The diffusion of Cr in [100]/[001] symmetrical bi-crystals with various tilt angles was investigated at temperatures ranging from 958 to 1197C (tables 98 and 99). It was found that, in low-angle boundaries, diffusion was dominated by a dislocation pipe mechanism whose activation energy was independent of the tilt angle, while the pre-exponential factor was a linear function of the sine of the tilt semi-angle. In the case of high-angle boundaries, the diffusion coefficients exhibited minima, and the activation energies exhibited maxima, for coincidence site lattice boundaries with = 13 (22.6, 67.4), = 17 (28.1, 61.9) and = 5 (36.9, 53.1). The pre-exponential factor also varied with the tilt angle, but the variation was random. The results confirmed that grain boundary diffusion was strongly affected by boundary structures and their associated energies.
X.M.Li, Y.T.Chou: Acta Materialia, 1996, 44[9], 3535-41
Table 98
Diffusion of Cr in [100]/[001] Nb Bicrystals as a Function of Tilt Angle
(°) | Temperature (C) | sD (m3/s) |
2.0 | 958 | 3.92 x 10-23 |
2.0 | 997 | 6.08 x 10-23 |
2.0 | 1040 | 1.01 x 10-22 |
2.0 | 1078 | 1.58 x 10-22 |
2.0 | 1121 | 2.21 x 10-22 |
2.0 | 1161 | 3.57 x 10-22 |
2.0 | 1197 | 5.28 x 10-22 |
8.0 | 958 | 5.64 x 10-23 |
8.0 | 997 | 8.82 x 10-23 |
8.0 | 1040 | 1.56 x 10-22 |
8.0 | 1078 | 2.07 x 10-22 |
8.0 | 1121 | 3.06 x 10-22 |
8.0 | 1161 | 5.28 x 10-22 |
8.0 | 1197 | 7.82 x 10-22 |
15.0 | 958 | 6.40 x 10-23 |
15.0 | 997 | 9.31 x 10-23 |
15.0 | 1040 | 1.58 x 10-22 |
15.0 | 1078 | 2.43 x 10-22 |
15.0 | 1121 | 4.00 x 10-22 |
15.0 | 1161 | 5.78 x 10-22 |
15.0 | 1197 | 8.02 x 10-22 |
20.0 | 958 | 8.73 x 10-23 |
20.0 | 997 | 1.42 x 10-22 |
20.0 | 1040 | 2.22 x 10-22 |
20.0 | 1078 | 3.01 x 10-22 |
20.0 | 1121 | 5.56 x 10-22 |
20.0 | 1161 | 9.63 x 10-22 |
20.0 | 1197 | 1.25 x 10-21 |
22.6 ( = 13) | 958 | 7.58 x 10-24 |
22.6 ( = 13) | 997 | 1.33 x 10-23 |
22.6 ( = 13) | 1040 | 1.70 x 10-23 |
22.6 ( = 13) | 1078 | 2.45 x 10-23 |
22.6 ( = 13) | 1121 | 8.71 x 10-23 |
22.6 ( = 13) | 1161 | 1.07 x 10-22 |
22.6 ( = 13) | 1197 | 1.16 x 10-22 |
26.0 | 958 | 7.47 x 10-23 |
26.0 | 997 | 1.13 x 10-22 |
26.0 | 1040 | 1.84 x 10-22 |
26.0 | 1078 | 2.50 x 10-22 |
26.0 | 1121 | 4.43 x 10-22 |
26.0 | 1161 | 7.39 x 10-22 |
26.0 | 1197 | 1.17 x 10-21 |
28.1 ( = 17) | 958 | 1.49 x 10-23 |
28.1 ( = 17) | 997 | 2.47 x 10-23 |
28.1 ( = 17) | 1040 | 4.55 x 10-23 |
28.1 ( = 17) | 1078 | 7.03 x 10-23 |
28.1 ( = 17) | 1121 | 1.08 x 10-22 |
28.1 ( = 17) | 1161 | 1.75 x 10-22 |
28.1 ( = 17) | 1197 | 2.96 x 10-22 |
31.0 | 958 | 6.66 x 10-23 |
31.0 | 997 | 1.22 x 10-22 |
31.0 | 1040 | 1.54 x 10-22 |
31.0 | 1078 | 2.56 x 10-22 |
31.0 | 1121 | 4.40 x 10-22 |
31.0 | 1161 | 7.82 x 10-22 |
31.0 | 1197 | 9.89 x 10-22 |
36.9 ( = 5) | 958 | 3.07 x 10-24 |
36.9 ( = 5) | 997 | 5.13 x 10-24 |
36.9 ( = 5) | 1040 | 9.33 x 10-24 |
36.9 ( = 5) | 1078 | 1.77 x 10-23 |
36.9 ( = 5) | 1121 | 3.37 x 10-23 |
36.9 ( = 5) | 1161 | 6.29 x 10-23 |
36.9 ( = 5) | 1197 | 9.22 x 10-23 |
43.0 | 958 | 1.57 x 10-22 |
43.0 | 997 | 2.67 x 10-22 |
43.0 | 1040 | 3.91 x 10-22 |
43.0 | 1078 | 5.70 x 10-22 |
43.0 | 1121 | 1.10 x 10-21 |
43.0 | 1161 | 1.49 x 10-21 |
43.0 | 1197 | 2.30 x 10-21 |
46.0 | 958 | 6.75 x 10-23 |
46.0 | 997 | 1.35 x 10-22 |
46.0 | 1040 | 1.66 x 10-22 |
46.0 | 1078 | 2.76 x 10-22 |
46.0 | 1121 | 3.64 x 10-22 |
46.0 | 1161 | 8.77 x 10-22 |
46.0 | 1197 | 1.02 x 10-21 |
53.1 ( = 5) | 958 | 3.94 x 10-24 |
53.1 ( = 5) | 997 | 7.91 x 10-24 |
53.1 ( = 5) | 1040 | 1.18 x 10-23 |
53.1 ( = 5) | 1078 | 1.59 x 10-23 |
53.1 ( = 5) | 1121 | 3.32 x 10-23 |
53.1 ( = 5) | 1161 | 7.36 x 10-23 |
53.1 ( = 5) | 1197 | 1.04 x 10-22 |
56.0 | 958 | 5.66 x 10-23 |
56.0 | 997 | 7.67 x 10-23 |
56.0 | 1040 | 1.09 x 10-22 |
56.0 | 1078 | 2.21 x 10-22 |
56.0 | 1121 | 3.01 x 10-22 |
56.0 | 1161 | 4.78 x 10-22 |
56.0 | 1197 | 8.69 x 10-22 |
61.9 ( = 17) | 958 | 4.61 x 10-24 |
61.9 ( = 17) | 997 | 7.86 x 10-24 |
61.9 ( = 17) | 1040 | 1.67 x 10-23 |
61.9 ( = 17) | 1078 | 1.58 x 10-23 |
61.9 ( = 17) | 1121 | 3.49 x 10-23 |
61.9 ( = 17) | 1161 | 6.39 x 10-23 |
61.9 ( = 17) | 1197 | 1.05 x 10-22 |
67.4 ( = 13) | 958 | 4.69 x 10-24 |
67.4 ( = 13) | 997 | 7.87 x 10-24 |
67.4 ( = 13) | 1040 | 1.36 x 10-23 |
67.4 ( = 13) | 1078 | 2.11 x 10-23 |
67.4 ( = 13) | 1121 | 3.90 x 10-23 |
67.4 ( = 13) | 1161 | 7.32 x 10-23 |
67.4 ( = 13) | 1197 | 1.01 x 10-22 |
69.0 | 958 | 4.50 x 10-23 |
69.0 | 997 | 8.88 x 10-23 |
69.0 | 1040 | 1.58 x 10-22 |
69.0 | 1078 | 1.92 x 10-22 |
69.0 | 1121 | 3.93 x 10-22 |
69.0 | 1161 | 5.37 x 10-22 |
69.0 | 1197 | 8.47 x 10-22 |
74.0 | 958 | 1.93 x 10-23 |
74.0 | 997 | 4.32 x 10-23 |
74.0 | 1040 | 4.76 x 10-23 |
74.0 | 1078 | 4.47 x 10-23 |
74.0 | 1121 | 9.78 x 10-23 |
74.0 | 1161 | 2.26 x 10-22 |
74.0 | 1197 | 4.15 x 10-22 |
78.0 | 958 | 1.27 x 10-23 |
78.0 | 997 | 1.85 x 10-23 |
78.0 | 1040 | 2.53 x 10-23 |
78.0 | 1078 | 5.01 x 10-23 |
78.0 | 1121 | 7.02 x 10-23 |
78.0 | 1161 | 1.25 x 10-22 |
78.0 | 1197 | 2.19 x 10-22 |
83.0 | 958 | 1.45 x 10-23 |
83.0 | 997 | 2.28 x 10-23 |
83.0 | 1040 | 3.28 x 10-23 |
83.0 | 1078 | 5.04 x 10-23 |
83.0 | 1121 | 8.36 x 10-23 |
83.0 | 1161 | 1.58 x 10-22 |
83.0 | 1197 | 2.34 x 10-22 |
Table 99
Arrhenius Parameters for Cr Grain Boundary Diffusion in
[100]/[001] Symmetrical Nb Bicrystals
at Temperatures Ranging from 958 to 1197C
(°) | sD (m3/s) | Q (kJ/mol) |
2.0 | 2.86 x 10-16 | 162.0 |
8.0 | 4.15 x 10-16 | 162.1 |
15.0 | 4.91 x 10-16 | 162.8 |
20.0 | 1.35 x 10-16 | 170.1 |
22.6 ( = 13) | 6.17 x 10-16 | 187.4 |
26.0 | 1.29 x.10-15 | 171.7 |
28.1 ( = 17) | 9.02 x 10-16 | 183.7 |
31.0 | 1.23 x 10-15 | 171.7 |
36.9 ( = 5) | 6.28 x 10-15 | 220.6 |
43.0 | 1.92 x 10-15 | 167.4 |
46.0 | 1.00 x 10-15 | 169.0 |
53.1 ( = 5) | 1.66 x 10-15 | 204.0 |
56.0 | 9.18 x 10-16 | 171.8 |
61.9 ( = 17) | 5.43 x 10-16 | 190.8 |
67.4 ( = 13) | 9.62 x 10-16 | 196.7 |
69.0 | 1.79 x 10-15 | 178.5 |
74.0 | 4.55 x 10-16 | 174.6 |
78.0 | 3.74 x 10-16 | 177.8 |
83.0 | 3.40 x 10-16 | 175.0 |