The tracer diffusion of 95Zr and 95Nb was measured, in ß-phase alloys which contained 5.5, 16.3 or 28.1at%Nb, at temperatures ranging from 1035 to 1871K (table 21). The experimental data were analyzed in terms of Manning's random alloy model, and the partial correlation factors were calculated as a function of temperature. These factors varied smoothly over the entire temperature range, whereas the diffusivity exhibited a pronounced curvature in Arrhenius plots (tables 22 and 23). A correlation was found to exist between the degree of deviation from Arrhenius behavior of the diffusion coefficients of both components, and the lattice dynamics of the measured phonon dispersions, with regard to their dependence upon the Nb content. The temperature dependence of the isotope effect in Zr diffusion was measured for the 5.5at%Nb alloy (table 24). The isotope-effect parameter tended to increase with temperature, and the energy-transfer factor for the alloy was somewhat larger than the corresponding values for pure ß-Zr; especially at low temperatures. The data led to the overall conclusion that the vacancy mechanism alone operated within the present temperature range.
Tracer Diffusion and Mechanism of Non-Arrhenius Diffusion Behavior of Zr and Nb in Body-Centered Cubic Zr-Nb Alloys. C.Herzig, U.Köhler, S.V.Divinski: Journal of Applied Physics, 1999, 85[12], 8119-30
Table 21
Bulk Diffusivity of 95Zr and 95Nb in Zr-Nb Alloys
Temperature (K) | Nb (at%) | Tracer | D (m2/s) |
994 | 16.3 | 95Zr | 1.38 x 10-15 |
1035 | 16.3 | 95Nb | 7.48 x 10-16 |
1065 | 16.3 | 95Zr | 3.50 x 10-15 |
1057 | 28.1 | 95Nb | 1.65 x 10-16 |
1091 | 16.3 | 95Nb | 1.74 x 10-15 |
1113 | 5.5 | 95Zr | 3.16 x 10-14 |
1098 | 28.1 | 95Nb | 2.95 x 10-16 |
1124 | 28.1 | 95Zr | 1.68 x 10-15 |
1136 | 16.3 | 95Zr | 9.52 x 10-15 |
1146 | 16.3 | 95Nb | 3.12 x 10-15 |
1156 | 28.1 | 95Nb | 1.01 x 10-15 |
1178 | 5.5 | 95Nb | 1.73 x 10-14 |
1178 | 5.5 | 95Zr | 5.80 x 10-14 |
1194 | 5.5 | 95Nb | 2.07 x 10-14 |
1194 | 5.5 | 95Zr | 6.08 x 10-14 |
1203 | 5.5 | 95Nb | 1.99 x 10-14 |
1203 | 5.5 | 95Zr | 6.41 x 10-14 |
1203 | 28.1 | 95Nb | 2.11 x 10-15 |
1202 | 28.1 | 95Zr | 5.97 x 10-15 |
1218 | 16.3 | 95Zr | 2.54 x 10-14 |
1218 | 16.3 | 95Nb | 8.27 x 10-15 |
1287 | 5.5 | 95Zr | 1.65 x 10-13 |
1287 | 5.5 | 95Nb | 5.84 x 10-14 |
1270 | 28.1 | 95Zr | 1.23 x 10-14 |
1270 | 28.1 | 95Nb | 4.70 x 10-15 |
1291 | 16.3 | 95Nb | 2.30 x 10-14 |
1291 | 16.3 | 95Zr | 5.61 x 10-14 |
1324 | 28.1 | 95Nb | 1.06 x 10-14 |
1324 | 28.1 | 95Zr | 2.58 x 10-14 |
1352 | 5.5 | 95Zr | 2.10 x 10-13 |
