Grain Boundary Groove Research Articles

Delayed fracture of ceramics caused by stress-dependent surface reactions

Consider a ceramic in an environment, corroding gradually by a surface reaction. When in addition subject to a mechanical load, the ceramic loses mass preferentially at grain-boundary grooves where stress concentrates, so that atomistically sharp cracks may nucleate. Before becoming a crack, a groove maintains local equilibrium at its root; after, it loses local equilibrium. The crack further propagates by breaking atomic bonds, often assisted by environmental molecules. This paper models the groove-to-crack evolution. The groove changes shape to reduce the free energy due to the combined effects of surface tension, grain-boundary tension, elasticity, and chemical potential difference between the solid and the environment. At any point on the surface, the reaction rate is taken to be proportional to the free energy reduction per unit volume of mass loss. The ceramic body is modeled by a half plane bounded by a curve, whose shape is described by a conformal mapping of many terms, allowing the elastic field in the body to be solved analytically. A variational method leads to a set of ordinary differential equations to evolve the shape. The model predicts threshold loads, and the times required, for crack nucleation.

Sintering in a dry snow cover

The basic shape of bonds in snow is dictated by the geometrical requirements of grain-boundary grooves and is not a simple concave neck as has long been assumed. In fact, all of the earlier work on the theory of sintering in snow was based on an incorrect assumption about the geometry. A theory of the growth of bonds in snow is given here based on observations of their actual shape which is dominated by grain-boundary grooves. The theory describes the growth of the bond by the removal of water molecules from the grain boundary by diffusion due to the stress gradient. Three-dimensional grains are described and the dihedral angle is allowed to increase with time.

Grain-boundary grooves and surface diffusion in polycrystalline alumina measured by atomic force microscope

Grain-boundary grooving was studied on polished surfaces of polycrystalline alumina, after it was annealed at 1370~1600 °C in air. The groove angles and the groove widths were measured by AFM and it was determined that surface diffusion is the dominant mechanism for the mass transport and the ratio of grain-boundary energy to surface energy decreased with increasing temperature. The surface diffusion coefficient calculated was D s = 8.22 × 10 7 × exp[ −577 ± 30(kJ mol −1) RT ] which is the smallest among those reported in the literature.

Morphological transition in Ni/C nanoscale multilayers

Annealing of nanoscale Ni/C multilayers and C/Ni/C trilayers at temperatures above about 670 K leads to the formation of separated Ni particles embedded in carbon. The agglomeration of the Ni layers starts by the formation of holes in the Ni layer and proceeds by hole growth and hole coalescence. Different thermodynamic driving forces and kinetic processes which can affect the observed agglomeration are discussed. The formation of holes by thermal grooving of Ni grain boundaries is analyzed quantitatively.

Capillarity driven motion of solid film wedges

A solid film freshly deposited on a substrate may form a non-equilibrium contact angle with the substrate, and will evolve. This morphological evolution near the contact line is investigated by studying the motion of a solid wedge on a substrate. The contact angle of the wedge changes at time t = 0 from the wedge angle α to the equilibrium contact angle β, and its effects spread into the wedge via capillarity-driven surface diffusion. The film profiles at different times are found to be self-similar, with the length scale increasing at t 1 4 . The self-similar film profile is determined numerically by a shooting method for α and β between 0 and 180°. In general, we find that the film remains a wedge when α = β. For α < β, the film retracts, whereas for α > β, the film extends. For α = 90°, the results describe the growth of grain-boundary grooves for arbitrary dihedral angles. For β = 90°, the solution also applies to a free-standing wedge, and the thin-wedge profiles agree qualitatively with those observed in transmission electron microscope specimens.

Time-Dependent Small-Scale Fracture in Metallic Materials at High Temperatures

This paper deals with time-dependent small-scaleintergranular fracture in metals at high temperatures. First, diffusional cavitation during fatigue isdiscussed in terms of its mechanism. Creep cavitiesand cavity-type cracks nucleate and grow inside thematerial under combined very slow tension and fastcompression cycling at relatively high temperatures,and they are extinguished by the succeeding fatigueunder the inverse cycling of combined fast tension andvery slow compression. Second, small-scale fractureis discussed in terms of its process. Fracture of athin aluminum wire in micro-electronic packages isdemonstrated through a numerical simulation of grainboundary grooving caused by surface and grain boundarydiffusion. Third, cavities and microcracks appearingin polycrystalline steels are discussed in terms ofthe effects of their microstructures. Characterization of multiple microcracking isattempted on the bases of a numerical simulation.

