Ternary chemical diffusion was studied, in the γ-phase of this system at 1223K, via the electron probe microanalysis of penetration profiles. The major and cross-diffusion coefficients were evaluated by using the Boltzmann-Matano method, as extended to the ternary system. It was found that the major coefficients were positive, whereas the cross-diffusion coefficients were negative (table 76). The concentration dependence of the diffusion coefficients could be expressed as a function of the Ni and Cr contents. The deduced interaction parameters indicated that the diffusive interaction between NI and Fe was much stronger than that between Cr and Ni or Ni and Fe. The tracer diffusion coefficients were deduced from the ternary diffusion coefficients, and decreased in the order, DCr - DFe - DNi (table 77).
G.B.Kale, K.Bhanumurthy, S.K.Khera, M.K.Asundi: Materials Transactions, 1991, 32[11], 1034-41
Table 76
Ternary Interdiffusion Coefficients in the Fe-Ni-Cr System at 1223K
Ni (wt%) | Cr (wt %) | Coefficient | Value (m2/s) |
70.3 | 17.8 | DNiNiFe | 1.58 x 10-15 |
71.3 | 19.6 | DNiNiFe | 1.56 x 10-15 |
64.8 | 5.9 | DNiNiFe | 2.70 x 10-15 |
66.6 | 11.6 | DNiNiFe | 3.80 x 10-15 |
75.9 | 23.6 | DNiNiFe | 1.05 x 10-15 |
42.0 | 23.0 | DNiNiFe | 2.30 x 10-15 |
54.0 | 24.0 | DNiNiFe | 2.50 x 10-15 |
83.6 | 13.2 | DNiNiFe | -1.23 x 10-15 |
91.9 | 1.8 | DNiNiFe | 2.35 x 10-15 |
90.5 | 3.1 | DNiNiFe | 8.05 x 10-15 |
58.1 | 24.2 | DNiNiFe | 2.40 x 10-15 |
63.7 | 24.5 | DNiNiFe | 1.79 x 10-15 |
67.4 | 24.4 | DNiNiFe | 1.99 x 10-15 |
75.4 | 24.4 | DNiNiFe | 2.7 x 10-16 |
54.8 | 25.9 | DNiNiFe | 3.78 x 10-15 |
46.5 | 9.0 | DNiNiFe | 2.52 x 10-15 |
49.2 | 15.3 | DNiNiFe | 3.20 x 10-15 |
45.0 | 28.4 | DNiNiFe | 1.90 x 10-15 |
57.0 | 28.8 | DNiNiFe | 1.80 x 10-15 |
59.0 | 30.0 | DNiNiFe | 5.7 x 10-16 |
42.0 | 9.8 | DNiNiFe | 5.5 x 10-16 |
35.4 | 18.5 | DNiNiFe | 7.2 x 10-16 |
42.4 | 29.6 | DNiNiFe | 7.0 x 10-16 |
43.9 | 9.5 | DNiNiFe | 2.40 x 10-15 |
43.4 | 16.6 | DNiNiFe | 1.30 x 10-15 |
45.1 | 5.8 | DNiNiFe | 8.80 x 10-15 |
42.3 | 28.5 | DNiNiFe | 1.25 x 10-15 |
44.7 | 4.5 | DNiNiFe | 7.3 x 10-16 |
28.8 | 22.7 | DNiNiFe | 1.50 x 10-15 |
70.3 | 17.8 | DNiCrFe | -1.1 x 10-16 |
71.3 | 19.6 | DNiCrFe | -2.7 x 10-16 |
64.8 | 5.9 | DNiCrFe | -2.0 x 10-17 |
66.6 | 11.6 | DNiCrFe | -5.4 x 10-16 |
75.9 | 23.6 | DNiCrFe | -2.1 x 10-16 |
