Tilt Boundaries Research Articles

数理的手法による電子顕微鏡像の解析と構造予測

数理的手法による電子顕微鏡像の解析と構造予測

A relaxation method for the energy and morphology of grain boundaries and interfaces

The energy density of crystal interfaces exhibits a characteristic “cusp” structure that renders it non-convex. Furthermore, crystal interfaces are often observed to be faceted, i.e., to be composed of flat facets in alternating directions. In this work, we forge a connection between these two observations by positing that the faceted morphology of crystal interfaces results from energy minimization. Specifically, we posit that the lack of convexity of the interfacial energy density drives the development of finely faceted microstructures and accounts for their geometry and morphology. We formulate the problem as a generalized minimal surface problem couched in a geometric measure-theoretical framework. We then show that the effective, or relaxed, interfacial energy density, with all possible interfacial morphologies accounted for, corresponds to the convexification of the bare or unrelaxed interfacial energy density, and that the requisite convexification can be attained by means of a faceting construction. We validate the approach by means of comparisons with experiment and atomistic simulations including symmetric and asymmetric tilt boundaries in face-centered cubic (FCC) and body-centered cubic (BCC) crystals. By comparison with simulated and experimental data, we show that this simple model of interfacial energy combined with a general microstructure construction based on convexification is able to replicate complex interfacial morphologies, including thermally induced morphological transitions.

Dynamics of formation of low-angle tilt boundaries in metals and alloys at high loading rates

A computer model has been developed in which the process of formation of low-angle tilt boundaries and fragmentation of initial subgrains during shock loading of metals and alloys is clearly demonstrated by the of two-dimensional discrete dislocation–disclination dynamics method. The formation and evolution of such grains proceeds under the action of an external stress and the stress field of grain boundary disclinations distributed on the subgrain boundaries. With the D16 aluminum alloy as an example, three cases of fragmented structures formed in accordance with the initial configuration of the disclination ensemble have been considered for a dipole, quadrupole, and arbitrary octupole of wedge disclinations. It has been shown that, in all these cases, the formation of a stable fragmented structure requires a stress of ~0.5 GPa and time of 10 ns. The main results of computer simulation (the finite form of a fragmented structure, typical level of applied stress, and small fragmentation time) agree well with known experimental results on shock compression of the D16 aluminum alloy.

Mechanisms and kinetics of the migration of grain boundaries containing extended defects

A full understanding of the basic processes of grain boundary migration is a fundamental prerequisite for predictive models of microstructural evolution in polycrystalline materials in processing and in service. In a detailed study of the kinetics of a $[111] \mathrm{\ensuremath{\Sigma}}7$ symmetric tilt boundary, we have previously shown that defect-free, flat grain boundaries, below their roughening temperature, can be strictly immobile in the experimental limit. Here we present the results of molecular dynamics simulations of grain boundaries containing a variety of ``defects.'' These simulations show that the presence of some of these defects restores the mobility of flat boundaries, even well below the roughening transition temperature. These defects fundamentally alter the mesoscale mechanism of grain boundary migration from one involving homogeneous nucleation to a heterogenous process. At the atomistic level, the crystal lattice reorients via coordinated shuffling of groups of atoms. In the case of flat boundaries, these shuffles must accumulate to form critically stable nuclei, but in the case of boundaries containing defects the shuffling of a small number of atoms at the defects can be sufficient, fundamentally altering the mechanism and kinetics of migration.

Continuous description of the atomic structure of grain boundaries using dislocation and generalized-disclination density fields

An atomistic-to-continuum method is developed to derive dislocation, generalized-disclination density fields and the associated elastic strain, rotation, curvature and second-distortion fields from the atomic structure of grain boundaries. From the relaxed and un-relaxed atomic positions, calculation of the transformation gradient feeds a mechanical framework, where discontinuities of the lattice elastic displacement and distortion (rotation and strain) are captured by smooth incompatible strain and second-distortion fields associated with the dislocation and generalized-disclination density fields, respectively. The method is applied to a copper symmetrical tilt boundary as obtained from molecular dynamics simulations. The core structure of the boundary is found to contain edge dislocations and dipoles of generalized-disclinations, including standard wedge-disclination dipoles. The latter reflect in particular localized shear and stretch discontinuities across the interface, in addition to the overall rotation discontinuity.