Liquid grooving at grain boundaries

The kinetic dissolution and diffusion regimes of liquid grooving of grain boundaries with zero (or near-zero) dihedral angle at the top are discussed, and their perdominance criteria formulated. A new model of liquid grooving is proposed, according to which the top of the channel propagates in a diffusion regime, while its widening proceeds kinetically. Analytical (for the particular case of low solubility) and numerical solutions are obtained. The linear dimensions (depth and width) of the channel are estimated for the mixed regime.

Grain boundary grooving by surface diffusion: an analytic nonlinear model for a symmetric groove

The fourth-order nonlinear boundary-value problem for the evolution of a single symmetric grain-boundary groove by surface diffusion is modelled analytically. A solution is achieved by partitioning the surface into subintervals delimited by lines of constant slope. Within each subinterval, the advance of the surface is described by an integrable nonlinear evolution equation. The model is capable of incorporating the actual nonlinearity arbitrarily closely. The surface profile is determined for various values of the central groove slope including the limiting case of a groove which has a root that is vertical. Such a solution exists only because of the nonlinearity.

Grain Boundary Grooving as the Mechanism of the Blech Electromigration in Interconnects

AbstractWe present a new approach to understand the mechanism of "homogeneous", or Blech electromigration (EM). This phenomenon describes macroscopically homogeneous displacement of the up-wind edge of thin film lines in microelectronic devices and is responsible for openings at contact windows, "vias" and other sites of perfect diffusion flux divergence.Our SEM, EPMA and EM drift velocity experiments have revealed the gradual transition from the microscopically homogeneous EM displacement to the highly nonhomogeneous mode wherein copious islands of residual material remain behind the drifting cathode edge of aluminum stripes. The transition is shown to occur due to an increase in either the current density, j, or in the stripe length, 1. The latter case suggests, that the transition results from the growth of the net grain boundary (GB) diffusion flux, I=le-Ib ,where Ie∝j and 1b∝1/1 are the EM flux and stress-gradient-driven back flux, respectively.Based upon recent progress in the theory of GB grooving under "external" GB fluxes, with surface diffusion acting as the healing mechanism, grooves' propagation along the line and their merging is considered to be the micromechanism of the "homogeneous" EM. In terms of the simple model described, the transition from the slow receding of the cathode butt edge slightly wrinkled by shallow grooves (A-regime of EM) to the fast extension and merging of slot -like grooves (B-regime) accounts for the transition observed in EM mode, while in both regimes the EM displacement velocity, V, is presumed to represent the groove propagation rate.The theory developed reduces to Blech formulae for V for the truly homogeneous A-regime and predicts quite different EM kinetics for the B-regime of microscopically nonhomogeneous EM. The latter is expected to dominate for films loaded by high current density with large grains and low surface diffusion.The dependence obtained for the residual mass left behind the drifted edge vs the displacement velocity, V, for unpassivated aluminum stripes of various lengths, loaded by j=2-106 A/cm2 at 548K provides a good evidence in support of a new approach.

Numerical simulation of grain-boundary grooving by surface diffusion

A numerical investigation of grain-boundary grooving by surface diffusion has been carried out. The surface diffusion is driven by surface curvature gradients, and a fixed dihedral angle is assumed at the groove tip. The corresponding mathematical system is an initial boundary value problem in a one-dimensional nonlinear partial differential equation. The numerical results show excellent agreement with Mullins' analytical “small slope” (i.e. dihedral angle close to 180 °) solution of the linearized mathematical system. Our simulation extends Mullins' solution, since it is applicable to larger groove widths and a complete range of dihedral angles. As an example, we apply our technique to two adjacent grooves. The evolution of the surface profile shows clearly that the two grooves grow initially independently, while they interact at a later stage, resulting in changes in their growth kinetics.

