The relation between the distribution of dihedral angles and the wetting angle during liquid phase sintering

This study presents a Monte Carlo method to simulate the effect of the wetting angle on a dihedral angle distribution and on a degree of the grain boundary penetration of a liquid phase during liquid phase sintering. For the high probability for wetting, the number of the grain boundary penetration of a liquid phase increased while the wetting angle decreased and a few bonded grains maintained a stable grain boundary with high dihedral angles. This finding contradicts the classical prediction that smaller values of mean dihedral angles produce superior wettability.     

The Fascination of Grain Boundary Grooves

An investigation of the topography of grain boundary thermal grooves in Ni‐rich NiAl by atomic force microscopy is presented. The authors demonstrate how the shape of the grooves is modified by grain boundary sliding and surface faceting and develop a quantitative theory of grain boundary grooving that takes into account the above complications. The great potential of grooving studies for the analysis of microstructure evolution is emphasized.     

The fascination of grain boundary grooves

Abstract

Studies of the topography of grain boundary thermal grooves in nickel rich NiAl by atomic force microscopy are reported. It is demonstrated how the processes of grain boundary sliding and surface faceting modify the shape of the grooves. A quantitative theory of grain boundary grooving that takes into account the above complications is developed. A high potential of grooving studies for the analysis of microstructure evolution is demonstrated.     

Temperature-dependent surface diffusion near a grain boundary

Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain–grain–fluid triple intersection, involve a prescribed slope at the groove axis. The well-known similarity reduction is no longer valid when the dihedral angle and surface diffusivity depend on time due to variation of the surface temperature. We adapt a nonlinear fourth-order model that can be discerned from symmetry analysis to be integrable, equivalent to the fourth-order linear diffusion equation. The connection between classical symmetries and separation of variables allows us to develop the correction to the self-similar approximation as a power series in a time-like variable.     

Grain boundary grooving in molybdenum bicrystals

The morphologies of grain boundary grooves formed after annealing of three Mo bicrystals at the temperature close to the melting point were studied with the aid of scanning force microscopy. The ratio of grain boundary to surface energy was calculated from the surface slopes measured at the root of the groove. This ratio was about 0.3 for the grain boundary grooves with the sharp roots, and it was significantly lower than 0.3 for the grooves with the blunted roots. It was shown that the blunting of the root of the grain boundary grooves is associated with the grain boundary migration during annealing. A model of grain boundary grooving accompanied by the instantaneous boundary shift was formulated. The surface topographies predicted by the model were in a good agreement with the experimentally measured ones. It was shown that grain boundary grooving process can be completely suppressed at the singular surfaces. This, together with the grain boundary migration during annealing results in characteristic groove morphology with the blunted root and leads to a significant underestimation of the grain boundary energy calculated from surface slopes.     

Void growth in thin silver films

A high density of small voids was observed in thin films of silver on examination with a high resolution transmission electron microscope. Void growth was studied in these films by annealing them in a vacuum as well as in the electron microscope using a specimen heating stage. Heating of the films to 700°C led to thermal grooving at the grain boundaries and finally to grain separation. It appears that the void growth occurs essentially as a result of annihilation of excess vacancies trapped in the film. The observed phenomena of thermal grooving and grain separation can be explained in terms of surface diffusion of silver atoms.     

On the role of indium underlays in the prevention of thermal grooving in thin gold films

Thin gold films are potentially important for metallizations in microelectronic devices because of the high activation energy of gold for electrotransport. A high activation energy ensures a longer lifetime of microelectronic devices compared with those in which aluminum metallizations are used. When electromigration is no longer the principal failure mechanism, other failure mechanisms, caused by d.c. stressing, might become important. One possibility is grain boundary grooving. Preliminary studies have shown that grain boundary grooving in thin gold films is prevented by inserting an indium underlay between the gold film and the substrate. The objective of this work was to investigate the mechanisms for the prevention of grain boundary grooving in In/Au composite films by comparing the microstructural evolution of pure gold films with In/Au composite films during isothermal annealing. Microstructures were characterized in terms of grain size, grain size distribution, preferred orientation and surface morphology utilizing transmission electron microscopy (TEM), cross-sectional TEM, scanning electron microscopy and X-ray diffraction. The chemical reactions and the distributions of the phases were monitored by selected area diffraction in TEM, and by Auger electron spectroscopy sputter profiling.It was found that the principal mechanisms that inhibit grain boundary grooving in IN/Au composite films area as follows.

