R. M. Cannon

Toughening of brittle solids by martensitic transformations

A review of toughening mechanisms in transformable brittle solids is presented. Primary emphasis is given to transformation toughening, although microcrack and deflection toughening are also considered. Models of toughness are developed using concepts from applied mechanics, but within the context of the thermodynamics and kinetics of the transformation process. The predictions are compared with experimental data for various ZrO/sub 2/ containing ceramic alloys. The predominant toughening mechanism depends on composition and microstructure; dilatational transformation toughening with shear modifications dominates in partially stabilized zirconia; uniaxial transformation and microcrack mechanisms prevail in zirconia alumina; transformation toughening with partial reversibility in tetragonal zirconia polycrystals.

VISCOELASTIC STRESSES AND SINTERING DAMAGE IN HETEROGENEOUS POWDER COMPACTS

Abstract A method for calculating viscoelastic stresses that develop around heterogeneities during sintering is developed. The method uses constitutive laws derived from experimental data obtained on porous, partially sintered bodies. Analysis of stresses using literature data for A1 2 O 3 reveal that the stresses around heterogeneities vary appreciably with density, particle size and temperature. The largest stresses occur in association with hard agglomerates.

Ridging effects on wetting and spreading of liquids on solids

Analysis of the triple junction for a liquid on a solid has emphasized conditions pertinent for metal and ceramic systems. Complementary experiments are largely for liquid metals on Al2O3 and also liquid silicates on metals. Ridges can form at the triple line in response to the vertical component of force from surface tension. These are very small elastic distortions at lower temperatures. Where any local diffusion or solution-precipitation of the solid in the liquid can occur, the ridge can exceed atomic dimensions readily, and at high temperatures can become microns in size. If the liquid front stays attached, drag from these ridges can limit the spreading velocity of the liquid. Four time regimes of interest are identified. First, at short times or low temperatures, inelastic ridges do not form and motion can be controlled by viscous flow of the fluid. In regime II, a small ridge can be carried by the front, whilst the macroscopic angle can simultaneously approach that from the Young-Dupre relationship. Owing to the existence of this latter regime, a range of conditions exists wherein it is possible to satisfy the classical Young equation macroscopically, and a more complete equilibrium locally. Finally, at longer times more complex geometries will prevail while the system is evolving toward equilibrium, regime IV, which entails significantly deforming the solid.

Reactive spreading: adsorption, ridging and compound formation

Reactive spreading, in which a chemically active element is added to promote wetting of noble metals on nonmetallic materials, is evaluated. Theories for the energetics and kinetics of the necessary steps involved in spreading are outlined and compared to the steps in compound formation that typically accompany reactive wetting. These include: fluid flow, active metal adsorption, including nonequilibrium effects, and triple line ridging. All of these can be faster than compound nucleation under certain conditions. Analysis and assessment of recently reported experiments on metal/ceramic systems lead to a focus on those conditions under which spreading proceeds ahead of the actual formation of a new phase at the interface. This scenario may be more typical than believed, and perhaps the most effective situation leading to enhanced spreading. A rationale for the pervasive variability and hysteresis observed during high temperature wetting also emerges.

Space charge, elastic field, and dipole contributions to equilibrium solute segregation at interfaces

The interaction potentials between solute ions and grain boundaries in ionic solids are identified as (1) the electrostatic interaction between the charged solutes and grain boundaries, (2) the elastic energy due to the size misfit of solutes in the matrix, and (3) the dipole interactions between the solute‐vacancy dipoles and the electric field in the grain‐boundary region. We include these interaction potentials to evaluate the minimum free energy and the equilibrium solute and defect distributions in the grain‐boundary region. Numerical calculations show that these interaction mechanisms, either acting individually or coupling with each other, lead to a nonuniform solute distribution near the grain boundary. Under certain conditions, both the elastic and dipole interactions can significantly modify the electrostatic potential near the boundary. Calculations also show that the grain‐boundary segregation of an aliovalent solute can be induced or altered by another aliovalent solute of different size misf...

Overview no. 48: Toughening of brittle solids by martensitic transformations

A review of toughening mechanisms in transformable brittle solids is presented. Primary emphasis is given to transformation toughening, although microcrack and deflection toughening are also considered. Models of toughness are developed using concepts from applied mechanics, but within the context of the thermodynamics and kinetics of the transformation process. The predictions are compared with experimental data for various ZrO/sub 2/ containing ceramic alloys. The predominant toughening mechanism depends on composition and microstructure; dilatational transformation toughening with shear modifications dominates in partially stabilized zirconia; uniaxial transformation and microcrack mechanisms prevail in zirconia alumina; transformation toughening with partial reversibility in tetragonal zirconia polycrystals.

Energetics and atomic transport at liquid metal/Al2O3 interfaces

Abstract The objective is to study interfacial mass transport mechanisms and to estimate interfacial energies for metal/Al2O3 systems. Experiments have been performed with molten drops of Ni, Cu, or Au on pure, polycrystalline alumina at oxygen partial pressures for which no adsorption is expected and with Al to determine the effect of extremely low p(O2). After removing the metal drops, grain boundary grooves at the interface and oxide surface have been analyzed using AFM and SEM. Several sources of error are assessed, and corrections are proposed for large systematic errors that occur for root angles. These experiments yield higher grain boundary energies and lower M/Al2O3 interfacial energies than previously reported. Transport rates near the metal/ceramic interface are two to four orders of magnitude faster than on the oxide surface and the results suggest that diffusion through the liquid metal is usually the main atomic transport mechanism. Experiments with Al indicate that, at the far lower oxygen activities, transport is faster at both the interface and alumina surface and that the interfaces are more anisotropic and have lower energy.

