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LOW TEMPERATURE ULTRASONIC RELAXATION
IN A DILUTE Ta-H ALLOY
K. Maschhoff, A. Granato
To cite this version:
K. Maschhoff, A. Granato.
LOW TEMPERATURE ULTRASONIC RELAXATION IN A
LOW TEMPERATURE ULTRASONIC RELAXATION IN A DILUTE Ta-H ALLOY
K.R. MASCHHOFF AND A.V. GRANATO
Physics Department and Materials Research Laboratory, University of Illinois, 104 S. Goodwin, Urbana, IL 61801. U.S.A.
Abstract
-
The ultrasonic attenuation of tantalum containing approximately
500 atomic
ppmof hydrogen has been measured as a function of temperature
below 5
Ka t frequencies between 10 and 55
MHz.In addition t o hydrogen,
the tantalum contains approximately 120 atomic ppm of carbon and 100 atomic
ppmof oxygen i n t e r s t i t i a l s .
Apeak in the attenuation
i nthe C11 mode was
found below
2K.
The peak i s caused by the relaxation of hydrogen trapped
near the carbon and/or oxygen impurities. No peak was seen in the C44 mode
in the same temperature range.
Simi 1 ar re1 axation processes have previously
been observed in d i l u t e Nb-O-H alloys,
b u tthe peak temperatures observed in
those systems are higher than those observed in Ta.
I
-
INTRODUCTION
I t i s known t h a t l i g h t i n t e r s t i t i a l s such as
C, N,and
0act as traps f o r hydrogen
in the group Vb transition metals
V,Nb, and Ta / I / .
The formation of a hydride
phase in these metals a t low temperatures i s suppressed i f the hydrogen
concentration i s below t h a t of the trapping i n t e r s t i t i a l s . In addition, an
anelastic relaxation process has been observed in
Nb-O-Hbelow 4 K using ultrasonic
attenuation and velocity measurements
/2/.The re1 axation process was ascribed
t o the redistribution of hydrogen among various tunnel-split s t a t e s localized
around the oxygen trap centers in response t o the perturbing s t r e s s wave.
W
e
report here measurments of ultrasonic attenuation a t low temperatures in Ta
containing d i l u t e amounts of
C,0, and
Has
a
function of temperature, frequency
and polarization.
Arelaxation peak i s found near 1.25
Ka t 12
MHz
in
this
alloy.
I1
-
EXPERIMENTAL
PROCEDUREThe sample used in the experiment was cut from a single crystal of Ta purchased
form the Materials Research Corp., Orangeburg. New York.
The chemical analysis
revealed the120
a p p of C and90
a p p of 0. Ohter contaminants occurin
concentrations below 10 appm. The sample had a nearly circular crossection with
an average diameter of 11
mn
with the cylindrical axis parallel t o
a
<loo>
direction. The ultrasonic faces were cut perpendicular t o the cylindrical axis and
were lapped f l a t and parallel t o tolerances of 2 microns and 1x10-5 radians
respectively.
C10-88 JOURNAL
DE
PHYSIQUEThe sample was charged w i t h approximately 500 appm o f hydrogen from the gas phase using an e q u i l i b r i u m technique /3/ and t h e f a c i l i t i e s o f H. K. Birnbaum.
Attenuation was measured v i a t h e u l t r a s o n i c p u l s e echo technique using a s i n g l e transducer as sender and r e c e i v e r . The l o n g i t u d i n a l and shear modes were produced w i t h .3 i n . diameter X-cut and 2.5 i n . diameter AC-cut transducers a t room
temperature using t h i o k o l . The bond was weak a t room temperature b u t became strong and s t a b l e a f t e r t h e bonding agent freezes near 190 K.
The f i r s t measurements were performed i n a He4 c r y o s t a t described by Hultman /4/. L a t e r measurements were performed i n a He3 c r y o s t a t described by Poker 151. I n both cases t h e sample was f i r s t cooled t o t h e base temperature and then s l o w l y heated w h i l e t h e a t t e n u a t i o n was measured.
