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INTRODUCTION

In the last decades the development of larger and faster computers has progressed at a tremendous rate, doubling the capabilities of a typical computer every 18 months. This development has enabled the field of ``computational materials physics'' to contribute significantly to the understanding of materials and their properties. In this paper we focus on the modelling of mechanical properties of nanocrystalline metals, i.e. of metals with a grain size in the nanometer range. The main focus is on atomic-scale simulations, but we also look at other simulation techniques for modelling materials at coarser length-scales.

As matter is made of atoms, and as the quantum mechanical equations governing the interactions of atoms (and the associated electrons) are known, one could imagine that it is -- at least in principle -- possible to solve these equations and predict the properties of matter from first principles. For simple properties of single-crystalline defect-free metals this is indeed possible. With quantum mechanical methods one is, however, only able to treat up to a few hundred atoms, and even there one has to resort to approximations when solving the fundamental equations. When treating complicated processes such as plastic deformation, this is clearly inadequate. One has to give up the ambition of retaining a full quantum mechanical description of the atomic interactions, and describe them by interatomic potentials.

Using parallel supercomputers, one can handle up to 108 atoms for times up to a nanosecond, when the interactions are described using simple pair potentials (Abraham 1997; Abraham, Schneider, Land, Lifka, Skovira, Gerner and Rosenkranz 1997; Bulatov, Abraham, Kubin, Devincre, and Yip 1998), or up to 35 million atoms using more realistic many-body potentials (Zhou, Beazley, Lomdahl and Holian 1997). In most cases one is limited to significantly smaller systems by the need to run a large number of simulations (and often by economical factors as well). The length scale of typical processes in plastic deformation is 1$\mu$m or more, and the time scale is typically seconds or longer. This corresponds to 1011 atoms in 109 nanoseconds, requiring a computational power of 1012 times what is possible today. Even if computers continue to improve at the current rate, such computational power will not become available in a foreseeable future. One is therefore forced to abandon using an atomistic approach to the whole problem, but will have to split up the problem according to the different length scales involved, and reserve the atomistic approach to the processes at the smallest length scales, see e.g. Carlsson and Thomson (1998).

In this paper we will give an overview over how this gap between different length scales can be bridged in simulations of plastic behaviour. In the first part we describe simulations of systems where the characteristic length scales are so small that the entire system can be studied atomistically. The system we have chosen is nanocrystalline metals. In the second part we give an overview of different simulation techniques at the micro and mesoscale, and how the different scales can be combined.


next up previous
Next: ATOMIC-SCALE SIMULATIONS OF NANOCRYSTALLINE Up: No Title Previous: ABSTRACT
Jakob Schiotz
1998-08-18