Center for Advanced Materials Research

Materials Research Science and Engineering Center on
"Micro- and Nano- Mechanics of Materials"

RESEARCH ACCOMPLISHMENTS AND PLANS
in the period 4/1/2006 - 3/31/2007

IRG1	IRG 2	Seed

The research activities within the MRSEC are central to its success. They are the base from which all other parts of the Center develop. The research proposed in the current project reflects a natural evolution of the work that has been performed under our past MRSEC and builds in new directions on two key themes: Stress in Thin Film and Small scale Structires and Multiscale Mechanics of Complex Microstructures. At the completion of this work, we will have developed a wide range of computational methods that can be applied to many materials problems and that have been validated with experimental studies. The results will provide insight at the atomic and microstructural scales into the central mechanics features of such problems as quantum dot formation, fracture of lamellar structures, and the fracture resistance of tailored interfaces. These particular systems have been chosen for study because they are excellent model systems and because they have relevance to many industrial applications. Hence, the detailed information we gather and the insight we gain will be of direct technological importance.

IRG1: STRESS IN THIN FILM AND SMALL SCALE STRUCTURES

Faculty participants: A.F. Bower, E. Chason, L.B. Freund, P. Guduru, K.S. Kumar, B.W. Sheldon, V. Shenoy, (7 students, 1 post-docs)

A major unifying theme of IRG1 is the coupling between stress, surface kinetics and surface energetics to understand dynamical evolution at small length scales. In this respect, Shenoy’s work has focused on understanding and modeling the evolution of nanostructures and surfaces. In a collaboration with Jim Hannon of IBM, they have performed detailed calculations to interpret LEEM measurements of the evolution of the technologically important Si(100) surface during deposition. The 2x1 reconstruction on this surface induces an anisotropic surface stress that rotates 90 deg between different atomic levels. Their calculations explain the complex spiral motion observed around dislocation cores intersecting the surface, due to a surface chemical potential that depends on the step energetics and the surface stress. These calculations make it possible to quantitatively evaluate critical surface kinetic parameters as well as increase our understanding of the effect of stress on controlling surface evolution.

On Si(111) surfaces, they have studied the evolution of 7x7 domains as the surface is cooled through the transition from a 1x1 surface reconstruction. As shown in figure 1, the island shape can evolve from a concave shape to a branched morphology, with the evolution controlled by a complex interplay of surface energetics and kinetics. Their calculations (shown in figure 1b) are able to explain the critical features of the evolution, such as how the balance between elastic relaxation around the edges and step edge energy creates an equilibrium island size and how the dependence of the step edge energy on orientation drives the shape to bifurcate from smooth edges to notches. The excellent agreement between the calculations and the measurements enables important surface parameters such as the step stiffness to be evaluated.

Bower et al. have made substantial progress in developing a front-tracking finite element method to predict the evolution of stress during the deposition of a thin polycrystalline film on a substrate. The film simulations consider both elastic interactions in the solid and transport along the film surface. A cohesive zone model (as shown schematically in figure 2) is used to model the attractive interaction between island surfaces as individual clusters coalesce to form grain boundaries. The effects of mass diffusion inside the grain boundary and differences in surface and grain boundary diffusivity are also included in the model. During the past year, changes to the numerical procedure have enabled them to dramatically increase the speed of the computer simulations, making it possible to conduct parametric studies of the effect of material properties and processing conditions on the stress evolution. Representative results are illustrated in figure 3, showing a sequence of stress contours during the coalescence of two islands – note the formation of grain boundary, and the complex stress distribution that develops in the triple junction. A characteristic three-stage process of (i) zero stress prior to coalescence; (ii) tensile stress at the instant of coalescence; and (iii) compressive stress after full coalescence emerges naturally from our simulations, in excellent qualitative and quantitative agreement with experiment. The dependence of the steady state stress on growth flux over a large range has been modeled showing the conditions for which the stress reaches a compressive maximum. The modeling studies have been complemented by experimental work on physical vapor deposition of low mobility materials (Sheldon) and electrodeposition of high mobility materials (Sheldon and Chason) to cover a wide range of kinetic parameters. These experiments are enabling the effect of surface mobility and grain size on residual stress to be quantified for comparison with the model predictions.

