We suggest a dislocation based constitutive model to incorporate the mechanical interaction between mobile dislocations and grain boundaries into a crystal plasticity finite element framework. The approach is based on the introduction of an additional activation energy into the rate equation for mobile dislocations in the vicinity of grain boundaries. The energy barrier is derived by using a geometrical model for thermally activated dislocation penetration events through grain boundaries. The model takes full account of the geometry of the grain boundaries and of the Schmid factors of the critically stressed incoming and outgoing slip systems and is formulated as a vectorial conservation law. The new model is applied to the case of 50% (frictionless) simple shear deformation of Al bicrystals with either a small, medium, or large angle grain boundary parallel to the shear plane. The simulations are in excellent agreement with the experiments in terms of the von Mises equivalent strain distributions and textures. The study reveals that the incorporation of the misorientation alone is not sufficient to describe the influence of grain boundaries on polycrystal micro-mechanics. We observe three mechanisms which jointly entail pronounced local hardening in front of grain boundaries (and other interfaces) beyond the classical kinematic hardening effect which is automatically included in all crystal plasticity finite element models owing to the change in the Schmid factor across grain boundaries. These are the accumulation of geometrically necessary dislocations (dynamic effect; see [Ma A, Roters F, Raabe D. A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 2006;58:2169–79]), the resistance against slip penetration (dynamic effect; this paper), and the change in the orientation spread (kinematic effect; this paper) in the vicinity of grain boundaries.

We show how information about the elastic stiffness and compliance of an orthotropic polycrystal may be obtained from measurements of the statistical properties of the microstructure. We begin by discussing the statistical properties of the governing equations and the hierarchy that results when the equations are averaged. Perturbation solutions are obtained in terms of low-order statistical information. Using methods previously developed, we derive bounds for the elastic stiffnesses and compliances. A hierarchy of bounds is derived using the statistical information obtained from measurement of the microstructure. We discuss the methods used to obtain the correlation functions of the microstructure and provide a specific example, using data obtained from a copper sample.

We review current progress in the understanding of interfaces in bulk thermoelectric materials. Following a brief discussion of the mechanisms by which embedded interfaces can enhance the electronic and thermal transport properties, we focus on emerging routes to engineer the nanoscale grain and interfacial structures in bulk thermoelectric materials. We address in particular (i) control of crystallographic texture, (ii) reduction of grain size to nanocrystalline dimensions, and (iii) formation of nanocomposite structures. While these approaches are beginning to yield promising improvements in performance, continued progress will require an improved fundamental understanding of the mechanisms governing the formation, stability, and properties of thermoelectric interfaces.

We investigate orientation selection during grain growth by computer simulation in two-dimension using the phase-field method. The model characterizes misorientation in three-dimension with all three degrees of freedom. The systems considered consist of a single cube component embedded in a matrix of randomly oriented grains in the initial microstructure. The average grain size and size distribution are similar for both textured and randomly oriented grains. Starting from various fractions and spatial distributions of the cube component, we show that the effect of boundary energy anisotropy on texture development differs drastically from that of mobility anisotropy. In all cases the fraction of the cube component increases if boundary energy is anisotropic, and decreases if boundary mobility is anisotropic while energy is isotropic. Similar to previous studies, when boundary energy is anisotropic the misorientation distribution is no longer time-invariant and grain growth kinetics deviates from the behavior of isotropic grain growth. However, mobility anisotropy could also alter misorientation distribution and hence affect grain growth kinetics, which is different from the results obtained previously for systems of either random or single-component texture. The initial spatial distribution of the texture component plays an important role in determining the time-evolution of the misorientation distribution and hence affects the overall kinetics of texture evolution and grain growth. The simulation results are analyzed using Turbull's theory on grain growth. It is found that even though many individual factors affect texture evolution during grain growth, the key factor that really controls the process is the local grain boundary energy density.

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.

