A multiscale Green's function method is described for modeling of point defects such as vacancies and interstitals together with extended defects such as free surfaces and interfaces in a general anisotropic solid. The method treats the point defects at the atomistic level and extended defects at the macroscopic continuum level in the same formalism. The point defects are represented using the lattice statics Green's function that can model a large crystallite containing a million atoms without excessive CPU effort. The method is especially useful for modeling the elastic response of nanomaterials in which surfaces and interfaces play relatively important roles. The method bridges the length scales by relating the microscopic lattice distortion near a point defect to measurable macroscopic parameters of the solid such as stress and strain. The method is applied to a vacancy and a free surface in fcc copper assuming a many-body potential derived by Cleri and Rosato. Using the lattice statics Green's function method, the lattice distortion, relaxation energy, and the relaxation volume due to a vacancy is calculated in an otherwise perfect copper lattice for a million-atom model. The calculated value of the relaxation volume is in excellent agreement with the observed value. Further, a free (1,0, 0) surface is modeled along with the vacancy using the multiscale Green's function method. Numerical results are presented for the displacement field and the strains at the free surface due to a vacancy and its interaction energy with a free surface in anisotropic copper.
Citation: Physical Review B (Condensed Matter and Materials Physics)
Issue: No. 9
Pub Type: Journals
continuum Green's function, copper, lattice distortion, lattice Green's function, multiscale modeling, vacancy