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

Abstract

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.