An analysis for estimating the probability of particle coalescence in liquid phase sintered systems

During liquid phase sintering solid particles move about within the liquid and make contact with each other. Microstructural examination of liquid phase sintered alloys clearly indicates that some of these contacts lead to particle coalescence even in systems in which wetting of the solid by the liquid is presumed to occur. Under these circumstances, the grain boundary formed by the particles must have a rather low energy and hence, misorientation. In this study, attention is directed at the problem of calculating the probability of a collision between particles that lead to the formation of a low angle grain boundary and hence, coalescence. By making simple but physically plausible assumptions about the nature of low angle grain boundaries, the coalescence probabilityp _c can be determined as a function of a parameterθ where θ = withγ _SL =solid-liquid surface energy,γ _ss = average solid-solid grain boundary energy and У is the angular extent of the energy cusp associated with a low angle grain boundary. A simple analytical expression ofp _c ,p _c = 0.1θ (1-cosθ) is derived and found to be in excellent agreement with other techniques for calculatingp _c for values ofθ ≲ 10 deg, the range most probable for liquid phase sintered alloys. Some discussion of the accuracy and assumptions of the present model is also given.