The objective of this Faculty Early Career Development (CAREER) Program award is to develop a seamless multi-scale computational technique to study crystalline solids with defects by resolving all the relevant length-scales -- from quantum-mechanical interactions at the sub-Angstrom length-scale to the elastic fields on the continuum scale. This will be achieved by (i) developing a real-space finite-element formulation of Kohn-Sham Density Functional Theory (KSDFT) which will scale linearly with the number of electrons; and (ii) developing the quasi-continuum reduction of KSDFT using a hierarchy of adaptive finite-element triangulations which will resolve the quantum-mechanical interactions where necessary (like the core of a defect), while seamlessly coarse-graining away to capture the long-ranged elastic fields. The developed multi-scale scheme will be used to investigate the origins of plasticity in surface dominated structures like nano-pillars.
The proposed research will enable quantum-mechanics informed calculations on continuum scales by seamlessly bridging the quantum-mechanical length-scale with the continuum. Importantly, this multi-scale scheme links the material description at any length-scale to their fundamental origin -- the electronic structure. Thus, the developed method is expected to be transferable and predictive. This effort will enable an accurate quantum-mechanical description of defects in materials, and in effect will promote predictive simulations of deformation and failure mechanisms in solids. The educational efforts include developing a core-curriculum for the field of nanoscience, and developing educational modules involving simulations of materials behavior to demonstrate the importance of computations in science and technology to high school students.
