Much of nanotechnology and nanoscience is devoted to the fabrication, control, and analysis of surfaces and solid defects. The nucleation, growth, and evolution of nanoscale defects and structures stands at the nexus of Materials Engineering, Mechanics, and Statistical Physics. Nanoscale science in this area requires the solution to fundamental and technical questions such as “When is a collection of atoms just a collection of atoms and when is it material?” or its more applied cousin, “How can we quantitatively describe the behavior of nanoscale materials and structures taking into account their atomic makeup and bonding?” Although of fundamental scientific importance, answering these questions will provide the quantitative tools necessary to define the next generation of nanoscale measurements and facilitate the design and optimization of the next generation of nanotechnology. These studies will look at fluctuating motion and material evolution to create quantitatively accurate statistical models usable in materials analysis and design, focusing on nanoscale randomness and fluctuations as entities to be modeled and measured. Areas of application include nanoscale self-assembly such as the famed self-assembled quantum dots, strained films and film growth, solid solution intermixing, stress-assisted nucleation of crystal defects, and free energies of fracture surfaces.