Multiscale Modeling of Point Defects and Free Surfaces in Semi-infinite Solids
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Multiscale Modeling of Point Defects and Free Surfaces in Semi-infinite Solids V.K. Tewary Materials Reliability Division, National Institute of Standards and Technology Boulder, CO 80305 ([email protected]) ABSTRACT A Green’s function method is described for multiscale modeling of point defects such as vacancies and interstitials at the atomistic level and extended defects such as free surfaces and interfaces at the macroscopic continuum level in a solid. The point defects are represented in terms of Kanzaki forces using the lattice-statics Green’s function, which can model a large crystallite containing a million atoms without excessive CPU effort. The lattice-statics Green’s function reduces to the continuum Green’s function in the asymptotic limit which is used to model the extended defects by imposing continuum- model boundary conditions. Numerical results are presented for the displacement field on the free surface due to a vacancy in semi-infinite fcc copper. INTRODUCTION We describe a Green’s function method for multiscale modeling of point defects such as vacancies and interstitials and extended defects such as free surfaces and interfaces in thin films and semi-infinite solids . Our model treats the point defects at the atomistic level and extended defects at a macroscopic level in the same formalism. We use the lattice-statics Green’s function for atomistic modeling of a point defect and the elastic continuum Green’s function for modeling an extended defect. In contrast to direct computer simulation methods for lattice statics which are CPU intensive, the advantage of the Green’s function method is that it is semi-analytic. Our method can model a large crystallite containing a million atoms without excessive CPU effort. The lattice-statics Green’s function reduces asymptotically to the continuum Green’s function that we use to model the extended defects. We use our method to calculate strain fields in the solid that contains both point and extended defects. Many physical properties of thin films and semi-infinite solids depend upon the strains caused by the point defects near the free surfaces and the interfaces. Strain is a macroscopic quantity that can be measured near a free surface. In order to interpret the experimental results, one needs a model to calculate the strains caused by the point defects in the presence of the free surface. Whereas the continuum model is adequate to represent macroscopic extended defects in solids, it is not fully reliable for modeling point defects where the discrete atomistic structure of the crystal lattice is very important (see, for example, [1,2]). It is therefore necessary to use a multiscale model that accounts for the discrete lattice structure of the solid near a point defect and the macroscopic effects near an extended defect. This explains the upsurge of current interest in multiscale modeling of solids. Recent papers on multiscale modeling are based upon purely numerical techniques using the finite element method and/or computer simulation of the lattice W
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