries have been studied and satisfactory agreement with available experimental data has been found.
The early developments of the dislocation theory were mainly in the framework of the continuum theory of elasticity. However, the importance of understanding the dislocation cores became apparent as investigations turned away from materials with close-packed structures to materials with more complex crystal structures. A necessary precursor for theoretical studies of the atomic structure of dislocations and other lattice defects is an understanding of atomic interactions. Until recently pair potentials were used almost exclusively in such studies. In this paper we first discuss the origin, merits and limitations of pair potentials. In particular, we analyse which features of pair potentials, as well as of the problems studied, are most important for the success of such atomistic studies. This is then demonstrated on two examples: the core structures of screw dislocations in intermetallic compounds with the Ll2 crystal structure and the cores of intrinsic grain-boundary dislocations. Finally we discuss possible future developments in dislocation studies, in particular the replacement of pair potentials by empirical many-body potentials and quantum-mechanically based total-energy calculations.
Normal grain growth in polycrystals is an important example of a capillarity driven coarsening phenomenon where topological structure of the system plays a major role. The process is practically important and attracts much interest, in particular in two-dimensional (2D) polycrystals because of the growing technological importance of thin polycrystalline films. In the present paper we discuss various approaches to normal grain growth in 2D polycrystals. We stay mostly within the framework of the uniform boundary model. This model provides a reasonable simplification leading to the Von Neumann-Mullins relation that relates the rate of growth of an individual grain to its local topology. Comparing different approaches---relatively simple mean-field theories, more sophisticated models incorporating real topology, and computer simulations adequately reproducing local equations of motion---we identify the principal factors responsible for different features of the phenomenon.
The Read-Shockley equation describing the dependence of grain boundary energy on misorientation of grains has been reformulated using the recently developed structural unit model of the atomic structure of grain boundaries so that it is applicable to general high angle boundaries. The boundary energy then consists of the energy of a reference structure, and of the core and elastic energies of the corresponding DSC dislocations. While the latter part of the boundary energy is determined using the elastic theory of dislocations the former two parts are determined on the basis of atomistics of grain boundaries employing the structural unit model. In the framework of this analysis the minimum number of reference structures in a give misorientation range as well as the extent of misorientations related to a given reference structure are determined. The positions of cusps in the energy vs misorientation dependence and their relative depths and extent are also determined. The validity of this model is demonstrated for tilt boundaries studied by atomistic computer simulations.
Interfaces are a critical determinant of the full range of materials properties, especially at the nanoscale. Computational and experimental methods developed a comprehensive understanding of nanograin evolution based on a fundamental understanding of internal interfaces in nanocrystalline nickel. It has recently been shown that nanocrystals with a bi-modal grain-size distribution possess a unique combination of high-strength, ductility and wear-resistance. We performed a combined experimental and theoretical investigation of the structure and motion of internal interfaces in nanograined metal and the resulting grain evolution. The properties of grain boundaries are computed for an unprecedented range of boundaries. The presence of roughening transitions in grain boundaries is explored and related to dramatic changes in boundary mobility. Experimental observations show that abnormal grain growth in nanograined materials is unlike conventional scale material in both the level of defects and the formation of unfavored phases. Molecular dynamics simulations address the origins of some of these phenomena.
Recent experimental and computational studies have produced two large grain boundary energy data sets for Ni. Using these results, we perform the first large-scale comparison between measured and computed grain boundary energies. While the overall correlation between experimental and computed energies is minimal, there is excellent agreement for the data in which we have the most confidence, particularly the experimentally prevalent Sigma 3 and Sigma 9 boundary types. Other CSL boundaries are infrequently observed in the experimental system and show little correlation with computed boundary energies. Because they do not depend on observation frequency, computed grain boundary energies are more reliable than the experimental energies for low population boundary types. Conversely, experiments can characterize high population boundaries that are not included in the computational study. Together the experimental and computational data provide a comprehensive catalog of grain boundary energies in Ni that can be used with confidence by microstructural scientists. (C) 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
There is an increasing amount of interest in grain boundary engineering (GBE) to improve the properties of the grain boundary network. In general, research has concentrated on use of a grain boundary misorientation based approach, namely, the coincidence site lattice (CSL), to categorise 'special' boundaries. The present paper presents the case that the specialness of grain boundaries is based on having at least one low index plane at the boundary, rather than because the boundary is a CSL type. It is shown that grain boundary planes play a pivotal role in GBE, and hence, an approach which focuses on the plane is advocated. Some potential routes for 'grain boundary plane engineering' are discussed.
