Non-equilibrium thermodynamics and kinetics of the sintering process: A relaxation model describing cold sintering

Sintering is a complex process that involves a number of competing mechanisms. There are many types of sintering processes. The most recently introduced is cold sintering, which is based largely on a chemo-mechanical pressure solution mechanism that mainly involves dissolution, transport, and precipitation to drive the densification. Using the cold sintering of zinc oxide as a model system, here we consider the kinetics of the densification process under isothermal and isobaric conditions at various applied pressures. Here, the time-dependent densification data are considered in terms of a relaxation model. The data are also analyzed in the frequency domain to aid in the separation of different densification mechanisms. As an analogy to dielectric spectroscopy methods, we introduce a modulus form of strain data to aid the identification of relaxation modes. We identify the activation energies of fast and slow processes, along with pressure dependence. Through the superposition of these identified relaxation modes, we can accurately model across a broad number of sintering conditions. The approach is discussed broadly with respect to all forms of sintering and the data obtained here is considered under a modified Kingery model to identify critical exponents. The models developed herein may be applicable to all sintering techniques, and the modulus representation of time domain relaxation may be a universal tool for detangling concurrent relaxation in many other types of relaxation phenomena.