Interdiffusion in the β-phase of various alloys was studied at temperatures ranging from 1000 to 1900C (tables 16 to 18). The interdiffusion coefficients were deduced, using the Den Broeder method, from concentration profiles which had been determined by means of electron-probe micro-analysis. These coefficients depended strongly upon the composition. The interdiffusion coefficient for lower Ta concentrations was some 1000 times greater than that for higher concentrations. The activation energies of 150 to 240kJ/mol were characteristic of a mono-vacancy diffusion mechanism. Diffusion in these alloys was characterized by a large Kirkendall effect, which resulted in marker movement towards the Ti-rich part of the sample. The intrinsic diffusion coefficients were calculated, at temperatures between 1000 and 1600C and at the composition of the Kirkendall plane, by using Heumann's method. It was found that the intrinsic diffusion coefficient of Ti was about 5 times greater than that of Ta.
Interdiffusion in the Body-Centered Cubic β-Phase of Ta-Ti Alloys D.Ansel, I.Thibon, M.Boliveau, J.Debuigne: Acta Materialia, 1998, 46[2], 423-30
Table 16
Interdiffusion in the Ta-Ti System
Ta (at%) | Temperature (C) | D (cm2/s) |
0 | 1000 | 4.60 x 10-10 |
0 | 1100 | 9.30 x 10-10 |
0 | 1200 | 2.50 x 10-9 |
0 | 1300 | 5.80 x 10-9 |
0 | 1400 | 1.30 x 10-8 |
0 | 1500 | 2.20 x 10-8 |
0 | 1600 | 4.50 x 10-8 |
5 | 1000 | 2.97 x 10-10 |
5 | 1100 | 6.16 x 10-10 |
5 | 1200 | 1.81 x 10-9 |
5 | 1300 | 3.66 x 10-9 |
5 | 1400 | 8.56 x 10-9 |
5 | 1500 | 1.78 x 10-8 |
5 | 1600 | 3.20 x 10-8 |
10 | 1000 | 1.39 x 10-10 |
10 | 1100 | 3.24 x 10-10 |
10 | 1200 | 1.07 x 10-9 |
10 | 1300 | 2.25 x 10-9 |
10 | 1400 | 6.00 x 10-9 |
10 | 1500 | 1.02 x 10-8 |
10 | 1600 | 2.23 x 10-8 |
15 | 1000 | 7.64 x 10-11 |
15 | 1100 | 1.77 x 10-10 |
15 | 1200 | 5.67 x 10-10 |
15 | 1300 | 1.47 x 10-9 |
15 | 1400 | 3.51 x 10-9 |
15 | 1500 | 6.88 x 10-9 |
15 | 1600 | 1.35 x 10-8 |
15 | 1700 | 3.05 x 10-8 |
20 | 1000 | 3.69 x 10-11 |
20 | 1100 | 8.59 x 10-11 |
20 | 1200 | 3.30 x 10-10 |
20 | 1300 | 8.95 x 10-10 |
20 | 1400 | 2.13 x 10-9 |
20 | 1500 | 4.09 x 10-9 |
20 | 1600 | 9.15 x 10-9 |
20 | 1700 | 2.11 x 10-8 |
25 | 1000 | 1.71 x 10-11 |
25 | 1100 | 4.35 x 10-11 |
25 | 1200 | 1.84 x 10-10 |
