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QUANTUM BEHAVIOUR OF TRAPPED H AND D IN Nb AND Ta
G. Cannelli, R. Cantelli, F. Cordero
To cite this version:
G. Cannelli, R. Cantelli, F. Cordero. QUANTUM BEHAVIOUR OF TRAPPED H AND D IN Nb AND Ta. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-227-C2-232.
�10.1051/jphyscol:1987831�. �jpa-00227135�
QUANTUM BEHAVIOUR OF TRAPPED H AND D IN Nb AND Ta
G. CANNELLI, R. CANTELLI' and F. CORDER0
~ s t i t u t o d i Acustica "O.M. Corbino", CNR, via Cassia 1216, I-00189 Roma, Italy
'11 Universit.2 d i Roma, Dipartimento d i Fisica, Via 0.
Raimondo, I-00173 Roma, Italy
ABSTRACT
Internal friction measurements at liquid helium temperature on Nb and Ta specimens containing oxygen (nitrogen) and doped with hydrogen (deuterium) show peaks due to the tunnelling of H(D) trapped by O(N). The peak at higher temperature in Nb-O(N)-H(D) and that observed in Ta-0-D are interpreted as due to a two-level system (TLS), and fits to the relaxation curves have been made. In Nb- O(N)-H(D) both 2-phonon and electron transitions gave nearly equivalent fits, while in Ta-0-D the predominance of the TLS-electrons interaction is revealed both by a sharp discontinuity of the slope of the relaxation curve at the normal- superconductor transition temperature and by the fit of the exprimental points.
The parameters characterizing the TLS and their coupling with phonons and electrons have been estimated.
1. INTRODUCTION
The diffusion regimes of interstitial hydrogen and its isotopes drastically vary with temperature. Interstitial hopping occurs at liquid nitrogen temperature, whilst at liquid helium temperature the particle is confined in trap sites created by heavier impurity atoms, among which it exhibits tunnelling. The geometry of the tunnel system and the nature of the transitions of H among the quantized levels is at present object of investigation. The two-level system (TLS) model explains many features observed in Nb and Ta by acoustic, neutron scattering and specific heat measurements and, as regards the type of its transitions, one-phonon, two-phonon and electron interactions have been proposed. Presently, it seems that the TLS interacts more effectively with electrons than with phonons.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987831
JOURNAL DE PHYSIQUE
2. EXPERIMENTAL
The specimens were p o l y c r y s t a l l i n e d i s c s s u p p l i e d by M a t e r i a l s Research C o r p o r a t i o n . The Nb d i s c (30 mm i n d i a m e t e r and 2 . 5 mm t h i c k ) was c u t from a 9 9 . 9 % p u r e s l a b and c o n t a i n e d 0.13 a t % 0 and 0.015 a t % N, a s e s t i m a t e d from t h e h e i g h t o f t h e Snoek peaks. The Ta sample was 99.996 % p u r e w i t h 0 . 0 5 3 a t % 0 and 0.016 a t % N. D i s l o c a t i o n a n n e a l i n g was o b t a i n e d by thermal t r e a t m e n t s a t 1500°C i n a vacuum b e t t e r t h a n lo-' mbar. Hydrogen and d e u t e r i u m doping were c a r r i e d o u t by t h e r m a l t r e a t m e n t s i n a p p r o p r i a t e g a s a t m o s p h e r e s .
F i g . 1 I n t e r n a l f r i c t i o n o f Nb-O(N)-D a t two v i b r a t i o n f r e q u e n c i e s . The s o l i d and dashed l i n e s r e p r e s e n t t h e e s t i m a t e d c o n t r i b u t i o n o f H
t r a c e s which have been
s u b s e q u e n t l y s u b t r a c t e d .
- - CH = 0.2 at.%
-
F i g . 2 Peak P2 i n Nb-O(N)-Ha a t two v i b r a t i o n f r e q u e n c i e s .
n Also shown a r e t h e b e s t f i t s
z
o b t a i n e d assuming r e l a x a t i o n o ft h e TLS v i a two-phonon and e l e c t r o n i n t e r a c t i o n .
