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Self-diffusion in niobium
PART
CONTRIBUTED
PAPERS
1I
Journal of Nuclear Materials 69 & 70 (1978) 0 North-Holland Publishing Company
SELF-DIFFUSION R.E. EINZIGER,
523-525
IN NIOBIUM * J.N. MUNDY and H.A. HOFF
Argonne National Laboratory, Argonne, Illinois 60439,
USA
tained from Materials Research Corporation, New York (Marz Grade). Single crystal samples were used for all diffusion anneals below 1800 K. Samples annealed at temperatures above 1673 K were sectioned with a precision parallel grinder, samples annealed at temperatures below 1670 K by anodizing. Despite previous experience in the sectioning of niobium by anodic oxidation [5,6] and considerable efforts at this Laboratory, a completely satisfactory technique was not developed. The large experimental scatter found in the previous measurement of niobium self-diffusion [ 1] show that the anodizing technique may have also been less than satisfactory. The diffusion anneals were made in an ultra high vacuum system using an electron beam furnace. The anneal conditions maintained the oxygen content of the niobium samples at a pre-established value. Two types of samples were annealed: the clean samples had an oxygen content less than 50 wt.ppm (see ref. [3]), the doped samples had an oxygen content between 600 and 800 wt.ppm. In the temperature range 1770-2570 K the measured diffusion coefficients were the same for clean or doped samples. The range of oxygen content was similar to that used in the work on self-diffusion in cr-Fe although the homologous temperature range was somewhat higher [(0.65-0.90) r, for Nb, (0.58-0.65) Tm for a-Fe]. An oxygen effect on diffusion in niobium might have been expected because niobium, a Group-V bee metal, has a high oxygen solubility . The temperature measurements were made with an optical pyrometer focused on a black body hole defined by a pair of sample surfaces. The pyrometer was calibrated through the furnace window against a standard tungsten strip lamp before and after each diffusion run. The pyrometer measured the average temperature in the black body cavity and the temperature gradient in the system results in slightly different values for the
Niobium self-diffusion was investigated as part of a continuing program designed to understand atomic transport in bee metals. Earlier measurements on sodium and potassium had shown curved Arrhenius plots similar to the results for diffusion in a number of fee metals. These plots had been interpreted as diffusion by single vacancies with an increasing contribution from divacancies at temperatures close to the melting point. Measurements‘of the isotope effect for self-diffusion in sodium and in (Yand 6-iron showed a strong temperature dependence which was also interpreted in terms of the single/divacancy concept. Selfdiffusion in chromium also shows a strongly temperature dependent isotope effect but the Arrhenius plot showed no measurable curvature. The present niobium self-diffusion work had three main aims. (1) A determination of the linearity of the Arrhenius plot. Previous measurements [ 1] had been made over ten orders of magnitude in the diffusion coefficient and although the Arrhenius plot is apparently linear -there is considerable scatter in the data. (2) A study of the effect of oxygen on diffusion. Previous measurements [2] on self-diffusion in &iron had shown that small changes of oxygen content had a large effect. However, measurements on chromium self-diffusion [3], a Group-VI bee metal, showed no measurable effect of oxygen. (3) An attempt to measure the isotope effect over a wide range of diffusion coefficients than has previously been possible. The method used was to observe the diffusion of a thin surface layer of 95Nb by sectioning. A detailed description of the experimental techniques will be given in another paper [4]. The niobium metal was obl
Work supported
by the US Energy ment Administration.
Research
and Devdop-
523
R.E. Einziger et al. /Self-diffusion
524
D-7:
2673 1
T(K)
2073 1
I673 I
1373 1 J
in niobium
t (8 + 3) X lop3 exp(-3F)cm2
s-r .
(1)
I
kq.5
1 5.5
I 4.5 IO./1
I 6.5
7.5
(K-l)
Fig. 1. Diffusion of 95Nb in niobium as a function of temperature.
