Structure and morphology of nanosized lead inclusions in aluminum grain boundaries

Grain boundary lead inclusions formed by ion implantation of mazed bicrystal aluminum films have been investigated by transmission electron microscopy. The vapor-grown bicrystal films contained mainly 90°(110) tilt boundaries with fixed misorientation but variable inclination, as well as some growth twins with 70.5°(110) symmetrical tilt boundaries and a few small-angle boundaries. It was found that the shape, size and orientation of the inclusions in the grain boundaries depend on the orientation of the aluminum grain boundary plane. Inclusions at 90°(110) tilt boundaries were invariably sharply faceted toward one aluminum grain and more rounded toward the other grain. The faceted side was a section of the cuboctahedral equilibrium shape of bulk lead inclusions in parallel topotaxy with the aluminum matrix. The rounded side, where the aluminum grain was rotated by 90° with respect to the lead lattice, approximated a spherical cap. At specific low-energy segments of the grain boundary where a (100) plane in grain 1 meets an (011) plane in grain 2, only two of several possible shapes were observed. One of these was preferred in as-implanted samples while both types were found after melting and re-solidification of the lend inclusions. The observations are discussed in terms of a modified Wulff construction.     

Microstructures of grain boundaries in (001)-oriented strontium bismuth tantalate thin films grown by pulsed laser deposition

(001)-oriented strontium bismuth tantalate thin films have been grown on Pt/TiO₂/SiO₂/Si (100) substrates by pulsed laser deposition. The room-temperature current–electric field dependence of the films has been investigated, which revealed a space-charge-limited conduction mechanism. The microstructures of grain boundaries and structural defects in these films were also examined by transmission electron microscopy and high-resolution transmission electron microscopy, respectively. The grains of the films deposited at 550 °C exhibited polyhedral morphologies, and the average grain size was about 50 nm in length and 35 nm in width. At a small misorientation angle (8.2°) tilt boundary, a regular array of edge dislocations with about 3-nm periodic distance was observed, and localized strain contrast near the dislocation cores was also observed. The Burgers vector b of the edge dislocation was determined to be [110]. At a high misorientation angle (39.0°) tilt grain boundary lattice strain contrast associated with the distortion of lattice planes was observed, and the mismatching lattice images occurred at about 2 nm along the boundary. The relationship between microstructural defects at grain boundaries and leakage currents of these films is also discussed. Received: 8 September 2000 / Accepted: 18 December 2000 / Published online: 28 February 2001     

Coupled motion of [10−10] tilt boundaries in magnesium bicrystals

Magnesium bicrystals were grown with symmetric and asymmetric tilt boundaries about the [10–10] axis using the vertical Bridgman technique. Isothermal constant load tensile tests were conducted on these bicrystals in the temperature range 300–500°C and relative displacements of the two grains were measured to obtain an appreciation for grain boundary motion characteristics. Coupled grain boundary motion was noted in almost all cases with the degree of tangential motion versus migration changing with tilt misorientation, temperature and applied stress. Specifically, within the family of symmetric bicrystals evaluated, a minimum in grain boundary displacement in the specimen plane was observed at a tilt misorientation of 20°. In specific stress/temperature regimes, rigid body sliding was observed for the particular case of a 35° asymmetric tilt misorientation. The ease of basal and prism slip in magnesium at the temperatures considered and the consequential impingement of intragranular dislocations on the bicrystal boundary and their decomposition and motion along the boundary are thought to play an important role in the observed coupled motion of these tilt boundaries.     

To the Question of Forming Geometrically Necessary Disclinations in Triple Junctions of Grain Boundaries in Metals

The Bollman and King models are tested by means of molecular dynamics simulation for the formation of geometrically necessary disclinations in triple junctions of grain boundaries in metals. It is shown that the stresses arising in a triple junction due to the non-multiple lengths of low-angle tilt boundaries to the distance between grain boundary dislocations is not compensated for mainly by the formation of an additional disclination in the junction (the King model) but by the bending of one or several grain boundaries, accompanied by the displacement of grain boundary dislocations. A triple junction of the Bollman U-type (containing a geometrically necessary disclination) is not formed at the conjugation of tilt boundaries with common misorientation along the junction or at the conjugation of mixed-type boundaries.     