42.0 | 23.0 | DNiCrFe | -2.4 x 10-16 |
54.0 | 24.0 | DNiCrFe | 1.9 x 10-16 |
83.6 | 13.2 | DNiCrFe | -2.10 x 10-15 |
91.9 | 1.8 | DNiCrFe | -2.5 x 10-16 |
90.5 | 3.1 | DNiCrFe | -1.20 x 10-15 |
58.1 | 24.2 | DNiCrFe | 8.6 x 10-16 |
63.7 | 24.5 | DNiCrFe | 3.7 x 10-16 |
67.4 | 24.4 | DNiCrFe | 2.67 x 10-15 |
75.4 | 24.4 | DNiCrFe | 5.27 x 10-15 |
54.8 | 25.9 | DNiCrFe | 4.1 x 10-16 |
46.5 | 9.0 | DNiCrFe | -3.4 x 10-16 |
49.2 | 15.3 | DNiCrFe | -5.0 x 10-16 |
45.0 | 28.4 | DNiCrFe | -1.10 x 10-15 |
57.0 | 28.8 | DNiCrFe | 4.1 x 10-16 |
59.0 | 30.0 | DNiCrFe | 1.33 x 10-15 |
42.0 | 9.8 | DNiCrFe | -1.12 x 10-15 |
35.4 | 18.5 | DNiCrFe | -1.80 x 10-15 |
42.4 | 29.6 | DNiCrFe | -5.6 x 10-16 |
43.9 | 9.5 | DNiCrFe | -1.50 x 10-15 |
43.4 | 16.6 | DNiCrFe | -8.7 x 10-16 |
45.1 | 5.8 | DNiCrFe | -2.10 x 10-15 |
42.3 | 28.5 | DNiCrFe | -3.9 x 10-16 |
44.7 | 4.5 | DNiCrFe | 2.5 x 10-16 |
28.8 | 22.7 | DNiCrFe | 3.9 x 10-16 |
70.3 | 17.8 | DCrNiFe | -7.5 x 10-16 |
71.3 | 19.6 | DCrNiFe | -9.9 x 10-16 |
64.8 | 5.9 | DCrNiFe | -2.5 x 10-16 |
66.6 | 11.6 | DCrNiFe | -8.9 x 10-16 |
75.9 | 23.6 | DCrNiFe | -4.30 x 10-15 |
42.0 | 23.0 | DCrNiFe | -4.8 x 10-16 |
54.0 | 24.0 | DCrNiFe | 2.6 x 10-16 |
83.6 | 13.2 | DCrNiFe | -9.8 x 10-16 |
91.9 | 1.8 | DCrNiFe | -3.7 x 10-16 |
90.5 | 3.1 | DCrNiFe | -2.90 x 10-15 |
58.1 | 24.2 | DCrNiFe | 2.8 x 10-16 |
63.7 | 24.5 | DCrNiFe | 2.5 x 10-16 |
67.4 | 24.4 | DCrNiFe | 2.5 x 10-16 |
75.4 | 24.4 | DCrNiFe | 2.1 x 10-16 |
54.8 | 25.9 | DCrNiFe | -1.10 x 10-15 |
46.5 | 9.0 | DCrNiFe | 1.3 x 10-16 |
49.2 | 15.3 | DCrNiFe | -7.4 x 10-16 |
45.0 | 28.4 | DCrNiFe | -1.0 x 10-15 |
57.0 | 28.8 | DCrNiFe | -1.10 x 10-15 |
59.0 | 30.0 | DCrNiFe | -2.5 x 10-16 |
42.0 | 9.8 | DCrNiFe | 4.60 x 10-15 |
35.4 | 18.5 | DCrNiFe | 9.0 x 10-16 |
42.4 | 29.6 | DCrNiFe | 7.2 x 10-16 |
43.9 | 9.5 | DCrNiFe | 3.7 x 10-16 |
43.4 | 16.6 | DCrNiFe | 1.10 x 10-15 |
45.1 | 5.8 | DCrNiFe | -9.70 x 10-15 |
42.3 | 28.5 | DCrNiFe | -2.7 x 10-16 |
44.7 | 4.5 | DCrNiFe | -3.6 x 10-16 |
28.8 | 22.7 | DCrNiFe | -2.0 x 10-16 |
70.3 | 17.8 | DCrCrFe | 9.2 x 10-16 |
71.3 | 19.6 | DCrCrFe | 1.15 x 10-15 |
64.8 | 5.9 | DCrCrFe | 1.50 x 10-15 |
66.6 | 11.6 | DCrCrFe | 1.08 x 10-15 |
75.9 | 23.6 | DCrCrFe | -3.30 x 10-15 |
42.0 | 23.0 | DCrCrFe | 5.70 x 10-15 |
54.0 | 24.0 | DCrCrFe | 2.40 x 10-15 |
83.6 | 13.2 | DCrCrFe | 4.50 x 10-15 |
