RELATIONSHIP BETWEEN MODELING OF THE ATOMIC-STRUCTURE OF GRAIN-BOUNDARIES AND STUDIES OF MECHANICAL-PROPERTIES

The main objective of the majority of the microscopic atomic level stu dies of interfaces has been investigation of the dominant atomic level structural features and their relation to geometrical and crystallogr aphic characteristics of grain boundaries. At the same time extensive studies of mechanical properties of materials with interfaces have bee n made in the framwork of continuum mechanics but without taking eithe r structure or properties of the interfaces into account. In this pape r we attempt, at least partially, to bridge the gap between atomistic and continuum approaches. Since the most fundamental properties of mat erials entering continuum treatments are the elastic moduli, we demons trate first that atomic-level elastic properties of interfaces can be rigorously defined and that the fourth-order tenser of effective elast ic moduli of grain boundary regions can be determined in atomistic sim ulations. We then proceed to employ these concepts in the continuum an alysis of long wavelength phonons corresponding to acoustic interface waves. It is then shown that only when the local elastic properties of interfaces are incorporated into the contiuum model, via boundary con ditions derived directly from the atomic-level elastic properties of i nterfaces, are the interfacial waves deduced from this model in good a greement with the phonon calculations.