Groove Angles and Surface Mass Transport in Polycrystalline Alumina

Grain‐boundary grooving was studied on polished surfaces of polycrystalline alumina, after annealing, in air, under vacuum, and in argon atmospheres in the temperature range 1273 to 1736 K. The groove angles, measured by optical interferometry, showed no significant change with experimental conditions, giving a mean value of 138.57°± 0.08° and a ratio of the grain‐boundary energy to surface energy of 0.707 ± 0.001. From the experiments it was determined that surface diffusion was the dominant mechanism for the mass transport. The surface diffusion coefficient, Ds(cm2/s) = 0.48 exp(−256(kJ/mol)/RT), was practically independent of the furnace atmosphere, and, in the low‐temperature region examined, depended on the structural damage in the near‐surface region which occurred during mechanical polishing.

Real time electron microscopy inspection of high temperature processes in W free standing wires

High temperature structural changes in a W wire are studied in situ by scanning electron microscopy. This is made possible by the microscopic size of the wire. Grain-boundary grooving and faceting are observed in real time. The constriction exhibits a strong thermal gradient (∼100 K μm−1) which is the driving force for the migration mechanisms responsible for the observed phenomena.

Pore removal during diffusion bonding of Nb[sbnd]Al2O3 interfaces

Results from a brief study of pore removal during diffusion bonding of interfaces between Nb and Al2O3 are presented. Sequential observations of the evolution of interface microstructure during the later stages of diffusion bonding indicates that pore removal occurs by the growth of bonding fronts in particular crystallographic directions dependent on the orientation of Nb, but not on that of the Al2O3. Bonding fronts meet, resulting in cylindrical voids which then breakup into uniformly distributed spherical voids. Characterization of the breakup suggests that the process is volume diffusion controlled. Finally, the effect of thermal grooving of Nb grain boundaries on mass transport during diffusion bonding is discussed.

Dihedral Angles in Magnesia and Alumina: Distributions from Surface Thermal Grooves

Dihedral angles, Ψs, from surface thermal grooves were measured using a metal reference line technique for polycrystalline MgO, undoped Al2O3, and MgO‐doped Al2O3. The values of Ψs span the following ranges: 89° to 116° for MgO at 1520 K, 76° to 166° for undoped Al2O3 at 1870 K, and 90° to 139° for MgO‐doped Al2O3 at 1870 K. For all three systems, the median Ψs values are 105° to 113°, implying that the median γgb/γs is 1.1 to 1.2, in contrast to metals where γgb/γs ranges typically from 1/4 to 1/2. The widths in Ψs distributions were different for the three materials with the width increasing in the following order: MgO, MgO‐doped Al2O3, undoped Al2O3. For all three materials, the grainboundary grooves and their corresponding Ψs were not symmetrical with respect to the surface normal. The asymmetry for MgO was due to the pinning of the grain boundaries by the surface thermal grooves. The range of inclination angles of the grain boundary to the surface was a function of Ψs, with the maximum inclination angles of ∼13°, in quantitative agreement with theory.

Metal Reference Line Technique for Obtaining Dihedral Angles from Surface Thermal Grooves

A metal reference line (MRL) technique is described for the measurement of surface–grain‐boundary dihedral angles, Ψs, from thermal grooves at a sample surface using scanning electron microscopy (SEM). Metal lines deposited onto a thermally grooved surface using photolithography conform to the contours of the grain‐boundary groove and provide a high‐contrast reference line for measuring Ψs by SEM. Measurements of Ψs from optical interferometry and calculated from groove dimensions using surface diffusion models of thermal grooving are compared with the metal reference line measurements from the same thermally grooved surface of MgO‐doped Al2O3. Distributions of Ψs are found to shift to lower angles and approach the true Ψs value as the resolution of the technique increases, with the MRL technique having the highest resolution, a median angle of 113°± 1° and a distribution of angles from 90°± 5° to 139°± 3°.

Surface diffusion in CaTiO3

The surface diffusion of CaTiO3 was examined using grain-boundary grooving. Measurements of groove widths were taken over the temperature range 1200 to 1 500° C on dense, sintered polycrystalline samples. A new approach for measuring groove widths on polycrystalline samples is described. For the temperature range from 1200 to 1350° C grooving was found to proceed by a surface diffusion mechanism. The activation energy for surface diffusion of CaTiO3 is 330±30 kJ mol−1. At 1450° C and above, grooving occurs by a volume diffusion mechanism.