diffusion coefficients from the samples defining the cavity. In the Arrhenius plot of the diffusion data shown in fig. 1, the geometric mean of the diffusion coefficients from each pair of samples has been used as the diffusion coefficient for the window-corrected black body temperature. Analysis of the previous data [ 1] for niobium selfdiffusion showed the linear Arrhenius relation with Do = 1 .l cm2 s-l and Q = 4.16 eV. However, Neumann [7] and Mehrer et al. [8] both assumed a single/ divacancy mechanism to govern diffusion in the Group-V bee metals and re-analyzed all the previous bee diffusion data. Their results for niobium were similar, and yielded (De)av/(Wrv - 4 X 102, QdAv * 1.35 and indicated that at the melting point divacancies were responsible for at least half of the diffusion. The present work shows definite curvature in the In D vs. l/T plot and has been fitted to the following expression. D = (3.7 k 0.3)exp(-4q)
The ratios of the pre-exponential terms and the activation energies are similar to both previous analyses, however, there are significant differences. The divacancy contribution to diffusion at the melting point resulting from eq. (1) is as high as 90% and suggests strongly the value of measuring the isotope effect for niobium selfdiffusion over a wide range of temperature. The low value of the isotope effect for self-diffusion in bee metals [3,9,10] together with the present analysis showing large divacancy contribution at high temperatures, gave a strong incentive to measure the isotope effect for niobium self-diffusion over a wide range of temperature. After considerable effort we have concluded that the measurements could not be made. The two isotopes 95Nb and 90Nb would appear to ne suitable but each isotope contains small traces of radioactive zirconium which would mask out any niobium mass effect. The significance of small traces (< 100 ppm) of radioactive impurity is not obvious and details of the problem can be found in ref. [ 111. In eq. (1) the absolute values of the pre-exponential factors are considerably lower than those from the previous analyses and if interpreted in terms of single and divacancy components would yield more conventional values for the activation entropies (-0.7 and 7 k, respectively). The ratio of the activation energies in eq. (1) is 1.25 and if the single/divacancy interpretation is assumed then,
(2) where EFv, Eg are the formation and migration energy of a single vacancy, and E& is the binding energy and Eyv the migration energy of divacancies. If E& and Ey? are assumed small (-0.1 ET”) then eq. (2) yields E$Eyv = 0.44 which is higher than expected for a Group-V bee metal [ 121. Adjustment of the assumed values of EFv and Eyv by factors of two or less can reduce the ratio Ey?‘,IEyv to only 0.35. References [l] T.S. Lundy, F.R. Winslow, R.E. Pawe and C.J. McHargue, Trans. Met. Sot., AIME 233 (1965) 1533. [2] V. Irmer and M. Feller-Kniepmeyer, Phil. Mag%.U (1972) 1345.
R.E. Einziger et al. / Self-diffusion (31 J.N. Mundy, C.W. Tse and W.D. McFall, Phys. Rev. B13 (1976) 2349. [4] R.E. Einziger, J.N. Mundy and H.A. Hoff, to be published [S] R.E. Pawel and T.S. Lundy, J. Appl. Phys. 35 (1964) 435. [6] M.R. Arora and R. Kelly, Electrochim. Acta 19 (1974) 413. [7] G.M. Neumann, Diffusion Processes (Gordon and Breach, London, 1971) p. 329.
in niobium
525
[ 81 H. Mehrer, P. Kuntz and A. Seeger, Defects in Refractory Metals, International Conference Proceedings (MO], 1972) p. 183. [9] J.N. Mundy, Phys. Rev. B3 (1971) 2431. [lo] C.M. Walter and N.L. Peterson, Phys. Rev. 178 (1966) 464. [ 111 R.E. Einziger and J.N. Mundy, to be published. [12] H. Schultz, Ser. Met. 8 (1974) 721.
CONTRIBUTED
PAPERS
1I
Journal of Nuclear Materials 69 & 70 (1978) 0 North-Holland Publishing Company
SELF-DIFFUSION R.E. EINZIGER,
523-525
IN NIOBIUM * J.N. MUNDY and H.A. HOFF
Argonne National Laboratory, Argonne, Illinois 60439,
USA
tained from Materials Research Corporation, New York (Marz Grade). Single crystal samples were used for all diffusion anneals below 1800 K. Samples annealed at temperatures above 1673 K were sectioned with a precision parallel grinder, samples annealed at temperatures below 1670 K by anodizing. Despite previous experience in the sectioning of niobium by anodic oxidation [5,6] and considerable efforts at this Laboratory, a completely satisfactory technique was not developed. The large experimental scatter found in the previous measurement of niobium self-diffusion [ 1] show that the anodizing technique may have also been less than satisfactory. The diffusion anneals were made in an ultra high vacuum system using an electron beam furnace. The anneal conditions maintained the oxygen content of the niobium samples at a pre-established value. Two types of samples were annealed: the clean samples had an oxygen content less than 50 wt.ppm (see ref. [3]), the doped samples had an oxygen content between 600 and 800 wt.ppm. In the temperature range 1770-2570 K the measured diffusion coefficients were the same for clean or doped samples. The range of oxygen content was similar to that used in the work on self-diffusion in cr-Fe although the homologous temperature range was somewhat higher [(0.65-0.90) r, for Nb, (0.58-0.65) Tm for a-Fe]. An oxygen effect on diffusion in niobium might have been expected because niobium, a Group-V bee metal, has a high oxygen solubility . The temperature measurements were made with an optical pyrometer focused on a black body hole defined by a pair of sample surfaces. The pyrometer was calibrated through the furnace window against a standard tungsten strip lamp before and after each diffusion run. The pyrometer measured the average temperature in the black body cavity and the temperature gradient in the system results in slightly different values for the
Niobium self-diffusion was investigated as part of a continuing program designed to understand atomic transport in bee metals. Earlier measurements on sodium and potassium had shown curved Arrhenius plots similar to the results for diffusion in a number of fee metals. These plots had been interpreted as diffusion by single vacancies with an increasing contribution from divacancies at temperatures close to the melting point. Measurements‘of the isotope effect for self-diffusion in sodium and in (Yand 6-iron showed a strong temperature dependence which was also interpreted in terms of the single/divacancy concept. Selfdiffusion in chromium also shows a strongly temperature dependent isotope effect but the Arrhenius plot showed no measurable curvature. The present niobium self-diffusion work had three main aims. (1) A determination of the linearity of the Arrhenius plot. Previous measurements [ 1] had been made over ten orders of magnitude in the diffusion coefficient and although the Arrhenius plot is apparently linear -there is considerable scatter in the data. (2) A study of the effect of oxygen on diffusion. Previous measurements [2] on self-diffusion in &iron had shown that small changes of oxygen content had a large effect. However, measurements on chromium self-diffusion [3], a Group-VI bee metal, showed no measurable effect of oxygen. (3) An attempt to measure the isotope effect over a wide range of diffusion coefficients than has previously been possible. The method used was to observe the diffusion of a thin surface layer of 95Nb by sectioning. A detailed description of the experimental techniques will be given in another paper [4]. The niobium metal was obl
Work supported
by the US Energy ment Administration.
