The fundamental question as to whether thin intergranular films can adopt an equilibrium thickness in polycrystalline ceramics is addressed. Two continuum approaches are presented, one based on interfacial energies and the other on the force balance normal to the boundary. These indicate that there will exist a stable thickness for the intergranular film and that it will be of the order of 1 nm. The origin of an equilibrium thickness is shown to be the result of two competing interactions, an attractive van der Waals-disperson interaction between the grains on either side of the boundary acting to thin the film and a repulsive term, due to the structure of the intergranular liquid, opposing this attraction. As both of these interactions are of short range (<lo nm), it is a natural consequence that the equilibrium thickness is of the order of 1 nm, a value commensurate with that observed experimentally in a wide range of ceramics. Two further consequences of importance are indicated. The first is that thin intergranular liquid phases can support a normal stress. The second is that the dielectric constants of the adjacent grains play an important role in determining the thicknesses of the intergranular phase. This leads to the conclusion, consistent with observations, that the thickness of the intergranular phase in polyphase ceramics is expected to be different at boundaries between dissimilar phases than that between like phases. NE of the most revealing findings produced during the ex0 amination of ccramic microstructures using the techniques of high-resolution transmission electron microscopy has been the fact that many of these materials contain a thin intergranular (generally siliceous) glass phase. The thickness of the intergranular glass phase can be quite small, being =0.5 to =2 nm in some silicon nitride and zirconia ceramics and upward of =5 nm in some alumina-based materials. In the majority of materials the intergranular phase is both continuous throughout the microstructure and, significantly, located at the two-grain junctions. As presently understood, the presence of a remnant intergranular glass phase can be produced by a number of different processes. In many ceramics, the phase results from the liquid-phase sintering process used to densify them. Examples of these include the silicon nitride alloys, the zinc oxide varistor materials, and alumina substrate materials. In others, such intergranular films are present because the materials are prepared by the controlled but incomplete crystallization of a glass (glass-ceramics). A third, but practically important, category is that in which the phase forms from the impurities present in the starting materials. For instance, a number of the ceramics developed for nuclear waste encapsulation4 and certain of the polycrystalline, tetragonal zirconia ceramics’ contain such intergranular films.

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On the Equilibrium Thickness of Intergranular Glass Phases in Ceramic Materials

Grain Boundary Complexions

The general mathematical constraints for thermomechanical equilibrium of partial melts under hydrostatic or nearly hydrostatic stress conditions are well known. However, melt phase geometries under equilibrium conditions have previously been understood only qualitatively. Because of its importance in determining bulk physical and chemical properties of partially molten regions of the crust and the mantle, we have computed the geometries of the liquid phase for a range of melt fractions and dihedral angles. We describe here a theoretical interfacial topology model and its associated calculational algorithms which yield numerically precise equilibrium solid-liquid interfacial surfaces where the only constraints imposed on the system are constant mean curvature and constant wetting angle in accordance with equilibrium. The calculated geometries are used to determine the permeability of partial melts to fluid flow, interfacial areas, surface energy, minimum channel cross section, surface mean curvature, and maximum trappable melt fraction for melt fractions up to 5% and wetting angles between 20° and 80°. For wetting angles less than 60° the melt is distributed in an interconnected network of channels along the grain edges, and therefore melt mobilization is possible as soon as melt forms. For wetting angles greater than 60° the melt phase will be distributed in isolated pockets at the grain corners if the melt fraction is less than a critical value, whereas an interconnected network of melt channels will be established if the critical melt fraction is exceeded. Wetting angle exerts a first-order control on the permeability of partially molten systems through its effect on the connectivity of the melt phase. Once a connected melt phase has formed, the permeability is only mildly sensitive to wetting angle.

Permeabilities, interfacial areas and curvatures of partially molten systems: Results of numerical computations of equilibrium microstructures

Solution-precipitation creep in glass ceramics

The London dispersion forces, along with the Debye and Keesom forces, constitute the long-range van der Waals forces. London's and Hamaker's work on the point-to-point dispersion interaction and Lifshitz's development of the continuum theory of dispersion are the foundations of our understanding of dispersion forces. Dispersion forces are present for all materials and are intrinsically related to the optical properties and the underlying interband electronic structures of materials. The force law scaling constant of the dispersion force, known as the Hamaker constant, can be determined from spectral or parametric optical properties of materials, combined with knowledge of the configuration of the materials. With recent access to new experimental and ab initio tools for determination of optical properties of materials, dispersion force research has new opportunities for detailed studies. Opportunities include development of improved index approximations and parametric representations of the optical properties for estimation of Hamaker constants. Expanded databases of London dispersion spectra of materials will permit accurate estimation of both nonretarded and retarded dispersion forces in complex configurations. Development of solutions for generalized multilayer configurations of materials are needed for the treatment of more-complex problems, such as graded interfaces. Dispersion forces can play a critical role in materials applications. Typically, they are a component with other forces in a force balance, and it is this balance that dictates the resulting behavior. The ubiquitous nature of the London dispersion forces makes them a factor in a wide spectrum of problems; they have been in evidence since the pioneering work of Young and Laplace on wetting, contact angles, and surface energies. Additional applications include the interparticle forces that can be measured by direct techniques, such as atomic force microscopy. London dispersion forces are important in both adhesion and in sintering, where the detailed shape at the crack tip and at the sintering neck can be controlled by the dispersion forces. Dispersion forces have an important role in the properties of numerous ceramics that contain intergranular films, and here the opportunity exists for the development of an integrated understanding of intergranular films that encompasses dispersion forces, segregation, multilayer adsorption, and structure. The intrinsic length scale at which there is a transition from the continuum perspective (dispersion forces) to the atomistic perspective (encompassing interatomic bonds) is critical in many materials problems, and the relationship of dispersion forces and intergranular films may represent an important opportunity to probe this topic. The London dispersion force is retarded at large separations, where the transit time of the electromagnetic interaction must be considered explicitly. Novel phenomena, such as equilibrium surficial films and bimodal wetting/dewetting, can result in materials systems when the characteristic wavelengths of the interatomic bonds and the physical interlayer thicknesses lead to a change in the sign of the dispersion force. Use of these novel phenomena in future materials applications provides interesting opportunities in materials design.

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Origins and Applications of London Dispersion Forces and Hamaker Constants in Ceramics

Impurity phases in commercial hot-pressed Si3N4 were investigated using transmission electron microscopy. In addition to the dominant, β-Si3N4 phase, small amounts of Si2N2O, SiC, and WC were found. Significantly, a continuous grain-boundary phase was observed in the ∼ 25 high-angle boundaries examined. This film is ∼ 10 A thick between, β-Si3N4 grains and ∼ 30 A thick between Si2N2O and β-Si3N4 grains.

L. K. V. Lou

Papers

Impurity Phases in Hot-Pressed Si3N4

Impurity phases in hot-pressed silicon nitride

Measuring cohesive energy of van der Waals heterostructures by nanoparticle intercalation method