The most frequent interfaces in olivine aggregates: the GBCD and its importance for grain boundary related processes

Rocks consist of crystal grains separated by grain boundaries that impact the bulk rock properties. Recent studies on metals and ceramics showed that the grain boundary plane orientation is more significant for grain boundary properties than other characteristics such as the sigma value or disorientation (in the Earth’s science community more frequently termed misorientation). We determined the grain boundary character distribution (GBCD) of synthetic and natural polycrystalline olivine, the most abundant mineral of Earth’s upper mantle. We show that grain boundaries of olivine preferentially contain low index planes, in agreement with recent findings on other oxides (e.g. MgO, TiO2, Al2O3 etc.). Furthermore, we find evidence for a preferred orientation relationship of 90° disorientations about the [001] direction forming tilt and twist grain boundaries, as well as a preference for the 60° disorientation about the [100] axis. Our data indicate that the GBCD, which is an intrinsic property of any mineral aggregate, is fundamental for understanding and predicting grain boundary related processes.

Experimental and computational analysis of abnormal grain growth

The mechanisms involved in the abnormal grain growth of the iron based oxide dispersion strengthened alloys are analysed in the present work. Its microstructural evolution takes place at high temperatures (0.9Tm) and is characterised by an initial submicrometre size microstructure and a strong < 110>|| rolling direction (RD) texture that evolves into a few extremely coarse grains (mm sizes) with < 112>||RD orientation. The analysis of the observed grain boundaries has been completed by molecular dynamics simulations. Microstructure evolution consists of an extended recovery process, followed by an abnormal grain growth stage, consequence of the orientation pinning mechanism and the proximity to a symmetric tilt boundary family between the < 110>||RD and < 112>||RD grains.

Dislocation-Mediated Deformation in Solid Langmuir Monolayers: Plastic Bending and Tilt Boundary.

The shear response of three types of textures (mosaic, striation, and stripe) in 10,12-pentacosadiynoic acid solid Langmuir monolayers has been investigated with Brewster angle microscopy. Low temperature mosaic textures respond to an applied stress elastically. Upon the application of shear the change of contrast appears in the form of propagation of fronts roughly perpendicularly to the shear direction within a single domain reversibly, while the domain shape keeps constant since it is presumably frozen kinetically. The striation and stripe textures at high temperatures show a viscoplastic behavior (plastic bending) in its rheological response, being consistent with the formation of a dislocation wall (tilt boundary) through dislocation dynamics (dislocation glide and climb). The stress-induced formation of a tilt boundary provides a manifestation of the collective motion of a number of dislocations.

The roles of crystallographic orientation, high-angle grain boundary, and indenter diameter during nano-indentation

Molecular dynamics simulation of nano-indentation of single-crystal and bicrystal FCC aluminum is performed. The role of crystallographic orientation during nano-indentation of single-crystal aluminum is assessed. Then, the influence of the presence of a grain boundary is analyzed by adding high-angle symmetric tilt boundaries of Σ5 /(100) and Σ5 /(100) parallel to the surface on which the indentation is performed. Furthermore, in both cases, the size of the indenter is changed to investigate how the surface curvature of the indenter affects the nano-indentation process. The results suggest that in each crystallographic orientation, the presence of a grain boundary increases the required force for indentation, while the distance of a grain boundary from the indentation surface could affect the increase in the required force. Simulations prove that the grain boundary acts as a source of generation and emission of dislocations and restricts the penetration of the indenter by limiting the slip band formation and plastic deformation. The dislocation emission from the grain boundary restricts the penetration of the indenter and limits the formation of the octahedral slip systems of type {111} and consequently increases the required force for indentation in bicrystals.

