ACMD Seminar: Why are crystal facets mathematically interesting? A continuum-scale story with a microscale touch

Professor Dionisios Margetis
Department of Mathematics and Institute of Physical Science and Technology, University of Maryland, College Park

Tuesday, April 3, 2018, 15:00 - 16:00
Building 222, Room B263
Gaithersburg

Tuesday, April 3, 2018, 13:00 - 14:00
Room 1-4072
Boulder

Host: Paul Patrone

Abstract: Recent advances in materials science enable the observation and control of microstructures such as nanoscale defects with remarkable precision. In this talk, I will discuss recent progress and open challenges in understanding how small-scale details in the kinetics of crystal surfaces can macroscopically influence the surface morphological evolution. In particular, the evolution of crystal surface plateaus, facets, is characterized by an effective behavior at the macroscale that is not necessarily only the outcome of averaging, but instead may be dominated by certain discrete (microscopic) events. This "idiosyncrasy" of facet evolution raises challenging but interesting mathematical questions. The talk will explore via selected examples and methods how the kinetics of microscale defects near facets can plausibly leave their imprints at larger scales. The main tool is a class of partial differential equations (PDEs) for the surface height profile. I address the question: Can this continuum description be reconciled with the motion of line defects (steps) at the nanoscale, and how?

Bio: Dionisios Margetis is a professor in the Department of Mathematics and the Institute for Physical Science and Technology at the University of Maryland, College Park. Professor Margetis received his PhD in Applied Physics in 1999 from Harvard University and has been at the University of Maryland since 2006. He is also affiliated with The Center for Scientific Computation and Mathematical Modeling and the Maryland NanoCenter. Professor Margetis's research lies broadly in materials modeling and analysis, at the triple point of applied mathematics, theoretical physics, and materials science. His research is motivated by physical experiments and primarily explores the connection of continuum laws (e.g. PDEs) to discrete or microscopic models (e.g. ODE systems) in classical and quantum mechanics. Of particular interest are microscale effects that leave their signatures even at large scales.