• 1.(1) Indium underlays modify the microstructure of gold films by randomizing the orientation of the grains, refining the grain size, narrowing the grain size distribution and roughening the surface of the gold films.
• 2.(2) Indium is redistributed on gold films and forms In₂O₃ on the free surface and within the film during air annealing.
• 3.(3) The In₂O₃ on the surface “caps” the surface of gold films and limits mass transport during annealing.
• 4.(4) The In₂O₃ within the gold film, presumably residing at grain boundaries, impedes grain growth by pinning the grain boundary migration.

     

Finite element analysis for surface diffusion-controlled shape instabilities of plate-like grains

Based on classical theory of surface diffusion and evaporation–condensation, a finite element program is developed to simulate the unstable shape evolution of plate-like grains. The program is used to analyze thermal grooving on a polycrystalline surface and compared with a non-linear solution and finite difference analysis. It shows that the finite element method used is robust, accurate and efficient. Then, the shape evolution kinetics of the plate-like grains are simulated as a function of the thermal grooving angle θ at the grain boundary–surface junctions and the initial aspect ratio of the plate β (plate width to thickness). When θ=0 (without internal boundary), the plate-like grain will evolve into cylinders directly. When an internal boundary exists, there is a critical thermal grooving angle θ_min for given β. If θ<θ_min, the plate cannot split, otherwise, the plate will split along the internal boundary of the plate-like grain. An approximate formulation of θ_min as a function of β is given based on a number of finite element analyses. The effect of initial termination shape of the plate on θ_min is also examined, and a weak effect was found. When β>10, its effect can be neglected.     

The grain boundary geometry for optimum resistance to growth of short fatigue cracks in high strength Al-alloys

In this paper, recent work on the effects of micro-texture on the growth behavior of short fatigue cracks in high strength aluminum alloys (such as Al-Li 8090 alloys and AA 2026 Al alloys) was first reviewed. The twist and tilt angles of crack plane deflection at a grain boundary were identified as the key factors that controlled the growth of a short fatigue crack across the grain boundary in these alloys. A large twist angle of the crack plane deflection at the grain boundary gave rise to a higher resistance to crack growth across the grain boundary, while a small twist angle represented a smaller resistance.The possible smallest twist angle of crack deflection at a boundary between a grain with a typical orientation (such as brass and goss orientations) and a randomly orientated grain was calculated and mapped in Euler space. The orientation of the neighboring grain that showed high resistance to crack growth was identified as a peak in these twist angle plots. The theoretical results were consistent with the results obtained from studies of short crack growth in AA 8090 and AA 2026 Al alloys. The results from this work paved the way to quantification of the texture effects on early growth of fatigue cracks in planar slip alloys.     