Motion of Grain Boundaries: Experiments on Bicrystals

Recent research on grain boundary migration is reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and the experimental results obtained on specially grown bicrystals are presented. Particularly, the investigated faceting and migration behavior of low angle grain boundaries under the curvature force in aluminum bicrystals was addressed. In contrast to the pure tilt boundaries, which remained straight/flat and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The migration of planar grain boundaries induced by a magnetic field was measured in bismuth and zinc bicrystals. Various structurally different boundaries were investigated. The results revealed that grain boundary mobility essentially depends on the misorientation angle and the inclination of the boundary plane. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonously with misorientation angle, whereas for low angle boundaries the migration activation enthalpy was virtually the same. The motion of the mixed tilt-twist boundaries under stress was observed to be accompanied by both the translation of adjacent grains parallel to the boundary plane and their rotation around the boundary plane normal.

Low‐Temperature Processable High‐Performance Electrochemically Deposited p‐Type Cuprous Oxides Achieved by Incorporating a Small Amount of Antimony

The development of an electrochemically robust method for the low‐temperature deposition of cuprous oxide (Cu2O) thin films with reliable and conductive p‐type characteristics could yield breakthroughs in earth abundant and ecofriendly all oxide‐based photoelectronic devices. The incorporation of the group‐V element antimony (Sb) in the solution‐based electrodeposition process has been investigated. A small amount of Sb (1.2 at%) in the Cu2O resulted in rapid nucleation and coalescence at the initial stage of electrochemical reaction, and finally made the surface morphology smooth in 2D. The growth behavior changed due to Sb addition and produced a strong diffraction intensity, single‐domain‐like diffraction patterns, and low angle tilt boundaries in the Cu2O:Sb film, implying extremely improved crystallinity. As a result, these films exhibited extraordinary optical transmittance and band‐to‐band photoluminescence emission as well as higher electrical conductivity. The Cu/Cu2O:Sb Schottky diode showed good rectifying characteristics and more sensible photoresponsibility.

Grain boundary motion and grain rotation in aluminum bicrystals: recent experiments and simulations

The results of experimental and computational efforts over recent years to study the motion of geometrically different grain boundaries and grain rotation under various driving forces are briefly reviewed. Novel in-situ measuring techniques based on orientation contrast imaging and applied simulation techniques are described. The experimental results obtained on specially grown aluminum bicrystals are presented and discussed. Particularly, the faceting and migration behavior of low angle grain boundaries under the curvature force is addressed. In contrast to the pure tilt boundaries, which remained flat/faceted and immobile during annealing at elevated temperatures, mixed tilt-twist boundaries readily assumed a curved shape and steadily moved under the capillary force. Computational analysis revealed that this behavior is due to the inclinational anisotropy of grain boundary energy, which in turn depends on boundary geometry. The shape evolution and shrinkage kinetics of cylindrical grains with different tilt and mixed boundaries were studied by molecular dynamics simulations. The mobility of low angle <100> boundaries with misorientation angles higher than 10°, obtained by both the experiments and simulations, was found not to differ from that of the high angle boundaries, but decreases essentially with further decrease of misorientation. The shape evolution of the embedded grains in simulations was found to relate directly to results of the energy computations. Further simulation results revealed that the shrinkage of grains with pure tilt boundaries is accompanied by grain rotation. In contrast, grains with the tilt-twist boundaries composed of dislocations with the mixed edge-screw character do not rotate during their shrinkage. Stress driven boundary migration in aluminium bicrystals was observed to be coupled to a tangential translation of the grains. The activation enthalpy of high angle boundary migration was found to vary non-monotonically with misorientation angle, whereas for low angle boundaries the migration activation enthalpy was virtually the same. The motion of the mixed tilt-twist boundaries under stress was observed to be accompanied by both the translation of adjacent grains parallel to the boundary plane and their rotation around the boundary plane normal.

Uranium vacancy mobility at the Σ5 symmetric tilt and Σ5 twist grain boundaries in UO2

Ionic transport at grain boundaries in oxides dictates a number of important phenomena, from ionic conductivity to sintering to creep. For nuclear fuels, it also influences fission gas bubble nucleation and growth. Here, using a combination of atomistic calculations and object kinetic Monte Carlo (okMC) simulations, we examine the kinetic pathways associated with uranium vacancies at two model grain boundaries in UO2. The barriers for vacancy motion were calculated using the nudged elastic band method at all uranium sites at each grain boundary and were used as the basis of the okMC simulations. For both boundaries considered – a simple tilt and a simple twist boundary – the mobility of uranium vacancies is significantly higher than in the bulk. For the tilt boundary, there is clearly preferred migration along the tilt axis as opposed to in the perpendicular direction while, for the twist boundary, migration is essentially isotropic within the boundary plane. These results show that cation defect mobility in fluorite-structured materials is enhanced at certain types of grain boundaries and is dependent on the boundary structure with the tilt boundary exhibiting higher rates of migration than the twist boundary.

