- Email: [email protected]
Diffusion of hydrogen in niobium under hydrostatic high pressure
Journal of the Less-Common
Met&,
129 (1987)
305 - 309
305
DIFFUSION OF HYDROGEN IN NIOBIUM UNDER HYDROSTATIC HIGH PRESSURE* A. PUSCH, W. FENZL and J. PEISL Sektion
Pkysik der Universitiit
Miinchen,
8000 Miinchen
22 (F.R.G.)
(Received May 5,1986)
Summary To understand the kinetics of phase separation or hydrogen embrittlement, the influence of lattice deformations on the diffusion coefficient should be known. We have measured the diffusion coefficient of hydrogen in niobium under hydrostatic pressure up to 3.5 GPa. A non-uniform distribution of hydrogen in the sample, which is mounted in a high pressure cell, is generated by means of electrotransport. After reaching a stationary concentration gradient the electric field is switched off and the relaxation of hydrogen distribution towards equilibrium is measured. We found that the diffusion coefficient increased by about 10% after the application of 1 GPa at T= 285 K. We compared our results with recent calculations which predict a decrease of the diffusion coefficient with increasing pressure.
1. Introduction The diffusion coefficient of hydrogen in niobium, tantalum and vanadium is well known over a wide range of temperatures and hydrogen concentrations [ 11. Although a great number of experimental results on hydrogen ,diffusion are available, the theoretical explanation is still unsatisfactory. The deviation from the classical Arrhenius behaviour at low temperatures as reported by VSlkl and Alefeld [l] has stimulated many theoretical attempts to understand the underlying diffusion mechanism. Most of the calculations are based on the mechanism of phonon-assisted tunnelling. The tunnelling matrix elements should depend in a characteristic way on the distance between the lattice sites where the tunnelling occurs. From recent experiments a considerable enhanced diffusion of hydrogen in vanadium under tensile stress has been claimed by Suzuki et al. [2]. To cast some light on this “puzzle” we set up an experiment to measure the diffusion of hydrogen in metals under hydrostatic pressure. *Paper presented at the ~ternation~ Symposium on the Properties and Applications of Metal Hydrides V, Mauhuisson, France, May 25 - 30,1986. 0022-5068/87/$3.50
@ Elsevier Sequoia/Printed in The Netherlands
306
2. Experimental
details
The experiments were performed with polyc~s~line foils 50 pm thick and single crystals. We used niobium samples of “Marz” grade (Materials Research GmbH), which were degassed at 2300 K in a vacuum of better than lo-” Torr. Subsequently they were loaded with hydrogen at 360 K using a palladium window to prevent the penetration of oxygen into the sample. The hydrogen concen~ation (see Table 1) was obtained by measuring the hy~ogen-induced resistivity increase of the samples. We employed the method of electrotransport combined with a resistivity measurement to determine the diffusion coefficient D. A potential difference of 1 - 2 mV caused a drift of the protons in the sample to the cathode and created a nearly linear density gradient of hydrogen atoms in the sample. After reaching s~tion~ conditions the electric field was switched off and the relaxation of the hydrogen distribution towards equilibrium was monitored by measuring the resistivity change across one half of the sample as a function of time. A typical measurement is shown in Fig. 1. During the decay of the concentration gradient the resistivity was measured by the use of alternating current with a period of eight seconds which is very small compared with the relaxation period T of the decay (about 12 000 s). The diffusion coefficient D may be calculated from 7 and the length of the sample.
TABLE 1 Hydrogen concentration
of the niobium samples
Nb, polycrystalline Nb, single crystal
Residual resistiuity ratio of the unloaded sample
Hydrogen concentration
830 480
0.0015 0.002
[HlI[Nb 1
'GASKET GASKET
250
12s
irkI + +
f
rl ji
R nl
+
+
++i +I -?+ + + + tm[hl
2
4
6
8
10
Fig. 1. The resistivity change R of one half of the sample as a function of time t. Fig. 2. Enlargement of the pressure cell.
