Search

The surface stress distribution in an ordered quantum dot superlattice is investigated using classical molecular dynamics simulations. We find that the surface stress field induced by various numbers~ from 1t o 9! of Ge islands embedded in a Si~001! substrate is in good agreement with analytical expressions based on pointlike embedded force dipoles, explaining the tendency of layered arrays to form vertically aligned columns. The short-ranged nature of this stress field implies that only the uppermost layers affect the surface growth and that their influence decreases rapidly with layer depth. @S0163-1829~99!52028-6#

A series of molecular-dynamics simulations has been performed in order to evaluate the effects of several physical factors on dynamic crack stability. These factors are the crystalline structure and the interatomic interaction modeled by various empirical potentials. For brittle crack propagation at low temperature we find that steady-state crack velocities are limited to a band of accessible values. Increasing the overload beyond ${\mathrm{K}}_{\mathrm{Ic}}$, the crack can propagate with a steady-state velocity, which quickly reaches the terminal velocity of about 0.4 of the Rayleigh wave speed. The magnitude of the terminal velocity can be related to the nonlinearity of the interatomic interaction. Further increasing the overload does not change the steady-state velocity dramatically, but significantly increases the amplitude of acoustic emission from the crack tip. Loading the crack even further leads to instabilities which take the form of cleavage steps, dislocation emission, or branching. The instability is closely related to the buildup of a localized coherent, phononlike field generated by the bond-breaking events. The form of the instability depends critically on crystal structure and on the crystallographic orientation of the crack system but can also be correlated with the relative ease of dislocation generation (and motion).

A series of atomistic calculations is performed in order to explore dislocation core-core interactions and the Peierls stress in a model hexagonal lattice. The method of calculation is the lattice Green`s function method, using several pair potentials with variable parameters. We confirm that dislocation cores broaden as a pair of dislocations with opposite sign move closer to each other. Continuum theories are surprisingly accurate in describing the dislocation-dislocation interaction force even in the range of strong core-core overlap. However, our atomistic calculations show that while the relation between the Peierls stress and dislocation width is exponential as the Peierls-Nabarro model predicts, that model underestimates the Peierls stress by nearly a factor of 10{sup 4}.

A series of atomistic calculations is performed in order to evaluate the effects of several physical factors on dislocation emission in a model hexagonal lattice. The method of calculation is the lattice Green's-function method, together with several pair potentials with variable parameters. The physical factors of interest are the dislocation width (or, more precisely, maximum strain) and ``unstable stacking energy'' suggested by several continuum-based calculations, as well as the mode-I loading. We find that the continuum theories are surprisingly accurate, provided that some modifications are made. Typical discrepancies are of order 10% in the emission stress intensity. However, the atomistic calculations indicate that several of the assumptions underlying the continuum theories are inaccurate. In addition, we find strong mode-I--mode-II interactions, which are summarized in the form of a crack-stability diagram.

This paper explores the use of lattice Green's functions for calculating the static structure of defects in lattices, in that the atoms of the lattice interact with their neighbors with an arbitrary nonlinear (short-range) potential. The method is hierarchical, in which Green's functions are calculated for the perfect lattice, for increasingly complicated defect lattices, and finally the nonlinear structure problem is iterated until a converged solution is found. For the case where the defect must be embedded within a very large linear system, and the slip plane, cleavage plane, nonlinear zone, etc., can be made small compared to the system size, Green's functions are a very powerful method for studying the physics of defects and their interactions. As an illustration of the method, we report numerical calculations for an interfacial crack emitting dislocations from an interface between two joined two-dimensional hexagonal lattices. The supercell size was 4{times}10{sup 6}, and the crack length was 101 lattice spacings. After the Green's functions were obtained for the defective lattice, the dislocation and crack structures were obtained in a minute or less, making possible detailed studies of the defects with various external loads, force laws, defect relative positions, etc., with negligible computer time. Withmore » practical supercomputer times, supercell and defect sizes one or two orders larger are feasible, thus making possible a realistic calculation of three-dimensional nucleation events on cracks, etc.« less