Tilt Boundary Formation in GeSi/Si (001) Vicinal Heterosystem

The structural state of Ge x Si 1 − x films grown on Si substrates with the vicinal orientation (1 1 13) has been studied. The (1 1 13) orientation has been obtained by rotating the singular plane (001) around the [11 − 0] axis. The x parameter of Ge x Si 1 − x films in different samples ranged from 0.083 to 0.268. Triclinic distortions arising in film crystal lattice have been analyzed using our technique developed for the determination of epitaxial layer structural parameters based on the X − ray diffractometry data. It has been established that during the epitaxial process the film lattice turns around the direction of surface steps due to the introduction of misfit dislocations into the interface. Dislocations with Burgers vector a /2 which is not parallel to the interface create an analog of a tilt boundary. The turning angle value ψ is proportional to the misfit dislocation density. This phenomenon is associated with a decrease of the interface symmetry that leads to a change in the efficiency of stress relieving by dislocations belonging to different families. The influence of these families on the low − angle boundary formation is considered. Experimental values of the ψ angle and shear strain for the [13 13 2 − ] and [1 − 10] directions lying in the interface (1 1 13) have been defined. A comparison of the experimental and calculated values of ψ for the [13 13 2 − ] direction is provided.

Dense Mg x Ni1−x O nanocubes with special grain boundaries and paracrystalline distribution of defect clusters by pulsed laser ablation

Pulsed laser ablation of reactively sintered MgO–NiO (9:1, 1:1, 1:9 molar ratio) disks was used to fabricate dense rocksalt-type Mg x Ni1−x O in the form of submicron-sized spherical particulate and nanocubes for X-ray diffraction and transmission electron microscopic characterizations. The rapidly solidified particulates and the condensed nanocubes have internal compressive stress increasing up to ca. 1 GPa with the increases in Ni content. The nanocubes were coalesced over well-developed polar surfaces, i.e., {100}, minor {110} and their vicinal surfaces with growth ledges, to form special grain boundaries, i.e., (100) 15° and 45° twist boundaries and [100] {001}/{011} asymmetric tilt boundaries. The Mg x Ni1−x O nanocubes also showed 3-D paracrystalline distribution of defect clusters with 2 nm and 1.5–2 nm interspacing for M1N9 and M1N1 compositions, respectively, but G.P. zone-like features for M9N1 composition. The Mg x Ni1−x O particulates and nanocondensates have UV–visible absorption edge in the range 4.0–3.3 eV, decreasing with increasing Ni content for potential engineering applications.

Three-dimensional evaluation of gettering ability for oxygen atoms at small-angle tilt boundaries in Czochralski-grown silicon crystals

Three-dimensional distribution of oxygen atoms at small-angle tilt boundaries (SATBs) in Czochralski-grown p-type silicon ingots was investigated by atom probe tomography combined with transmission electron microscopy. Oxygen gettering along edge dislocations composing SATBs, post crystal growth, was observed. The gettering ability of SATBs would depend both on the dislocation strain and on the dislocation density. Oxygen atoms would agglomerate in the atomic sites under the tensile hydrostatic stress larger than about 2.0 GPa induced by the dislocations. It was suggested that the density of the atomic sites, depending on the tilt angle of SATBs, determined the gettering ability of SATBs.

