Stress-driven instability in growing multilayer films

We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system recursively in terms of that of the old states of the buried layers. In turn, we use the result for the elastic state to derive the morphological evolution equation of surface profile to first order of perturbations, with the solution explicitly expressed by the growth conditions and material parameters of all the deposited layers. We apply these results to two kinds of multilayer structures. One is the alternating tensile/compressive multilayer structure, for which we determine the effective stability properties, including the effect of varying surface mobility in different layers, its interplay with the global misfit of the multilayer film, and the influence of asymmetric structure of compressive and tensile layers on the system stability. The nature of the asymmetry properties found in stability diagrams is in agreement with experimental observations. The other multilayer structure that we study is one composed of stacked strained/spacer layers. We also calculate the kinetic critical thickness for the onset of morphological instability and obtain its reduction and saturation as number of deposited layers increases, which is consistent with recent experimental results. Compared to the single-layer film growth, the behavior of kinetic critical thickness shows deviations for upper strained layers.Comment: 27 pages, 11 figures; Phys. Rev. B, in pres

Are Vicinal Metal Surfaces Stable?

Quantum Matter and Optic

A study of nano-indentation using coupled atomistic and discrete dislocation (CADD) modeling

The phenomenon of nano-indentation into a thin film bonded to a rigid substrate is simulated using a recently developed technique whereby a fully atomistic region is coupled to a continuum region. There are three unique features of the model, as compared to several other coupled techniques that are available. First, the continuum region may contain any number of discrete dislocations, modeled as elastic defects. Second, these dislocations are mechanically coupled to one another and to the atomistic region, thus providing the atomistic region with the appropriate stress environment due to the long-range interaction with the dislocations. Finally, the method includes algorithms for automatically detecting and passing dislocations between the atomistic and continuum regions, taking care of the kinematics of slip at the atomistic/continuum interface

A coupled atomistic/continuum model of defects in solids

A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the "passing" of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to "exact" fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads. (C) 2002 Elsevier Science Ltd. All rights reserved

Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics

A computational method (CADD) is presented whereby a continuum region containing dislocation defects is coupled to a fully atomistic region. The model is related to previous hybrid models in which continuum finite elements are coupled to a fully atomistic region, with two key advantages: the ability to accomodate discrete dislocations in the continuum region and an algorithm for automatically detecting dislocations as they move from the atomistic region to the continuum region and then correctly "converting" the atomistic dislocations into discrete dislocations, or vice-versa. The resulting CADD model allows for the study of 2d problems involving large numbers of defects where the system size is too big for fully atomistic simulation, and improves upon existing discrete dislocation techniques by preserving accurate atomistic details of dislocation nucleation and other atomic scale phenomena. Applications to nanoindentation, atomic scale void growth under tensile stress, and fracture are used to validate and demonstrate the capabilities of the model. (C) 2003 Elsevier Ltd. All rights reserved

A coupled atomistics and discrete dislocation plasticity simulation of nanoindentation into single crystal thin films

The phenomenon of 2D nanoindentation of circular "Brinell" indenter into a single crystal metal thin film bonded to a rigid substrate is investigated. The simulation method is the coupled atomistics and discrete dislocation (CADD) model recently developed by the authors. The CADD model couples a continuum region containing any number of discrete dislocations to an atomistic region, and permits accurate, automatic detection and passing of dislocations between the atomistic and continuum regions. The CADD model allows for a detailed study of nanoindentation to large penetration depths (up to 60 Angstrom here) using only a small region of atoms just underneath the indenter where dislocation nucleation, cross-slip, and annihilation occur. Indentation of a model hexagonal aluminum crystal shows: (i) the onset of homogeneous dislocation nucleation at points away from the points of maximum resolved shear stress; (ii) size-dependence of the material hardness, (iii) the role of dislocation dissociation on deformation; (iv) reverse plasticity, including nucleation of dislocations on unloading and annihilation; (v) permanent deformation, including surface uplift, after full unloading; (vi) the effects of film thickness on the load-displacement response; and (vii) the differences between displacement and force controlled loading. This application demonstrates the power of the CADD method in capturing both long-range dislocation plasticity and short-range atomistic phenomena. The use of CADD permits for a clear study of the physical and mechanical influence of both complex plastic flow and non-continuum atomistic-level processes on the macroscopic response of material under indentation loading. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved

Coupled atomistic and discrete dislocation plasticity

A computational method for multiscale modeling of plasticity is presented wherein each dislocation is treated as either an atomistic or continuum entity within a single computational framework. The method divides space into atomistic and continuum regions that communicate across a coherent boundary, detects dislocations as they approach the boundary, and seamlessly converts them from one description to another. The method permits the study of problems that are too large for fully atomistic simulation while preserving accurate atomistic details where necessary, but is currently limited to a 2D implementation. A validation test is performed by comparing the method against full atomistic simulations for a D nanoindentation problem

A study of nano-indentation using coupled atomistic and discrete dislocation (CADD) modeling

The phenomenon of nano-indentation into a thin film bonded to a rigid substrate is simulated using a recently developed technique whereby a fully atomistic region is coupled to a continuum region. There are three unique features of the model, as compared to several other coupled techniques that are available. First, the continuum region may contain any number of discrete dislocations, modeled as elastic defects. Second, these dislocations are mechanically coupled to one another and to the atomistic region, thus providing the atomistic region with the appropriate stress environment due to the longrange interaction with the dislocations. Finally, the method includes algorithms for automatically detecting and passing dislocations between the atomistic and continuum regions, taking care of the kinematics of slip at the atomistic/continuum interface