LOCAL AND EFFECTIVE ELASTIC PROPERTIES OF GRAIN-BOUNDARIES IN SILICON

When considering the mechanical behaviour of materials an important pr operty is the tensor of elastic moduli. Recently, local elastic moduli of interfaces have been defined and studied for metallic materials [1 to 3]. In these works grain boundaries are regarded as heterogeneous continua composed of 'phases' associated with individual atoms which p ossess elastic moduli identified with the atomic-level moduli evaluate d at corresponding atomic positions. From this representation it is po ssible to define the 'effective' moduli of the grain boundary region. In this paper this concept is developed for materials with covalent ch aracter of bonding, specifically silicon. Using the Tersoff's potentia l [4, 5], the atomic-level and effective elastic moduli of the interfa cial region have been evaluated for three alternate structures of the Sigma = 3 (11(2) over bar)/[<1(1)over bar>0] tilt boundary. These calc ulations: are then compared with the continuum bounds on the effective moduli evaluated using the classical minimum-energy principles of ela sticity. The effective moduli calculated in the atomistic framework ar e generally within the continuum bounds and thus the present study dem onstrates that the heterogeneous continuum model of the interfaces is appropriate for the description of the elastic properties of grain bou ndaries in silicon. An important aspect addressed in this study is the uniqueness of interfacial elastic moduli since their evaluation invol ves the energy associated with an atom which cannot be defined uniquel y. The calculations have been made for two different partitions of the total energy into energies associated with individual atoms. These tw o partitions lead to almost identical results for the effective moduli and continuum bounds when the tensor of the atomic-level moduli is po sitive definite. When some atomic-level moduli are not positive defini te tie results may depend on the chosen energy partition.