Mechanisms of Liquid-Phase Sintering

Similarly, the mechanisms of liquid-phase sintering can be described by dividing the process into three stages. The first stage involves the redistrihulion of the liquid 

A two-dimensional model of circular particles has been developed to describe the liquid redistribution behaviors, which assumes that the chemical potential of the liquid in all the pores in a given particle array is the same at equilibrium [84]. When an atom is located under the surface of a liquid-vapor meniscus, with an average radius of curvature r, its chemical potential is given by 

Due to presence of the compressive capUlaiy force, the solubUily at the contact points between the particles is higher than that at other surfaces of the particles [89, 90]. Because of this dUference in solubilily, matter transport occurs Ifom the contact points to other places, so as to form a flat contact region, as shown in Fig. 5.38 [1]. With increasing radius of the contact region, the stress along the interface decreases, so that the densification slows down. The rate of the matter transport is controlled by the slower one of the two mechanisms (i) difiusion through the liquid layer and (ii) solution-precipitation via interface reaction. 

The rate control by diffusion through the liquid layer can be described by using the two spherical particle model. The two particles have the same radius a, if each sphere is dissolved away along the center-to-center line by a distance h to form a circular contact region with radius X, these parameters can be related through the following expression  

The volume of material removed from each sphere is given hyV X hl2, which is combined with Eq. (5.236), there is 

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Huppmann WJ, Riegger H, Kayssta- WA, Smolej V, Pejovnik S (1979) Elementary mechanisms of liquid-phase sintering. 1. Rearrangement Zeitschrift Fur Metallkunde 70 707-713... 

Cannon, H. S. and Lenel, F. V., Some observations on the mechanism of liquid phase sintering, in Pulvermetallurgie (Plansee Proceedings 1952), F. Benesovsky (ed.), Metallwerk Plansee GmbH, Reutte, 106-22, 1953. 

The mechanisms of liquid-phase sintering processes have been described in detail by Kingery (213, 214], Petzow (215), and German [216]. The sintering process can be treated as a sequence of three stages particle rearrangement solution-reprecipitation and skeleton sintering. 

Figure 2. Schematic diagram illustrating the three stages of liquid phase sintering, with the dominant mechanisms and processes for each stage. (After Ref 1.)...

Fig. 5.43 The three mechanisms of grain-shape accommodation and neck growth during solution reprecipitation controlled densification of liquid-phase sintering a contact flattening, b dissolution of small grains, and c solid-state bonding. Reproduced with permission from [73]. Copyright 2009, Springer...

Derive Eq. (10.38) for the shrinkage during the solution-precipitation stage of liquid-phase sintering when the phase boundary reaction is the rate controlling mechanism. 

Figure 1. Microstructure of a ceramic produced by liquid phase sintering showing rounded grains, some residual porosity, and the intergranular glassy phase resulting from the liquid phase. (From R. W. Davidge, Mechanical Behavior of Ceramics, copyright 1979, p. 14. Reprinted with the permission of Cambridge University Press.)...

This mechanism is similar to the one occurring during liquid-phase sintering, where the dissolution of crystalline material into the glassy phase occurs at the interfaces loaded in compression and their reprecipitation on interfaces loaded in tension. The rate-limiting step in this case can be either the dissolution kinetics or transport through the boundary phase, whichever is slower. This topic was discussed in some detail in Chap. 10, and will not be repeated here. 

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