Topological transformation of grains in three-dimensional normal grain growth
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S. Ishihara Ceramic Superplasticity Project, ICORP, Japan Science and Technology Corporation 2-4-1 Mutsuno, Atsuta, Nagoya 456-8587, Japan
A. Domı´nguez-Rodrı´guez Departmento de Fisı´ca de la Materia Condensada, Universidad de Sevilla, Aptdo. 1065, 41080 Sevilla, Spain (Received 6 February 2001; accepted 19 April 2001)
The topological transformation of grains in three-dimensional normal grain growth was analyzed by Brakke’s Surface Evolver method that simulated the boundary motion by curvature. The statistics on elemental processes, which change the number of faces f of a grain, were determined from the simulation. The distribution function of the number of faces P( f ) in a steady structure could be predicted from the difference in the current of grains arriving at and leaving from state f. For the disappearance of one grain, face-creation switching occurred 3.7 times and face-elimination switching occurred 13.2 times on the average.
I. INTRODUCTION
The polycrystalline solids consist of a huge number of grains. The grain boundary moves toward minimizing its total energy, which is proportional to total boundary area, and then the motion changes the size and shape of grains at elevated temperatures. The small grains shrink and disappear, and the mean size of the remaining grains increases. The grain boundary network reaches to a steady structure that is geometrically similar in a statistical sense.1– 6 In normal grain growth, the distribution function of grain size F(R/〈R〉) maintains the self-similar shape where 〈R〉 is the mean grain size.7–9 The state of a grain is classified according to its number of faces, f, which is equivalent to the number of nearest-neighbor grains.10,11 The distribution function of the number of faces P( f ) maintains a steady shape in normal grain growth also. As a grain changes its size, it varies the topological state f as shown in Fig. 1. Rhines and Craig10 examined the topological path of transformation in grain growth. The elemental processes of topological change are grain switching (T1 process) and disappearance of grain (T2 process).2,6 Grain switching is a process to make or lose contact with other grains, namely creation and elimination of a face of the grain.10,12–15
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J. Mater. Res., Vol. 16, No. 7, Jul 2001 Downloaded: 25 Mar 2015
In their pioneering paper, Kurtz and Carpay11 constructed a model of grain growth by considering the transfer rate of a grain between classes divided according to f. The transition of a grain from the state f to f − 1 occurs by loss of its neighbor grain through faceelimination switching or disappearance of the neighbor. The transition to f + 1 occurs by the formation of contact with a new grain through a face-creation switching. Computer simulation enables us to track microstructural evolution in grain growth. The analysis of detailed simulation gives information about individual acts of topological transformation and their stati
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