Design and synthesis of multigrain nanocrystals via geometric misfit strain.

The impact of topological defects associated with grain boundaries (GB defects) on the electrical, optical, magnetic, mechanical and chemical properties of nanocrystalline materials1,2 is well known. However, elucidating this influence experimentally is difficult because grains typically exhibit a large range of sizes, shapes and random relative orientations3-5. Here we demonstrate that precise control of the heteroepitaxy of colloidal polyhedral nanocrystals enables ordered grain growth and can thereby produce material samples with uniform GB defects. We illustrate our approach with a multigrain nanocrystal comprising a Co3O4 nanocube core that carries a Mn3O4 shell on each facet. The individual shells are symmetry-related interconnected grains6, and the large geometric misfit between adjacent tetragonal Mn3O4 grains results in tilt boundaries at the sharp edges of the Co3O4 nanocube core that join via disclinations. We identify four design principles that govern the production of these highly ordered multigrain nanostructures. First, the shape of the substrate nanocrystal must guide the crystallographic orientation of the overgrowth phase7. Second, the size of the substrate must be smaller than the characteristic distance between the dislocations. Third, the incompatible symmetry between the overgrowth phase and the substrate increases the geometric misfit strain between the grains. Fourth, for GB formation under near-equilibrium conditions, the surface energy of the shell needs to be balanced by the increasing elastic energy through ligand passivation8-10. With these principles, we can produce a range of multigrain nanocrystals containing distinct GB defects.

GPU-accelerated minimum distance and clearance queries.

We present practical algorithms for accelerating distance queries on models made of trimmed NURBS surfaces using programmable Graphics Processing Units (GPUs). We provide a generalized framework for using GPUs as coprocessors in accelerating CAD operations. By supplementing surface data with a surface bounding-box hierarchy on the GPU, we answer distance queries such as finding the closest point on a curved NURBS surface given any point in space and evaluating the clearance between two solid models constructed using multiple NURBS surfaces. We simultaneously output the parameter values corresponding to the solution of these queries along with the model space values. Though our algorithms make use of the programmable fragment processor, the accuracy is based on the model space precision, unlike earlier graphics algorithms that were based only on image space precision. In addition, we provide theoretical bounds for both the computed minimum distance values as well as the location of the closest point. Our algorithms are at least an order of magnitude faster and about two orders of magnitude more accurate than the commercial solid modeling kernel ACIS.

Performing efficient NURBS modeling operations on the GPU.

We present algorithms for evaluating and performing modeling operations on NURBS surfaces using the programmable fragment processor on the Graphics Processing Unit (GPU). We extend our GPU-based NURBS evaluator that evaluates NURBS surfaces to compute exact normals for either standard or rational B-spline surfaces for use in rendering and geometric modeling. We build on these calculations in our new GPU algorithms to perform standard modeling operations such as inverse evaluations, ray intersections, and surface-surface intersections on the GPU. Our modeling algorithms run in real time, enabling the user to sketch on the actual surface to create new features. In addition, the designer can edit the surface by interactively trimming it without the need for retessellation. Our GPU-accelerated algorithm to perform surface-surface intersection operations with NURBS surfaces can output intersection curves in the model space as well as in the parametric spaces of both the intersecting surfaces at interactive rates. We also extend our surface-surface intersection algorithm to evaluate self-intersections in NURBS surfaces.