Kinetic Monte Carlo Simulation of the Aging of Nanoporous Metals
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1263-Y04-04
Kinetic Monte Carlo Simulation of the Aging of Nanoporous Metals Gregory J. Wagner1, Dariush Seif1,2, and Markus Ong1 1 Sandia National Laboratories, Livermore, CA 94551, U.S.A. 2 Current address: UCLA, Westwood, CA 90024, U.S.A. ABSTRACT A kinetic Monte Carlo model for the simulation of the coarsening of nanoporous metals is developed and demonstrated. The model treats surface evolution through the mechanism of surface diffusion by following atoms hopping between sites on an FCC lattice. Using a generic model for event energy barriers, we are able to demonstrate trends in the simulation and show that at high temperatures, coarsening follows approximately the scaling law predicted by continuum surface diffusion theory; the behavior is less clear at low temperatures. By selecting event energies to model palladium we show that we are able to reach temperatures and time scales that have relevance to experiments and applications. INTRODUCTION Nanoporous metallic particles are of great interest for a range of applications including catalysis, gas storage, and electrical energy storage. In particular, recent work has shown that bulk powders of porous palladium, with pore sizes in the 2-5 nm range, can be produced at scales suitable for hydrogen storage applications [1]. However, because of their small pore size these materials are very susceptible to morphological evolution during aging, especially at elevated temperatures, leading to degradation of their storage properties. To better understand and predict the phenomena at work in nanoporous metal aging, we have developed a kinetic Monte Carlo (kMC) model for the simulation of atomic diffusion in a metal lattice. Our goals in this work are twofold: to use kMC to directly predict nano-structural evolution at elevated temperatures, and to explore the range of validity over time and temperature of continuum models of surface diffusion-driven evolution. THEORY The continuum theory of morphological evolution due to surface diffusion was developed by Mullins and coworkers in a series of papers beginning in the 1950s [2]. This simple model is based on the motion of surface atoms under the influence of a free energy gradient. The Mullins equation states that the growth rate of the surface in the normal direction, wn wt , is proportional to the Laplacian of the surface curvature N: wn (1.1) B 2s N wt where B is the surface mobility and the subscript s on the derivatives indicates that derivatives are taken with respect arc length along the surface tangent directions. In this work we will study the time evolution of statistically homogeneous nanoporous structures. To predict this evolution using the Mullins theory of surface diffusion, we will assume that the coarsening of these structures occurs through the mechanism of surface diffusion only, and that the coarsening of the material can be measured through the growth of a single characteristic length scale L. In this work we will define L to be the reciprocal of the surface area per volume of the material:
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