Atomistic Computer Simulation of Diffusion

Abstract

The past decades have seen a tremendous increase in the application of computer modeling and simulation methods to diffusion processes in materials. Along with continuum modeling aimed at describing diffusion processes by differential equations, atomic-level modeling is playing an increasingly important role as a means of gaining fundamental insights into diffusion phenomena.One of the reasons for the growing interest in the atomistic modeling of diffusion is the recognition that experimental methods only deliver effective diffusion coefficients, i.e., coefficients averaged over the diffusion zone and over many atomic jumps contributing to the diffusion flux. Recovering information relating to individual diffusion mechanisms, their activation barriers, correlation factors, and other atomic-level characteristics is extremely difficult, if not impossible. As a result, many experimental measurements produce useful reference numbers for handbooks and immediate technological applications (which is very important too) but do not add much to our basic understanding of diffusion processes. In the long run, however, it is highly desirable to be able to predict diffusion coefficients by calculation. This ability is critical for the ongoing effort to reduce the dramatic costs associated with the development of new technologically advanced materials by the traditional empirical approach. Atomistic modeling appears to offer the only viable way of gaining insights into mechanisms of complex diffusion processes and thus creating a fundamental framework for predictive diffusion calculations.A second reason for this growing interest is that drastically increased computer speeds have enabled computer simulations that could only be dreamed about just two decades ago. New methods have been developed that provide a realistic description of atomic interactions in materials, accelerate molecular dynamics (MD) and Monte Carlo simulations, and allow more reliable calculations of transition rates. The new methods provide

Molecular dynamics study of self-diffusion in Zr

“…In principle, the diffusivity can be obtained from molecular dynamics (MD) simulation but such simulation would require establishing equilibrium vacancy concentration which may require very large simulation cell and rather long simulation time. The formation and migration energies can be rather easily obtained from T=0 calculations (e.g., see [2] or [3]) but using these values at finite temperatures at which the diffusion actually occurs is based on assumption that these quantities do not depend on temperature. The formation and migration energies can be also obtained from more expansive MD simulations where one vacancy is introduced in the simulation cell (e.g., see [4], [5], [6]).…”

“…The formation and migration energies can be also obtained from more expansive MD simulations where one vacancy is introduced in the simulation cell (e.g., see [4], [5], [6]). The calculation of the formation and migration entropies, correlation factor is more complex and based on further assumptions [2]. Finally, the presence of just one vibration frequency in Eq.…”

“…Because of complexity of determination of all parameters in Eq. (2), it is seldom used to determine the diffusivity and in the most works, only the activation energy, E D , calculated via Eq. (4) at T=0 is compared with the experimental activation energy.…”

Predicting Ion Diffusion from the Shape of Potential Energy Landscapes

“…These transitions between Li sites are related to the macroscopic transport. In other words, site-to-site transitions become so-called “rare-event” processes relative to the within-site dynamics . To simplify, the diffusion rate depends on the availability of vacant sites and the height of the energy barriers between the sites.…”

Predicting ion diffusion from the shape of potential energy landscapes

“…In other words, site-to-site transitions become so-called "rare-event" processes relative to the within-site dynamics. 14 To simplify, the diffusion rate depends on the availability of vacant sites and the height of the energy barriers between the sites.…”