In addition to the development of residual stress, Sheldon has used changes in film stress to provide information about the energetics and kinetics of point defects in non-stoichiometric oxide materials (e.g., TiO2-x, CeO2-x, etc.). The point defect concentration plays a critical role in controlling film stress as well as atomic and electronic transport in these materials. As shown in figure 3, the stress in the film changes depending on the ambient environment (i.e., oxidizing or reducing atmosphere). The relationship between the steady state stress and the temperature/pressure of the surrounding gas is used to determine the energetics of defect formation and the rate of change of the stress is used to determine the kinetics of defect diffusion. The defect concentration and defect kinetics are difficult to measure directly, and monitoring film stress provides important information that is not readily obtained from other techniques (e.g., impedance spectroscopy). The temperature and pressure dependence of the resulting stress has been used to determine the formation energy for oxygen vacancies in TiO2-x and CeO2-x films. The time-evolution of the stress in TiO2-x films has been used to determine the temperature-dependent point defect diffusivity. They are also performing experiments on stress evolution during constrained sintering of Gd-doped ceria, which is of interest as an electrolyte for solid oxide fuel cells.

Chason and Kumar have been studying the formation of Sn whiskers in coatings on Cu conductors. Whisker formation has become a critical problem in electronics manufacturing due to environmental regulations requiring the removal of Pb. Pb-Sn alloys coatings (that have been used in commercial applications up until now) do not form whiskers, but lead-free pure Sn coatings (that are being substituted for Pb-Sn) produce many whiskers that create short circuits and system failures, including several documented satellite crashes. Several major results have been obtained in the past year. The simultaneous evolution of intermetallic (IMC) volume, film stress and whisker nucleation has been measured on layers of different thickness and composition. They find that the stress saturates at a value comparable to the yield stress, even though the IMC continues to grow, which indicates the onset of plastic deformation in the Sn layers to accommodate the volumetric expansion around the growing IMC particles. The presence of dislocation-mediated plasticity was confirmed by cross-sectional TEM measurements (as shown in figure 5) which show that the highly mobile dislocations form into subgrain boundaries. The oxide plays a critical role by preventing dislocations form escaping to the top surface and relieving the stress. In contrast with pure Sn layers, alloy layers of Pb-Sn do not build up large stresses even though the growth of IMC is comparable to the pure Sn. This is attributed to the different microstructure of the Pb-Sn layers, with many horizontal grain boundaries that can absorb the dislocations without creating stress. In the future, these will be extended to different layered structures to identify underlying materials processes and explore mitigation strategies. The experimental results will also be used as a basis for developing models of IMC growth and stress evolution to develop a predictive capability for whisker formation and to interpret accelerated aging studies.

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IRG2: Multiscale Mechanics of Complex Microstructures

Faculty participants: Bower, Curtin, Gao, Kim, Kumar, Needleman (4 students, 1 post-doc)

The goal of IRG 2 is to elucidate the mechanisms of deformation and failure in complex multiphase and nanoscale microstructures. The project is motivated by the need to develop advanced materials that are capable of withstanding stress, often combined with an extreme environment, for applications such aircraft structures, gas turbines, and lightweight engines for automotive applications. Our approach is to use multi-scale computer simulations that include cohesive zone models of fracture and fatigue, discrete dislocation models of plasticity, and several atomistic simulations methods to model material processes at continuum, meso- and atomic scales. Our simulations are guided and verified by in-situ observations of failure in both model systems, as well as by experiments designed to provide quantitative measurements of strength associated with specific processes.

