An analysis of microstructural parameters in the minimum contact area model for ultrasonic velocity–porosity relations

The relationship between the normalised ultrasonic velocity (vv0) and the volume fraction (P) of pores in porous materials has been derived on the basis of a minimum solid area of contact model. It considers the development of the minimum solid area of contact during the sintering of an assembly of monosized spheres stacked in simple cubic packing. It is shown that by using a single model parameter “c”, related to the effective aspect ratio “α” of spheroidal pores; it is possible to predict the trends in variation of the experimental (vv0 versus P) data of hot pressed silicon carbide (SiC), hot pressed silicon nitride (HPSN), reaction bonded silicon nitride (RBSN), porcelain, ceramic superconductors based on YBCO system, sintered iron and tungsten powder compacts as well as alumina. In addition, it was found that a single relation describes the behaviour of both longitudinal and transverse wave velocity as a function of pore volume fraction in all but the ceramic superconductors of the aforesaid materials. Finally, it is proposed that for all practical purposes, the analytical relation derived in the present work, can be efficiently approximated by an empirical relationship: vv0=1−a1Pn, where the subscript zero refers to the material of theoretical density and a1, n are fitting parameters.