A model of diffusion/viscous mass transport in silicates during liquid-phase sintering
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The model of capillary transport of liquid metals driven by shear stress resulting from the displacement of menisci [J.W. Nowok, Scripta Metall. Mater. 29, 931 (1993); Acta Metall. Mater. 42, 4025 (1994)] is applicable to liquid-phase sintering of silicate/aluminosilicate glasses. The movement of a liquid phase between adjacent particles is compared with that in capillaries. It appears that the transport property of intergranular melt may be expressed by the viscosity (77) and volume diffusion (D) parameters if mean displacement of menisci is compared with the mean diffusive jump lengths of atoms/molecules (L). This leads to the following relation: (y/r))La = D c a p , where a and £>cap are a specific permeability and volume diffusion coefficient. The use of this model requires the assumption that the diffusing species are also the viscous flow units, and they can be either atoms or structural units. This assumption seems to be applicable for depolymerized silicate melts if the dominant mass transport is initiated by the diffusion of both nonbridging oxygen and silicon atoms.
I. GENERAL PRINCIPLES Liquid-phase sintering is usually divided into three stages: (i) The formation of necks and rearrangement of particles caused by plastic deformation of necks, (ii) solution-precipitation with simultaneously occurring pore shrinkage, and (iii) final pore removal resulted from fluxing of melt.3-4 The maximum densification may be achieved in systems with sufficient quantity of liquid phase that intergranular thickness be above some critical level. The criterion for liquid phase flow between adjacent grains can be analyzed either by pressure gradients in the melt or by the gradients in chemical potential along interfaces.5 In a capillary the pressure difference (inside and outside the capillary) is determined by the surface tension (Laplace equation). Therefore, in our model the fundamental driving force responsible for the mass flux in the capillary-like media is assumed driven by the surface tension of the melt. Opposing this transport is the viscous force in the melt. The meniscus velocity as it progresses along the channel is dependent on the surface tension-to-viscosity ratio, 7/17 [m/s]. The motion of melt originates from the activated motion of the meniscus at the neck with simultaneous dissolution of silicate into the neck (Fig. 1). As a result liquid from the neck may move either by viscous flow or by volume diffusion; however, the dissolution of silicate into melt is governed by the diffusion process at the solid/melt interface. Thus, the migration of liquid phase can realistically be treated as: dissolution of particles into the melt (diffusion) volume transport of the melt (diffusion = viscous flow) —• pore filling and pore shrinkage. J. Mater. Res., Vol. 10, No. 2, Feb 1995 http://journals.cambridge.org
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All fluxes in the above relation are not independent, but must satisfy the conservation of mass and the electroneutrality constraint. The displacive movements of menisci by the amount AL
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