On the completion of recrystallization process, strainfree TiB2grains substitute the deformed TiB2grains and the boundaries of grain slowly drift apart, thus producing a uniform increase in the size of grains, as shown in Fig.1a, at the expense of adjacent recrystallized grains of smaller size. Here, the energy associated with the grain boundaries acts as the driving force for growth of the grain. Therefore, as the grain size of TiB2increases, the total area of grain boundary decreases leading to lowering of the total energy of Al–4.5%Cu–xTiB2composite. The two-dimensional model of TiB2grains in Al–4.5%Cu–xTiB2after the recrystallization process is represented in Fig.1a where irregular TiB2grains of different sizes and different number of sides are being shown. In Fig.1b, a triple point from Fig.1a schematic is shown in an exploded view for better understanding of the mechanism. Here, the surface tension can be assumed to be approximately equal for different TiB2grain boundaries of Al–4.5%Cu–xTiB2composite.Now, at this triple point, the forces should be balanced, and Eq. (1) shows the output from these balanced forces equations, where under the conditions of equilibrium, the grain boundaries of these three grains should meet at relative angles of 120?at the triple point, making TiB2 grains to be hexagonal in shape.
Thus, for obtaining stable equilibrium, the two-dimensional TiB2grains model should comprise of regular hexagons with linear and straight sides. For attaining surface tension equilibrium and makingθ=120°,boundaries of TiB2grain should drift and bend along with simultaneous triple-point displacements from X to Y as shown in Fig.1c, where dotted lines represent the original position of grain boundaries. Since a boundary with curve has more energy, under the force of surface tension, the grain boundary uncurls by moving toward the center of curvature direction and is shown in Fig.1d.
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