  In this work, we present a variational and quantitative phase-field model for
non-isothermal sintering processes. The model is derived via an extended
non-diagonal phase-field model. The model evolution equations have naturally
cross-coupling terms between the conserved kinetics (i.e., mass and thermal
transfer) and the non-conserved one (grain growth). These terms are shown via
asymptotic analysis to be instrumental in ensuring the elimination of interface
artefacts, while also examined to not modify the thermodynamic equilibrium
condition (characterized by dihedral angle). Moreover, we demonstrate that the
trapping effects and existence of surface diffusion in conservation laws are
direction-dependent. An anisotropic interpolation scheme of the kinetic
mobilities which differentiates the normal and the tangential directions along
the interface is discussed. Numerically, we demonstrate the importance of the
cross-couplings and the anisotropic interpolation via presenting
thermal-microstructural evolutions.
