Diffusion of Small Interstitial Solute Atoms

Small solute atoms in the interstices between the larger host atoms in a relaxed metallic glass diffuse by the direct interstitial mechanism (see Section 8.1.4). The host atoms can be regarded as immobile. A classic example is the diffusion of H solute atoms in glassy Pd8oSi2o- For this system, a simplified model that retains the essential physics of a thermally activated diffusion process in disordered systems is used to interpret experimental measurements [20-22]. 

The following quantities will be of use in describing the interstitial self-diffusion and intrinsic chemical diffusion  

N = total number of interstitial sites p = fraction of all interstitial sites that are occupied p = fraction of all sites that are tracer-interstitial occupied p°k = fraction of all sites that are type k sites (Fig. 10.4a) p(k) = fraction of type k sites that are occupied Pk = fraction of all sites that are occupied type k sites Pk = fraction of all sites that are tracer-occupied type k sites 

The occupation probability at the various sites should follow Fermi-Dirac statistics because each site can accommodate only one interstitial. Therefore, 

A model for the tracer self-diffusivity of the interstitials is now developed for a system in which the total concentration of inert interstitials and chemically similar radioactive-tracer interstitials is constant throughout the specimen but there is a gradient in both concentrations. Since the inert and tracer interstitials are randomly intermixed in each local region, 

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Another system obeying Fick s law is one involving the diffusion of small interstitial solute atoms (component 1) among the interstices of a host crystal in the presence of an interstitial-atom concentration gradient. The large solvent atoms (component 2) essentially remain in their substitutional sites and diffuse much more slowly than do the highly mobile solute atoms, which diffuse by the interstitial diffusion mechanism (described in Section 8.1.4). The solvent atoms may therefore be considered to be immobile. The system is isothermal, the diffusion is not network constrained, and a local C-frame coordinate system can be employed as in Section 3.1.3. Equation 2.21 then reduces to... 

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