I 1 1
-
EXPERIMENTAL RESULTSAttenuation vs temperature data f o r t h e C11 e l a s t i c mode a t an u l t r a s o n i c frequency o f 12 MHz are shown i n Fig. 1. A peak i n t h e a t t e n u a t i o n i s seen near 1.25 K when t h e sample i s charged w i t h hydrogen. The a t t e n u a t i o n was also observed i n
measurements a t 31.7 MHz and 55 MHz. The background a t t e n u a t i o n increases r a p i d l y w i t h i n c r e a s i n g temperature, r i s i n g t o a l a r g e value near t h e superconducting c r i t i c a l temperature, Tc. The background a t t e n u a t i o n v a r i e s as t h e square o f the frequency, and makes higher frequency measurements d i f f i c u l t . The measured a t t e n u a t i o n f o l l o w s t h e p r e d i c t i o n s o f t h e BCS t h e o r y o f s u p e r c o n d u c t i v i t y f o r the e l e c t r o n i c absorption except i n t h e r e g i o n o f t h e hydrogen peak. This p r o p e r t y
w i l l be used l a t e r t o separate t h e hydrogen peak from t h e e l e c t r o n i c absorption f o r analysis.
The a t t e n u a t i o n was also measured f o r t h e Cqq on t h e same sample. No peak was seen i n t h i s mode.
I V
-
ANALYSISThe background a t t e n u a t i o n i s composed o f a p a r t t h a t v a r i e s w i t h frequency and from r u n t o r u n b u t n o t w i t h temperature and a p a r t t h a t increases w i t h t h e square o f t h e frequency and e x p o n e n t i a l l y w i t h i n v e r s e temperature below Tc. The f i r s t term i s p r i m a r i l y due t o loses i n t h e bond and i s e a s i l y d e a l t w i t h . The second term i s t h e e l e c t r o n i c absorption and must be c a r e f u l l y subtracted from t h e data t o permit analysis o f t h e hydrogen peak.
The BCS t h e o r y o f s u p e r c o n d u c t i v i t y p r e d i c t s t h a t t h e normalized a t t e n u a t i o n
A f i t ( T ) = A0 + Ael x %/%(T) ( 2 ) where A0 and Ael are constants and %/a,, i s given by Eq. 1. I n Eq. 1, 4.45 K was used f o r t h e Tc o f tantalum, and i t s zero temperature energy gap was given by
2 x A (0) = 3.5 x kTc. The data were f i t t o Eq. 2 i n a temperature r e g i o n above t h e hydrogen peak using a nonlinear l e a s t squares technique w i t h A0 and Ael as f i t t i n g parameters. The r e s u l t s o f the f i t f o r 12
MHz
are shown i n Fig. 1 as t h e s o l i d curve. A background o f t h i s form was subtracted from t h e data a t each frequency l e a v i n g t h e peaks shown i n Fig. 2.The a t t e n u a t i o n f o r an a n e l a s t i c r e l a x a t i o n process i s given by t h e Debye r e l a t i o n which can be expressed as
where w i s t h e s t r e s s wave r a d i a n frequency, T i s t h e r e l a x a t i o n time, and LR i s t h e r e l a x a t i o n strength. Since L!R v a r i e s s l o w l y w i t h temperature, the temperature dependence o f t h e r e l a x a t i o n time can be found by n o t i n g t h e temperature o f t h e peak at several frequencies and usinq Eq. 3. For t h e l i m i t e d range o f frequencies
used i n the experiment t h e relaxation time is fit by an Arrhenius form with an
a c t i v a t i o n energy, Q = .64
'
.1 meV and a frequency f a c t o r of vo = 4xlOY/s. The r e l a x a t i o n s t r e n g t h was determined from t h e peak heights, and was about 2 x10-5. V-
DISCUSSIONOne o f t h e p r i n c i p l e advantages o f using u l t r a s o n i c techniques f o r p o i n t d e f e c t s t u d i e s i s t h a t the measurements p r o v i d e symmetry i n f o r m a t i o n on t h e p o i n t d e f e c t s t r u c t u r e . I n t h e experiment we f i n d a r e l a x a t i o n i n t h e C11 e l a s t i c mode b u t not i n C44. Since
and since r e l a x a t i o n s o f t h e bulk modulus have o n l y been r e p o r t e d i n cases where t h e defect concentration i s h i g h we conclude t h a t t h e r e l a x a t i o n i s i n t h e C' e l a s t i c mode. This i s t h e same as t h e mode dependence r e p o r t e d f o r the Nb-0-H system
121.
