ATOMIC-LEVEL ELASTIC PROPERTIES OF INTERFACES AND THEIR RELATION TO CONTINUA

The relationship between atomic structure and elastic properties of grain boundaries is investigated from both discrete and continuum points of view. The complete fourth-order tensors of both the atomic-level and the effective elastic moduli are defined for the discrete system, where the latter corresponds to sub-blocks from an infinite bicrystal and are calculated here for a relatively few atomic layers above and below the grain boundary. Then, a heterogeneous continuum model of the boundary is introduced where distinct phases are associated with individual atoms and possess their atomic-level moduli. Only estimates (upper and lower bounds) of the effective moduli can be determined for the continuum model. Comparison between the atomistic results and those for the continuum model establishes the validity of this definition of elastic properties for heterogeneous structures at atomic scales. Furthermore, these comparisons as well as algebraic properties of the fourth-order tensor of moduli lead to criteria to assess the stability of a given grain boundary structure.