25 | 1300 | 4.66 x 10-10 |
25 | 1400 | 1.31 x 10-9 |
25 | 1500 | 2.65 x 10-9 |
25 | 1600 | 5.66 x 10-9 |
25 | 1700 | 1.26 x 10-8 |
25 | 1800 | 1.82 x 10-8 |
30 | 1000 | 3.72 x 10-12 |
30 | 1100 | 1.50 x 10-11 |
30 | 1200 | 9.20 x 10-11 |
30 | 1300 | 2.82 x 10-10 |
30 | 1400 | 7.39 x 10-10 |
30 | 1500 | 1.60 x 10-9 |
30 | 1600 | 3.33 x 10-9 |
30 | 1700 | 8.97 x 10-9 |
30 | 1800 | 1.33 x 10-8 |
30 | 1900 | 3.23 x 10-8 |
35 | 1000 | 2.17 x 10-12 |
35 | 1100 | 4.81 x 10-12 |
35 | 1200 | 3.07 x 10-11 |
35 | 1300 | 1.32 x 10-10 |
35 | 1400 | 4.24 x 10-10 |
35 | 1500 | 9.17 x 10-10 |
35 | 1600 | 2.03 x 10-9 |
35 | 1700 | 5.08 x 10-9 |
35 | 1800 | 7.28 x 10-9 |
35 | 1900 | 2.15 x 10-8 |
40 | 1000 | 1.86 x 10-12 |
40 | 1100 | 3.88 x 10-12 |
40 | 1200 | 1.53 x 10-11 |
40 | 1300 | 3.22 x 10-11 |
40 | 1400 | 2.25 x 10-10 |
40 | 1500 | 4.99 x 10-10 |
40 | 1600 | 1.08 x 10-9 |
40 | 1700 | 3.28 x 10-9 |
40 | 1800 | 4.77 x 10-9 |
40 | 1900 | 1.26 x 10-8 |
45 | 1000 | 1.68 x 10-12 |
45 | 1100 | 3.6 x 10-12 |
45 | 1200 | 1.23 x 10-11 |
45 | 1300 | 2.57 x 10-11 |
45 | 1400 | 7.97 x 10-11 |
45 | 1500 | 1.69 x 10-10 |
45 | 1600 | 3.85 x 10-10 |
45 | 1700 | 2.00 x 10-9 |
45 | 1800 | 2.92 x 10-9 |
45 | 1900 | 8.34 x 10-9 |
50 | 1000 | 1.51 x 10-12 |
50 | 1100 | 3.16 x 10-12 |
50 | 1200 | 1.08 x 10-11 |
50 | 1300 | 2.28 x 10-11 |
50 | 1400 | 5.50 x 10-11 |
50 | 1500 | 1.07 x 10-10 |
50 | 1600 | 2.69 x 10-10 |
50 | 1700 | 1.11 x 10-9 |
50 | 1800 | 1.77 x 10-9 |
50 | 1900 | 5.14 x 10-9 |
55 | 1000 | 1.36 x 10-12 |
55 | 1100 | 2.84 x 10-12 |
55 | 1200 | 9.54 x 10-12 |
55 | 1300 | 2.06 x 10-11 |
55 | 1400 | 4.53 x 10-11 |
55 | 1500 | 8.89 x 10-11 |
55 | 1600 | 2.18 x 10-10 |
55 | 1700 | 5.02 x 10-10 |
55 | 1800 | 9.33 x 10-10 |
55 | 1900 | 3.15 x 10-9 |
60 | 1000 | 1.21 x 10-12 |
60 | 1100 | 2.54 x 10-12 |
60 | 1200 | 8.47 x 10-12 |
60 | 1300 | 1.84 x 10-11 |
60 | 1400 | 4.00 x 10-11 |
60 | 1500 | 7.86 x 10-11 |
60 | 1600 | 1.92 x 10-10 |
60 | 1700 | 3.13 x 10-10 |
60 | 1800 | 4.85 x 10-10 |
60 | 1900 | 1.79 x 10-9 |
65 | 1000 | 1.08 x 10-12 |
65 | 1100 | 2.24 x 10-12 |
65 | 1200 | 7.44 x 10-12 |
65 | 1300 | 1.62 x 10-11 |
65 | 1400 | 3.51 x 10-11 |
65 | 1500 | 6.93 x 10-11 |
65 | 1600 | 1.69 x 10-10 |
65 | 1700 | 2.47 x 10-10 |
65 | 1800 | 3.47 x 10-10 |
65 | 1900 | 1.02 x 10-9 |
