Surface diffusion of atoms plays a significant role in the evolution of the shape of a material in the nanometer regime because it becomes the dominant mechanism for mass transport as the surface area to volume ratio increases. In this dissertation, I present a theoretical study of the shape evolution of a particular nanostructure: the nanowire. At non-zero temperatures, atomic steps are always present on the surface of a nanostructure and their growth and motion causes a change of shape and can cause the wire to break.

I have studied the morphological evolution of nanowires before and after a break develops, the resulting segments of a broken nanowire whose tips are nanoneedles. My approach is to develop and compare a step motion model and atomistic simulations and test them against available experimental data and classical continuum theory. My approach also allowed me to derive the scaling relations and exponents describing the morphological evolution of nanowires and study the microscopic nature of the instability that causes them to break.