Shear modulus of sintered 'house of cards'-like assemblies of crystals

A cell model of a 'house of cards'-like assembly of crystals is used for the study of the evolution of the shear modulus during sintering. The crystals are assumed to have a lozenge shape. The cell model takes different crystal-crystal contacts into account. The force needed to separate two sintered crystals is calculated using the minimum surface area (MSA) approximation. By varying the thickness, long axis, and short axis of the crystals, it is possible to make space-filing configurations which have a nonzero shear modulus at crystal volume fraction that can be as low as phi = 0.03. This is significantly lower than the volume fractions phi > 0.52 that are found in studies where the MSA approximation is applied to assemblies of spherical particles. It is found that sintering may cause a nonlinear volume fraction dependence of the shear modulus, which depends on the shape of the crystals, the type of crystal-crystal contacts, and the character of the crystal assembly. The calculated shear modulus is analyzed using the phenomenological expression (phi - phi0)beta, where phi0 represents the volume fraction at the start of sintering. The exponent beta is found to vary between 1 and 2. The interpretation of the shear modulus using a fractal model is also discussed.