Carl E. Hoge

Thermodynamic and geometric considerations of solid state sintering

Abstract Thermodynamic analysis of model sintering systems indicates that the minimum free energy configuration is represented geometrically by interpenetrating spheres of increasing size with no neck formation. The dihedral angle formed at the grain boundary increases as densification proceeds; the limit is the equilibrium angle determined by the ratio of the solid/solid and solid/vapor interfacial energies for the system. An intermediate free energy configuration favored by kinetic factors is the formation of a neck at grain/grain contacts with an equilibrium dihedral angle; the resulting reverse curvature in the surfaces of the particles provides the driving force for densification in this case. Conditions and mechanisms under which both configurations develop are discussed and are illustrated by experiments on MgO powder compacts that density considerably more rapidly in flowing water vapor than in static air.

Thermodynamic Aspects of Solid State Sintering

The kinetic approach, initially developed by Kuczynski,(1) based on the use of a two-sphere model has led to an understanding of the mass transport processes that can occur during solid state sintering. The factors that lead to the grain growth that is practically always observed during sintering, however, are not as well understood. The following phenomenological analysis based on a thermodynamic approach provides additional understanding of the densification processes, driving forces for mass transport, and the conditions under which grain boundary movement and consequently grain growth occur.

Phase Distribution in Solid-Liquid-Vapor Systems

Spatial distribution of phases in a solid-liquid-vapor system are described by the classical Young’s equation1

Interfacial Reactions and Wetting Behavior of Glass-Iron Systems

{\gamma _{sv}} - {\gamma _{s\ell }} = {\gamma _{\ell v}}\cos \theta ,

THERMODYNAMICS OF WETTING

(1) where γ is the interfacial tension between solid-vapor (sv), solid-liquid (sl), and liquid-vapor (lv) phases, γsv-γsl is the driving force for wetting, and θ is the contact angle at a solid-liquid-vapor triple point as measured through the liquid phase. Furthermore, in systems where the solid phase is polycrystalline

THERMODYNAMIC CONSIDERATIONS OF SOLID STATE SINTERING

{\gamma _{ss}} = 2{\gamma _{sf}}\cos \frac{\Phi }{2},