The influence of tilt grain boundaries on the mechanical properties of bicrystalline graphene nanoribbons

The mechanical properties of bicrystalline graphene nanoribbons with various tilt grain boundaries (GBs) which typically consist of repeating pentagon–heptagon ring defects are investigated based on the method of molecular structural mechanics. The GB models are constructed via the theory of disclinations in crystals, and the elastic properties and ultimate strength of bicrystalline graphene nanoribbons are calculated under uniaxial tensile loads in perpendicular and parallel directions to grain boundaries. The dependence of mechanical properties is analyzed on the chirality and misorientation angles of graphene nanoribbons, and the experimental phenomena that Young's modulus and ultimate strength of bicrystalline graphene nanoribbons can either increase or decrease with the grain boundary angles are further verified and discussed. In addition, the influence of GB on the size effects of graphene Young's modulus is also analyzed.     

Pressure effect on grain boundary wetting at various temperatures

Bicrystals of Fe-6 at.% Si alloy containing <001> 5 tilt grain boundaries with a deposited zinc layer have been annealed at various hydrostatic pressure at four temperatures between 700° and 905°C. After the anneals the dihedral angle of the grain boundary groove formed at the site of the grain boundary intersection with the solid-melt interphase boundary has been measured. The transition from complete to incomplete wetting of the grain boundary by the zinc-rich melt (dewetting phase transition) has been found to occur as the pressure increased at all temperatures studied. The temperature dependence of the dewetting transition pressure p _w has been determined. That dependence has a minimum at a temperature of 790°C, which is close to the peritectic temperature in the Fe–Zn system (782°C). A thermodynamic analysis of the wetting phenomena in the two-component system, based on Becker's regular solution model for the surface tension of the interphase boundary, explains the minimum in the p _w (T) dependence.     

Energies of formation and structures of point defects at tilt grain boundaries in molybdenum

The structure and formation energy of vacancies and interstitials at symmetrical tilt grain boundaries in molybdenum have been investigated by means of classical molecular dynamics. The dependence of the formation energy of these boundaries on the grain misorientation angle has been calculated. The structures of defects, energies of their formation, and diffusion mechanisms have been determined for the most stable grain boundaries.     

Molecular dynamic simulation of the CsCl–Al2O3 interface

The interface between solid cesium chloride and α-aluminum oxide was simulated by molecular dynamics technique. It was shown that due to a misfit between lattices of the components the interfacial contact may be presented as a small-angle boundary saturated with dislocations. Also a domain structure is formed. The dislocations and interdomain boundaries act as a source of defects and give rise to the total ionic mobility along the interface and boundaries. According to the calculation at a temperature of nearly 70% of the melting point, the diffusion coefficients of ions along misfit dislocation cores and domain walls, ∼ 10^– 6 cm²/s, are only an order of magnitude lower than the corresponding values for molten salts.     

Interdiffusion in two-layer Pd/Ag films III. TEM investigation of diffusion-induced grain boundary migration

Diffusion-induced grain boundary migration (DIGM) is studied by the transmission electron microscopy method in polycrystalline two-layer Pd/Ag thin films with a grain size (100–2000 nm). In addition to the typical features of DIGM known for coarse-grained bulk objects and foils, new features are found which are caused by a quite dense network of triple junctions and by misfit dislocations: fast increase of grain boundary curvature and inclination; back motion of grain boundaries owing to recrystallization forces and termination of DIGM. Homogenization resulted from diffusion-induced migration of misfit dislocations is observed in addition to DIGM.     