70 | 1000 | 9.40 x 10-13 |
70 | 1100 | 1.94 x 10-12 |
70 | 1200 | 6.46 x 10-12 |
70 | 1300 | 1.39 x 10-11 |
70 | 1400 | 3.04 x 10-11 |
70 | 1500 | 5.98 x 10-11 |
70 | 1600 | 1.47 x 10-10 |
70 | 1700 | 2.12 x 10-10 |
70 | 1800 | 2.93 x 10-10 |
70 | 1900 | 6.34 x 10-10 |
75 | 1000 | 8.00 x 10-13 |
75 | 1100 | 1.64 x 10-12 |
75 | 1200 | 5.57 x 10-12 |
75 | 1300 | 1.17 x 10-11 |
75 | 1400 | 2.55 x 10-11 |
75 | 1500 | 5.02 x 10-11 |
75 | 1600 | 1.23 x 10-10 |
75 | 1700 | 1.80 x 10-10 |
75 | 1800 | 2.46 x 10-10 |
75 | 1900 | 4.84 x 10-10 |
80 | 1000 | 6.50 x 10-13 |
80 | 1100 | 1.33 x 10-12 |
80 | 1200 | 4.59 x 10-12 |
80 | 1300 | 9.40 x 10-12 |
80 | 1400 | 2.08 x 10-11 |
80 | 1500 | 4.05 x 10-11 |
80 | 1600 | 9.98 x 10-11 |
80 | 1700 | 1.46 x 10-10 |
80 | 1800 | 2.02 x 10-10 |
80 | 1900 | 3.94 x 10-10 |
85 | 1000 | 4.90 x 10-13 |
85 | 1100 | 1.01 x 10-12 |
85 | 1200 | 3.52 x 10-12 |
85 | 1300 | 7.10 x 10-12 |
85 | 1400 | 1.60 x 10-11 |
85 | 1500 | 3.06 x 10-11 |
85 | 1600 | 7.57 x 10-11 |
85 | 1700 | 1.11 x 10-10 |
85 | 1800 | 1.58 x 10-10 |
85 | 1900 | 3.10 x 10-10 |
90 | 1000 | 3.40 x 10-13 |
90 | 1100 | 6.80 x 10-13 |
90 | 1200 | 2.41 x 10-12 |
90 | 1300 | 4.80 x 10-12 |
90 | 1400 | 1.09 x 10-11 |
90 | 1500 | 2.06 x 10-11 |
90 | 1600 | 5.10 x 10-11 |
90 | 1700 | 7.54 x 10-11 |
90 | 1800 | 1.11 x 10-10 |
90 | 1900 | 2.20 x 10-10 |
95 | 1000 | 1.80 x 10-13 |
95 | 1100 | 3.40 x 10-13 |
95 | 1200 | 1.25 x 10-12 |
95 | 1300 | 2.40 x 10-12 |
95 | 1400 | 5.70 x 10-12 |
95 | 1500 | 1.06 x 10-11 |
95 | 1600 | 2.58 x 10-11 |
95 | 1700 | 3.83 x 10-11 |
95 | 1800 | 6.04 x 10-11 |
95 | 1900 | 1.17 x 10-10 |
Table 17
Impurity Diffusion of Ta in Ta-Ti Alloys
Temperature (C) | D (cm2/s) |
1000 | 5.31 x 10-10 |
1100 | 1.08 x 10-9 |
1150 | 1.68 x 10-9 |
1200 | 3.13 x 10-9 |
1250 | 4.42 x 10-9 |
1300 | 6.39 x 10-9 |
1350 | 9.31 x 10-9 |
1400 | 1.49 x 10-8 |
1450 | 1.89 x 10-8 |
1500 | 2.36 x 10-8 |
1550 | 3.38 x 10-8 |
1600 | 5.13 x 10-8 |
Table 18
Diffusion Parameters for Ta in Ta-Ti Alloys
Ta (at%) | Do (cm2/s) | E (kJ/mol) |
0 | 1.16 x 10-3 | 153 |
10 | 1.22 x 10-3 | 171 |
20 | 2.32 x 10-3 | 193 |
30 | 6.37 x 10-3 | 223 |
40 | 4.34 x 10-3 | 237 |
50 | 1.99 x 10-4 | 206 |
60 | 1.24 x 10-5 | 174 |
70 | 5.15 x 10-6 | 167 |
80 | 3.45 x 10-6 | 166 |
90 | 1.84 x 10-6 | 167 |