Evolving Small Structures

A polished polycrystal has a flat surface. At room temperature, the surface remains flat for a long time. At an elevated temperature atoms move. The surface grows grooves along triple junctions, where the surface meet grain boundaries. The grooves reveal the grain boundaries in the microscope. Atoms may move in many ways. They may diffuse in the lattice, diffuse on the surface, or evaporate into the vapor phase. Here we will only consider surface diffusion. Atoms diffuse on the surface away from the triple junction, making a dent along the junction, and piling two bumps nearby.

Some phenomena due to surface diffusion:

• Flattening a surface.
  
• Spherodizing.
  
• Rayleigh instability.
  
• Grain boundary grooving.
• Sintering
  Self-assembled quantum dots

Diffusion and creep involve the same atomic process: atoms must change neighbors, aided by thermal energy. We explore their relation in this lecture.

I have taught this course four times before, but have never devoted lectures on basic thermodynamics. It is a subject I’m not good at, but I have used it often in research, in a loose way. One can ride a bicycle without knowing Newton’s laws, even though bicycle-riding is governed by Newton’s law. If thermodynamics gives me so much trouble, perhaps it also gives my students a lot of trouble. I have taken lectures from many teachers on the subject. None have really made me feel comfortable with it. Now I’m trying to teach you. I hope that I can help you become comfortable with the subject. Maybe you already are. Maybe you never will. I have no evidence that I can be more effective than these other teachers, but I have the enthusiasm of an amateur.

Cavity Growth Is Caused by a Series of Tiny Effects

• A tiny fraction of lattice sites are vacant.
• The tensile stress increases the vacancy concentration at the external surface by a tiny fraction.
  
• The tiny nonunifomity in the vacancy concentration drives diffusion.
• A tiny fraction of vacancies change site, by an atomic distance.
  

A solid contains a spherical cavity, subject to a hydrostatic stress. For now, we assume that the solid is stiff so we ignore its deformation. The cavity can still change its size by a special mechanism: atoms diffuse through the solid between the cavity surface and the external surface. We will concentrate in this lecture on the question, Will the cavity shrink or enlarge? We will consider the diffusion process in some detail in the next lecture, and answer the question, How fast will the cavity change its size?