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Surface Roughening and Unstable Neck Formation in Faceted Particles: II, Mathematical Modeling
Author(s) -
Sheldon Brain W.,
Rankin Janet
Publication year - 1999
Publication title -
journal of the american ceramic society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.9
H-Index - 196
eISSN - 1551-2916
pISSN - 0002-7820
DOI - 10.1111/j.1151-2916.1999.tb02011.x
Subject(s) - facet (psychology) , surface energy , curvature , surface (topology) , materials science , instability , microstructure , particle (ecology) , condensed matter physics , chemical physics , mechanics , geometry , composite material , chemistry , physics , mathematics , geology , psychology , social psychology , oceanography , personality , big five personality traits
Unstable neck formation between two isolated particles was analyzed by considering the effects of both faceted and rounded (i.e., “atomically rough”) surfaces. Mathematical descriptions of both neck growth and rupture are devel‐oped here. Calculations conducted with these formulations can explain the neck instability observed by Rankin and Boatner. The analysis and the experimental data suggest that the energy barrier associated with forming a new atomic layer on top of a faceted surface can restrict the shape evolution of a crystalline particle, even at moderately high temperatures. The analysis also indicates that this en‐ergy barrier can be overcome when the positive curvature which initially exists at a facet/rough surface boundary re‐verses as a result of neck growth. This latter effect offers an explanation for neck rupture which is consistent with the experimental results. In addition to providing an explana‐tion for this phenomenon, the analyses presented here also demonstrate that surface phase boundaries and step energy barriers can have a significant effect on microstructure evolution during solid‐state sintering.