Diffusion induced grain boundary migration (DIGM) is a phenomenon in which the sideways migration of grain boundaries accompanies the diffusion of solute along them. This results in the deposition of solute in, or its removal from, the matrix through which the boundaries sweep. In this review, the detailed phenomenology of DIGM is described, and the theories which have been proposed to explain it are compared critically with the phenomenology itself. The potential uses of DIGM in engineering the properties of materials are discussed.
Dynamic in situ X-ray topographic deformation studies have been performed on polycrystalline ice. Based on these observations, a new and dominant mechanism for dislocation nucleation, which is related to stress concentrations observed in the vicinity of grain boundaries, is proposed. It was found that the areas near grain boundaries always deform before the grain interiors. Lattice dislocations were nucleated continuously at large-angle grain boundaries, driven by internal stresses that are higher than the external stress. The dislocations, once generated, glide on the basal plane as semi-hexagonal loops. The shape of these loops is a result of a balance of the stresses present. The dislocation generation mechanism at grain boundaries was found to depend strongly on the basal plane orientation relative to both the loading direction and the grain boundary plane.
Some recent experimental results on boundary dislocations are discussed with reference to the concepts of extrinsic and intrinsic boundary dislocations and the associated stress and displacement fields. It is shown that the presence of a long-range stress field is not only dependent on the origin of the boundary dislocations, but also results from the external displacement conditions allowed at the outer limits of the crystals. The conditions for this long-range stress field to vanish are specified. The difficulties in experimental studies of the mechanical aspects of boundary dislocations arrays are commented on, and some suggestions are made to help in their analysis.
The effects of non-central forces in atomistic studies of grain boundaries in molybdenum and tungsten, the transition metals with half-filled d-band, are investigated. For this purpose we have used two different types of potential which include different number of moments of the local density of electronic states when evaluating the total energy: the central-force Finnis-Sinclair potentials which include the scalar second moment and the potentials constructed by Carlsson which include the fourth and the matrix second moments. The energy terms associated with these two moments represent non-central interactions and assure that the bcc-fcc structural energy difference is reproduced with good accuracy. For the three boundaries studied, the non-central forces have been found to be very important in determining the lowest energy structures. In particular, the energy differences between multiple structures depend on specific orientations and geometries of the atomic clusters at and near the interface. On the other hand, central-force potentials favour structures with atomic separations close to those found in the bulk with no regard to bond orientation. As a consequence the lowest-energy structures predicted by the two potential schemes differ in details in both the local atomic relaxations and the magnitude of the rigid-body displacements of the grains, although many general features of the boundary structures remain the same, independent of the potentials used. The calculations also show that it is not possible to identify the major non-central contribution with the fourth moment alone. Thus inclusion of both the matrix second moment and the fourth moment energy contributions is essential for an appropriate description of non-central atomic interactions.