Another s i m i l a r i t y o f t h e present system w i t h Nb-0-H i s t h a t both show a r e l a x a t i o n r a t e o f t h e Arrhenius type w i t h a c t i v a t i o n energies and frequency f a c t o r s much smaller than those t y p i c a l l y seen i n c l a s s i c a l p o i n t d e f e c t systems. T h i s
Arrhenius r a t e was o r i g i n a l l y i n t e r p r e t e d by Poker e t . al. as evidence f o r a m u l t i - l e v e l system w i t h a 2-phonon Orbach type r e l a x a t i o n mechanism. However, r e c e n t measurements o f a t t e n u a t i o n i n Nb-N-H i n t h e normal and superconducting s t a t e by Wang e t . a l . 191 and o f a t t e n u a t i o n and v e l o c i t y i n Nb-0-H as a f u n c t i o n o f magnetic f i e l d by Drescher-Krasika and Granato
/lo/
have shown t h a t t h e r a t e i ss t r o n g l y a f f e c t e d by t h e e l e c t r o n i c s t a t e o f t h e Nb host. This allows f o r t h e p o s s i b i l i t y o f using a two-level formal ism w i t h the Arrhenium f a c t o r a r i s i n g from t h e e l e c t r o n i c i n t e r a c t i o n w i t h t h e t u n n e l i n g system. Black and Fulde /9/ have shown i n c a l c u l a t i o n s on t u n n e l i n g systems i n superconducting m e t a l l i c glasses t h a t t h e r e l a x a t i o n r a t e follows an Arrhenius form w i t h an "activation energy" close to
C10-90 JOURNAL
DE
PHYSIQUEthe suggestion that interaction with the quasiparticles or conduction electrons is
an important relaxation mechanism for trapped
H
is consistent with previous
measurements in Nb and in the present work in Ta.
VI
-
CONCLUSION
In conclusion, we have found a re1 axation in the Cll;
elastic due to trapped Hin a dilute Ta alloy. There is no corresponding relaxation seen in the C44 mode.
The relaxatyon time of this defect obeys an Arrhenius equation with an energy
exponent of .64 meV. This trapped hydrogen system is similar in many respects to
the Nb-0-H defect system.
Fig. 1. Attenuation
vs.temperature for Fig. 2. Attenuation vs. temperature for
the C11 mode at 12
MHz.The solid curve the C11 mode at 3 frequencies after back-
is a computed background.
ground subtraction.
ACKNOWLEDGEMENTS
The authors would like to thank H. K. Birnbaum for his help in charging the sample
with hydrogen. We would also like to thank E. Johnson and W. Johnson for their
assistance with the measurements. This work was supported by the U.
S. Department
of Energy, Division of Materi a1 s Sciences under Contract DE-AC02-76ER01198.
REFERENCES
/I/ C. A. Wert, in Topics in Applied Phys., Vol. 29, Hydrogen in Metals 11, eds.
G. Alefeld and J. Vol kl, Springek-Verlag, Berlin-Heidelburg-New York, 1978.
/2/
D. B.Poker, G. G. Setser, A. V. Granato, and H. K. Birnbaum,
Z.
Phys. Chem.
116, 439 (1979).
T. Schober and H. Wenzl, in Topics in Ap lied Ph s., Vol. 29, Hydro en in
Metals 11, eds.
6.
Alefeld and J. Vol kl, ~prigger-Veriag,
~ e r l
w
&
e
H
-
n
i
York, 1978.
/4/ K. L. Hultman Thesis, Univ. of Illinois, 1979.
151
D. B. Poker Thesis, Univ. of Illinois, 1978.
161 Superconductivity, Vol. 1, ed. R. D. Parks, Marcel Dekker Inc., New York,
1969.
/7/ M. Levy and I. Rudnick, Phys. Rev. 132, 1073 (1963).
/8/
