HRTEM study of [001] low-angle tilt grain boundaries in fiber-textured BaTiO3 thin films

Low-angle tilt grain boundaries in [001] fiber-textured BaTiO₃ thin films were investigated by high-resolution transmission electron microscopy. Extensive observation revealed a very high density of low-angle tilt grain boundaries in the film. The low-angle tilt grain boundaries can be described as periodical arrays of dislocations on {100} and {110} boundary planes. The boundaries with (100) plane on {100} planes are composed of perfect dislocations with Burgers vectors b = a < 100 > (a = lattice constant of BaTiO₃: 0.3992 nm), while the boundaries with (110) plane on {110} planes are composed of the dissociated dislocations with Burgers vectors a/2 < 110 >. It was thus found that the difference in the boundary plane leads to different dislocation structures along the low-angle grain boundaries.     

Structures of a Σ = 9, [110]/{221} symmetrical tilt grain boundary in SrTiO<Subscript>3</Subscript>

In this study, we fabricated a bicrystal of SrTiO₃ containing a Σ = 9, [110]/{221} symmetric tilt grain boundary (GB) and its atomistic structure was directly observed by transmission electron microscopy (TEM) and scanning TEM (STEM). We theoretically estimated the most stable structure by first principles calculations, and by combining this with TEM images determined the atomistic structure of the Σ = 9 grain boundary. We found that when the grain boundary is slightly tilted from the coincident site lattice (CSL) orientation, displacement shift complete (DSC) dislocations are introduced at the grain boundary to accommodate the misorientation between the two adjacent crystals while the most stable atomic structure remains unchanged.     

Dislocations in yttrium orthoaluminate single crystals

The dislocations present in single crystals of yttrium orthoaluminate grown by the Czochralski technique have been studied by means of etch pits and electron microscopy. They are shown to be predominantly edge in character with Burgers vectors which are principallya [1 0 0] andb [0 1 0]. In most instances, the dislocations form simple tilt boundaries. A few dislocations of a more random nature occur in association with twin boundaries. Dislocation formation is shown to be a characteristic of c-axis growth related to stresses caused by the anisotropic contraction of the material;b-axis crystals can be grown in a dislocation-free form.     

On brittle crack advance by double kink nucleation

A Mode I brittle crack is simulated by a pile-up of edge dislocations. The leading dislocation is a perfect lattice dislocation and the remaining dislocations are sub-dislocations with fractional Burgers vectors. A double kink at the crack-tip is represented by a set of double jogs on the dislocations. The equilibrium jog array is determined for several examples. The calculations give results for the activation energy for double-kink formation and for the elastic field of double kinks. The results are applicable to theoretical estimates of crack-growth rates and in providing boundary conditions for atomic simulations.     

Further refinements in the energy of grain boundaries

Earlier surface dislocation analysis of a grain boundary recognized the tendency of the grain-boundary surfaces to coalesce in order to reduce surface energy. The coalescence process is described by a distribution of surface dislocations on the grain-boundary surfaces. In the present paper, previous analysis is further refined. In particular, the sum of the Burgers vectors of the surface array of grain-boundary dislocations is not equal to the Burgers vector of the grain-boundary lattice dislocation. Instead, the Burgers vector of the surface array is determined as a function of the coalescence of the grain-boundary surfaces. The conservation of Burgers vectors of dislocations is used to predict the presence of a screening array of dislocations. The screening array of dislocations is determined by minimization of the total energy of the configuration. The distortion around the boundary is relaxed by the screening array. In general, the distribution of the screening array is two dimensional. This result has been proved by the presence of a minimum energy configuration for two sets of screening arrays of dislocations situated at different distances from the boundary.     

Deformation of internal boundaries

A geometrical analysis of the deformation of internal boundaries is presented using the slip systems as reference co-ordinate axes to describe the orientation of the two phases adjacent to the boundary. The present analysis can be applied to any type of boundary such as a grain boundary, a twin boundary or a two-phase interface. The nature of the disturbance left by a dislocation cutting through the boundary is characterized by a boundary dislocation, the Burgers vector of which can be determined from the orientation relationship between the adjacent slip systems. Whenever the crystal dislocation, cutting through the boundary, has a Burgers vector component normal to the boundary, the disturbance also possesses a ledge character, the motion of which may cause both grain boundary sliding as well as migration. The formulae derived are applied to simple cases to determine the nature of the boundary dislocations.     

Properties of tilt grain boundaries in ordered alloys

Computer simulation of symmetric tilt grain boundaries (GB) Σ = 5 [100](012) in ordered alloys Ni₃Al and NiAl was carried out. The energy of GB ws calculated by a method construction of γ-surface construction using Morse's empirical centralforce potentials. Results show GB having several steady states: (i) one is stable; or (ii) metastable. These states differ by energy and atomic structure of GB. Transition of GB from one state to the other is investigated and Burgers vector of GB dislocations are determined. It is shown that a direction fo GB slip in both alloys is [100].     