91.9 | 1.8 | DCrCrFe | 3.6 x 10-16 |
90.5 | 3.1 | DCrCrFe | 1.10 x 10-15 |
58.1 | 24.2 | DCrCrFe | 2.77 x 10-15 |
63.7 | 24.5 | DCrCrFe | 3.03 x 10-15 |
67.4 | 24.4 | DCrCrFe | 2.19 x 10-15 |
75.4 | 24.4 | DCrCrFe | 3.41 x 10-15 |
54.8 | 25.9 | DCrCrFe | 1.50 x 10-15 |
46.5 | 9.0 | DCrCrFe | 3.00 x 10-15 |
49.2 | 15.3 | DCrCrFe | 3.70 x 10-15 |
45.0 | 28.4 | DCrCrFe | 1.30 x 10-15 |
57.0 | 28.8 | DCrCrFe | 8.0 x 10-16 |
59.0 | 30.0 | DCrCrFe | 2.5 x 10-16 |
42.0 | 9.8 | DCrCrFe | 2.83 x 10-15 |
35.4' | 19.5 | DCrCrFe | 5.50 x 10-15 |
42.4 | 29.6 | DCrCrFe | 4.30 x 10-15 |
43.9 | 9.5 | DCrCrFe | 4.40 x 10-15 |
43.4 | 16.6 | DCrCrFe | 6.30 x 10-15 |
45.1 | 5.8 | DCrCrFe | 5.40 x 10-15 |
42.3 | 28.5 | DCrCrFe | 3.70 x 10-15 |
44.7 | 4.5 | DCrCrFe | 3.40 x 10-15 |
Table 77
Tracer Diffusion Coefficients in the Fe-Ni-Cr System at 1223K
Ni (wt%) | Cr (wt%) | Coefficient | Value (m2/s) |
70 | 18 | DNi | 6.1 x 10-14 |
71 | 20 | DNi | 5.0 x 10-14 |
72 | 21 | DNi | 4.3 x 10-14 |
67 | 12 | DNi | 1.36 x 10-13 |
54 | 24 | DNi | 5.5 x 10-14 |
85 | 9 | DNi | 2.03 x 10-13 |
85 | 11 | DNi | 1.51 x 10-13 |
84 | 13 | DNi | 6.6 x 10-14 |
30 | 26 | DNi | 1.34 x 10-14 |
58 | 24 | DNi | 1.18 x 10-13 |
75 | 24 | DNi | 7.5 x 10-14 |
50 | 15 | DNi | 3.0 x 10-15 |
45 | 28 | DNi | 6.6 x 10-14 |
57 | 29 | DNi | 4.19 x 10-13 |
35 | 19 | DNi | 2.91 x 10-13 |
42 | 30 | DNi | 1.50 x 10-13 |
70 | 18 | DFe | 8.1 x 10-14 |
71 | 20 | DFe | 7.9 x 10-14 |
72 | 21 | DFe | 8.1 x 10-14 |
67 | 12 | DFe | 1.01 x 10-13 |
54 | 24 | DFe | 2.45 x 10-13 |
85 | 9 | DFe | 2.08 x 10-13 |
85 | 11 | DFe | 2.33 x 10-13 |
84 | 13 | DFe | 4.0 x 10-14 |
30 | 26 | DFe | 2.20 x 10-13 |
58 | 24 | DFe | 2.02 x 10-13 |
75 | 24 | DFe | 1.26 x 10-13 |
50 | 15 | DFe | 4.7 x 10-14 |
45 | 28 | DFe | 1.21 x 10-13 |
57 | 29 | DFe | 2.46 x 10-13 |
35 | 19 | DFe | 4.31 x 10-13 |
42 | 50 | DFe | 3.57 x 10-13 |
70 | 18 | DCr | 9.30 x 10-13 |
71 | 20 | DCr | 1.13 x 10-12 |
72 | 21 | DCr | 2.87 x 10-13 |
67 | 12 | DCr | 1.84 x 10-12 |
54 | 24 | DCr | 4.60 x 10-13 |
85 | 9 | DCr | 3.21 x 10-13 |
85 | 11 | DCr | 7.38 x 10-13 |
84 | 13 | DCr | 3.45 x 10-12 |
30 | 26 | DCr | 5.98 x 10-13 |
58 | 24 | DCr | 6.33 x 10-13 |
75 | 24 | DCr | 8.29 x 10-13 |
50 | 15 | DCr | 7.12 x 10-13 |
45 | 28 | DCr | 8.75 x 10-13 |
57 | 29 | DCr | 2.76 x 10-12 |
35 | 19 | DCr | 4.21 x 10-13 |
42 | 30 | DCr | 1.42 x 10-12 |