Critical current of an inhomogeneous Josephson junction at an intergrain boundary with a random distribution of dislocations

The critical current J _c(θ) of an intergrain boundary is calculated as a function of the contact misorientation angle θ of the granules. It is assumed that the ordering parameter is suppressed in regions near boundaries with an enhanced mechanical stress induced by randomly distributed surface dislocations. The stress distribution function is determined using a probabilistic approach. Assuming that the weak coupling at the boundary is Josephson coupling, an analytic expression is found for the angular dependence J _c(θ) (for tilt and twist boundaries). The magnitude of the residual critical current of a boundary in a strong magnetic field is estimated. Fiz. Tverd. Tela (St. Petersburg) 40, 393–402 (March 1998)     

Theoretical study of the critical current of YBa2Cu3O7−δ bicrystals with hole-deficient grain boundaries

We develop a theory of the critical current across grain boundaries in YBa₂Cu₃O_7−δ bicrystals. Experiments have shown that there is hole depletion near a boundary and the concentration profiles have been determined for specific cases. These results mean that the critical temperature is a function of distance from the boundary. Taking this function from experiment as input into the theory, we study two specific boundaries: a boundary with a 7° misorientation angle about [100] which is known to be strongly coupled for the purposes of current flow, and a 31° boundary which is known to be weakly coupled. Using Ginzburg-Landau theory, we determine the dependence of the critical current density (j_c) on temperature and the spatial dependence of the order parameter for these boundaries. The results show that the oxygen depletion can account for a major portion of the change from weak to strong coupling of boundaries as the misorientation angle is increased.     

Mobility of low-angle grain boundaries in pure metals

The mobility of low-angle grain boundaries in pure metals is reviewed and several theoretical treatments are provided. The approach that provides the best agreement with the available experimental data is one in which the mobility is controlled by vacancy diffusion through the bulk to (and from) the dislocations that comprise the boundary that are bowing out between pinning points. The pinning points are presumed to be extrinsic dislocations swept into the boundaries or grown in during the prior processing of the material. This approach yields a mobility that is constant with respect to misorientation angle, up to the transition to the high-angle regime. For small misorientations of the order 1°, however, the mobility appears to increase with decreasing misorientation angle.     

Microstructure and transport properties of various 90° grain boundaries in YBa2Cu3O7 thin films

The microstructure and transport properties of various 90° grain boundaries in (103) oriented YBa₂Cu₃O₇(YBCO) thin films grown epitaxially in situ by 90° off-axis sputtering are compared. The (103) films grown on (101) LaAlO₃ and (101) SrTiO₃ substrates have specific sets of 90° grain boundaries in both principal in-plane directions: 90° [010] twist boundaries along the [101] direction, and 90° [010] symmetrical tilt boundaries and 90° [010] basal-plane-faced tilt boundaries along the (301) direction. No weak-link behavior is observed across some of these boundaries by transport critical current density and normalized magnetic field dependence of J _c measurements along both those in-plane directions. High-resolution transmission electron microscopy reveals variations in the structure and microfaceting of the 90° boundaries, which may contribute to the absence of weak-link behavior. These results have important implications for understanding the behavior of step-edge Josephson junctions.     

First observation of a wetting phase transition in low-angle grain boundaries

The wetting phase transition at low-angle intercrystallite grain boundaries has been experimentally observed. In contrast to the high-angle grain boundaries with the misorientation angels θ > 15°, the low-angle grain boundaries (θ < 15°) are not continuous two-dimensional defects, but constitute a discrete wall (network) of lattice dislocations (edge and/or helical). The theory predicts that, depending on θ, either a continuous layer of the liquid phase or a wall (network) of microscopic liquid tubes on wetted dislocation nuclei is formed at completely wetted low-angle grain boundaries. It has been shown that the continuous liquid layers at low-angle grain boundaries in the Cu-Ag alloys appear at the temperature T _wminL = 970°C, which is 180°C higher than the onset temperature T _wmin = 790°C and 50°C lower than the finish temperature of the wetting phase transition at high-angle grain boundaries, T _wmax = 1020°C.     