307
The pressure was created in a high pressure apparatus with supported opposed Al@, anvils. The niobium samples and a lead foil were connected to the electrical feed~roughs within the pressure cell (see Fig. 2) by welding. The lead foil served as a pressure measuring device, using the well-known resistivity change of lead with pressure [ 31.
3. Results and discussion The diffusion coefficient D at 285 K us. the pressure p is shown in Fig. 3. A considerable increase of about 10% can be seen after the application of 1 GPa. The increase of L) as measured for the polyc~s~line sample (see Fig. 3(a)) is smaller than for the single crystal (see Fig. 3fb)). Owing to the large experimental error in the dedication of the pressure, this effect may be less significant, A real physical reason for this effect is unlikely because the polycrystalline sample is purer and contains less hydrogen. From the results of Fig. 3 it is clearly demonstrated that the diffusion coefficient increases with pressure up to 3.5 GPa, while the corresponding lattice parameter change amounts to only about half a per cent.
-.i-
I
p
I
‘?.0
1
2
[GPaI
I”
3
L
(4
3.8 i
’ P 0
1
2
?
in
iGPa
j
1‘
(b) Fig. 3. The diffusion coefficient of hydrogen in niobium at T = 285 K us. the pressure p: (a) for the polycryst~line sample with a hydrogen concentration of e = 0.0015 [I-i J/E Nb J; (b) for the single crystal with a hydrogen concentration of c = 0.002 [H]f[Nb].
308
It should be emphasized that the diffusion coefficients of the hydrogen atoms in the samples were the same when no pressure was applied. The measured absolute value of D is, however, smaller than the value obtained by Gorskyeffect measurements [l]. Inspection of other electrotransport and thermotransport measurements [4,5] shows the same discrepancy, which may be caused by systematic errors of a still unexplained origin. The only calculation of D under pressure known to the authors has been performed by A. Klamt (personal communication) using the quantum mechanical approach as reported by Teichler et al. [ 63. Klamt’s results and our preliminary theory based on classical considerations of the pressure dependence of D are shown in Fig. 4. Both of the c~c~ations contradict the experimental results. In the case of the quantum mechanical treatment the pressure dependence of some of the quantities used is still not verified by experimental proofs. Therefore, the discrepancy between theory and experiment as shown in Fig. 4 may not be significant. In the palladium-hydrogen system at room temperature and high hydrogen concentrations Baranowski and Majorowski found a decreasing diffusion coefficient at pressures up to 1 GPa [ 71. These results cannot be compared with ours because the details of the diffusion mechanism of hydrogen in f.c.c. and b.c.c. metals are quite different. Moreover, the pressure dependence of the diffusion coefficient at high hydrogen concentrations is more difficult to interpret owing to the strong H-H interaction.
r-:_-
.lO .20 -30
-LO
‘\
1.0
'\
'.
20
3.0
p 1nlGPa
'\
'\
LO
I
b.
'.
“Y
quantum Fig. 4. Relative change of the diffusion coefficient D vs. the pressure p: mechanical approximation; - - - -, classical approximation; - a-, experimental rkults.
Acknowledgments The authors wish to thank Prof. J. S. &hilling for the high pressure apparatus and A. Klamt for his calculations.
309
References 1 J. Vijlkl and G. Alefeld, Hydrogen in Metals I, Topics in Applied Physics, Vol. 28, Springer, Berlin, 1978. 2 T. Suzuki, H. Namazue, S. Koine and H. Hayakawa, Phys. Rev. Lett., 51 (1983) 798. 3 A. Eilling and J. S. Schilling, J. Phys. F, 11 (1981) 623. 4 S. Schuppler, personal communication. 5 H. Wipf, Jiilich-Bericht (1972) 876. 6 H. Teichler and A. Klamt, Phys. Lett. A, 108 (1985) 281. 7 B. Baranowski and S. Majorowski, J. Less-Common Met., 98 (1984) L27.
