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.
Fig. 1 Movement of boundaries at a triple point during TiB2grain growth:atwo-dimensional representation of grains after recrystallization along with a triple-point exploded view,bboundaries heading for the center of curvature (direction of arrow),btriple-point illustration just before TiB2grain growth process,cbending of boundaries for achieving equilibrium due to surface tension forces at the triple point (where X to Y movement of triple point is observed), anddstraightening of boundaries to reduce energy with disturbance of the equilibrium
Here, boundaries straighten out, but stable equilibrium is disturbed, i.e., anglehbecomes less than 120°. This process is repeated multiple times leading to the gentle disappearance of grain 1, while progressive growth is observed for grain 2 and grain 3. Overall, the average size of these grains surges. As represented in Fig.2a, the grain boundary drifts toward the curvature center, with concave boundary grains growing at the cost of convex boundary grains, which are ultimately consumed. Also, Fig.2b represents the expansion mechanism and the phenomenon of grain growth.
Fig. 2 Diffusion of atoms and boundaries:aAtom is more stable in concave shaped grain,since having more neighbors (thus, more bonds) compared to convex grain, causing then boundary to move toward the center of curvature (diffusion of atoms,/ boundary movement), and bschematic representing growth of a grain;cboundaries migrating toward the center of curvature, and 4th grain consumed leading to grain growth of the remaining three,done side reduced for each of the three grains, andenumber of sides increasing during grain growth (for grains 1 and 4)
The grain growth generally starts at a particular place inside Al–4.5%Cu–xTiB2 composite where recrystallization has already taken place, while recrystallization still happens in other parts of the metal mixture. Here, the number of sides of the growing grains may decrease, as illustrated in Fig.2c, d, or may increase, as shown in Fig.2e. Further, geometrical coalescence, represented in Fig.3a–d, may occur in the composite mixture having resilient preferential orientation with two TiB2grains such as 1 and 2 (initially, placed far) of almost same orientation gathering and making an individual grain during the growth. The growth of TiB2 grains taking place is small when time is increased at a constant temperature, compared to the condition of increasing temperature at a particulartime.
Fig. 3 Geometrical coalescence of grains 1 and 2 taking place having similar orientation of atoms (XY is similar to a sub-boundary of a single grain growing out from grain 1 and 2)
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