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Neighborhood topological effect on grain topology-size relationship in three-dimensional polycrystalline microstructures |
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| Authors: | Ullah Asad GuoQuan Liu Hao Wang Khan Matiullah Faraz Khan Dil Iqbal M Zubair |
| Institution: | 1. School of Materials Science and Engineering, University of Science and Technology Beijing, Beijing, 100083, China 2. Department of Mathematics, Karakoram International University Gilgit-Baltistan, Gilgit, 15100, Pakistan 3. State Key Laboratory for Advanced Metals and Materials, University of Science and Technology Beijing, Beijing, 100083, China 4. Department of Physics, University of Science and Technology Bannu, 28100, Bannu, Pakistan 5. School of Applied Sciences, University of Science and Technology Beijing, Beijing, 100083, China |
| Abstract: | A new grain topology-size relationship in three-dimensional (3D) polycrystalline microstructures has recently been established by considering the effects of non-random first nearest neighbor grains. In this contribution, a generalized form for this relationship is presented by considering the interactions of kth (k=1, 2, 3…) nearest neighbor grains, and large scale Monte Carlo-Potts model simulation is used to investigate the general neighborhood topological effect on the topology-size relationship. The results show that, unlike their first nearest neighbors (k=1), the topological correlations of 3D grains with their kth layers (k?2) of nearest-neighbors may have trivial effect on the topology-size relationship. |
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