0 1 2 3 4 5 6
T ( K l
3 . RESULTS
The r e l a x a t i o n spectrum o f Nb-O(NI-H(D) is c o n s t i t u t e d by two t h e r m a l l y a c t i v a t e d peaks l a b e l l e d a s P I ( a t lower t e m p e r a t u r e ) and P2 111. F i g u r e 1 shows t h e two peaks i n Nb-O(N) doped w i t h 0.14 a t % D a t two v i b r a t i o n f r e q u e n c i e s (20 and 73 kHz). The s m a l l c o n t r i b u t i o n due t o unwanted t r a c e s of hydrogen ( s o l i d and
The i n t e r n a l f r i c t i o n (Q-') measurement i n t h e same specimen c o n t a i n i n g 0.2 a t % H (open and c l o s e d t r i a n g l e s i n F i g . 2 ) d i s p l a y s peak P2 and t h e t a i l o f PI, which however h a s been r e s o l v e d by u l t r a s o n i c a t t e n u a t i o n 121.
F i g u r e 3 shows t h e Q"' c u r v e v e r s u s r e c i p r o c a l t e m p e r a t u r e o f t h e Ta sample doped with 0.25 a t % D a t 7 . 5 and 30 kHz.
The i n t e r n a l f r i c t i o n o f t h e H- and D-free samples was always l e s s t h a n 5x10-' and t h i s background was s u b t r a c t e d from t h e c u r v e s o f Figs.1-3. A l l t h e measurements were c a r r i e d o u t o n c o o l i n g .
Hydride and d e u t e r i d e p r e c i p i t a t i o n were avoided i n niobium and t h e peaks observed were r e t r a c e d i n subsequent measurements. On t h e c o n t r a r y , p r e c i p i t a t i o n o c c u r r e d i n Ta d u r i n g c o o l i n g and, because t h e p r e c i p i t a t e p a r t i c l e s p a r t i a l l y remove H o r D from t h e O(N) t r a p s , s l i g h t l y lower peaks were observed d u r i n g subsequent c o o l i n g r u n s . A s t h e peak a t 30 kHz was measured twice, i n F i g . 3 t h e d a t a o f t h e f i r s t r u n have been r e s c a l e d i n o r d e r t o o v e r l a p them t o t h o s e o f t h e second one.
F i g . 3 I n t e r n a l f r i c t i o n o f Ta-0-D a t two v i b r a t i o n f r e q u e n c i e s a s a f u n c t i o n o f r e c i p r o c a l t e m p e r a t u r e . The c o n t i n u o u s l i n e s a r e t h e b e s t f i t o b t a i n e d assuming r e l a x a t i o n o f t h e TLS v i a e l e c t r o n s .
