Dispersion forces and Hamaker constants for intergranular films in silicon nitride from spatially resolved-valence electron energy loss spectrum imaging

French, {RH }, Müllejans H, Jones {DJ }, Duscher G, Cannon {RM }, Rühle M.  1998.  


The van der Waals {(vdW)} dispersion forces represent one of the fundamental long range interfacial and surface forces in materials. The dispersion forces, for a set of materials in close proximity, arise from the electronic structure of the materials wherein the electrons in interatomic bonds acting as oscillating dipoles exhibit an attractive interaction energy. These {vdW} dispersion forces, represented by a proportionality constant, the full spectral Hamaker constant {(A)}, can be calculated directly from optical property based electronic structure spectra such as the interband transition strength {(Jcv)} using the Lifshitz theory. {Si3N4} exhibits equilibrium intergranular films {(IGFs)} whose thickness is determined by a force balance where the contribution of the van der Waals dispersion force is dictated by the {IGF} chemistry. Using spatially resolved-valence electron energy loss {(SR-VEEL)} spectroscopy in the {STEM} with a 0.6 nm probe permits the in situ determination of {vdW} forces on the {IGFs} in viscous sintered polycrystalline systems. In addition local variations in {IGF} chemistry and dispersion forces throughout the microstructure of individual silicon nitride samples can be determined using these methods. From multiplexed zero loss/plasmon loss optimized {SR-VEEL} spectra across {IGFs} with subsequent single scattering deconvolution, Kramers Kronig analysis and London dispersion analysis, the index of refraction and Hamaker constants can be determined. The method proved to be accurate and reproducible with comparison to {VUV} measurements for the bulk materials and repeated measurements on numerous individual {IGFs.} For these optimized {Si3N4} materials, the dispersion forces varied over a range from 2 to 12 {zJ.} These showed standard deviations on the order of 1 {zJ} for systems with {IGFs.} Additional systematic errors can not be excluded. Local variations in Hamaker constants within the microstructure of a single sample correlate to the distribution of {IGF} thicknesses observed i.e. the thickness varies inversely with Hamaker constant. The technique of measuring Hamaker constants in situ represents an important new tool for dispersion force and wetting studies. For the first time it is observed that the thickness of the {IGF} scales with the local Hamaker constant of the investigated grain boundary region.


Acta Materialia










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