Surface growth topography of grain boundaries in Al thin films

Surface growth topography of grain boundary (GB) areas has been studied on aluminium films deposited at 570 K on mica, NaCl and glass substrates at different levels of oxygen contamination. Broad and deep GB grooves decorated by secondary nuclei were found in highly contaminated films, while hills bordered by pinned growth steps were present at very low oxygen contamination in films deposited on NaCl. Hills were observed at all types of [III] tilt boundaries independent on their azimuthal orientations. A model has been proposed for the interpretation of the development of GB grooves and hills. The model was based on the processes of monolayer crystal growth controlled by the purity of GBs. Pure GBs can be active in the nucleation of monolayers growing the crystals, while contaminated GBs are adsorption sites where impurity species are preferentially segregated and incorporated. Transmission electron microscopy of Pt shadowed films was used to study the GB displacements taking place in high purity films.

Effect of diffusivity variation on capillarity and electromigration-induced surface and grain boundary diffusion

The authors present a detailed analysis of capillarity effect in the presence of surface diffusivity variation and use this as a basis to describe evolution of the surface profiles generated by the electromigration-induced surface and grain boundary (GB) diffusion in a bicrystal film. Thermal GB grooving is asymmetric in the presence of diffusivity variation across the GB, but the extent of asymmetry is rather significant, less than 0.14% from the symmetric case, but up to 60% in diffusivity variation considered. Surface profiles of the electromigration-induced surface and GB diffusion for the samples with and without prior heat treatments have been carefully analysed and compared. The surface morphological changes can be understood in terms of the combined action of the following effects: (i) Dynamic balance between the surface tension and the GB tension incorporation with surface diffusivity variation across the GB generates further disparity in the profile changes. The effect lasts as long as the sample is under power stressing. (ii) The non-vanishing surface flux divergence with the GB acting either as a sink or source of the flux contributes dominantly to the GB disfiguration. (iii) Four additional transient terms originating from the capillarity effect aggravate the surface profile changes in the early stage of electromigration, causing surface undulation and so on, but gradually, the effect is overshadowed. Electromigration damages are mainly dictated by a quantity M which in turn is determined by the interplay between the GB flux and the surface diffusivity variation. With a negative M the profile starts with a sharp cusp which in time turns obtuse, then the minimum moves downstream into the grain. When M is positive, the GB profiles change rapidly with a small increase in M and in power stressing time. The profiles contract and protrude like a mound, and quickly rise above the x axis. Beyond this point, the shape of the surface morphology becomes relatively unchanged. Furthermore, when two or more GB diffusions are activated simultaneously, the superpositional effect of the GB fluxes may lead to trapezoidal growth and/or faceted voids, among other types of profiles. Finally, the problems with respect to further quantification of the quantity M are briefly discussed.

The identification of thin amorphous films at grain-boundaries in Al2O3

The presence of amorphous grain-boundary phases in ceramic materials can significantly influence their properties. Such grain-boundary films can be identified by the dark-field diffuse scattering technique, the Fresnel fringe technique, and analytical electron microscopy (energy-dispersive spectroscopy). However, spectrum artefacts can present major problems for the use of such techniques. Specifically, grain-boundary grooving, surface damage of the specimen and silicon contamination are shown experimentally to arise from ion-milling during the preparation of TEM specimens. It is experimentally shown that, with the above techniques, these artefacts can cause grain-boundaries in commercial alumina specimens to appear to contain glassy phases. The ambiguity in interpreting the results from the use of each of these techniques is discussed in detail.

Evaluation of surface-diffusion coefficients from grain-boundary grooving data on Mo, Mo—Re, and Cr

AbstractThe grain-boundary grooving (GBG) technique has been widely used to obtain surface-diffusion coefficients of metals since this method offers great experimental simplicity in companson to methods such as sinusoidal profile decay. However, the evaluation of grain-boundary groove data has always posed a problem: in many cases, it is found that the same experimental data can be analysed to obtain values for Ds or Dv by assuming only one of the two diffusion mechanisms to be solely responsible for matter transport. The values of Ds and Dv thus obtained are in good agreement with those determined by other techniques. Some workers have used parameters such as the ratio of groove height to groove depth as criteria to determine the predominant transport mechanisms. However, it has been shown by Robertson that the height/depth ratio for grooving under surface-diffusion conditions can approach that for volume-diffusion conditions if the slope of the groove at the root is large. Therefore, such parameters can...