RESISTANCE STUDIES OF HYDROGEN DIFFUSION IN NIOBIUM

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RESISTANCE STUDIES OF HYDROGEN

DIFFUSION IN NIOBIUM

E. Clark, P. Tzanetakis, H. Birnbaum

To cite this version:

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C10-83

RESISTANCE STUDIES OF HYDROGEN DIFFUSION IN NIOBIUM

E.A. CLARK, P. TZANETAKIS* AND H.K. BIRNBAUM

Department

o f

M e t a l l u r g y and Mining E n g i n e e r i n g and M a t e r i a l s

R e s e a r c h L a b o r a t o r y , U n i v e r s i t y

of

I l l i n o i s , Urbana,

I L

61801,

U.S.A.

A b s t r a c t

-

Hydrogen d i f f u s i o n i n Nb was s t u d i e d u s i n q thermotransport t o e s t a b l i s h c o n c e n t r a t i o n g r a d i e n t s i n a p e r i o d i c w i d t h modul ated sample. The r e s i s t a n c e o f t h e sample was measured as a f u n c t i o n o f time, by a K e l v i n b r i d g e c i r c u i t , as t h e p e r t u r b e d hydrogen d i s t r i b u t i o n r e t u r n e d t o uniform concentration. Results f o r a H/Nb = 0.001 sample, measured i n t h e

temperature range 300 K and 180 K show t h e d i f f u s i v i t y o f H t o be two t o f o u r times l a r g e r than t h a t measured by t h e Gorsky e f f e c t . When f i t t e d tt t h Arrhenius r e l a t i o n , Q = 0.078

₅

+

.001 eV/atom and Do = 3.0

+

0.7 x 10- cm /s.

INTRODUCTION

The d i f f u s i v i t y o f hydrogen and i t s isotopes i n Nb has been e x t e n s i v e l y s t u d i e d u s i n g t h e Gorsky e f f e c t ; a s t r a i n r e l a x a t i o n technique /I/. Results f o r t h e s o l i d s o l u t i o n a phase a t low concentrations i n d i c a t e a change o f slope i n t h e Arrhenius p l o t ( l o g D vs. 1/T), a t about 250 K, f o r hydrogen, b u t n o t f o r deuterium o r t r i t i u m . Also, hydrogen shows a s i g n i f i c a n t l y smaller a c t i v a t i o n enthalpy of d i f f u s i o n (both below and above 250 K) than e i t h e r deuterium o r t r i t i u m /2/. E f f o r t s t o apply c l a s s i c a l o r quantum t h e o r i e s o f d i f f u s i o n t o these r e s u l t s are u n s a t i s f a c t o r y /3/. This r e p o r t describes r e s u l t s o f a l t e r n a t i v e method t o t h e Gorsky e f f e c t : using thermotransport t o c r e a t e a c o n c e n t r a t i o n gradient, i n s t e a d of stress. I n t h i s technique, t h e r e l a x a t i o n o f t h e r e s i s t a n c e o f a p e r i o d i c a l l y w i d t h modulated sample i s used as a measure o f t h e hydrogen d i f f u s i v i t y .

*present address : Department of Physics, University of Crete, Heraklion, Crete, Greece.

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C10-84 JOURNAL

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PHYSIQUE EXPERIMENTAL

A f t e r outgassing 25

urn

t h i c k Nb f o i l t o 2 x T o r r and 2500 K, t h e samples were shaped u s i n g p h o t o r e s i s t techniques and electrochemical e t c h i n g t o produce a specimen shown i n Fig. 1. The samples were used i n p a i r s w i t h one, used as a reference, having H/Nb = 0. The o t h e r was charged w i t h low l e v e l s o f hydrogen using a coulombical l y t i t r a t e d cathodic charging method (which avoids oxygen and n i t r o g e n contamination). The hydrogen concentration was measured by t h e r e s i s t a n c e

increment. The specimens were clamped t o a temperature c o n t r o l 1 ed copper block.

Fig. 1

-

Drawing o f a w i d t h modulated specimen.

