# Robert Sekerka

## Emeritus University Professor, Physics and Mathematics

**Office:**Wean Hall 6416

**Phone:**412-268-2362

**Fax:**412-681-0648

**Email:**rs07@andrew.cmu.edu

**Website:**http://sekerkaweb.phys.cmu.edu/

## Education

Ph.D., Harvard University## Research

Most of my research is interdisciplinary and is concerned with theoretical problems in materials science that lead to challenging problems in physics and mathematics. Examples are the thermodynamics of stressed solids, transport phenomena, surfaces and interfaces, phase transformations, the definition of chemical potentials in stressed solids, the fundamental basis of the Onsager reciprocal relations in multi-component diffusion and heat flow, and the influence of anisotropic surface tension and kinetics on crystal shape. Problems dealing with phase transformations lead to difficult free boundary problems that are generalizations of the classical Stefan problem because of boundary conditions that depend on the curvature of the free boundary. One seeks to calculate and understand the factors that determine the shapes of the interfaces that separate the growing phase from the nutrient phase. Linear stability theory is used to analyze the conditions under which bodies of simple shape evolve spontaneously into more complex patterns. Non-linear analyses, frequently requiring numerical techniques, are used to track freely growing shapes and to ascertain fundamental aspects of the cellular and dendritic patterns that often result. We employ the phase field model (diffuse interface) in which an additional PDE is solved in lieu of boundary tracking. The phase field model has been used to calculate the operating state (tip speed and radius of curvature) of dendrites grown at large supercoolings, as well as cell shapes and solute segregation during directional solidification of alloys. We have also used Lattice-Boltzmann models to treat buoyancy drivers, interdiffusions and the patterns that form when one really immiscible fluid displaces another. Recently, attention has turned to quantitative modeling of high temperature creep in stressed crystalline solids.## Selected Publications

- E. Yokoyama, R. F. Sekerka and Y. Furukawa,
*Growth of an Ice Disk: Dependence of critical thickness for disk instability on supercooling of water*, J. Phys. Chem. B (March 2009). - R. F. Sekerka,
*Phase Field Modeling of Crystal Growth Morphology,*in "Perspectives on Inorganic, Organic and Biological Crystal Growth: From Fundamentals to Applications", editors M. Skowronski, J. DeYoreo, C. A. Wang, AIP Conference Proceedings 916, 176 (2007). - J. A. Dantzig, W. J. Boettinger, J. A. Warren, G. B. McFadden, S. R. Coriell, and R. F. Sekerka,
*Numerical Modeling of Diffusion-induced Deformation,*Met. Mat. Trans. 37A, 2701 (2006). - W. J. Boettinger, G. B. McFadden, S. R. Coriell, R. F. Sekerka, and J. A. Warren,
*Lateral deformation of Diffusion couples,*Acta Materialia 53, 1995 (2005). - R. F. Sekerka,
*Analytical criteria for missing orientations on three-dimensional equilibrium shapes,*J. Crystal Growth 275, 77 (2005). - R. F. Sekerka,
*Equilibrium and growth shapes of crystals: How do they differ and why should we care?*(Czochralski Lecture), Crystal Res. Tech. 40, 291 (2005). - V. Sofonea and R. F. Sekerka,
*Diffusivity of Two Component Isothermal Finite Difference Lattice Boltzmann Models,*Int. J. Mod. Phys. C 16, 1075 (2005). - V. Sofonea and R. F. Sekerka,
*Diffuse reflection boundary conditions for a thermal lattice Boltzmann model in two dimensions: Evidence of temperature jump and slip velocity in micro-channels,*Phys. Rev. E 71, 066709 (2005).