2024-03-29T10:17:44Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/691722022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Modeling grain boundaries using a phase field techniqueKobayashi, R.Warren, J. ACarter, W. Copen access410We propose a two dimensional frame-invariant phase field model of grain imĀpingement and coarsening. One dimensional analytical solutions for a stable grain boundary in a bicrystal are obtained, and equilibrium energies are comĀputed. We are able to calculate the rotation rate for a free grain between two grains of fixed orientation. For a particular choice of functional dependencies in the model the grain boundary energy takes the same analytic form as the microscopic (dislocation) model of Read and Shockley [11]. 64.70.Dv, 64.60.-i, 81.30.Fb, 05.70.LnDepartment of Mathematics, Hokkaido University1998-09-01engdepartmental bulletin paperVoRhttps://doi.org/10.14943/83568http://hdl.handle.net/2115/6917210.14943/83568Hokkaido University Preprint Series in Mathematics422112https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69172/1/pre422.pdfapplication/pdf499.93 KB1998-09-01