Met&,
129 (1987)
305 - 309
305
DIFFUSION OF HYDROGEN IN NIOBIUM UNDER HYDROSTATIC HIGH PRESSURE* A. PUSCH, W. FENZL and J. PEISL Sektion
Pkysik der Universitiit
Miinchen,
8000 Miinchen
22 (F.R.G.)
(Received May 5,1986)
Summary To understand the kinetics of phase separation or hydrogen embrittlement, the influence of lattice deformations on the diffusion coefficient should be known. We have measured the diffusion coefficient of hydrogen in niobium under hydrostatic pressure up to 3.5 GPa. A non-uniform distribution of hydrogen in the sample, which is mounted in a high pressure cell, is generated by means of electrotransport. After reaching a stationary concentration gradient the electric field is switched off and the relaxation of hydrogen distribution towards equilibrium is measured. We found that the diffusion coefficient increased by about 10% after the application of 1 GPa at T= 285 K. We compared our results with recent calculations which predict a decrease of the diffusion coefficient with increasing pressure.
1. Introduction The diffusion coefficient of hydrogen in niobium, tantalum and vanadium is well known over a wide range of temperatures and hydrogen concentrations [ 11. Although a great number of experimental results on hydrogen ,diffusion are available, the theoretical explanation is still unsatisfactory. The deviation from the classical Arrhenius behaviour at low temperatures as reported by VSlkl and Alefeld [l] has stimulated many theoretical attempts to understand the underlying diffusion mechanism. Most of the calculations are based on the mechanism of phonon-assisted tunnelling. The tunnelling matrix elements should depend in a characteristic way on the distance between the lattice sites where the tunnelling occurs. From recent experiments a considerable enhanced diffusion of hydrogen in vanadium under tensile stress has been claimed by Suzuki et al. [2]. To cast some light on this “puzzle” we set up an experiment to measure the diffusion of hydrogen in metals under hydrostatic pressure. *Paper presented at the ~ternation~ Symposium on the Properties and Applications of Metal Hydrides V, Mauhuisson, France, May 25 - 30,1986. 0022-5068/87/$3.50
@ Elsevier Sequoia/Printed in The Netherlands
306
2. Experimental
details
The experiments were performed with polyc~s~line foils 50 pm thick and single crystals. We used niobium samples of “Marz” grade (Materials Research GmbH), which were degassed at 2300 K in a vacuum of better than lo-” Torr. Subsequently they were loaded with hydrogen at 360 K using a palladium window to prevent the penetration of oxygen into the sample. The hydrogen concen~ation (see Table 1) was obtained by measuring the hy~ogen-induced resistivity increase of the samples. We employed the method of electrotransport combined with a resistivity measurement to determine the diffusion coefficient D. A potential difference of 1 - 2 mV caused a drift of the protons in the sample to the cathode and created a nearly linear density gradient of hydrogen atoms in the sample. After reaching s~tion~ conditions the electric field was switched off and the relaxation of the hydrogen distribution towards equilibrium was monitored by measuring the resistivity change across one half of the sample as a function of time. A typical measurement is shown in Fig. 1. During the decay of the concentration gradient the resistivity was measured by the use of alternating current with a period of eight seconds which is very small compared with the relaxation period T of the decay (about 12 000 s). The diffusion coefficient D may be calculated from 7 and the length of the sample.
TABLE 1 Hydrogen concentration
of the niobium samples
Nb, polycrystalline Nb, single crystal
Residual resistiuity ratio of the unloaded sample
Hydrogen concentration
830 480
0.0015 0.002
[HlI[Nb 1
'GASKET GASKET
250
12s
irkI + +
f
rl ji
R nl
+
+
++i +I -?+ + + + tm[hl
2
4
6
8
10
Fig. 1. The resistivity change R of one half of the sample as a function of time t. Fig. 2. Enlargement of the pressure cell.