4. DISCUSSION
We b r i e f l y e x p l a i n t h e main f e a t u r e s o f t h e TLS model 13-4/, which, up t o now, is t h e o n l y one used t o q u a n t i t a v e l y e x p l a i n t h e low t e m p e r a t u r e e x p e r i m e n t a l d a t a . I t is supposed t h a t H ( D ) is d e l o c a l i z e d n e a r t h e O ( N ) t r a p i n two e q u i v a l e n t s i t e s , which may d i f f e r i n energy o f A due t o t h e e l a s t i c i n t e r a c t i o n s with t h e o t h e r d e f e c t s ; t h e f i r s t two l e v e l s o f t h e t u n n e l system a r e s p l i t o f E = (A:
+
where& is t h e m a t r i x element o f t u n n e l l i n g . The change o f E with strain^
is:
b u t up t o now t h e c o n t r i b u t i o n ofAo t o D h a s been c o n s i d e r e d n e g l i g i b l e by t h e v a r i o u s a u t h o r s . The v i b r a t i o n o f t h e sample changes t h e e n e r g y s p l i t t i n g E, g i v i n g r i s e t o a n e l a s t i c r e l a x a t i o n , whose i n t e n s i t y is:
where n i s t h e volume c o n c e n t r a t i o n o f TLS, c t h e e l a s t i c s t i f f n e s s coupled t o t h e TLS and ,9 = l1kT. The r e l a x a t i o n peak is g i v e n by t h e Debye formula:
JOURNAL
DE
PHYSIQUE( 3 ) Q-'(TI
= d ( ~ ) wr
I + (ui)2
where J,,( i s t h e a n g u l a r frequency o f v i b r a t i o n and T ( T ) t h e r e l a x a t i o n time o f t h e TLS; T ( T ) depends o n ' t h e t y p e o f i n t e r a c t i o n between TLS and l a t t i c e , which can occur through phonons and through t h e c o n d u c t i o n e l e c t r o n s . The one-phonon c o n t r i b u t i o n t o t h e r e l a x a t i o n frequency is:
w i t h
I;,:,
is slowly v a r y i n g with temperature, and t h e r e f o r e g i v e s r i s e t o very broad peaks. The c o n t r i b u t i o n from two-phonon t r a n s i t i o n s h a s a much s t r o n g e r dependence on T, b e i n g r l o c T7 i n t h e h i g h t e m p e r a t u r e l i m i t , and t h e r e f o r e g i v e s r i s e t o narrow peaks. Higher o r d e r t r a n s i t i o n s s h o u l d be r e l e v a n t a t h i g h e r t e m p e r a t u r e s and w i l l n o t be c o n s i d e r e d .Another t y p e o f i n t e r a c t i o n of t h e TLS with t h e c r y s t a l i s through t h e c o n d u c t i o n e l e c t r o n s , s i m i l a r l y t o t h e electron-phonon c o u p l i n g , where i n s t e a d o f t h e phonons we have t h e s m a l l d i s p l a c e m e n t s o f t h e atoms c o r r e s p o n d i n g t o t h e occupied l e v e l o f t h e TLS. The temperature dependence ofTel is i d e n t i c a l with t h a t f o r one-phonon r e l a x a t i o n :
where ~ ( E F ) is t h e e l e c t r o n d e n s i t y of s t a t e s a t t h e Fermi l e v e l and K,,is analogue t o , t h e phonon c o u p l i n g y . The r e l a x a t i o n frequency d r o p s when t h e metal becomes superconductor, because t h e number o f f r e e e l e c t r o n s a b l e t o ... i n t e r a c t with t h e TLS i s reduced 151. When t h e e n e r g y gap f o r s u p e r c o n d u c t i v i t y , ~ ~ , i s g r e a t e r t h a n t h e energy s p l i t E o f t h e TLS, t h e e x p r e s s i o n f o r t h e r e l a x a t i o n t i m e i s a p p r o x i m a t e l y :
which is a g a i n s t r o n g l y dependent on t e m p e r a t u r e .
Some f e a t u r e s o f i n e l a s t i c n e u t r o n s c a t t e r i n g , s p e c i f i c h e a t , u l t r a s o n i c a t t e n u a t i o n and v e l o c i t y measurements o n Nb-0-H(D) have been a s s o c i a t e d with t h e mechanism g i v i n g r i s e t o peak P1 and have been i n t e r p r e t e d i n terms o f a TLS, mainly i n t e r a c t i n g w i t h e l e c t r o n s and c h a r a c t e r i z e d by a n energy s p l i t E of about 2 K f o r H and 0.24 K f o r D /2,6-101. The p r o c e s s g i v i n g r i s e t o P2 h a s been d e t e c t e d o n l y by i n t e r n a l f r i c t i o n / 1 / and u l t r a s o n i c a t t e n u a t i o n measurements 121, and was a t t r i b u t e d by t h e a u t h o r s o f Ref.2 t o p a i r s o f H t r a p p e d by 0, on t h e b a s i s o f its dependence on a n n e a l i n g i n t h e p r e s e n c e o f p r e c i p i t a t e s . This p r o c e s s t o o was i n t e r p r e t e d a s a TLS by t h e p r e s e n t a u t h o r s I l l . I t must be noted t h a t t h e t h e o r y o f t h e TLS i s independent o f t h e e x a c t a t o m i s t i c c o n f i g u r a t i o n which e x h i b i t s t u n n e l l i n g , and t h e r e f o r e c a n be a s well a p p l i e d t o c o n f i g u r a t i o n s d i f f e r e n t from t h a t g i v i n g r i s e t o PI by changing t h e p a r a m e t e r s o f t h e TLS.