An investigation into the influence of grain boundary misorientation on the tensile strength of SiC bicrystals

In this work, molecular dynamics (MD) and Car-Parrinello molecular dynamics (CPMD) simulation-based analyses are performed to understand the influence of grain boundary (GB) misorientation on the tensile strength of SiC bicrystals. The tensile strength is governed by the changes in electron density and bond strength of atoms in GBs. An investigation of dislocation activity during mechanical deformation shows that the extent of the propagation of dislocations across the bicrystal grains is directly proportional to the extent of GB misorientation. An analytical relation that predicts the tensile strength as a function of GB misorientation is developed.     

The structure of a migrating low-angle tilt grain boundary in strontium titanate

Weak beam transmission electron microscopy and stereomicroscopy have been used to characterize the three-dimensional structure of a severely deformed low-angle tilt grain boundary in a strontium titanate ceramic. Various interactions between crystal lattice dislocations and grain boundary dislocations in this boundary have been analysed. The deformed low-angle tilt grain boundary is a result of partial glide. The boundary is composed of dislocations with Burgers vectorsa [¯100] and the deformation of the boundary is interpreted as having occurred by the interactions of the boundary with crystal lattice dislocations during grain boundary migration. Observed dislocation network in the grain boundary are a result of the reactionb ₃=b₁+b₂=a [¯100]+a [00¯1]=a [¯10¯1], and the resultant dislocations are sessile. Also, many crystal lattice dislocations are pinned by the grain boundary and produce a complex dislocation structure for the boundary.M. Fujimoto is a Visiting Scientist at the Massachusetts Institute of Technology on leave from Taiyo Yuden Co., Ltd., Tokyo, Japan.     

Molecular dynamics simulation of crack growth under cyclic loading

The mechanical behaviors around a crack tip for a system including both a crack and two tilt grain boundaries under cyclic loading are examined using a molecular dynamics simulation. Not only a phase transition but also the emission of edge dislocations is observed in order to relax stress concentration around a crack tip during the first loading. Then, a dislocation pile-up is formed near the grain boundary after the edge dislocations reach the grain boundary, because they cannot move beyond the grain boundary. During the first unloading, the edge dislocations emitted from the crack tip return to the crack tip and disappear in the system. We observe several vacancies generated around the crack tip and crack growth corresponding to an atomic scale during cyclic loading. Conclusively, we propose the fatigue crack growth mechanism for the initial phase of the fatigue fracture. That is, a fatigue crack propagates due to coalescence of the crack and the vacancies caused by the emission and absorption of dislocations.     

Characterization of Cu(InGa)Se2 grain boundary properties by electron- and tip-probe methods

Grain boundary (GB) properties of Cu(InGa)Se₂ thin film were measured using electron beam induced current (EBIC), electron back scatter diffraction patterns (EBSD) and scanning spreading resistance microscopy (SSRM) methods. The weak EBIC signal was observed in back-side grains which were separated by the random grain boundaries (GBs) running parallel to the substrate. Furthermore, it was shown by the SSRM that the tilt GBs had low resistivity. The two phenomena were explained by our previous proposed GB model [1]. Finally, the grain with a weak EBIC signal was assessed by the transmission electron microscope (TEM), and it was found that the grain had a twin cluster. The edge of the cluster reached at the CdS/CIGS interface, and the interface was disordered, which caused the minority carrier to sink, limiting the solar cell performance.     

Motion of the faceted 57° [11\overline{2} 0] tilt grain boundary in zinc

The impact of faceting on the high-angle grain boundary motion was studied. The non-steady-state motion of the 57° tilt grain boundary (GB) half-loop in a Zn bicrystal has been studied in situ. Above 678 K the slowly migrating GB half-loop was continuously curved. Below this temperature moving GB was fully or partially faceted. The transformation of curved GB into a GB facet with increasing temperature was observed for the first time. Overlapping faceting/roughening of three crystallograpically different GB facets lead to the complicated non-steady-state motion. As a result, the GB mobility values and migration enthalpy were not unique, but lay in a certain interval.     

