“From defects to cracks: Optimal scaling laws in ductile fracture”

In 2003, researchers at Toyota introduced a TiNb based alloy that they named Gum Metal. The alloy displays super strength, super elasticity and considerable ductility. In fact the alloy's observed strength approaches the its ideal strength. These properties fully emerge only after extensive cold swaging. However, postdeformation microstructures reveal few (if any) dislocations. These observations (amongst others) led Toyota researchers to claim that Gum Metal is the first bulk engineering alloy to deform at ideal strength. The interesting properties of Gum Metal beg the question: Where are the dislocations? In this talk, I will present our studies of dislocations within Gum Metal, and discuss how the elastic anisotropy that emerges near a concentration driven phase transformation results in easy pinning and extreme spreading of the dislocation cores, ultimately leading to the impressive mechanical properties of Gum Metal. Large-scale electronic structure calculations and studies on defects Vikram Gavini Department of Mechanical Engineering, University of Michigan, Ann Arbor Defects play a crucial role in influencing the macroscopic properties of solids—examples include the role of dislocations in plastic deformation, dopants in semiconductor properties, and domain walls in ferroelectric properties. These defects are present in very small concentrations (few parts per million), yet, produce a significant macroscopic effect on the materials behavior through the long-ranged elastic and electrostatic fields they generate. The strength and nature of these fields, as well as other critical aspects of the defect-core are all determined by the electronic structure of the material at the quantummechanical length-scale. Hence, there is a wide range of interacting length-scales, from electronic structure to continuum, that need to be resolved to accurately describe defects in materials and their influence on the macroscopic properties of materials. This has remained a significant challenge in multi-scale modeling, and a solution to this problem holds the key for predictive modeling of complex materials systems. In an attempt to address the aforementioned challenge, this talk presents the development of a seamless multi-scale scheme to perform electronic structure calculations at macroscopic scales. The key ideas involved in its development are (i) a real-space variational formulation of electronic structure theories, (ii) a nested finite-element discretization of the formulation, and (iii) a systematic means of adaptive coarse-graining retaining full resolution where necessary, and coarsening elsewhere with no patches, assumptions or structure. This multi-scale scheme has enabled, for the first time, calculations of the electronic structure of multi-million atom systems using orbital-free density-functional theory, thus, paving the way for an accurate electronic structure study of defects in materials. The accuracy of the method and the physical insights it offers into the behavior of defects in materials is highlighted through studies on vacancies and dislocations. Current efforts towards extending this multi-scale method to Kohn-Sham density functional theory will also be presented, which include: (i) the development of higher-order adaptive finite-element formulation for efficient real-space Kohn-Sham DFT calculations; (ii) the development of a linear-scaling approach that is applicable to both insulating and metallic systems. Electronic and plasmonic phenomena at graphene grain boundaries Zhe Fei, Physics Department of UC San Diego Line defects that are omnipresent in graphene films fabricated with chemical vapor deposition method (CVD) were studied with scattering-type scanning near-field microscope (sSNOM) –a unique technique allowing efficient excitation and high-resolution imaging of graphene plasmons [1,2]. The characteristic sSNOM features of line defects are plasmonic twin fringes, which are generated due to interference between surface plasmons of graphene launched by a scanning probe and reflected by the line defects. The twin fringes allow us to visualize and distinguish various types of line defects including cracks, wrinkles, and most interestingly grain boundaries. Unlike other line defects, grain boundaries are in the atomic length scale. Therefore it remains challenging to characterize their physical properties with traditional methods. I will show that our technique together with modeling and analysis provide a convenient way to uncover the electronic and plasmonic properties associated with grain boundaries in graphene [3]. [1] Z. Fei et al. Nano Lett. 11(11), 4701-4705 (2011). [2] Z. Fei et al. Nature 487, 82–85 (2012). [3] Z. Fei et al. Nature Nanotech. 8, 821–825 (2013). Towards the ab-initio study of defects: Coarse-graining Density Functional Theory Phanish Suryanarayana Georgia Institute of Technology Crystal defects, though present in relatively minute concentrations, play a significant role in determining macroscopic properties. The accurate characterization of defects represents a unique challenge since both the electronic structure of the defect core as well as the long range elastic field need to be resolved simultaneously. Unfortunately, accurate ab-initio electronic structure calculations are limited to a few hundred atoms, which is orders of magnitude smaller than that necessary for a complete description at physically relevant concentrations. We present a real-space formulation for coarse-graining Density Functional Theory [1] that significantly speeds up the analysis of crystal defects without appreciable loss of accuracy. The proposed technique consists of two steps. First, we develop a linearscaling method [1, 2] in terms of quantities amenable to coarse-graining. Next, we introduce a spatial approximation scheme which is adapted so as to furnish fine resolution where necessary and to coarsen elsewhere. We validate the formulation through selected examples.