In work on microstructural effects on fracture, Kumar is using both in-situ experiments and finite-element/cohesive-zone computations to study crack deflection at twist boundaries, using bi-crystals of Zn as a model system. Crack deflection and twisting are the dominant toughening mechanisms in intermetallics such as lamellar Ti46Al, polycrystalline ceramics, and brittle lamellar composites. Principal results from this project during the past year are (i) measurement of toughening caused by a twist grain boundary as a function of orientation (Fig 1) (ii) development and calibration of cohesive zone based continuum finite element model of crack propagation through a twist boundary, based on models developed with Gao. Continued work will focus on extending the simulations to account for crystal plasticity, and more detailed comparisons between theory and experiment.

Our continuum fracture models use cohesive zones to model material failure at the crack tip. We are using mesoscale and atomistic simulations, as well as experiments, to calibrate these constitutive relations and provide insight into the underlying processes that lead to material failure. Needleman is using discrete dislocation simulations to study dislocation emission and organization near crack tips during fracture, Kumar is using in-situ microscopy to provide direct observations of these processes, and Kim is using model experiments to measure the influence of fluctuating stress fields near a crack tip on the effective fracture toughness of the material.

Many failure mechanisms in complex microstructures are controlled to a large extent by meso-scale interactions between defects, at length scales between 100nm and 1000nm. Needleman and Curtin are using discrete dislocation simulations to study a range of problems where meso-scale deformation mechanisms play an important role. Three significant studies were completed during the past year

In association with Northrop-Grumman Corporation, Curtin and Needleman have used discrete dislocation simulations to model fatigue crack growth rates for cracks emanating from cracked inclusion particles, a typical defect in Al-7075 alloys used for aircraft structures. A set of representative results are illustrated in Fig. 2. The DD model reveals that particles having a higher elastic modulus than the matrix show faster fatigue crack growth. Specifically, the threshold stress intensity for the onset of crack growth is much lower, primarily due to the increased local stresses generated by the particle, and the subsequent Paris-law exponent is lower. These results are consistent with experimental data obtained at Northrop-Grumman.
Curtin has used the discrete dislocation method to model fracture in confined thin metals films having applications in microelectronic devices, with recent emphasis has been on predicting the role of residual stress on fracture toughness for different film thicknesses. Experimental results (Lane M, Dauskardt RH. J Mat Res 2000; 15:2758-2769) show a marked decrease in toughness with increased residual stress, a result that cannot be adequately explained by standard continuum plasticity. The DD model predict that tensile residual stresses do decrease the fracture toughness significantly for thicker films (~2 microns), in agreement with experiments. These results show that the DD model captures the simultaneous interactions among numerous constraints – elastic confining layers; crack tips; residual stresses - that cause size-dependent plasticity phenomena, through treatment of plasticity at the fundamental dislocation level, eliminating the need for ad-hoc introduction of size effect corrections in continuum plasticity models. Furthermore, our results make quantitative contact with experimental data, indicating that the DD models can be quantitative, particularly when phenomena are dominated by dislocation pile-up effects at boundaries.
Needleman has continued efforts to understand the underlying mechanisms responsible for size effects on plastic flow in single crystal and polycrystalline metals. In previous work we used two-dimensional discrete dislocation plasticity to investigate the origins of the single crystal size effect. During the past year, a similar study was completed for polycrystalline specimens. Our calculations showed that the role of grain boundaries in blocking slip is key to the difference between the size dependence of single crystal and polycrystalline specimens. For a sufficiently small single crystal specimen, the distance a dislocation needs to glide to exit the specimen is less than the mean distance between obstacles and dislocations are likely to leave the specimen without encountering an obstacle. Continued plastic deformation thus requires the stress to be maintained at the nucleation strength. For larger specimens, dislocation glide is more likely to be blocked by obstacles. The stress concentrations associated with the elastic fields of the dislocations then enable the activation of dislocation sources at applied stress values less than the nucleation strength. Thus, the same discrete dislocation framework that accounts for the size effect in single crystals gives size independence for polycrystals.