One-phonon t r a n s i t i o n s f o r t h e r e l a x a t i o n time o f P2 a r e e a s i l y excluded because t h e y would g i v e r i s e t o a peak markedly broader t h a n t h a t measured. On t h e o t h e r hand, f o r both i s o t o p e s i t is i m p o s s i b l e t o d i s c e r n between two-phonon and e l e c t r o n i n t e r a c t i o n s because t h e y g i v e e q u i v a l e n t f i t s , a s d i s p l a y e d i n F i g s . 2 and 4 .
I n t h e tantalum-deuteripm system t h e r e l a x a t i o n c u r v e e x t e n d s i t s e l f i n both t h e normal andsuperconductingregions, and d i s p l a y s a s h a r p d i s c o n t i n u i t y i n t h e s l o p e a t TC s u g g e s t i n g t h a t t h e r e l a x a t i o n r a t e is mainly governed by t h e c o n d u c t i o n e l e c t r o n s . Indeed, t h e a n a l y s i s i n terms o f a TLS i n t e r a c t i n g with e l e c t r o n s , shown by t h e c o n t i n u o u s l i n e s i n Fig.3, is s a t i s f a c t o r y ; d e t a i l s on t h e a n a l y s i s w i l l be p u b l i s h e d e l s e w h e r e . Because o f t h e d i s t o r s i o n s c r e a t e d by p r e c i p i t a t i o n , a d i s t r i b u t i o n o f asymmetries was i n t r o d u c e d i n t h e f i t ; t h i s i s
3 I I I I 1 , I I I
Nb-O(N)-D P2 co = 0 . 2 4 at.%
- two phonons
Fig.4 Peak. P2 in Nb-O(N)-D after subtraction of P1 with the best fits obtained assuming relaxation of the TLS via two- phonon or electron interaction.
Table 1 shows the values of some parameters of the TLS deduced from the fits of Figs.2-4 when the electron interaction is supposed to be operative; the parameters are the tunnel splittingAo
,
the widthsP of the Gaussian distribution for the asymmetry energy A , the couplingy of A to phonons (longitudinal) and the coupling Kl,n(EF) of A to the electrons. The values of AO and y obtained for Nb supposing two-phonon transitions are practically unchanged 111. Because P2 in Nb is a narrow peak, as is seen in Figs.2 and 4, the fit is insensitive to the value of the width of the distribution in.& simply requesting that it is much less thanL$,
and therefore only a lower limit to Y can be given.TABLE 1
As explained in detail in Ref.1, such a high value of y implies a one-phonon relaxation rate much higher than the measured one; this inconsistency can be removed by taking into account also the dependence of the matrix elementAoon on strain, so that a high value of the intensity of relaxation and therefore of D does not necessarily imply a high value of ~ ; : t , through M (see Eqs. 1,2,4). In fact the usual assumption of neglectingy~ with respect to
y
is without ground, as already pointed out 1111.It is noteworthy that the theoretically expected isotope effect of& is not observed for P2 in Nb, whereas a strong effect is found for PI.
Concluding, the low temperature relaxation processes observed in Nb and Ta have been interpreted in terms of a TLS model, making fits of the peaks. While in Nb the fit is not conclusive for the type of interaction between TLS and crystal (phonons or electrons), in Ta the predominance of the electron interaction is revealed both by the discontinuity of the slope of the relaxation curve at the normal-superconducting transition temperature and.by the fit.
JOURNAL DE PHYSIQUE
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