Characterisation of fine-grained oxide ceramics

A range of high resolution techniques have been used to characterise the grain boundary segregation behaviour of rare earth (RE) doped (La, Gd, Eu and Yb) alumina and spinel. TEM based techniques (HR-TEM, HAADF STEM and EDS) have been used to study the structure and chemistry of grain boundaries. The use of a HAADF detector in STEM provides atomic number contrast and easy identification of heavy (RE) segregants. This has been used to produce high resolution RE elemental maps, showing the width of the segregated region to be less than the size of the electron probe (1 nm) for all boundaries studied. EDS showed that within a 1 nm thick boundary region (an upper limit) the RE cations would account for 10 (±2)% and 15 (±2)% of the cation total in alumina and spinel respectively. Preliminary results from ultra-high resolution STEM (probe size 0.1 nm) suggest that, in spinel, the segregated region is actually composed of a much thinner continuous monolayer of RE atoms at the grain boundary. This is consistent with HR-TEM, which showed spinel grain boundaries possessed minimal grain boundary structural disorder.AFM has been used to study the effect of RE grain boundary segregation on thermal grooving behaviour. The improvement in resolution that is achieved by operating in Tapping mode is shown to translate into an improved profile of the groove root. This has been used in conjunction with Electron Backscattered Diffraction (EBSD) to examine the relationship between grain boundary geometry and misorientation. The addition of RE dopants to alumina was found to significantly increase the size of grain boundary grooves. This can be attributed to the out-diffusion of RE segregants, an effect which compromises grain boundary energy calculations for materials with grain boundary segregation. AFM and EBSD are also used to relate anisotropic tribo-chemical polishing-wear with grain orientation.     

A stereoscopic method for dihedral angle measurement

A new method is presented for the measurement of equilibrium dihedral angles in intergranular inclusions, and illustrated with pure copper containing 1 wt% lead. The method is based on the selective dissolution of inclusions visible along a polished metallographic section. Scanning electron microscopy stereo image pairs are then taken and processed so as to enable a three-dimensional digital reconstruction of the inclusion/matrix interface along each inclusion. Spherical caps describing the Cu/Pb interface over non-facetted orientations are then fitted to the measured digital inclusion envelope reconstructions. Knowing the center and radius of these spheres, the true dihedral angle of each specific inclusion can then be deduced with good precision.It is found that the true dihedral angle in the Cu/Pb alloy is not a unique function of temperature, reflecting the (known) anisotropy of high-angle grain boundary energy in copper.     

Advancing nanograined/ultrafine-grained structures for metal implant technology: Interplay between grooving of nano/ultrafine grains and cellular response

Nanograined/ultrafine-grained (NG/UFG) metals provide surfaces that are different from conventional coarse-grained polycrystalline metals because of the high fraction of grain boundaries. In the context of osseointegration of metal implants, grooving of nanograins/ultrafine grains by electrochemical grooving is a potential approach to increase the biomechanical interlocking and anchorage with consequent enhancement of cellular response. The primary objective of the research described here is to advance science and technology of metal implants by making a relative comparison of osteoblast response of grain boundary grooved and planar NG/UFG surfaces. The NG/UFG substrates were obtained using an ingenious concept of controlled phase reversion and the grain boundaries were electrochemically treated to induce grooving of large fraction of grain boundaries of NG/UFG substrate. Experiments on the effect of grooving of grain boundaries of NG/UFG metal indicated that cell attachment, proliferation, viability, morphology, and spread are favorably modulated and significantly different from planar (non-grooved) NG/UFG substrates. Furthermore, immunofluorescence studies demonstrated stronger vinculin signals associated with actin stress fibers in the outer regions of the cells and cellular extensions on electrochemically grooved NG/UFG substrate. These observations are indicative of accelerated response of cell–substrate interaction and activity. The differences in the cellular response of planar and grain boundary grooved NG/UFG surface are attributed to favorable surface topography that accelerates the cellular activity.     

Fractal pattern formation in thermal grooving at grain boundaries in Ag films on Si(111) surfaces

Growth of Ag films on Br- and H-passivated Si(111) surfaces and the annealing behaviour have been investigated by Rutherford backscattering spectrometry, scanning electron microscopy and photoemission electron microscopy techniques. Upon annealing the phenomenon of thermal grooving was observed in the Ag films. Depending on the annealing temperature, at an intermediate annealing time Ag depletion (evaporation) from the grain boundaries produces fractal patterns of Ag-depleted regions. Continued annealing eventually produces a percolated network of Ag-depleted regions (thermal grooves) along the grain boundaries and isolated Ag grains appear as the depth of the grooves reaches the substrate. For the fractal structures produced by thermal grooving, the fractal dimension has been estimated to be 1.60 ± 0.04. Observation of a fractal pattern in thermal grooving was not hitherto reported. A thorough analysis of the experimental results has been carried out in the context of current theories. These theories are inadequate to describe the experimental results.     

