  A thermodynamically consistent phase-field model is developed to study the
non-isothermal grain coalescence during the sintering process, with a potential
application to the simulation in unconventional sintering techniques, e.g.
spark plasma sintering, field-assisted sintering, and selective laser
sintering, where non-equilibrium and high temperature gradient exist. In the
model, order parameters are adopted to represent the bulk and atmosphere/pore
region, as well as the crystallographic orientations. Based on the entropy
analysis, the temperature-dependent free energy density is developed, which
includes contributions from the internal energy (induced by the change of
temperature and order parameters) and the order parameter related
configurational entropy. The temperature-dependent model parameters are
determined by using the experimental data of surface and grain boundary
energies and interface width. From laws of thermodynamics, the kinetics for the
order parameters and the order-parameter-coupled heat transfer are derived. The
model is numerically implemented by the finite element method. Grain
coalescence from two identical particles shows that non-isothermal condition
leads to the unsymmetric morphology and curved grain boundary due to the
gradients of on-site surface and grain-boundary energies induced by the local
temperature inhomogeneity. More simulations on the non-isothermal grain
coalescence from two non-identical and multiple particles present the temporal
evolution of grain shrinkage/growth, neck growth, and porosity, demonstrating
the capability and versatility of the model. It is anticipated that the work
could provide a contribution to the research community of unconventional
sintering techniques that can be used to model the non-isothermal related
microstructural features.