We have examined the crystallographic structure of GaAs/InP interfaces obtained by wafer fusion following different procedures. Plan-view and cross-sectional transmission electron microscopy reveal that the interface is not only composed of a regular array of two sets of edge dislocations and is more complex than generally supposed. If a twist is created due to misalignment of the two substrates, the dislocations are not edge dislocations but also have a screw component. Dislocations for which the Burgers vectors have a component normal to the interface are also present. Those dislocations probably result from steps and some of them accommodate the tilt between the two substrates. Inclusions and voids as well as a low number of volume dislocations are present in all the samples. The observed volume dislocation density near the interface lies in the 105–107 cm−2 range and these volume dislocations may be associated with thermal mismatch. The origin of all these defects is discussed.

We determine the linear stability of a rod or wire subject to capillary forces arising from an anisotropic surface energy. The rod is assumed to be smooth with a uniform cross–section given by a two–dimensional equilibrium shape. The stability analysis is based on computing the sign of the second variation of the total energy, which is examined by solving an associated eigenvalue problem. The eigenproblem is a coupled pair of second–order ordinary differential equations with periodic coefficients that depend on the second derivatives of the surface energy with respect to orientation variables. We apply the analysis to examples with uniaxial or cubic anisotropy, which illustrate that anisotropic surface energy plays a significant role in establishing the stability of the rod. Both the magnitude and sign of the anisotropy determine whether the contribution stabilizes or destabilizes the system relative to the case of isotropic surface energy, which reproduces the classical Rayleigh instability.

Using modern wide-angle atom probes, it is possible to acquire atomic scale 3D data containing 1000 s of nm(2) of interfaces. It is therefore possible to probe the distribution of segregated species across these interfaces. Here, we present techniques that allow the production of models for interfacial excess (IE) mapping and discuss the underlying considerations and sampling statistics. We also show, how the same principles can be used to achieve thickness mapping of thin films. We demonstrate the effectiveness on example applications, including the analysis of segregation to a phase boundary in stainless steel, segregation to a metal-ceramic interface and the assessment of thickness variations of the gate oxide in a fin-FET.

Using in situ nanoindentation, we investigated dislocation–interface interactions in Al/Nb multilayers. Preferential storage of dislocations at interfaces, as opposed to within layers, was observed. Recovery of dislocations was observed to occur through climb in the interfaces. The rapid climb of dislocations is ascribed to high vacancy diffusivity and vacancy concentration in the interfaces. The vacancy formation energy at interfaces, 0.12 eV, as estimated from the experimentally measured climb rates, was found to be significantly lower than in the bulk.

Using a spherical aberration (Cs)-corrected scanning transmission electron microscopy (STEM) and electron energy-loss spectroscopy (EELS), we investigated a 6° low-angle [001] tilt grain boundary in SrTiO 3 . The enhanced spatial resolution of the aberration corrector leads to the observation of a number of structural variations in the edge dislocations along the grain boundary that neither resemble the standard edge dislocations nor partial dislocations for SrTiO 3 . Although there appear to be many variants in the structure that can be interpreted as compositional effects, three main classes of core structure are found to be prominent. From EELS analysis, these classifications seem to be related to Sr deficiencies, with the final variety of the cores being consistent with an embedded TiO x rocksalt-like structure.

Twinned 2H martensite is observed in copper-based shape memory alloys together with basal and non-basal plane stacking faults. Knowledge of the twin-boundary structure and its interaction with the faults is important to understand the deformation mechanism by twin coalescence. High-resolution electron microscopy coupled with image simulations have been used for these studies. The interface of the type I twinning in 2H martensite shows an atomic configuration with mirror antisymmetry. An atomic plane is shared by the twinned variants in such a way that the distance between the planes, parallel to the interface, is unchanged at the boundary and the mean atomic volume is conserved. The interaction of the boundary with a basal plane fault generates a shift in the interface. A mirror antisymmetrical boundary is maintained by introducing an imperfect interface dislocation.

