Semiclassical approach for isothermal densification of a solid body driven by diffusion-like mechanisms Original Research Article

A semiclassical theory is proposed to investigate the pressureless densification of a solid body governed by diffusion phenomena at constant temperature. We start from the state equation for a solid, where the Debye approximation for the Helmholtz free energy has been provided with a density of vibrational modes that accounts for the microstructural changes occurring at the frequency scale of the implied matter transport. Development of the stationary condition with respect to time yields the evolution of the mass density. It depends upon the absolute temperature, some characteristic features of the phonon spectrum (i.e. Debye temperature and Gruneisen parameter) and upon a parameter related to the microstructural disorder. Diffusion coefficient and surface tension are considered at a temperature value obtained from the energy of the phonon gas vibrations at the frequency scale of the matter transport. Densification rate turns out to be increasing with increasing Gruneisen parameter and increasing values of the ratio which can be interpreted as an effective energy fraction available for the process (θD is the Debye temperature). Application to experimental data are presented and discussed for samples made by rutile (titanium dioxide, TiO2), alumina (aluminium oxide, α-Al2O3) and copper (Cu). In the end, it is suggested a possible quasi-particle in sintering phenomena, resulting from the coupling between the phonon gas and the diffusional matter transport from the bulk phase to the grain boundary, and of energy given by ∼ℏω̃=kBθ.