The formation and migration of vacancies in (1121) twin boundaries in α-Ti and α-Zr are studied by computer modelling. Three empirical central force potentials constructed within the embedded-atom method are used to represent atomic interactions. Minimum-energy structures for the grain boundary are found first and the vacancy is then introduced by removing an atom and allowing further relaxation of the structure. Formation energies, entropies and relaxation volumes are calculated for different positions of vacancies. In order to analyse the vacancy migration, and thus the boundary self-diffusion, various vacancy jumps have been investigated and the corresponding migration energies and entropies calculated. The most probable paths composed of these simple jumps are then proposed. Both the formation and the migration free energies are significantly lower than in the bulk which demonstrates the role of the grain boundary as a vacancy sink and a fast diffusion channel. These free energies are then employed in evaluation of the diffusion coefficient tensor, the effective activation energies Qjj and the pre-exponential factors D0jj when the jj component of this tensor is assumed to follow an Arrhenius relationship Djj = D0jj exp (-Qjj/kBT). The boundary diffusion is then contrasted with the bulk diffusion and the calculated diffusion coefficients compared with available experimental data.
A model of grain boundary diffusion is considered in which the diffusivity in the boundary region is anisotropic and coordinate-dependent. For the usual experimental conditions, approximate analytical solutions of the model appear to coincide in form with those of Fisher's uniform isotropic slab model, but the role of the boundary diffusion coefficient and the boundary width is played by respective effective quantities related to the local diffusion behaviour. The accuracy of the analytical solutions obtained is estimated by comparing with the results of finite-difference calculations on the basis of exact diffusion equations. The model may be used for relating experimentally measured grain boundary diffusion characteristics to the results of modelling atomic jumps along grain boundaries.
It is shown that a hexagonal dislocation network in a low-angle twist boundary may be imaged either as a hexagonal pattern or as a triangular black-white contrast pattern, depending on the diffraction conditions employed. This may explain the apparent discrepancy between the recent results of Scott and Goodbew (1981) and those of previous workers.
The width of dislocations in grain boundaries is calculated by minimizing the interfacial energy of the boundary and the strain field energy of the dislocations. The calculations indicate that models, assuming equilibrium grain boundaries to consist of characteristic low energy structures with, if necessary, superimposed' arrays of localized misfit dislocations are of physical significance only for those boundaries whose energy depends strongly on the orientation relationship. For all other boundaries, dislocation models, although geometrically correct, seem to be of limited physical significance. Localized misfit dislocations are found to be unstable in these boundaries in the sense that their cores spread over the entire boundary area. The same applies to extrinsic grain boundary dislocations. They are found to be localized only in boundaries whose energy depends strongly on the mis-orientation. Measurements of the widths of misfit dislocations and observations on the width of extrinsic grain boundary dislocations agree with the results of the calculations.External forces (externally applied mechanical forces, thermal stresses, chemical forces) may result in the localization of dislocations in grain boundaries. This effect may be important for grain boundary sliding, phase transformations and the generation of dislocations from grain boundaries.
A theoretical analysis of grain-boundary stability and of the equilibrium positions of dislocations in all types of observed structures has been carried out using the method of Key and Saada (1976). It is concluded that for medium angles of tilt (θ = 2° to 5°), the symmetric position, i.e. the {022} grain-boundary plane (G.B.P.), is unstable. Furthermore the {211} G.B.P. is always the position of minimum energy.A superposition method has been developed to measure precisely the splitting separation of partial dislocations. The intrinsic-fault energy deduced from high-resolution observation, is equal to 100 erg/cm. The extrinsic-fault energy has been estimated to be of the same order of magnitude as this or lower.Although the core structure of dislocations is not yet completely determined, all our results are consistent with qualitative arguments on core energy based on open bonds; it explains why the sessile edge dislocation is not split.
It is shown that a range of interfacial defects can exist in non-holosymmetric and non-symmorphic crystals, and that these are distinct from previously recognized types. The crystallographic methodology used to predict the character of these defects is outlined. Examples of defects in grain boundaries of diamond-structure and sphalerite-structure materials and NiSi2/Si and GaAs/Ge interphase boundaries are discussed. Experimental observations of the defects in interphase boundaries are considered briefly.