Misorientation Dependence of the Grain Boundary Energy in Magnesia

Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the 3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes.     

Asymmetric tilt grain boundary structure and energy in copper and aluminium

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the ? 100 ? misorientation axis, and the Σ9 and Σ11 systems rotated about the ? 110 ? misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the ? 100 ? system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the ? 110 ? system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.     

Excess Volume of the Solid/Liquid Interface in Fe-6 at.%Si Bicrystals Wetted by Liquid Zinc

The pressure effect on grain boundary wetting in Fe-6 at.%Si bicrystals of different misorientation angles but constant misorientation axis has been studied. The wetting agent was liquid zinc. It was found that the pressure for the dewetting transition is higher for the near 5 boundary than for the other general boundaries, where is the inverse density of the coincidence sites in the two misoriented crystal lattices. This result was explained assuming a thinner liquid film wetting the near 5 boundary than in the case of nonperiodic grain boundaries. Furthermore, the wetting angle increased with increasing pressure. The wetting angle dependence on pressure could be understood assuming a excess surface volume of the solid/liquid (S/L) interface higher than 0.2 nm. This is considerably higher than the estimated excess volumes of grain boundaries based on computer simulations. To explain this result, it was postulated that in the system studied, where diffusion of Zn, Fe and Si perpendicular to the S/L interface takes place, the S/L interface is relatively thick and the interaction between the two crystals separated by the melt extends over more than 2 nm distance. This long-range interaction was rationalized in terms of clusters of several atoms, detaching from the solid and dissolving in the melt at some distance from the bulk.     

MOLECULAR DYNAMICS SIMULATION ON LOW ANGLE GRAIN BOUNDARIES

Molecular dynamics simulation has been performed to investigate the microstructure and properties of low angle grain boundaries, employing the embedded atom method(EAM) type interatomic potential for Ni-Al alloy. The energies of the low angle grain boundaries with different dislocation densities were calculated, and the results indicate that the low angle grain boundary energy varies as a function of misorientation angle. The simulation was found in good agreement with the calculation on the basis of the dislocation theories in the low angle scale. The low angle grain boundary energy goes up with the increase of misorientation angle and tends to go down after reaching a maximum. An energy cusp exists when the misorientation angle increases further, but in this scale the dislocation theories are invalid for energy calculation due to the strong interaction of the dislocations at the boundaries. The simulation results also indicate that the microstructure of low angle grain boundaries can still be described as dislocations when the misorientation angle is larger than 10°.     

Atomic configurations and diffusion mechanisms near the asymmetric grain boundaries in tetragonal CuAu I alloy with <100 > and <001 > tilt axes

The molecular dynamics method is used to investigate an atomic configuration in the structure of asymmetric tilted grain boundaries for the ordered CuAu I alloy with FCT symmetry and L10 structure. Investigations are performed for three misorientation angles: 7, 16, and 22° and grain boundaries with <100 > and <001 > tilt axes. The distinctive features of the structural grain boundary reorganization and diffusion mechanisms are elucidated at different temperatures.     

Theoretical study of hydrogen absorption near symmetric tilt grain boundaries in Pd and TiFe

The results of calculations of the atomic and electron structure of Pd and TiFe with symmetrical Σ5 tilt grain boundaries obtained using the methods of electron density functional theory are reported. Hydrogen sorption at tilt grain boundaries and corresponding surfaces is considered. It is shown that the hydrogen absorption energy increases in magnitude by ∼0.2 eV at the Pd Σ5(210) grain boundary and by ∼0.5 eV in B2-TiFe with the Σ5(310) grain boundary. The binding energy of hydrogen in palladium, as well as in TiFe, in the most preferred positions at the surface is higher than near grain boundaries. It is found that, as in the case of a defect-free material, the following tendency is observed at a symmetrical tilt grain boundary: the strong bond of the impurity at the grain boundary in the metal or alloy matrix reduces the sorption energy of hydrogen.