COMPOSITION AND CHEMICAL WIDTH OF ULTRATHIN AMORPHOUS FILMS AT GRAIN BOUNDARIES IN SILICON NITRIDE

Two different electron energy loss spectroscopy (EELS) quantitative analytical methods for obtaining complete compositions from interface regions are applied to ultrathin oxide-based amorphous grain boundary (GB) films of ∼ 1 nm thickness in high-purity HIPed Si 3 N 4 ceramics. The first method, 1, is a quantification of the segregation excess at interfaces for all the elements, including the bulk constituents such as silicon and nitrogen; this yields a GB film composition of SiN 0.49±1.4 O 1.02±0.42 when combined with the average film thickness from high resolution electron microscopy (HREM). The second method, II, is based on an EELS near-edge structure (ELNES) analysis of the Si– L 2,3 edge of thin GB films which permits a subtraction procedure that yields a completeEELS spectrum, e.g., that also includes the O– K and N– K edges, explicitly for the GB film. From analysis of these spectra, the film composition is directly obtained as SiN 0.63±0.19 O 1.44±0.33 , close to the one obtained by the first method but with much better statistical quality. The improved quality results from the fewer assumptions made in method II; while in method I uniform thickness and illumination condition have to beassumed, and correction of such effects yields an extra systematic error. Method II is convenient as it does not depend on the film thickness detected by HREM, nor suffer from material lost by preferential thinning at the GB. In addition, a chemical width for these films can be deduced as 1.33 ± 0.25 nm, that depends on an estimation of film density based on its composition. Such a chemical width is in good agreement with the structural thickness determined by HREM, with a small difference that is probably due to the different way in which these techniques probe the GB film. The GB film compositions are both nonstoichiometric, but in an opposite sense, this discrepancy is probably due to different ways of treating the surface oxidation layers in both methods.

Full spectral calculation of non-retarded Hamaker constants for ceramic systems from interband transition strengths

Abstract The van der Waals (vdW) interaction is one of the key terms in the force balances dictating wetting behavior and intergranular film thicknesses. The characteristics of thin intergranular or surficial glass films are of increasing importance due to their role in determining the properties of polycrystalline ceramics. The Hamaker constant scales the London dispersion force part of the vdW interaction for a particular configuration of grains and films and is a direct function of the interband optical properties of the interatomic bonds of the materials. For ceramics, much previous work focused on simplified models, such as the Tabor-Winterton approximation (TWA), to determine Hamaker constants based on refractive indices. Herein we develop full spectral calculations of the Hamaker constants for various ceramic systems using experimentally determined interband transition strengths (ĵcv(ω)) to directly derive the London dispersion spectra (e2(ξ)) from which spectral difference functions lead to direct determination of the Hamaker constants. The results affirm the expectation that transitions involving valence electrons provide the predominant contribution to the dispersion forces for the compounds examined. Calculations have been done for the planar case of a gap between two semi-infinite bodies containing either vacuum or an intervening glassy layer. The results indicate that the TWA is useful for oxides with relatively low refractive indices, i.e., n ~ 1.4–;1.8. However, when any of the materials have larger indices, this approximation becomes inexact, and no obvious, simple correction to the TWA gives uniformly good results, as the behavior differs for simple covalent materials and for oxides with partially filled d-shells but having similar refractive indices. An important consequence is that Hamaker constants are smaller for such high index materials, especially oxides, with intervening glassy films than might be expected from approximations. Calculations have also been done for two other geometries, i.e., for an intervening film with a layer of a third material at both interfaces and for glass coated free surfaces. The former of these provides first insights regarding the behavior with nonuniform films which often differs markedly from that expected for homogeneous films of the same average composition.

CERAMIC/METAL INTERFACIAL CRACK GROWTH: TOUGHENING BY CONTROLLED MICROCRACKS AND INTERFACIAL GEOMETRIES

Toughening of ceramic/metal interfaces through the use of controlled interfacial geometries and non-coplanar microcrack-like pores is examined with respect to both critical and subcritical crack growth. Patterned uniform arrays of inclined interfacial steps and of “microcracks/voids” (with width 22 μm and spacing 10 μm), out-of-plane to the main interfacial crack, were produced for glass/copper interfaces by photo-lithographic techniques combined with evaporation and diffusion bonding processes. Significant toughening and improved stress corrosion crack-growth resistance is achieved through the promotion of crack-tip shielding primarily from crack bridging. Specifically, plastic void growth within the copper is seen to generate bridged ligaments of metal film between the glass substrates; the resulting mechanical crack bridging leads to plastic stretching of the film and provides the dominant toughening mechanism, with a smaller contribution from crack deflection. Correspondingly, subcritical (pre-instability) crack-growth rates with the patterned arrays in “wet” and “dry” gaseous atmospheres are retarded by orders of magnitude compared to rates for plain interfaces. The toughness with the various patterned interfaces exhibits marked resistance-curve (R-curve) behavior with fracture toughness values increased by factors of 4–9 compared to intrinsic fracture toughness, G0, values of ∼2 J/m2 for these plain glass/copper interfaces. Surface roughness of the glass substrate is reasoned to be a controlling parameter for the shape and magnitude of such crack-resistance curves.