An analytical study of the static state of multi-junctions in a multi-phase field model |
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| Authors: | Wei Guo Robert Spatschek Ingo Steinbach |
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| Institution: | 1. Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-University Bochum, Germany;2. Max-Planck-Institut für Eisenforschung GmbH, 40237 Düsseldorf, Germany;1. Department of Materials Science and Engineering, Kunsan National University, Kunsan 514150, Republic of Korea;2. Department of Optical Engineering, Cheongju University, Cheongju 28503, Republic of Korea;3. School of Advanced Materials Engineering, Kookmin University, Seoul 02841, Republic of Korea;4. Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang 37673, Republic of Korea;5. Graduate Institute of Ferrous Technology, Pohang University of Science and Technology, Pohang 37673, Republic of Korea;6. Korea Institute of Materials Science, Changwon 51508, Republic of Korea;1. Institute of Materials and Processes, Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133 Karlsruhe, Germany;2. Institute of Applied Materials, Karlsruhe Institute of Technology, Straße am Forum 7, 76131 Karlsruhe, Germany;3. Institut für Materialphysik im Weltraum, Deutsches Zentrum für Luft- und Raumfahrt (DLR), 51170 Köln, Germany;1. Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr University Bochum, Stiepeler Str. 129, 44780, Bochum, Germany;2. Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, Lavrentyev prosp. 15, 630090, Novosibirsk, Russia;1. Department of Materials Engineering, Indian Institute of Science, 560012 Bangalore, India;2. Institute of Applied Materials, Karlsruhe Institute of Technology, 76131 Karlsruhe, Germany |
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| Abstract: | We investigate the properties of the multi-order parameter phase field model of Steinbach and Pezzolla I. Steinbach, F. Pezzolla, A generalized field method for multi-phase transformations using interface fields, Physica D 134 (1999) 385–393] with respect to the behavior in triple and higher order junctions. From the structure of this model, it was speculated that “dynamical” solutions may exist in the triple junction, which could lead to a violation of Young’s law. Here we confirm analytically recent numerical simulations showing that such dynamical states do not exist, and that an equilibrium solution therefore does indeed correspond to a minimum of the free energy; this implies that Young’s law must be satisfied in the framework of the model. We show that Young’s law is a consequence of the interface kinetic equilibrium and not due to a mechanical force balance, in agreement with earlier predictions C. Caroli, C. Misbah, On static and dynamical Young’s condition at a trijunction, J. Phys. I France 7 (1997) 1259–1265]. |
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