Sintering polydispersed spherical glass particles
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We used the Clusters model to study the densification kinetics and resulting porosity of a compact of polydispersed soda-lime-silica glass spheres. In addition to the physical data (viscosity, surface tension, particle size distribution) required by the Clusters model, for the first time in glass-sintering studies, we took extra variables into account: the average number of necks per sphere, the effects of pre-existing crystals on the particle surfaces, and sample size. The model predicted both the densification kinetics and the resulting pore-size distribution of sintered compacts. A cross section of a porous sample displayed a porosity pattern that agreed with computer-simulated cross sections, whose pore-size distributions was calculated via the Clusters model using a Monte Carlo technique. Its capacity to predict both density and pore-size distribution makes the Clusters model a valuable tool for designing sintered glasses with any desired microstructure.
I. INTRODUCTION
The viscous sintering kinetics of two spheres during neck formation and the shrinkage of a matrix having isolated spherical pores were long ago studied by Frenkel1 and Mackenzie–Shuttleworth,2 respectively. Frenkel’s model is valid for the first 10% of linear shrinkage (when starting with a relative density, ⳱ compact/glass, of about 0.6), while the MS model is valid for a greater than approximately 0.9. When starting with low-density compacts ( < 0.3) Scherer’s model is more appropriate for a wider range of relative densities.3–5 The sintering kinetics of real glass compacts, however, is far more complex, as we will demonstrate in this paper. A variety of factors are responsible for this intricacy, for example, wide particle size distribution rather than monodispersed systems, irregular particle shape, loose or anisotropic particle packing, pre-existing crystals or dust on the particle surfaces, concurrent surface crystallization, and degassing, which may occur during sintering.6–8 When a compact with a particle-size distribution sinters, the densification kinetics is faster for the smaller particles. This fact was considered in the development of the Clusters model for viscous flow sintering in which the word “cluster” refers to a group of particles of the same size.6 We will, hereafter, adopt the Clusters model due to the following reasons: it allows computation of both the relative density and the pore-size distribution of a)
On leave from the Comisio´n Nacional de Energı´a Ato´mica, Centro Ato´mico Bariloche, 8400-S.C.de Bariloche, Argentina. e-mail: [email protected] J. Mater. Res., Vol. 18, No. 6, Jun 2003
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the compact, taking into account not only the physical parameters discussed in Ref. 7 (particle-size distribution, glass-vapor surface energy, viscosity, surface nucleation density, and crystal growth rate), but also extra ones— the packing arrangement of the particles (the average number of neighbors) and the pre-existing or concurrently developed surface crystalliz
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