The kinetics of neck growth

In these equations, k, k2, k and 4 are constants which vary with temperature, and t is the time of reaction. 

Experiments have shown that sodium chloride (NaCl) and other volatile materials sinter by a predominantly vapour transport mechanism whereas refractory oxides and metals sinter mainly by way of bulk diffusion. 

The driving force for these reactions is the Gibbs energy of formation of the oxide (see Section S3.2). In favourable cases, such as that of aluminium, the product of corrosion may provide a protective coating, preventing fiuther reaction from taking place. In less favourable circumstances, such as the corrosion of iron, the product may be loose or flake off, continually exposing new surfaces for corrosion. 

The oxidation reaction will be influenced by the equilibrium oxygen pressure in the surroundings (Sections SI.5 and S3.2). Calculation of the equilibrium partial pressures over metal oxides shows that values lie between approximately 10 atmospheres to 10 atmospheres. As the oxygen partial pressure in air is about a fifth of an atmosphere it is clear that metals will have a tendency to oxidise. From the point of view of thermodynamics, there is always a considerable driving force for reaction. 

Corrosion of metals takes place by way of a variety of important chemical reactions. At ordinary temperatures, this process is often called tarnishing, and at high temperatures, scale formation. In this section, the reaction of metals with dry gases at relatively high temperatures is considered. This is referred to as direct corrosion, to distinguish it from many common forms of corrosion, including rust formation on iron, which need the presence of water. These latter reactions are considered in Section 9.4. 

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As the evaporation or condensation of material is basically controlled by reactions of atoms at the surface, the kinetics of sintering by the evaporation/ condensation mechanism is also determined by either evaporation or condensation of atoms. The kinetics of neck growth by this mechanism was derived from the Langmuir equation, a gas adsorption equation. The use of the Langmuir equation means that the condensation of atoms controls the neck growth. 

The relative neck size is defined by x/r, where x is the diameter of the neck and r the diameter of the particles. The kinetics of neck growth are modeled by the expression... 

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