Theory of normal grain growth in normalized size space |
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| Affiliation: | 1. Department of Materials Science and Engineering, UCLA, Los Angeles, CA 90095-1595, USA;2. Department of Theoretical Physics, Cherkasy State University, Cherkasy 18000, Ukraine;1. Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China;2. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China;3. Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Tsinghua University, Beijing 100084, China;1. Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang, 110016, China;2. College of Materials Science and Engineering, University of Science and Technology of China, Hefei, 230026, China;1. Department of Materials Science and Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890, USA;3. Department of Materials Science and Engineering, University of California, Berkeley, CA 94720, USA;4. Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, CA 94550, USA;1. Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China;2. State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, China;3. Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Beijing 100084, China |
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| Abstract: | Simple mean-field deterministic theory of normal grain growth in both 3-dimension and 2-dimension cases is presented, predicting the Rayleigh size distribution. The main idea is an application of standard thermodynamics to normalized size space with unit length proportional to average size. In the normalized space, the change of normalized free energy caused by the size change of an arbitrary grain is independent of the reservoir, which consists of all the other grains. Such “decoupling” enables us to use the original Burke-Turnbull approach to relate driving force to velocity of grain growth in the normalized space. |
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