The d e t e c t i o n c i r c u i t i s based on a double K e l v i n bridge, which was balanced so t h a t only t h e d i f f e r e n c e i n r e s i s ance between t h e sample and reference was measured

₅

/4/. Passing a 600 mA (6000 A/cm ) c u r r e n t through t h e sample and reference caused p r e f e r e n t i a l h e a t i n g o f t h e t h i n p a r t s , causing hydrogen thermotransport from t h e t h i n t o t h e t h i c k p a r t s o f t h e specimen. A f t e r t h e h i g h c u r r e n t was removed, t h e b r i d g e voltage was monitored as a f u n c t i o n o f t i m e by a l o c k - i n a m p l i f i e r . This voltage i s d i r e c t l y r e l a t e d t o t h e d i f f e r e n c e between t h e c o n c e n t r a t i o n i n t h e t h i n p a r t C1 and t h e average concentration Co by

where A and B are b r i d g e r e s i s t o r 8 (60P0 QJ, Vk i s t h e b r i d g e voltage, ks i s t h e sample geometrical f a c t o r (2 x 10 cm- ) pH i s t h e r e s i s t i v i t y p e r u n i t

concentration o f hydrogen (0.64 x Q -cm/at%), I i s t h e measuring c u r r e n t (50 mA) and dl and d2 a r e t h e t h i n and t h i c k widths o f t h e sample (0.4 mm and 1.6 mm, r e s p e c t i v e l y ) .

F o r he r e s u l t s reported herein, a t t h e s t a r t o f t h e d i f f u s i o n r e l a x a t i o n Vk = 2.5 x 10g V, and Co = 0.001 H/Nb so

The heat o f t r a n s p o r t o f H i n Nb i s 0.123 eV/atom /5,6/, and t h e e f f e c t i v e temperature r i s e o f t h e t h i n areas i s estimated t o be about 1 K.

RESULTS AND DISCUSSION

A t y p i c a l r e l a x a t i o n curve i s shown i n Fig. 2. The d a t a were f i t t e d u s i n g a method o f non-1 i n e a r l e a s t squares t o several r e l a x a t i o n f u n c t i o n s : a s i n g l e exponential, a s i n g l e exponential p l u s a l i n e a r ramp, and a sum o f two exponentials (double exponential). .The f u n c t i o n chosen t o be t h e best f i t was determined by t h e minimal r e s i d u a l sum o f squares and by i n s p e c t i o n o f t h e p l o t s o f t h e f i t t e d f u n c t i o n minus data p o i n t ( r e s i d u a l ) versus time. The double exponential was g e n e r a l l y observed t o provide t h e best f i t t o t h e data a t t h e h i g h e r temperatures w i t h t h e short, temperature independent r e l a x a t i o n time being associated w i t h t h e thermal r e l a x a t i o n o f t h e specimen a f t e r t h e h e a t i n g c u r r e n t was t u r n e d o f f . The longer, temperature dependent r e l a x a t i o n was associated w i t h hydrogen d i f f u s i o n . At t h e lowest temperatures t h e thermal r e l a x a t i o n was best described by t h e f i t s o f t h e s i n g l e exponential w i t h a small l i n e a r ramp f u n c t i o n . I n a l l cases, t h e hydrogen d i f f u s i o n r e l a x a t i o n i s described very we1 1 by a s i n g l e exponential r e l a x a t i o n .

Fig. 3 i s an Arrhenius p l o t o f t h e hydrogen d i f f u s i v i t y f o r a sample w i t h 0.1 at% H. The d i f f u s i v i t y i s c a l c u l a t e d from t h e r e l a x a t i o n t i m e T by

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Fig. 2

-

R e l a x a t i o n 0.001 H/Nb.

o f sample r e s i s t a n c e vs. t i m e due t o H d i f f u s i o n a t 220 K f o r

F i g . 3

-

Log d i f f u s i v i t y vs. r e c i p r o c a l t e m p e r a t u r e f o r 0.001 H/Nb. x = data, s o l i d l i n e = A r r h e n i u s f i t t o data, broken l i n e = Gorsky e f f e c t .

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C10-86

JOURNAL

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PHYSIQUE

r e l a x a t i o n t i m e and t h e l a r g e s t amp1 itude. The dominant r e l a x a t i o n time i s described by Eq. 1 which a l l o w s determination o f d i f f u s i v i t y from t h e experimental data.

