Equilibrium film thickness at interphase boundaries

Other than the wetting, non-wetting and dewetting behaviour of interfaces, the other striking TEM observation is that the thickness of intergranular films seems to be relatively constant from one interface to another in any given sample, but that it varies from material to material. 

Theoretical considerations by Clarke and co-workers (Clarke, 1987 Clarke etal., 1993) show that an equilibrium film thickness arises from the competition between attractive dispersion forces determined by the dielectric properties of the grains and repulsive disjoining forces which can be steric forces and/ or double-layer forces. Wetting will occur when the solid-solid boundary energy, yb, is less than that of the wetted boundary, 2y, where y is the liquid-solid interfacial energy (Clarke, 1985), provided that there is a suitable source of liquid, for example as a consequence of liquid-phase sintering at high temperatures. 

The most general equilibrium condition which applies to a thin film sandwiched between two phases when there is an applied pressure, P, and a capillary pressure, /cap. is 

Clarke (1987) examined the form of Eq. (17.1) for the situation where n, D = nADS = nHB = 0, in which case the repulsive force per unit area enabling an equilibrium film thickness to arise is simply Ilsx. Subsequently, Clarke etal. (1993) examined the situation where nx D 0, nADS = nHB = 0 for zero and finite values of nsx, concluding that it is only under certain restricted conditions that it is plausible for an electrical double-layer force to contribute significantly to the total repulsive force. 

If the only significant repulsive force per unit area is Ilsx, as is likely to be the case for interphase boundaries between non-oxide engineering ceramics such as SiC, Si3N4 and / -BN, the net force, F, per unit area pushing two grains together becomes 

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