1352 | 5.5 | 95Nb | 8.20 x 10-14 |
1374 | 16.3 | 95Zr | 1.47 x 10-13 |
1374 | 16.3 | 95Nb | 6.44 x 10-14 |
1415 | 28.1 | 95Nb | 3.37 x 10-14 |
1415 | 28.1 | 95Zr | 7.87 x 10-14 |
1461 | 5.5 | 95Nb | 2.21 x 10-13 |
1461 | 5.5 | 95Zr | 4.67 x 10-13 |
1456 | 16.3 | 95Nb | 1.75 x 10-13 |
1456 | 16.3 | 95Zr | 3.45 x 10-13 |
1502 | 28.1 | 95Nb | 1.10 x 10-13 |
1502 | 28.1 | 95Zr | 2.00 x 10-13 |
1540 | 5.5 | 95Nb | 5.40 x 10-13 |
1540 | 5.5 | 95Zr | 9.97 x 10-13 |
1545 | 16.3 | 95Nb | 4.31 x 10-13 |
1545 | 16.3 | 95Zr | 6.52 x 10-13 |
1583 | 28.1 | 95Nb | 2.30 x 10-13 |
1583 | 28.1 | 95Zr | 4.44 x 10-13 |
1630 | 5.5 | 95Zr | 1.17 x 10-12 |
1685 | 5.5 | 95Nb | 1.29 x 10-12 |
1685 | 5.5 | 95Zr | 1.98 x 10-12 |
1710 | 16.3 | 95Nb | 1.99 x 10-12 |
1710 | 16.3 | 95Zr | 2.68 x 10-12 |
1725 | 28.1 | 95Zr | 1.42 x 10-12 |
1725 | 28.1 | 95Nb | 9.07 x 10-13 |
1774 | 5.5 | 95Nb | 2.95 x 10-12 |
1774 | 5.5 | 95Zr | 3.94 x 10-12 |
1802 | 5.5 | 95Nb | 3.31 x 10-12 |
1802 | 5.5 | 95Zr | 4.34 x 10-12 |
1840 | 16.3 | 95Nb | 5.88 x 10-12 |
1840 | 16.3 | 95Zr | 6.92 x 10-12 |
1853 | 28.1 | 95Nb | 2.66 x 10-12 |
1853 | 28.1 | 95Zr | 3.74 x 10-12 |
1944 | 5.5 | 95Zr | 1.02 x 10-11 |
1944 | 5.5 | 95Nb | 9.41 x 10-12 |
1957 | 5.5 | 95Zr | 1.23 x 10-11 |
1957 | 5.5 | 95Nb | 1.23 x 10-11 |
2003 | 5.5 | 95Zr | 1.87 x 10-11 |
2003 | 5.5 | 95Nb | 1.94 x 10-11 |
Table 22
Parameters for Zr and Nb Diffusion in Zr-Nb Alloys
D = Doexp[-E/kT]exp[a(Tm/T)2]
Tracer | Nb (at%) | Do (m2/s) | E (eV) | a |
95Zr | 0 | 4.77 x 10-5 | 3.32 | 3.81 |
95Zr | 5.5 | 4.4 x 10-5 | 3.26 | 3.72 |
95Zr | 16.3 | 2.53 x 10-5 | 2.84 | 2.30 |
95Zr | 28.1 | 1.3 x 10-5 | 2.71 | 1.62 |
95Nb | 0 | 7.1 x 10-5 | 3.83 | 4.1 |
95Nb | 5.5 | 2.1 x 10-4 | 3.55 | 3.77 |
95Nb | 16.3 | 1.7 x 10-4 | 3.18 | 2.4 |
95Nb | 28.1 | 6.5 x 10-5 | 3.09 | 1.96 |
Table 23
Parameters for Zr and Nb Diffusion in Zr-Nb Alloys
D = D1exp[-E1/kT] + D2exp[-E2/kT]
Tracer | Nb (at%) | D1 (m2/s) | D2 (m2/s) | E1 (eV) | E2 (eV) |
95Zr | 0 | 3.7 x 10-7 | 2.5 x 10-11 | 1.75 | 0.60 |
95Zr | 5.5 | 2.2 x 10-4 | 2.6 x 10-9 | 2.88 | 1.09 |
95Zr | 16.3 | 1.7 x 10-6 | 1.2 x 10-9 | 1.99 | 1.18 |
95Zr | 28.1 | 1.5 x 10-6 | 2.35 x 10-10 | 2.07 | 1.21 |
95Nb | 0 | 2.8 x 10-6 | 2.7 x 10-10 | 2.11 | 0.99 |
95Nb | 5.5 | 9.8 x 10-4 | 1.4 x 10-8 | 3.13 | 1.36 |
95Nb | 16.3 | 5.0 x 10-6 | 3.8 x 10-11 | 2.17 | 0.98 |
95Nb | 28.1 | 9.6 x 10-6 | 1.7 x 10-8 | 2.44 | 1.70 |
Table 24
Isotope-Effect Parameter for Zr Diffusion in Zr-5.5at%Nb
Temperature (K) | IEP |
2003 | 0.383 |
1540 | 0.390 |
1352 | 0.380 |
1194 | 0.318 |
1178 | 0.335 |