Driving Forces of Sintering

Sintering process is an irreversible process, during which the free energy of the system is decreased. The sources responsible for such a decrease are called the driving forces of sintering. There are three potential driving forces, (i) the curvature of particle surfaces, (ii) externally applied pressure, and (iii) chemical reaction. 

Surface curvature is always present as the driving force of sintering, while external stress and chemical reaction may be absent. Therefore, surface curvature is the primary driving force of sintering. For one mole of ceramic powder, comprising of spherical particles with a radius a, the number of particles is given by ... 

Therefore, Es is the quantity of the decrease in surface free energy of the powder, if a fuUy dense body is formed from the one mole of particles, i.e., it is the driving force of sintering. 

The driving force of sintering is the reduction of the total interfacial energy. The total interfacial energy of a powder compact is expressed as yA, where y is the specific surface (interface) energy and A the total surface (interface) area of the compact. The reduction of the total energy can be expressed as... 

The driving force of sintering appears as differences in bulk pressure, vacancy concentration and vapour pressure — parallel phenomena — due to differences in surface curvature of the particles. For the geometry in Figure 4.2, the pressure difference AP is... 

The equations in Table 4.2 were derived for systems where the driving force of sintering is the capillary pressure difference due to curvature difference. However, when an external pressure Pappi. is applied, the total sintering pressure Pt is the sum of the capillary and external pressures,... 

In die operation of die first source, the driving force for sintering is the difference in curvature between the neck and the surface of the sphere. The curvature force A l, is given by... 

The values of m given above conform to Hemng s scaling law (1950) which states that since the driving force for sintering, the transport length, the area over which uansport occurs and the volume of matter to be transported are proportional to a, and respectively, the times for equivalent change in two powder samples of initial particle size ai q and 2,0 are... 

This experiment is discussed here in some detail both beeause it casts light on the driving force for sintering and because it is a beautiful example of the ingenious... 

The driving force for sintering is the reduction in the total free energy of the particulate system, AG, which is composed of free energy changes of volume, AGy, boundaries, AGb, and surfaces, AGt. 

Because the surface energy per volume is larger for small particles and because the fundamental driving force for sintering is surface-energy reduction, compacts composed of smaller powders will typically sinter more rapidly. Smaller powders are more difficult to produce and handle therefore, predictions of sintering rate dependence on size are used to make choices of initial particle size. Herring s... 

Figure 7.30 Two adjacent particles. (a) Before sintering, the particles have two solid-vapor surfaces, each with a surface energy ysv. (b) After the onset of sintering, a necked region forms between particles, replacing two solid-vapor surfaces with a lower-energy solid-solid surface. yss < ysv, providing the thermodynamic driving force for sintering.

Commonly, the applied pressure is much greater than the driving force for sintering, and as a result, equation (e) of (17.2.3.5.1) becomes ... 

In a rough approximation this driving force between sintering of two particles is given by the gradient of the "sintering pressure" Pg, with Pg given by ... 

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