Diffusion Fundamentals (E-Journal)
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Choice and ambiguity of diffusion paths during formation and growth of intermediate phases and two-phase zones in ternary systems
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New Analytical Results and Numerical Schemes for Irregular Diffusion Processes
Get PDFWe examine the transient diffusion equation with time- and space-dependent diffusion coefficients in 1D. Such transport equations can be easily derived from the Fokker-Planck equation and are essential to understand the diffusion mechanisms in general, e.g. in carbon nanotubes. With the help of the classical self-similar Ansatz we give new, nontrivial analytical solutions. Then we reproduce these by 16 explicit numerical time integration methods, 11 of which are recent and unconditionally stable. The results show that some of the algorithms, e.g. the leapfrog-hopscotch method, are very efficient and can outperform the standard FTCS method
Determination of the parameters of Heine and Abarenkov model potential in hcp crystals
Get PDFParameters of Heine and Abarenkov potential has been computed in this paper for twenty two hexagonal closed pack (hcp) crystals. From the minimization of structure dependent energy of the pure crystal the inter-relation between the two parameters of the potential is first determined. Calculation uses pseudopotential technique with nine different exchange and correlation functions and either only available experimental value of vacancy formation energy or that obtained from an empirical relation based on other experimental parameters as tool. Comparison is made with parameter of Ashcroft model also. For Aschroft this variation is almost flat showing averageness while for Heine and Abarenkov sharp variations are there from one hcp crystal to other