This work applies a constrained coincidence site lattice/constrained complete pattern shift lattice (CCSL/CDSCL) model and secondary O-lattice model to simulate the interfacial structure in the major side interface of Mg17Al12/Mg. The result shows that, at the orientation relationship (OR) with a small deviation (∼0.5 deg) from the Burgers OR, the secondary misfit in the interface normal to the parallel Δg vectors can be completely accommodated by the steps. The secondary dislocation networks in the habit plane and major side facet have been calculated.

This study examined the effect of CaO addition on grain-boundary conductivity in 10 mol % Gd 2 O 3 -doped CeO 2 containing 500 ppm SiO 2 as an impurity. The addition of CaO increased the grain-boundary conductivity ∼ 50 times without affecting the grain-interior conductivity significantly. CaO was incorporated into the CeO 2 lattice completely, which means that a scavenging reaction between a large CaO-related second phase and siliceous impurity was not the reason for the increased conductivity. After adding CaO, grain boundary structure changed from random to faceted. Configuration change in the grain-boundary segregation in relation to the boundary-structure variation is suggested as a possible reason.

This paper shows that in a higher-dimensional approach, quasicrystals and interfaces are formally equivalent. Interfaces and quasicrystals are interpreted here as a region in space where the atoms of interpenetrated crystal lattices compete for space. Based on this paradigm, a method derived from the strip-projection method developed for the study of quasicrystals has been introduced. The method is completely general, independent of the parent crystal lattice type, relative orientation, and translation and of the position and orientation of the boundary plane. In this approach the perpendicular space coincides with Bollmanns' displacement space, while the parallel space contains a physical structure characterized by a minimum local strain that includes both the interface and adjacent crystal lattices. A classification of interfaces in a finite number of well-defined equivalence classes (local isomorphisms) that include orientational and translational degrees of freedom has been introduced. This classification is based on the symmetry of the hyperlattice and the position and shape of the strip and incorporates concepts from previous structural units and symmetry breaking approaches. It is suggested that such classes can be related to physical properties of interfaces. The formalism defines ideal (minimum strain) structures assumed to play an analogous role in grain boundaries (GB's) to those played by the perfect crystal and quasicrystal concepts in the study of crystals and quasiperiodic structures. Also, a lattice, called the phason lattice, is introduced to account for the dislocation content of nonsingular interfaces. Accordingly, the properties of any GB are seen to be determined by the periodicity of isosymmetrical regions related to the O and phason lattices and not by the ill-defined and pathologically discontinuous index number Σ.

This chapter gives an introduction to the Potts model and a practical guide to programming and performing simulations. It shows how the beautiful but tyrannical surface tension effects can be investigated using the computational equivalent of soap bubble solution: the Potts model. Like soap bubble solution it is easy to use and provide fundamental insights into surface tension phenomena; but also like soap bubble solution, it can lead to a sticky mess. The aim of this chapter is to provide a best practice implementation guide to the model. It is divided into four sections. The first deals with the Ising model, which is considerably simpler than the Potts model but will allow us to discuss the physics of boundary motion that is encapsulated in the Potts model. It also allows the reader to get some experience of coding of simple Potts-like algorithms. In the second section, the Q-state Potts model is introduced and the diverse range of phenomena that can be simulated is shown. Section 3 is an algorithm section, allowing the reader to improve the efficiency of the Potts code should they wish. The final section introduces the reader to a range of industrial applications of the Potts model. © 2007 Elsevier Inc. All rights reserved.