Research
and Devdop-
523
R.E. Einziger et al. /Self-diffusion
524
D-7:
2673 1
T(K)
2073 1
I673 I
1373 1 J
in niobium
t (8 + 3) X lop3 exp(-3F)cm2
s-r .
(1)
I
kq.5
1 5.5
I 4.5 IO./1
I 6.5
7.5
(K-l)
Fig. 1. Diffusion of 95Nb in niobium as a function of temperature.
diffusion coefficients from the samples defining the cavity. In the Arrhenius plot of the diffusion data shown in fig. 1, the geometric mean of the diffusion coefficients from each pair of samples has been used as the diffusion coefficient for the window-corrected black body temperature. Analysis of the previous data [ 1] for niobium selfdiffusion showed the linear Arrhenius relation with Do = 1 .l cm2 s-l and Q = 4.16 eV. However, Neumann [7] and Mehrer et al. [8] both assumed a single/ divacancy mechanism to govern diffusion in the Group-V bee metals and re-analyzed all the previous bee diffusion data. Their results for niobium were similar, and yielded (De)av/(Wrv - 4 X 102, QdAv * 1.35 and indicated that at the melting point divacancies were responsible for at least half of the diffusion. The present work shows definite curvature in the In D vs. l/T plot and has been fitted to the following expression. D = (3.7 k 0.3)exp(-4q)
The ratios of the pre-exponential terms and the activation energies are similar to both previous analyses, however, there are significant differences. The divacancy contribution to diffusion at the melting point resulting from eq. (1) is as high as 90% and suggests strongly the value of measuring the isotope effect for niobium selfdiffusion over a wide range of temperature. The low value of the isotope effect for self-diffusion in bee metals [3,9,10] together with the present analysis showing large divacancy contribution at high temperatures, gave a strong incentive to measure the isotope effect for niobium self-diffusion over a wide range of temperature. After considerable effort we have concluded that the measurements could not be made. The two isotopes 95Nb and 90Nb would appear to ne suitable but each isotope contains small traces of radioactive zirconium which would mask out any niobium mass effect. The significance of small traces (< 100 ppm) of radioactive impurity is not obvious and details of the problem can be found in ref. [ 111. In eq. (1) the absolute values of the pre-exponential factors are considerably lower than those from the previous analyses and if interpreted in terms of single and divacancy components would yield more conventional values for the activation entropies (-0.7 and 7 k, respectively). The ratio of the activation energies in eq. (1) is 1.25 and if the single/divacancy interpretation is assumed then,
(2) where EFv, Eg are the formation and migration energy of a single vacancy, and E& is the binding energy and Eyv the migration energy of divacancies. If E& and Ey? are assumed small (-0.1 ET”) then eq. (2) yields E$Eyv = 0.44 which is higher than expected for a Group-V bee metal [ 121. Adjustment of the assumed values of EFv and Eyv by factors of two or less can reduce the ratio Ey?‘,IEyv to only 0.35. References [l] T.S. Lundy, F.R. Winslow, R.E. Pawe and C.J. McHargue, Trans. Met. Sot., AIME 233 (1965) 1533. [2] V. Irmer and M. Feller-Kniepmeyer, Phil. Mag%.U (1972) 1345.
R.E. Einziger et al. / Self-diffusion (31 J.N. Mundy, C.W. Tse and W.D. McFall, Phys. Rev. B13 (1976) 2349. [4] R.E. Einziger, J.N. Mundy and H.A. Hoff, to be published [S] R.E. Pawel and T.S. Lundy, J. Appl. Phys. 35 (1964) 435. [6] M.R. Arora and R. Kelly, Electrochim. Acta 19 (1974) 413. [7] G.M. Neumann, Diffusion Processes (Gordon and Breach, London, 1971) p. 329.
in niobium
525
[ 81 H. Mehrer, P. Kuntz and A. Seeger, Defects in Refractory Metals, International Conference Proceedings (MO], 1972) p. 183. [9] J.N. Mundy, Phys. Rev. B3 (1971) 2431. [lo] C.M. Walter and N.L. Peterson, Phys. Rev. 178 (1966) 464. [ 111 R.E. Einziger and J.N. Mundy, to be published. [12] H. Schultz, Ser. Met. 8 (1974) 721.