Sintering is a common process during which nanoparticles and microparticles are bonded, leading to the shrinkage of interstitial pore space. Understanding morphological evolution during sintering is a challenge, because pore structures are elusive and very complex. A topological model of sintering is presented here, providing insight for understanding 3-D microstructures observed by X-ray microtomography. We find that the topological evolution is described by Euler characteristics as a function of relative density. The result is general, and applicable not only to viscous sintering of glasses but also to sintering of crystalline particles. It provides criteria to distinguish the stages of sintering, and the foundations to identify the range of applicability of the methods for determining the thermodynamic driving force of sintering.

Sintering stress and bulk viscosity were derived as functions of relative density from microtomographic images in viscous sintering of glass particles. Three methods were proposed to estimate the sintering stress from relative density, specific surface area, and average of curvature on pore surface, which were directly measured by X‐ray microtomography. The surface energy method gave valid value in the final stage of sintering, while the mixed method gave better estimation in the intermediate stage. For the initial stage of sintering, the sintering stress was calculated from the average contact radius and the average coordination number observed by X‐ray microtomography. The sintering stress at the final stage increased in free sintering, but it decreased in constrained sintering due to pore coarsening. The bulk viscosity was calculated from the shrinkage rate and the sintering stress.

The representative volume element (RVE) is a basic concept in the continuum mechanics of sintering of random heterogeneous porous materials. A quantitative determination of its size was performed by using synchrotron X-ray microtomography data of constrained sintering of thin glass film on a rigid substrate. A RVE size is associated with a property of interest; we determined it for relative density, specific surface area, and hydrostatic component of sintering stress. The RVE size was estimated to be from 11 to 17 times larger than the average initial particle size. The RVE size was associated with a given precision of the property. It depended on the volume fraction of porous structure, or, relative density, so that it varied with microstructural evolution.