Thermodynamics of Densification: I, Sintering of Simple Particle Arrays, Equilibrium Configurations, Pore Stability, and Shrinkage

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Abstract
Equilibrium configurations for linear and closed arrays (rings and regular polyhedra containing a single pore) of identical particles (cylinders or spheres) were determined by minimizing the array's surface and grain‐boundary energies with the assumption that each particle conserves its mass. The change in free energy between the initial and equilibrium configuration increases with dihedral angle (i.e., the equilibrium angle). More significantly, it is shown that pores will shrink to an equilibrium size if the number (n) of coordinating particles is greater than a critical value. The critical pore coordination number (nc) increases with the dihedral angle. Only pores withnncare thermodynamically unstable during sintering. It is also shown that any mass‐transport mechanism can lead to pore shrinkage while a connecting path to the pore surface remains open. The effective sintering “stress” (i.e., driving force) increases with the dihedral angle and decreases to zero as the equilibrium configuration is reached. Sintering stresses increase with decreasing coordination number. It is also shown that the shrinkage strain for closed arrays increases with the pore coordination number. Rearrangement phenomena within a powder compact are discussed with regard to resultant sintering forces on nonsymmetrically coordinated particles.