This article is intended to acquaint the reader with the basic techniques that are currently available for acquiring maps of materials microstructure based on crystallographic orientation. Examples are given of the applications of the techniques with the aim of stimulating the imagination of the reader. Many readers will be familiar with the electron back scattered diffraction (EBSD) method because of its general availability but there is a wide variety of available methods, each of which is best suited to certain problems. All methods rely on generating diffraction patterns via the interaction of electrons or X-rays with (polycrystalline) matter. In some cases, especially electrons, patterns from individual crystallites are required whereas in others, especially with X-rays, overlapping patterns must be disaggregated. A working knowledge of the methods used to describe orientations is assumed. Likewise, a knowledge of the physics that governs the interaction of electrons or X-rays with matter is assumed and the origins of the diffraction patterns used in the methods described are not explained. Neutron diffraction is not included here because the method cannot afford sufficient spatial resolution to be useful for mapping. For the most part, the methods produce maps with the orientation specified at points on a regular grid. In general, the electron diffraction-based methods provide a direct measurement at each grid point whereas in the X-ray methods, the gridded map is derived from other diffraction data.

The ® rst atomistic simulations of orthogonal networks of screw dislocations in silicon have been performed to investigate the core structures of dislocation intersections. Structural models for the dislocation intersections are proposed and examined by the classical molecular dynamics method with the empirical interatomic potential of TersoA . The screw dislocations (b a/2 110 ) are assumed to be undissociated, according to experimental data on atomic structures of the synthetic low-angle Si/Si(001) twist boundaries. It is found that cores of the dislocation intersections are formed by closed characteristic groups of atoms (extended point defects). The structure of these defects depends on the fact whether the screw dislocation arrays generate a twist or a shear boundary. The former has a well-de® ned energy minimum, with the characteristic groups having the point-group symmetry 222 (D2). The latter is found to exhibit a degeneracy in the number of local energy minima, corresponding to non-symmetrical characteristic groups with a diA erent coordination of atoms.

The symmetry-dependence of electronic grain boundary (GB) properties in polycrystalline CuInSe2 thin films was investigated in a combined study applying scanning electron microscopy, electron backscatter diffraction, and Kelvin probe force microscopy. We find that highly symmetric Σ3 GBs have a higher probability to be charge neutral than lower symmetric non-Σ3 GBs. This symmetry-dependence can help to explain the large variations of electronic properties found for GBs in Cu(In,Ga)Se2.

The structure of the Σ3⟨110⟩{111} lateral twin boundary in tungsten has been studied using molecular static simulation. Two distinct boundary structures were found to be stable or metastable in the considered models. Multilayer oscillatory relaxation profiles were observed for the internal energy and local boundary dilatation. It was shown that the resulting structures are broad and alternate atomic planes in the immediate vicinity of the Σ3⟨110⟩{111} twin boundary may coalesce to form atomic planes with hexagonal-close-packed structure. The description of the incoherent twin boundary as a rigid ω-phase sandwich accounts almost entirely for the revealed atomic configuration.

The structural properties of LiFePO4 prepared by the hydrothermal route and chemically delithiated have been studied using analytical electron microscopy and Raman spectroscopy. High-resolution transmission electron microscopy and selected area electron diffraction measurements indicate that the partially delithiated particles include LiFePO4 regions with cross-sections of finite size along the ac-plane, as a result of tilt grain boundary in the bc-plane, and dislocations in other directions. Only the boundary along the bc-plane is accompanied by a disorder over about 2 nm on each side of the boundary. The Raman spectrum shows the existence of both LiFePO4 and FePO4 phases in the shell of the particles at a delithiation degree of 50%, which invalidates the core–shell model. This result also invalidates the recent model according to which each particle would be single-domain, i.e. either a LiFePO4 particle or a FePO4 particle. On the other hand, our results, like prior ones, can be understood within the framework of a model similar to the spinodal decomposition of a two-phase system, which is discussed within the framework of morphogenesis of patterns in systems at equilibrium. Both end-members, however, are well crystallized, suggesting a recovery similar to that observed in superplastic alloys, with dynamics that are due to the motion of nucleation fronts and dislocations, and not due to a diffusion phenomenon associated with a concentration gradient.