Stress relaxation of thin film due to coupled surface and grain boundary diffusion

A numerical scheme, based on an energy statement, is developed to simulate thin film morphology evolution and stress relaxation due to concurrent surface diffusion and grain boundary diffusion. Different from previously published works, this paper also explores the effects of mobility ratio of the two processes and the dihedral angle at the surface-grain boundary triple junction. The range of mobility ratio, in which the stress relaxation process is limited by either surface diffusion or grain boundary diffusion, is determined. It is found that, when the stress relaxation is limited by the rate of surface diffusion, the dihedral angle at the surface-grain boundary junction plays a significant role. A scheme of using both experimental and numerical results to determine grain boundary diffusivity is also presented. As an example, we obtain the activation energy and diffusivity for grain boundary diffusion in Cu thin film.     

Microstructural evolution and its influence on the impact toughness of GH984G alloy during long-term thermal exposure

The microstructure evolution and its effect on the impact toughness of a new Ni-Fe based alloy GH984 G,used in 700℃ ultra-super critical coal-fired power plant,were investigated during thermal exposure at 650℃-750℃ for up to 10,000 h.The results show that the impact toughness at room tempe rature drops rapidly at the early stage during thermal exposure at 700℃ and then has no significant change even if after exposure for 10,000 h.The significant decline of the impact toughness is attributed to the coarsening of M₂₃C₆ carbides at grain boundaries,which weakens the grain boundary strength and leads to the aging-induced grain boundary embrittlement.The M₂₃C₆ carbides have almost no change with further thermal exposure and the impact toughness also remains stable.Additionally,the impact toughness rises with the increase of thermal exposure temperature.The size of γ' after thermal exposure at 750℃ for10,000 h is much bigger than that at 650℃ and 700℃ for 10,000 h.There fore,the intragranular strength decreases significantly due to the transformation of the interaction between γ' and dislocation from stro ngly coupled dislocation shearing to Orowan bowing.More plastic deformation occurs within grains after thermal exposure at 750℃ for 10,000 h,which increases the impact toughness.     

Annealing,flux divergence and surface morphology

Mullins' thermal grooving analysis has been extended to cases where there is a ridge or notch. Annealing may blunt the ridge and shallow the notch under appropriate conditions. A quantity M which is held to be responsible for non-vanishing flux divergence, i.e.?·J ≠ 0, in thin film metallization in electromigration has been positively identified. Since the quantity M will never vanish unless the film is a single crystal, electromigration is expected to be operative at all current levels. The grain boundary grooving of the electromigration origin is shown to dominate the failure processes and the changes in surface morphology.     

Multiaxial behavior of ferroelectric single and polycrystals with pressure dependent boundary effects

The external electric and mechanical fields applied at angles to the initial poled direction of the ferroelectric ceramics produce a significantly different nonlinear behavior to that of external fields applied parallel to the poling direction. This angle dependent response of ferroelectric single and polycrystals are predicted by the model proposed based on irreversible thermodynamics and physics of domain switching. The dissipation associated with boundary constraints in thin ferroelectric single crystals are incorporated in the model. As well, the pressure dependent constraints imposed by the surrounding grains on the grain of interest at its boundary during domain switching is correlated with the resistance experienced by a ferroelectric single crystal on its boundary during domain switching. Taking all the domain switching possibilities, the volume fractions of each of the variants in a grain are tracked and homogenized for macroscopic behavior. Numerical simulations were carried out for the multiaxial behavior of ferroelectric single and polycrystals under electrical, mechanical and electromechanical loading conditions.     