Nanoscopic mechanism of Cu precipitation at small-angle tilt boundaries in Si

We investigate copper (Cu) precipitation at small-angle tilt boundaries on (220) in Czochralski-grown p-type silicon (Si) ingots using transmission electron microscopy, atom probe tomography, and ab initio calculations. In the initial stage of precipitation, Cu atoms agglomerate along the boundaries, forming coherent layers (less than about 2 nm thick) of ${\mathrm{Cu}}_{3}\mathrm{Si}$ with a body-centered-cubic structure in a metastable state ($a=0.285$ nm). As the layers thicken, they become semicoherent with misfit dislocations on the (220) interphase boundaries, reducing coherency strains. Subsequently, the metastable layers convert into incoherent polyhedrons of orthorhombic ${\ensuremath{\eta}}^{\ensuremath{'}\ensuremath{'}}\text{\ensuremath{-}}{\mathrm{Cu}}_{3}\mathrm{Si}$ in the equilibrium state, forming interphase boundaries on {112} in Si. These results are similar to the Cu precipitation processes found in metallic alloys: the formation of Guinier-Preston zones followed by a conversion into the equilibrium $\ensuremath{\theta}$ phase.

Assessment of Strain-Generated Oxygen Vacancies Using SrTiO₃ Bicrystals.

Atomic-scale defects strongly influence the electrical and optical properties of materials, and their impact can be more pronounced in localized dimensions. Here, we directly demonstrate that strain triggers the formation of oxygen vacancies in complex oxides by examining the tilt boundary of SrTiO3 bicrystals. Through transmission electron microscopy and electron energy loss spectroscopy, we identify strains along the tilt boundary and oxygen vacancies in the strain-imposed regions between dislocation cores. First-principles calculations support that strains, irrespective of their type or sign, lower the formation energy of oxygen vacancies, thereby enhancing vacancy formation. Finally, current-voltage measurements confirm that such oxygen vacancies at the strained boundary result in a decrease of the nonlinearity of the I-V curve as well as the resistivity. Our results strongly indicate that oxygen vacancies are preferentially formed and are segregated at the regions where strains accumulate, such as heterogeneous interfaces and grain boundaries.

Effects of incoherent nanoinclusions on stress-driven migration of low-angle grain boundaries in nanocomposites

Stress-driven migration of grain boundaries (GBs) is theoretically described as a plastic deformation mode in metal matrix nanocomposites containing incoherent reinforcing (ceramic or metallic) nanoinclusions. We considered the exemplary case of low-angle tilt boundaries migrating in nanocrystalline or ultrafine-grained metallic matrixes and analytically calculated the effects of reinforcing nanoinclusions on the GB migration process. In doing so, migrating low-angle tilt boundaries are represented as walls of edge lattice dislocations that cooperatively glide in a metal matrix but cannot penetrate wire nanoinclusions. It is theoretically revealed that the nanoinclusions typically hamper the stress-driven GB migration. At the same time, in the situation with small (ultrafine) nanoinclusions, they cause an anomalous effect enhancing (or, in other terms, decreasing the critical stress for unlimited migration) the stress-driven GB migration in metal–metal and metal–ceramic nanocomposites. The results of our theoretical examination are consistent with the corresponding experimental data reported in the literature.

Anomalous mechanical characteristics of graphene with tilt grain boundaries tuned by hydrogenation

Grain boundaries (GBs) as typical defective graphene structure have significant influence on its mechanical properties. The fracture strength of hydrogenated graphene with tilt GBs composed of pentagon–heptagon defects are systematically investigated using classical Molecular Dynamics (MD) method. Anomalous mechanical characteristics are revealed for graphene with hydrogenation either on or near the GBs. For graphene sheets with hydrogenation on tilt GBs under perpendicular pulling, the strength of hydrogenated GBs with large tilt angle is anomalously stronger than low-angle tilt boundary having fewer defects because of the interaction between polar stress fields of hydrogenated pentagon–heptagon defects. For graphene with hydrogenation near the GBs, the interaction between GBs and hydrogenated domains at different distance intervals is investigated. The strength is found to be governed by the peak normal stress in hydrogenated domain, and an exponential relationship between the normal strength and distance interval is revealed as a result of the stress field overlap between GB and hydrogenation interface. Our results gain meaningful insight into the effects of hydrogenation on the strength of graphene with tilt GBs, and provide guidelines for designing high-quality hydrogenated graphene-based nanodevices.