Structure of Crystalline Interfaces

The structure of crystalline interfaces, as observed by transmission electron microscopy, is reviewed with emphasis on the similarity of grain and interphase boundaries of the dislocation type. Small-angle grain boundaries and low misfit interphase boundaries between similar crystal structures largely condense their mismatch into arrays of interfacial dislocations having Burgers vectors in common with dislocations located in the bulk crystals. Large-angle grain boundaries near certain misorientations corresponding to good fit between the abutting grains contain dislocations with Burgers vectors which are not found in the bulk crystal. Partially coherent interphase boundaries between quite dissimilar crystals, for example, f.c.c. and b.c.c., may also contain such dislocations. Principally, because of the difficulties involved in the acquisition of interfacial dislocations, dislocation interphase boundaries, in particular, usually do not have the minimum energy structure.     

Grain growth prediction with inclination dependence of 〈1 1 0〉 tilt grain boundary using multi-phase-field model with penalty for multiple junctions

Multi-phase-field (MPF) model with a higher-order term representing energetic penalty for multiple junctions was proposed to predict the grain growth accompanying the inclination dependence of grain boundary (GB) energy and mobility. The inclination effect was introduced on the basis of GB energy obtained from molecular dynamics (MD) simulations. The preliminary grain growth simulation of an isolated grain surrounded by Σ3 GB certified that the analytical equilibrium shape was well reproduced. The augmented higher-order term added to conventional MPF model could improve convergence and stability of numerical calculations around triple junction (TJ) region even if there exists the large GB energy gap at the TJ. Moreover, the present MPF model can realize well the Young’s relation with no GB inclination effect and further extend to the case with that effect. For the polycrystalline grain growth simulations with the GB energy distribution according to the misorientation angle of Al 〈1 1 0〉 tilt GB, Σ3 GB inclination lead the weak anisotropy characterized by Σ3{111} twin boundary. Besides, the inclination dependence can effectively drive the GBs with low GB energy like the low-angle GB during grain growth.     

Rôle du support dans le mécanisme de formation des dislocations interfaciales et cohérence dans les systèmes épitaxiques Fe/Au(100) et Fe/Au(111)

We have studied the formation of interfacial dislocations during the epitaxial growth of iron on gold either in the (100) orientation or in the (111) orientation, when the epitaxial interfaces have different geometries. The conditions in which interfacial dislocations appears and the nature of their Burgers vectors are defined in both cases. In the case of Fe/Au(100) these dislocations are either pure edge dislocations with a Burgers vector parallel to the interface or mixed dislocations with a Burgers vector inclined with respect to the interface. In all cases these dislocations arise from dislocations pre-existing in the substrate either by slipping or by stepping. We study the coherence in both the epitaxial pairs.     

Simultaneous grain boundary motion,grain rotation,and sliding in a tricrystal

Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.     

Edge dislocations near a cracked sliding interface

The edge dislocations near a cracked sliding interface were investigated. A continuous distribution of edge dislocations with Burgers vector along the y direction was used to simulate a crack of finite length along the sliding interface. From the dislocation distribution the stress field in the entire space was obtained. The stress intensity factors at both crack tips and image force on the edge dislocation were derived. The effects of the dislocation source and shear modulus ratio on both stress intensity factors and image force were also studied. Only mode I stress intensity factors at both tips were found in the composite materials with a sliding interface. The edge dislocations with Burgers vector along the y direction emitted from the crack always shield it to prevent propagation. The above results may reduce to an edge dislocation near a semi-infinite crack along a sliding interface including a sliding grain boundary. This revised version was published online in August 2006 with corrections to the Cover Date.     

Estimation of grain boundary torques in bicrystalline specimens

A method for estimation of grain boundary torques τ(φ), based on displacement of a boundary in bicrystalline specimens, has been described and results obtained for certain 〈110〉 symmetric tilt boundaries in 99.998 a/o aluminum bicrystals have been presented. The (111) and (113) twin boundaries are characterized by large values of τ(φ) at all temperatures investigated, whereas the (112) twin boundary is characterized by a large value only at relatively low temperatures. A qualitative ranking of the magnitude of normalized values of τ(φ) suggests that the largest value is associated with the (111) twin boundary followed by, in order of decreasing magnitude, the (113), (112) and (221) twin boundaries and the 10° low-angle boundary. This ranking is in accord with progressively decreasing degrees of atomic fit at the boundary as predicted from coincidence-lattice theory. Magnitude of the normalized grain boundary torques is proportional to the depth of the cusp in the energy-inclination plots. Such cusps are consistent with the significant degree of dependence of grain boundary structure on inclination.     

Plane harmonic waves in the linearized gauge theory of dislocations

Dispersion relations and the associated eigenvectors for the linearized gauge theory of dislocations are calculated for an isotropic, centrosymmetric and homogeneous material. Plane harmonic waves of dislocation fields are connected to micro-voigts and micro-slips through appropriately chosen arrays of edge and screw dislocations with Burgers vectors that vary in position and time. The observable displacements that give rise to those internal waves are calculated together with the corresponding dislocation densities and currents.