307
The pressure was created in a high pressure apparatus with supported opposed Al@, anvils. The niobium samples and a lead foil were connected to the electrical feed~roughs within the pressure cell (see Fig. 2) by welding. The lead foil served as a pressure measuring device, using the well-known resistivity change of lead with pressure [ 31.
3. Results and discussion The diffusion coefficient D at 285 K us. the pressure p is shown in Fig. 3. A considerable increase of about 10% can be seen after the application of 1 GPa. The increase of L) as measured for the polyc~s~line sample (see Fig. 3(a)) is smaller than for the single crystal (see Fig. 3fb)). Owing to the large experimental error in the dedication of the pressure, this effect may be less significant, A real physical reason for this effect is unlikely because the polycrystalline sample is purer and contains less hydrogen. From the results of Fig. 3 it is clearly demonstrated that the diffusion coefficient increases with pressure up to 3.5 GPa, while the corresponding lattice parameter change amounts to only about half a per cent.
-.i-
I
p
I
‘?.0
1
2
[GPaI
I”
3
L
(4
3.8 i
’ P 0
1
2
?
in
iGPa
j
1‘
(b) Fig. 3. The diffusion coefficient of hydrogen in niobium at T = 285 K us. the pressure p: (a) for the polycryst~line sample with a hydrogen concentration of e = 0.0015 [I-i J/E Nb J; (b) for the single crystal with a hydrogen concentration of c = 0.002 [H]f[Nb].
308
It should be emphasized that the diffusion coefficients of the hydrogen atoms in the samples were the same when no pressure was applied. The measured absolute value of D is, however, smaller than the value obtained by Gorskyeffect measurements [l]. Inspection of other electrotransport and thermotransport measurements [4,5] shows the same discrepancy, which may be caused by systematic errors of a still unexplained origin. The only calculation of D under pressure known to the authors has been performed by A. Klamt (personal communication) using the quantum mechanical approach as reported by Teichler et al. [ 63. Klamt’s results and our preliminary theory based on classical considerations of the pressure dependence of D are shown in Fig. 4. Both of the c~c~ations contradict the experimental results. In the case of the quantum mechanical treatment the pressure dependence of some of the quantities used is still not verified by experimental proofs. Therefore, the discrepancy between theory and experiment as shown in Fig. 4 may not be significant. In the palladium-hydrogen system at room temperature and high hydrogen concentrations Baranowski and Majorowski found a decreasing diffusion coefficient at pressures up to 1 GPa [ 71. These results cannot be compared with ours because the details of the diffusion mechanism of hydrogen in f.c.c. and b.c.c. metals are quite different. Moreover, the pressure dependence of the diffusion coefficient at high hydrogen concentrations is more difficult to interpret owing to the strong H-H interaction.
r-:_-
.lO .20 -30
-LO
‘\
1.0
'\
'.
20
3.0
p 1nlGPa
'\
'\
LO
I
b.
'.
“Y
quantum Fig. 4. Relative change of the diffusion coefficient D vs. the pressure p: mechanical approximation; - - - -, classical approximation; - a-, experimental rkults.
Acknowledgments The authors wish to thank Prof. J. S. &hilling for the high pressure apparatus and A. Klamt for his calculations.
309
References 1 J. Vijlkl and G. Alefeld, Hydrogen in Metals I, Topics in Applied Physics, Vol. 28, Springer, Berlin, 1978. 2 T. Suzuki, H. Namazue, S. Koine and H. Hayakawa, Phys. Rev. Lett., 51 (1983) 798. 3 A. Eilling and J. S. Schilling, J. Phys. F, 11 (1981) 623. 4 S. Schuppler, personal communication. 5 H. Wipf, Jiilich-Bericht (1972) 876. 6 H. Teichler and A. Klamt, Phys. Lett. A, 108 (1985) 281. 7 B. Baranowski and S. Majorowski, J. Less-Common Met., 98 (1984) L27.