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Atomistic simulations of diffusional processes with elastic interactions

Date: 
Tuesday 21st January 2003 - 14:00 to 15:00
Venue: 
INI Seminar Room 1
Session Title: 
Mathematical Challenges in Scientific and Engineering Computation
Abstract: 
Diffusion is a process that takes place at the atomic scale through the motion of defects, notably vacancies. In the first part of my talk I will show that the atomistic mechanisms of diffusion have consequences at the macroscale for kinetics and morphologies of phases produced by transformations. Even the mechanism of coarsening of second phases can be strongly influenced by the trapping of vacancies at interfaces.

In the second part of my talk I shall describe our most recent work on including long-range elastic interactions in atomistic models of diffusional processes. There are many instances where elastic interactions are known to have a profound effect on diffusional processes. In elastically anisotropic materials, spatial correlations of precipitates arise along elastically soft directions. Very small amounts of certain impurities can influence the kinetics of diffusional phase changes in a seemingly disproportionate manner. When atoms are deposited from the vapour onto surfaces islands may form to relieve the elastic strain energy in the system. These are all diffusional processes in which elastic interactions play a crucial role. The challenge for atomistic modelling is how to include very long-range effects in a simulation involving millions, even billions, of vacancy hops. We have developed new computational techniques to meet this challenge, which I shall describe and illustrate.

This work was done in collaboration with Daniel R Mason, who was supported by EPSRC, and with Dr Robert Rudd of Lawrence Livermore National Laboratory.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons