Theoretical and experimental data on diffusion along moving and stationary boundaries in metals were reviewed. A model was presented, for diffusion in polycrystals, which contained both stationary and moving boundaries. The model predicted the occurrence of 3-step concentration depth profiles. The first step was caused by direct volume diffusion, the second was caused by diffusion along moving boundaries, and the third (with the deepest penetration) was caused by diffusion along stationary boundaries. By fitting the model to experimental profiles, the product, sD, for stationary boundaries, and the velocity and fraction of moving boundaries could be determined. The model was applied to experimental studies of grain-boundary self-diffusion in -Hf which had been carried out by using radiotracer sectioning techniques. The value of the product for self-diffusion in -Hf was described by:
sD(m3/s) = 3.5 x 10-13exp[-212(kJ/mol)/RT]
The product of velocity and temperature could be described by:
VT(mK/s) = 11.2 exp[-195(kJ/mol)/RT]
Due to a high grain boundary mobility, some of the boundaries moved during the experiments. The motion was clearly revealed by an unusual shape of the resultant penetration profiles. In the case of Hf, the activation energy for boundary migration appeared to be close to the activation energy for boundary self-diffusion. This agreement indicated that, at least in this particular case, the average activation barrier to atomic transport across the boundaries was the same as that to diffusion along the boundaries.
Y.M.Mishin, M.Köppers, C.Herzig: Solid State Phenomena, 1995, 41, 79-92
Table 117
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1820 | 10 | 1.01 x 10-7 |
1900 | 10 | 1.38 x 10-7 |
1820 | 15 | 1.03 x 10-7 |
1900 | 15 | 1.39 x 10-7 |
1820 | 20 | 1.05 x 10-7 |
1900 | 20 | 1.39 x 10-7 |
1820 | 25 | 1.07 x 10-7 |
1900 | 25 | 1.38 x 10-7 |
1600 | 30 | 4.41 x 10-8 |
1700 | 30 | 5.49 x 10-8 |
1820 | 30 | 1.08 x 10-7 |
1900 | 30 | 1.40 x 10-7 |
1600 | 35 | 4.46 x 10-8 |
1700 | 35 | 6.08 x 10-8 |
1820 | 35 | 1.09 x 10-7 |
1900 | 35 | 1.41 x 10-7 |
1500 | 40 | 2.45 x 10-8 |
1600 | 40 | 4.50 x 10-8 |
1700 | 40 | 6.29 x 10-8 |
1820 | 40 | 1.10 x 10-7 |
1900 | 40 | 1.42 x 10-7 |
1500 | 45 | 2.53 x 10-8 |
1600 | 45 | 4.56 x 10-8 |
1700 | 45 | 6.48 x 10-8 |
1820 | 45 | 1.10 x 10-7 |
1900 | 45 | 1.45 x 10-7 |
1500 | 50 | 2.59 x 10-8 |
1600 | 50 | 4.60 x 10-8 |
1700 | 50 | 6.57 x 10-8 |
1820 | 50 | 1.10 x 10-7 |
continued
Table 117 (continued)
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1400 | 55 | 1.30 x 10-8 |
1500 | 55 | 2.79 x 10-8 |
1600 | 55 | 4.73 x 10-8 |
1700 | 55 | 6.58 x 10-8 |
1820 | 55 | 1.11 x 10-7 |
1400 | 60 | 1.33 x 10-8 |
1500 | 60 | 2.80 x 10-8 |
1600 | 60 | 4.84 x 10-8 |
1700 | 60 | 6.46 x 10-8 |
1820 | 60 | 1.12 x 10-7 |
1300 | 65 | 7.53 x 10-9 |
1400 | 65 | 1.34 x 10-8 |
1500 | 65 | 2.68 x 10-8 |
1600 | 65 | 4.79 x 10-8 |
1700 | 65 | 6.35 x 10-8 |
1820 | 65 | 1.13 x 10-7 |
1300 | 70 | 7.55 x 10-9 |
1400 | 70 | 1.34 x 10-8 |
1500 | 70 | 2.66 x 10-8 |
1600 | 70 | 4.67 x 10-8 |
1700 | 70 | 6.36 x 10-8 |
1820 | 70 | 1.14 x 10-7 |
1200 | 75 | 4.11 x 10-9 |
1300 | 75 | 7.62 x 10-9 |
1400 | 75 | 1.41 x 10-8 |
1500 | 75 | 2.71 x 10-8 |
1600 | 75 | 4.55 x 10-8 |
1700 | 75 | 6.37 x 10-8 |
1820 | 75 | 1.15 x 10-7 |
1200 | 80 | 4.46 x 10-9 |
continued
Table 117 (continued)
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1300 | 80 | 7.82 x 10-9 |
1400 | 80 | 1.51 x 10-8 |
1500 | 80 | 2.69 x 10-8 |
1600 | 80 | 4.45 x 10-8 |
1700 | 80 | 6.39 x 10-8 |
1820 | 80 | 1.18 x 10-7 |
1100 | 85 | 2.36 x 10-9 |
1200 | 85 | 4.46 x 10-9 |
1300 | 85 | 8.17 x 10-9 |
1400 | 85 | 1.51 x 10-8 |
1500 | 85 | 2.56 x 10-8 |
1600 | 85 | 4.39 x 10-8 |
1700 | 85 | 6.45 x 10-8 |
1820 | 85 | 1.21 x 10-7 |
1100 | 90 | 2.78 x 10-9 |
1200 | 90 | 4.45 x 10-9 |
1300 | 90 | 8.42 x 10-9 |
1400 | 90 | 1.38 x 10-8 |
1500 | 90 | 2.49 x 10-8 |
1600 | 90 | 4.42 x 10-8 |
1700 | 90 | 6.46 x 10-8 |
1820 | 90 | 1.22 x 10-7 |
1000 | 95 | 9.60 x 10-10 |
1100 | 95 | 2.86 x 10-9 |
1200 | 95 | 4.55 x 10-9 |
1300 | 95 | 9.93 x 10-9 |
1400 | 95 | 1.34 x 10-8 |
1500 | 95 | 2.55 x 10-8 |
1600 | 95 | 4.52 x 10-8 |
1700 | 95 | 6.79 x 10-8 |
continued
Table 117 (continued)
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1820 | 95 | 1.22 x 10-7 |
1820 | 10 | 1.01 x 10-7 |
1900 | 10 | 1.38 x 10-7 |
1820 | 15 | 1.03 x 10-7 |
1900 | 15 | 1.39 x 10-7 |
1820 | 20 | 1.05 x 10-7 |
1900 | 20 | 1.39 x 10-7 |
1820 | 25 | 1.07 x 10-7 |
1900 | 25 | 1.38 x 10-7 |
1600 | 30 | 4.41 x 10-8 |
1700 | 30 | 5.49 x 10-8 |
1820 | 30 | 1.08 x 10-7 |
1900 | 30 | 1.40 x 10-7 |
1600 | 35 | 4.46 x 10-8 |
1700 | 35 | 6.08 x 10-8 |
1820 | 35 | 1.09 x 10-7 |
1900 | 35 | 1.41 x 10-7 |
1500 | 40 | 2.45 x 10-8 |
1600 | 40 | 4.50 x 10-8 |
1700 | 40 | 6.29 x 10-8 |
1820 | 40 | 1.10 x 10-7 |
1900 | 40 | 1.42 x 10-7 |
1500 | 45 | 2.53 x 10-8 |
1600 | 45 | 4.56 x 10-8 |
1700 | 45 | 6.48 x 10-8 |
1820 | 45 | 1.10 x 10-7 |
1900 | 45 | 1.45 x 10-7 |
1500 | 50 | 2.59 x 10-8 |
1600 | 50 | 4.60 x 10-8 |
1700 | 50 | 6.57 x 10-8 |
continued
Table 117 (continued)
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1820 | 50 | 1.10 x 10-7 |
1400 | 55 | 1.30 x 10-8 |
1500 | 55 | 2.79 x 10-8 |
1600 | 55 | 4.73 x 10-8 |
1700 | 55 | 6.58 x 10-8 |
1820 | 55 | 1.11 x 10-7 |
1400 | 60 | 1.33 x 10-8 |
1500 | 60 | 2.80 x 10-8 |
1600 | 60 | 4.84 x 10-8 |
1700 | 60 | 6.46 x 10-8 |
1820 | 60 | 1.12 x 10-7 |
1300 | 65 | 7.53 x 10-9 |
1400 | 65 | 1.34 x 10-8 |
1500 | 65 | 2.68 x 10-8 |
1600 | 65 | 4.79 x 10-8 |
1700 | 65 | 6.35 x 10-8 |
1820 | 65 | 1.13 x 10-7 |
1300 | 70 | 7.55 x 10-9 |
1400 | 70 | 1.34 x 10-8 |
1500 | 70 | 2.66 x 10-8 |
1600 | 70 | 4.67 x 10-8 |
1700 | 70 | 6.36 x 10-8 |
1820 | 70 | 1.14 x 10-7 |
1200 | 75 | 4.11 x 10-9 |
1300 | 75 | 7.62 x 10-9 |
1400 | 75 | 1.41 x 10-8 |
1500 | 75 | 2.71 x 10-8 |
1600 | 75 | 4.55 x 10-8 |
1700 | 75 | 6.37 x 10-8 |
1820 | 75 | 1.15 x 10-7 |
continued
Table 117 (continued)
Interdiffusion in the Hf-Zr System
Temperature (C) | Zr (at%) | D (cm2/s) |
1200 | 80 | 4.46 x 10-9 |
1300 | 80 | 7.82 x 10-9 |
1400 | 80 | 1.51 x 10-8 |
1500 | 80 | 2.69 x 10-8 |
1600 | 80 | 4.45 x 10-8 |
1700 | 80 | 6.39 x 10-8 |
1820 | 80 | 1.18 x 10-7 |
1100 | 85 | 2.36 x 10-9 |
1200 | 85 | 4.46 x 10-9 |
1300 | 85 | 8.17 x 10-9 |
1400 | 85 | 1.51 x 10-8 |
1500 | 85 | 2.56 x 10-8 |
1600 | 85 | 4.39 x 10-8 |
1700 | 85 | 6.45 x 10-8 |
1820 | 85 | 1.21 x 10-7 |
1100 | 90 | 2.78 x 10-9 |
1200 | 90 | 4.45 x 10-9 |
1300 | 90 | 8.42 x 10-9 |
1400 | 90 | 1.38 x 10-8 |
1500 | 90 | 2.49 x 10-8 |
1600 | 90 | 4.42 x 10-8 |
1700 | 90 | 6.46 x 10-8 |
1820 | 90 | 1.22 x 10-7 |
1000 | 95 | 9.60 x 10-10 |
1100 | 95 | 2.86 x 10-9 |
1200 | 95 | 4.55 x 10-9 |
1300 | 95 | 9.93 x 10-9 |
1400 | 95 | 1.34 x 10-8 |
1500 | 95 | 2.55 x 10-8 |
1600 | 95 | 4.52 x 10-8 |
1700 | 95 | 6.79 x 10-8 |
1820 | 95 | 1.22 x 10-7 |