Atomic structure and elastic properties of grain boundaries in materials with covalent character of bonding.

摘要

In this thesis the effects of non-central atomic interactions were first investigated in an atomistic study of grain boundaries in molybdenum and tungsten, the transition metals with half-filled d-band. For this purpose the potentials constructed by Carlsson have been used. They incorporate contributions of the fourth and the matrix second moments of the local density of electronic states (LDOS) which both lead to non-central character of interactions. For the three boundaries studied the energy differences between alternate structures were found to depend significantly on the angles between bonds of nearest neighbor atoms while central-force potentials, which only include the scalar second moment of the LDOS, favor structures with atomic separations close to those in the ideal lattice. Consequently, the lowest energy structures predicted by the two potential schemes differ in both the local atomic relaxations and the magnitude of the rigid-body displacements of the adjoining grains, although many general features of the boundary structures remain the same, independent of the potentials used.; The calculations of the atomic structure of grain boundaries in silicon, a model covalent system, were made using Tersoff's potentials and revealed two different tendencies that appear to govern the energetic preference among competing alternate structures. The first tendency is to preserve the tetrahedral four-fold coordination of the perfect crystal. For the structures where all the atoms are four-fold coordinated the factor which plays the decisive role in determining the lowest energy structure is the tendency to preserve the nearest neighbor bond-angles close to those found in the perfect crystal.; The atomistic study of the interfacial elastic properties showed that the reduced coordination at the interface leads to the loss of positive definiteness of the moduli associated with these regions. In parallel, by linking atomistic and continuum approaches, an improved continuum representation of the interface was developed which accounts for the distinct interfacial properties. Inclusion of these properties in the continuum framework of interface wave propagation was critical in reproducing the dispersive character of long wavelength interfacial acoustic waves in agreement with lattice dynamics calculations.