A.     Driving force for densification

Assuming as above that the liquid wets and spreads over the solid surfaces, the solid / vapor interface of the particulate system will be eliminated and pores will from in the liquid. The reduction of the liquid / vapor interfacial area provides a driving force for shrinkage and densification of the overall system. For a spherical pore of radius r in a liquid, the pressure difference across the curved surface by the equation of young and Laplace.

     
                 
 
              (10.1)






Where 2yiv is the surface energy of the liquid/ vapor interface. The pressure in there liquid is lower than that in the pore, and this generates a compressive stress on the particles. This compressive stress due to the liquid is equivalent to placing the system under an external hydrostatic pressure, the magnitude of which is given by eq. (10.1). taking yiv =  1 j/m2  and r  = 0.5 µm gives p  = 4 MPa. Pressures of this magnitude can provide a fairly appreciable force for sintering.

B.     Enhancement of densification

Compared to solid-state sintering, the presence of the liquid phase leads to enhanced densification through (i) enhanced rearrangement of the particulate solid and (ii) enhanced matter transport through the liquid.

Enhanced rearrangement
The friction between the particle is significantly reduced, so they can rearrange more easily under the actions of the compressive stress exerted by the liquid.

Enhanced Matter Transport
In solid –state sintering by, for example, grain boundary diffusion, an important parameter that controls the rate if diffusion is the product of the grain boundary diffusion coefficient Dgb and the grain boundary thickness δgb. In liquid-phase sintering, the corresponding parameter is the product of the diffusion coefficient DL of the solute atoms in the liquid and the thickness of the liquid bridge, δL. As noted earlier, δL is typically many times greater than δgb, and diffusion through a liquid is much faster than in solid. The liquid therefore provides a path for enhanced matter transport.

C.     Source of the Liquid Phase

The consolidated powder form for liquid-phase sintering is normally produced from a mixture of two powders : a major component an additive phase. On heating, the additive melts  or reacts with a small part of the major component to form a eutectic liquid. The production of the liquid phase by melting of a additive is fairly common in metallic systems, e.g., Fe(Cu) and W(Ni). In ceramic systems, the formation of a eutectic liquid is more common, e.g., MgO(CaO-SiO2) and ZnO(Bi2O3). For systems that rely on the formation of a eutectic liquid, phase diagrams play a key role in the selection of the additive and in the choice of the firing conditions. The use of phase diagrams in liquid-phase sintering will be discussed later in this chapter.

D.     Amount of Liquid Phase

For the production of most advanced ceramics by liquid-phase sintering, the amount of  liquid phase produced at the firing temperature is kept typically below =vol %, although in a few cases it csn be as high as =10 vol %. The volume of liquid is therefore insufficient to fill the interstices between the solid particles. However, many traditional ceramics are fabricated by a process in which a much higher volume of liquid is sufficient to fill the interstices between the solid particles (after some rearrangement of the system), and no further densification by other mechanisms is required for the production of the final article. As we will recall from chapter 1, this type of sintering in which the liquid volume is sufficient to fill up the interstices between the solid particles is referred to as vitrification.

E.      Persistent and Transient Liquid-Phase Sintering

In most system, the liquid persists throughout the firing process and its volume does not change appreciably. This situation is sometimes referred to as persistent liquid-phase sintering. On cooling, the liquid forms a glassy grain boundary phase, which, as outlined earlier, may lead to a deterioration in high-temperature mechanical properties. In a small number of systems, the liquid may be present over a major portion of the firing process but then disappears by (i) incorporation into the solid phase to produce a solid solution, e,g. , Si, N4(Al2O3-AIN); (ii)crystallization of the liquid, e,g., Si3N4(Al2O3-Y2O3); or (iiii) evaporation e,g., the system BaTiO3(LiF). The term transient liquid-phase sintering is used to describe the sintering in which the liquid phase disappears prior to the completion of firing. The interest in ceramic materials for mechanical engineering applications at high temperatures has led to the investigation of transient liquid-phase sintering in a few Si3N4 systems. However, the process is generally difficult to control and requires much  further work if it is to be practiced successfully on a larger scale.
In this book, the term liquid-phase sintering will refer most generally to the case of a persistent liquid. A distinction between persistent and transient liquid-phase sintering will be made only when it is convenient.

F.      Cohesion of the Particulate Solid During Firing
Despite the presence of a viscous liquid between the particles during liquid-phase sintering, the structure does not collapse unless the volume of liquid is very large. The capillary stress produced by the liquid holds the solid particles together. The creep (or shear) viscosity of the system is, however, much lower than that of a similar system without the liquid phase.

G.     Advantages and Disadvantages of Liquid-Phase Sintering

The major advantages of liquid-phase sintering, as discussed earlier, are (i) the enhanced densification leading to the production of high density and (ii) the economic benefits arising from the use of a lower firing temperature than that required for solid-state sintering of the major component. However, the use of liquid-phase sintering is not without its disadvantages. The liquid formed during firing normally remains as a grains boundary  phase on cooling (see Fig. 1.15). this grain boundary  phase can cause a deterioration of the properties of the fabricated article. An important example is the production of ceramics for structural applications at high temperature. The grain boundary phase may soften prematurely, thereby causing a reduction in the creep resistance of the solid. In many cases, causing it is not easy to control the grain growth during liquid-phase sintering. The liquid may also enhance the coarsening process so that the achievement of a fine-grained microstructure may be difficult. Finally, compared to solid-state sintering, the presence of an additional phase may make the analysis and understanding of certain aspects of liquid phase sintering more difficult.

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