The grain boundary self-diffusion of Hf was studied in the hexagonal close-packed phase of the alloy, at 910 to 1493K, by using radiotracer and serial sectioning techniques. It was not possible to stabilize the grain size fully by using pre-diffusion heat treatments, so some of the grain boundaries moved during diffusion annealing due to continuing grain growth. Consequently, the measured penetration profiles were untypical in shape and could not be treated by using standard grain boundary diffusion models which considered only stationary grain boundaries. A procedure for treating such profiles was developed on the basis of a simple model for tracer diffusion in a polycrystal which contained both stationary and moving grain boundaries. By using this method, it was possible to determine the product of the grain-boundary self-diffusion coefficient and grain boundary width for stationary grain boundaries. It was also possible to estimate the grain boundary migration velocities by assuming that the product values for stationary and migrating grain boundaries were the same. The activation enthalpy and pre-exponential factor of the product for self-diffusion along stationary boundaries (table 126) were deduced to be 212kJ/mol and 3.5 x 10-13m3/s. In spite of the presence of 3%Zr, these parameters were expected to describe closely the self-diffusion in pure -Hf. The data indicated the operation of a vacancy mechanism for grain boundary self-diffusion in the latter, and were consistent with previous results for other hexagonal close-packed transition metals. A rough estimate of the activation enthalpy for grain boundary migration (195kJ/mol) was in good agreement with that for grain boundary diffusion, and suggested that the activation barriers to atomic transport across, and along, the grain boundaries were almost identical.

F.Güthoff, J.Mishin, C.Herzig: Zeitschrift für Metallkunde, 1993, 84[8], 584-91

Table 121

Diffusivity of 95Zr in Hf-10at%Nb

 

Temperature (K)

D (m2/s)

1758

1.16 x 10-12

1863

2.96 x 10-12

2113

1.14 x 10-11

2268

2.42 x 10-11

 

Table 122

Diffusivity of 95Nb in Hf-10at%Nb

 

Temperature (K)

D (m2/s)

1758

8.22 x 10-13

1863

1.59 x 10-12

2113

7.53 x 10-12

2268

1.79 x 10-11

 

Table 123

Diffusion Parameters for 181Hf, 95Nb

 and 95Zr in Hf-Nb Alloys

 

Nb(at%)

Isotope

Do (m2/s)

E (kJ/mol)

18

Hf

2.23 x 10-6

219.4

18

Zr

3.07 x 10-6

219.3

18

Nb

4.82 x 10-6

234.7

10

Hf

4.15 x 10-7

189.5

10

Zr

6.97 x 10-7

193.3

10

Nb

7.26 x 10-7

200.9

Table 124

Partial Correlation Factors for 181Hf Diffusion in Hf-Nb Alloys

 

Temperature (K)

Nb (at%)

f

1300

18

0.702

1300

18

0.843

1400

18

0.705

1400

18

0.829

1500

18

0.708

1500

18

0.815

1600

18

0.711

1600

18

0.802

1700

10

0.721

1700

10

0.782

1700

18

0.713

1700

18

0.790

1800

10

0.722

1800

18

0.716

1900

10

0.723

1900

18

0.718

2000

10

0.724

2000

18

0.720

2100

10

0.725

2100

18

0.722

Table 125

Partial Correlation Factors for 95Nb Diffusion in Hf-Nb Alloys

 

Temperature (K)

Nb (at%)

f

2100

10

0.749

2100

18

0.750

2000

10

0.757

2000

18

0.759

1900

10

0.765

1900

18

0.770

1800

10

0.773

1800

18

0.779

 

Table 126

Grain Boundary Self-Diffusivity in -Hf

 

Temperature (K)

D (m2/s)

910

2.54 x 10-26

985

1.52 x 10-24

1068

1.89 x 10-23

1126

3.86 x 10-23

1187

1.84 x 10-22

1218

3.61 x 10-22

1244

7.96 x 10-22

1325

1.59 x 10-21

1393

4.24 x 10-21

1493

8.43 x 10-21