Atomistic and continuum models for phase change dynamics
2006 (English)In: Proceedings of the International Congress of Mathematicians, 2006, 1563-1582 p.Conference paper (Refereed)
The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and capillary forces acting on length scales compared to the nanometer width of the solid-liquid interface. Its modeling is useful for instance in processing techniques based on casting. The phase field method is widely used to study evolution of such microstructures of phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen�Cahn/Ginzburg�Landau equation modeling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitative correct result of dendritic side branching. This lecture presents some ideas to derive stochastic phase field models from atomistic formulations by coarse-graining molecular dynamics and kinetic Monte Carlo methods.
Place, publisher, year, edition, pages
2006. 1563-1582 p.
Phase transformation, phase-field, coarse-grained, molecular dynamics, Brownian
IdentifiersURN: urn:nbn:se:kth:diva-55367ScopusID: 2-s2.0-84878067528ISBN: 978-3-03719-022-7OAI: oai:DiVA.org:kth-55367DiVA: diva2:471528
International Congress of Mathematicians. Madrid, Spain. August 22-30 2006
QC 201201032012-01-022012-01-022012-02-25Bibliographically approved