In-situ TEM observations of abnormal grain growth, coarsening, and substrate de-wetting in nanocrystalline Ag thin films

Abnormal grain growth is studied in nanocrystalline sputtered Ag films. Eighty nanometer thick Ag films are DC sputter deposited onto back-etched amorphous silicon nitride membranes. Specimens are annealed in a heating stage in an in-situ TEM for various temperatures and hold times. With the same specimen, we proceed to higher temperatures after the apparent halt of growth for sufficiently long hold times. The grain size distribution of the as-deposited films is bi-modal, with large abnormal grains with 100 nm diameters, embedded in a matrix of smaller grains of 15 nm diameters. Coarsening begins at temperatures of approximately 100°C, and quickly reaches a plateau. The growth process restarts only after sufficient temperature increases, and plateaus at each succeeding temperature. Using a variation of the Mullins–Von Neumann law, the activation energy for the abnormal growth is found to be 0.274 eV, consistent with the value reported for pore formation during electromigration via surface diffusion in Ag. Grain growth appears to stop above temperatures of 350°C, eventually leading to triple junction pore formation at 350°C and de-wetting of the film from the substrate at 600°C. The de-wetting is the high temperature limit of the thermal grooving which cancels the driving force for grain growth at the lower temperatures. TEM images as evidence of this effect are presented, along with observations on the pore formation that support surface diffusion as the mass transport mechanism for grooving, pore fomation, and as the limiting mass transport mechanism for the grain growth.     

Accelerated precipitation behavior of cast Mg-Al-Zn alloy by grain refinement

This study demonstrates that the precipitation behavior of β-Mg₁₇Al₁₂ phase during aging and the resultant variation in hardness and mechanical properties of cast Mg-Al-Zn alloy are strongly dependent on initial grain size. Grain size reduction accelerates discontinuous precipitation at the early stage of aging treatment by increasing the area fraction of grain boundaries that can act as nucleation sites for discontinuous precipitates (DP), but it does not influence DP growth rate. Grain refinement also prematurely terminates continuous precipitation because the formation of a large number of DP reduces the amount of Al dissolved in the matrix, which is required for the formation of continuous precipitates (CP). This promotion of DP formation and early termination of CP formation significantly decrease the peak-aging time to one-third. The enhanced precipitation behavior also leads to an additional hardness improvement in the aged alloy, along with an increase in hardness owing to grain boundary strengthening by grain refinement. The amount of increase in hardness changes with aging time, which is determined by the variation of three variables with aging time: DP fraction difference between refined and nonrefined alloys, hardness difference between DP and matrix, and matrix hardness difference between the two alloys. Grain refinement improves both tensile strength and ductility of the homogenized alloy owing to grain boundary strengthening and suppression of twinning activation, respectively. However, the loss of ductility after peak-aging treatment is greater in the refined alloy because of the larger amount of DP acting as a crack source in this alloy.     

Evolution of tin whiskers and subsiding grains in thermal cycling

The evolution of surface morphology, including whisker formation, grain boundary cracking, and subsiding grains, was studied in Sn thin films on Si substrates with a Cu interlayer during thermal cycling from ?40 to 85 °C in air for up to 250 cycles and was compared with surface morphologies resulting from room temperature aging. Multiple areas were tracked, and the areal density of whiskers and the grain morphologies within these areas were monitored over time for room temperature aging and with increasing number of thermal cycles. During room temperature aging, the whisker density increased with time until saturation ~3 weeks after plating. As for thermal cycling, the whisker density was observed first to increase but then to decrease as a result of a whisker pinch-off phenomenon. The characteristic features of whiskers formed during thermal cycling included the formation of deep grooves along the in-plane grain boundaries of whiskers (“whisker root”), a decrease in whisker radii as they grew, striation rings on whiskers perpendicular to the whisker growth direction, corresponding striations along grooved surfaces in the film, albeit at different spatial periodicities than those on their corresponding whiskers, and whisker pinch-off as whiskers became prone to fracture as their radii decreased. Whiskers formed during room temperature aging did not display such grooving or pinch-off. A whisker pinch-off model was proposed to explain the observed morphological changes and the resulting decrease in whisker density during thermal cycling, with a calculated whisker growth rate that agrees with the experimental observation.