Equilibration of vacancies

Our first example of a reaction in inhomogeneous metallic systems will be the equilibration of vacancies. In close-packed elemental crystals such as Cu or Al, essentially the only point defects are vacancies - as long as the metal is sufficiently pure. According to Gibbs, the 

Interdiffusion in binary metal alloys and the Kirkendall effect 

In order that we may deal with a concrete situation, let us consider the experimental arrangement shown in Fig. 7-1. Two metal cylinders A and B are welded flush against one another. 

A and B should form a complete range of solid solutions. This means that they should have the same crystal structure as well as similar molar volumes. The phenomenological transport problem here is concerned with the solution of Fick s laws for the given experimental conditions in this inhomogeneous system. The atomistic problem is concerned with the interpretation of the chemical diffusion coefficient which, for example, might have been determined by a Boltzmann-Matano analysis. It was shown in section 5.5.3 that, for the case of binary diffusion via vacancies, the chemical diffusion coefficient may be written as  

For the case of an ideal (Raoultian) solution or an ideal dilute (Henryan) solution, is constant, and the thermodynamic factor is unity. Under these conditions  

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Acock et al. found that the loss of water from chrome alum when exposed to hard vacuum apparently occurs in two stages the first with a loss of 12 water molecules and the second with a loss of 4. Whether a phase change occurs in each stage is not known it is possible that the first stage is an equilibration of vacancies. The dehydration of ammonium and potassium alums may be a little more straightforward the loss of water from these salts increased from 19.8 to 20.6 of their original 24 water molecules as the temperatures was increased from 20 to 40°C. 

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