In the development of multi-scale simulation methods, Curtin and Needleman are currently creating a technique to couple the discrete dislocation method with continuum plasticity in a finite element framework. This will provide a direct connection to macroscopic (structural) length-scales, and, if combined with the Coupled Atomistic-Discrete Dislocation method recently developed by Curtin, will permit simulation of an entire component at all length scales. In addition, Needleman is using MD simulations to calibrate parameters such as dislocation nucleation criteria that are used in discrete dislocation models. Work during the past year focused on studies of dislocation nucleation at free surfaces. Important conclusions of this study are (i) stress magnitudes at the instant of dislocation nucleation are nearly an order of magnitude smaller than for homogeneous bulk dislocation nucleation and (ii) contrary to standard assumptions, dislocation nucleation is not well-represented by a critical value of the resolved shear stress but is reasonably well-represented by the critical stress gradient criterion.

Finally, Curtin has developed a new multi-scale approach that can predict the influence of solute chemistry and volume fraction in Al/Mg alloys, in association with the GM/Brown CRL. Understanding the influence of solutes on plastic flow in solute strengthened metals is a critical issue in designing lightweight Al and Mg alloys with improved formability. The new theory identifies Mg motion across the dislocation core, from the compression side to the tension side, as the operative mechanism (Fig 3). The activation enthalpy for this cross-core Mg diffusion is much lower than that for bulk Mg diffusion in Al, greatly accelerating the process in comparison to existing theories and in good agreement with experimental values (strain rate scale of 5x10-5/sec predicted and measured). The energy change upon the cross-core diffusion sets a strength scale that is comparable to experimental values (see Fig 3). The cross-core mechanism is expected to operate in other material systems as well.

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SEED: MICROMECHANICS OF CELL ADHESION

Faculty participants: L.B. Freund, J. Morgan, J. Tang (4 students, 1 post-doc)

A focus this past year has been on the experimental discovery that there appears to be a maximum spacing between molecular bonds for which adhesion of the cell to its substrate can occur [Arnold et al., ChemPhysChem 5 (2004) 383]. Freund has shown that thermal fluctuations arising from immersion of the membrane in a heat bath can account for the appearance of a critical bond site spacing in agreement with the observations. Current effort focuses on the kinetics of bonding in such a process and the synergy of adjacent bonds in effecting cell adhesion.

Morgan’s group has undertaken a series of experiments based on our novel micro-molded hydrogel developed in the first year of the project to study the self-assemble properties of different cell types. Using micro-molded non-adhesive agarose hydrogels seeded with Reuber-H35 rat hepatoma cell line (H35s), human fibroblasts (NHFs) or their mix (1:1), we showed that cells can self-assemble rods, tori and honeycombs. Figure 1 shows a 1:1 mix of labeled NHFs (red) and H35s (green) seeded onto gels with honeycomb features and viewed by fluorescent microscopy after 24 hours. We found that H35s readily formed stable rod-like structures that were 49% the original length of the mold’s trough feature up to 2.2 mm. They also formed intact tori (88%) and fully-intact honeycombs structures with patent lumens (9/9), even when released from the mold. In contrast, mono-dispersed NHFs seeded into trough features progressed rapidly to spheroids and formed fewer stable tori (30%) and honeycombs (0/9). Experiments with labeled cells in tori and honeycombs revealed that cells self-segregated in these complex structures, that H35s enveloped NHFs and that NHFs have different morphologies in taut versus relaxed structures. The experimental methodology and results introduced by Morgan below are providing a wealth of quantitative data on evolution of cell clusters through mutual interaction. To provide a framework for quantitative interpretation of the observations, Freund has begun development of a model of the kinetics of transport within such a cluster; this effort will carry over into the next project year.

Tang’s group has focused on the experimental study of the isotropic to nematic phase transition of F-actin. A current graduate student, Mr. Patrick Oakes, has played a key role in carrying this project to completion, resulting in two original publications. Another major effort in the last year has been acquisition and testing of the combined AFM-TIRF microscopy system supported under the MRSEC program. Through the fall and winter, various components have been delivered. As of Feb. 2007, the facility has been available for test experiments. The preliminary results are very exciting and much of the current year will be devoted to making use of this new experimental capability.

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