Collective and tracer diffusion of lattice gases in lattices with site-energy disorder

Using density functional theory to study hydrogen diffusion in metals: A brief overview

“…For disordered materials, however, the number of distinct local events that can occur is very large, even in the idealized case in which it is obvious how to define the character of these events in terms of the identities of atoms in the vicinity of the diffusing H. H diffusion in disordered materials can be defined in terms of lattice models provided that rules for defining local hop rates for each possible site are established. Various efforts to develop models of this type based on fitting to experimental data have been made [18][19][20][21][22][23], but the large number of parameters needed to fully define even relatively simple lattice models creates significant uncertainty in this approach. DFT calculations can play a useful role in this area because they can be used to predict the hopping rates of H with complete control over the identity of atoms surrounding the diffusing H.…”

Hydrodynamic limit of a disordered lattice gas

“…Moreover, because of the definition of A 0 , expression (6. 19) with 1I M c replaced by 1I M can be bounded by c s 2d e −s δ/2 . In conclusion…”

“…From the physical point of view, diffusion of lattice gases in systems with site disorder has been studied mainly by means of simulations and more or less rough approximations like mean field . We refer the interested reader to [19], [20], [21], [22], [24] and to [17] for an iterative procedure to compute corrections to the mean-field approximation.…”

Diffusion Coefficients of Single and Many Particles in Lattices with Different Forms of Disorder

“…6 is a very good approximation for the single particle diffusion coefficient in this model. Numerical simulations [25,26] verified that the coefficient of collective diffusion in the situation described above is given by Eq. 6.…”