DEPARTMENT COLLOQUIUM | The ABC's of Modeling Pattern Formation: From Classical DFT to the Hohenberg/Halperin Alphabet Soup of Models

Speaker: Ken Elder (Oakland University)

One of the most important and successful fields in physics is equilibrium statistical mechanics, which provides a well defined variational method for determining equilibrium states. Unfortunately it is extremely rare for solids to be in such states due to long transient times or external driving forces. Most naturally occurring or man made materials contain complex non-equilibrium spatial patterns that play a key role in determining material property and function. This talk will focus on the development of a continuum field theory that models processes on atomic length and diffusive time scales. This approach naturally incorporates elasticity and plasticity, both of which can be critical for determining microstructure formation and material properties. The model also provides a link between classical density functional theory and traditional continuum field theories of crystallization and phase segregation (i.e., Models A, B and C in the Hohenberg-Halperin classification scheme). Specific applications to epitaxial growth and strained surface ordering will also be discussed.