Probability densities of disorientation angles among randomly oriented grains in tricrystals

Disorientation Angles among Grains around Triple Junctions in Deformed and Annealed Aluminum

“…Before considering the triple junctions in deformed and annealed aluminum, we will first explain the disorientationangle diagram 6) that will be used to discuss the disorientation angles among three grains around the triple junctions. The three disorientations angles ª 12 , ª 23 and ª 31 among Grains 1, 2 and 3 for each triple junction, as shown in Fig.…”

“…A d v a n c e V i e w oriented grains were computationally generated and the dots in the triangle connecting points O, P and Q show the results of the sets of three disorientation angles around the triple junctions. 6) Point O is the origin with the coordinate (ª min , ª i ) = (0°, 0°). The coordinates of points P and Q are (ª MD , 3ª MD ) and (0°, 2ª MD ), respectively, where ª MD = 62.80°is the maximum disorientation angle for cubic grains.…”

“…The coordinates of points P and Q are (ª MD , 3ª MD ) and (0°, 2ª MD ), respectively, where ª MD = 62.80°is the maximum disorientation angle for cubic grains. 6,911) Using points of V and W in Fig. 5 with the coordinates (15°, 45°) and (0°, 30°), respectively, the disorientation-angle diagram is divided into three regions.…”

“…Considering one million sets of three randomly oriented grains, the probabilities of belonging to each region are 93.33% for region T, 6.63% for region B and 0.04% for region S. 6) Because the probability of belonging to region S is less than 0.1%, it is reasonable that there are no dots in region S in Fig. 5 for 1000 triple junctions.…”

“…Considering the disorientation angles among grains around triple junctions, a disorientation-angle diagram was proposed in a recent study. 6) Here, using the concept of this disorientation-angle diagram, we considered the distribution of disorientation angles around the triple junctions in deformed and annealed aluminum. By comparing the disorientation-angle diagrams before and after grain growth, the characteristics of the triple junctions during the grain growth are discussed.…”