Extrinsic secondary grain boundary dislocation (GBD) structures have been observed by weak-beam transmission electron microscopy in a variety of [001] twist boundaries in MgO. These structures were derived from segments of lattice dislocations embedded in the boundaries and could be interpreted as the result of the decomposition of the lattice dislocations into extrinsic GBDs and the subsequent interaction of the product GBDs with the intrinsic boundary structure. The results demonstrate that lattice dislocations in MgO are attracted to grain boundaries over a wide range of conditions and tend to remain embedded in the boundaries as extrinsic GBD structures. All observations could be rationalized on the basis of the CSL model for grain boundaries in cubic materials and were consistent with the intrinsic boundary structures described in Part I of the present work (Sun and Balluffi 1982). Furthermore, the results were similar in many respects to earlier results obtained with [001] twist boundaries in gold.
The mathematical relationship is presented between a coincidence site lattice and its related secondary dislocation Burgers vectors. These vectors are the displacement vectors which maintain the order in a grain boundary that is characteristic of c.s.l. orientation. Values of the vectors are given for low-order coincidence site lattices and their application to a random grain boundary distribution is discussed. Attention is drawn to some errors in the literature.
The dislocation aspects of the earlier model of Bishop and Chalmers for the structure of high angle symmetric tilt boundaries in metals is extended to twist and more general boundaries having both tilt and twist components. The expected strain contrast in high angle grain boundaries is discussed. It is concluded that strain contrast effects will be observed whenever there is not a long-range cancellation of the strain field of the boundary because of perturbations in the primary dislocation array, provided that the perturbations are sufficiently strong and widely spaced.Two types of contrast are discussed. One will occur at near-coincidence orientations due to perturbations in the periodicity of the primary dislocation array. This can be described in terms of secondary dislocations. The second is the result of a small tilt or twist about a second axis superimposed on an otherwise simple tilt boundary.
The core widths of grain boundary misfit dislocations in [001] twist boundaries close to coincidence site lattice misorientations have been studied by transmission electron microscopy on thin-film bicrystals of gold. Matching of experimental dark-field weak-beam images with profiles computed using the dynamical theory of electron diffraction shows that the core width for the 36·9°, Σ = 5 boundary is ~ 5 nm and may be even greater for the 22·6°, £ = 13 and 28·1°, Σ=17 boundaries. The results suggest that the coincidence site lattice plus dislocation network model of high-angle grain-boundary structures is applicable only to small angular ranges of misorientation close to angles corresponding to coincidence site lattice boundaries with relatively low energies.
The superlattice-fringe imaging technique in electron microscopy has been modelled for two ordering alloys, using multiple-beam dynamical diffraction theory. The transmitted beam and one first-order diffracted beam were combined to form the fringe image, and tilted illumination was used. Superlattice-fringe image contrast was studied as a function of degree of long-range order, specimen thickness, and diffracting conditions for an Fe3Al alloy with B2 order and for a Cu3Au alloy with Ll2 order. The results demonstrate that, for a given diffracting condition, there is a critical thickness below which superlattice-fringe contrast is a single-valued and monotonically increasing function of degree of long-range order. For an electron energy of 120 keV, in the Fe-Al alloy this thickness is approximately 50 nm, whereas for Cu3Au it is only 10 nm. Multiple-beam dynamical interactions were found to play an important role in determining the critical thickness. The implications of these results for using the technique to make quantitative measurements of degree of long-range order in inhomogeneous specimens are discussed.
Atomistic simulation methods have been used to calculate the structures and energies of a series of 001 symmetrical tilt grain boundaries in NiO. The configurations studied were all coincident twin boundaries, but the relaxation displaces the two crystal halves from the perfectly coincident structure. The (n10) boundaries are all qualitatively similar, and can be considered as arrays of left bracket 100 right bracket dislocations. Boundaries such as (320) and (430) consist of left bracket 110 right bracket dislocations. The boundary energies vary smoothly with angle, except for a cusp where the structure changes from left bracket 100 right bracket to left bracket 110 right bracket dislocations. All the boundaries are stable with respect to dissociation. The Coulomb interaction makes these boundaries qualitatively different from the analogous interfaces in fcc metals. The significance of the structures for grain-boundary diffusion is discussed.