A1 so shown i n Fig. 3 i s t h e best f i t o f V o l k l and A l e f e l d t o t h e Gorsky e f f e c t data, showing t h e change o f slope a t 250 K /I/. The present r e s u l t s a r e

c o n s i s t e n t l y above t h e Gorsky e f f e c t r e s u l t s (by a f a c t o r o f two a t 300 K and a f a c t o r o f 4 a t 180 K). C o r r e c t i o n o f t h e present r e s u l t s f o r t h e mean f i e l d i n t e r a c t i o n o f H would increase t h e d i f f u s i v i t y by 10%. The r e s u l t s o f a very s i m i 1 a r thermotransport experiment by Wipf and A l e f e l d /5/ gave values o f hydrogen d i f f u s i v i t y s l i g h t l y l e s s than t h e Gorsky e f f e c t and support t h e change o f slope a t about 250 K. However, s i n c e these p r e v i o u s experiments used o n l y one t h i n s e c t i o n

( i n s t e a d o f t h e 16 used here), t h e r e l a x a t i o n curves were n o t s i n g l e exponential and o b t a i n i n g t h e r e l a x a t i o n times u s i n g a more complex f i t t i n g procedure than t h a t used )!ere. D i f f e r e n c e s between t h e present r e s u l t s and those p r e v i o u s l y r e p o r t e d may a l s o stem from d i f f e r e n c e s i n p u r i t i e s o f t h e Nb. However, i t must be p o i n t e d o u t t h a t i m p u r i t y t r a p p i n g would r e s u l t i n a decrease o f d i f f u s i v i t y and an increase i n t h e a c t i v a t i o n enthalpy.

The present data were f i t t e d t o a s i n g l e Arrhenius curve and t o two Arrhenius curves. A l l t h e f i t t e d parameters a r e presented i n Table 1. W i t h i n t h e

experimental e r r o r , t h e choice between t h e s i n g l e Arrhenius o r t h e f i t t o t h e two Arrhenius temperature dependences o f t h e present data i s unclear. Understanding t h e r e l a t i o n s h i p o f t h e present r e s u l t s t o t h e previous Gorsky e f f e c t r e s u l t s w i l l requi r e a d d i t i o n a l experimental data.

Table I

Method Temp Range (K)

Q

(ev)

Gorsky E f f e c t > 250 .106+06

<

250 .068 f .004 Width Modulation a) 300-180 .078 f .001 Resistance R e l a x a t i o n b) [300-2501 .084 -f. .016 [250-1801 .075 f .002 CONCLUSIONS

The d i f f u s i v i t y o f hydrogen can be measured u s i n g a r e s i s t i v i t y re1 a x a t i o n technique i n which thermotransport o f hydrogen i n a w i d t h modulated specimen i s used t o p e r t u r b an i n i t i a l u n i f o r m hydrogen d i s t r i b u t i o n . The p e r i o d i c form o f t h e sample a1 lows a simple re1 a t i o n between measured re1 a x a t i o n t i m e and d i f f u s i v i t y t o e x i s t w i t h t h e r e l a x a t i o n curves showing t h e expected s i n g l e exponential behavior. Values o f hydrogen d i f f u s i v i t y i n a H/Nb= 0.001 sample, between 180 K and 300 K, a r e a f a c t o r o f two (300 K) t o f o u r (180 K) h i g h e r than previous measurements obtained using t h e Gorsky e f f e c t . The present data do n o t support t h e e x i s t e n c e o f a change of slope o f t h e Arrhenius p l o t o f t h e hydrogen d i f f u s i v i t y as was p r e v i o u s l y r e p o r t e d a t about 250 K.

ACKNOWLEDGEMENTS

T h i s work was supported by D.O.E. O f f i c e o f Basic Energy Sciences under c o n t r a c t DE-AC02-76ER01198.

REFERENCES

/1/ J. V o l k l and G. A l e f e l d , chap. 5 i n " D i f f u s i o n i n Solids: Recent Developments", ed. A.S. Nowick, J.J. Burton, Academic Press, New York (1975).

/2/ K.W. Kehr, i n " E l e c t r o n i c S t r u c t u r e and P r o p e r t i e s o f Hydrogen i n Metals", NATO Conference Series V I : 6, ed. P. Jena, C.B. Sattherthwaite, Plenum, New York (1983). /3/ Zh Qi, J. V o l k l , R. Lasser and H. Wenzl, J. Phys. F: Met. Phys.

13,

2053

11983).

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