ANELASTIC RELAXATION OF OXYGEN IN PURE NIOBIUM AND VANADIUM

HAL Id: jpa-00227137

https://hal.archives-ouvertes.fr/jpa-00227137

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

ANELASTIC RELAXATION OF OXYGEN IN PURE NIOBIUM AND VANADIUM

J. Diehl, G. Haneczok, G. Hörz, B. Purniah, K. Schulze, M. Weller

To cite this version:

J. Diehl, G. Haneczok, G. Hörz, B. Purniah, K. Schulze, et al.. ANELASTIC RELAXATION OF

OXYGEN IN PURE NIOBIUM AND VANADIUM. Journal de Physique Colloques, 1987, 48 (C8),

pp.C8-239-C2-244. �10.1051/jphyscol:1987833�. �jpa-00227137�

ANELASTIC RELAXATION OF OXYGEN I N PURE NIOBIUM AND VSNADIUM

J . D I E H L , G . H A N E C Z O K '1' , G . H 5 R Z , B . P U R N I A H *2' , K . SCHULZE a n d M. WELLER

Max-Planck-Instltut f u r Metallforschung, Institut f u r Werkstoffwissenschaften, D-7000 Stuttgart, F.R.G.

Résumé - Des expériences de f r o t t e m e n t i n t é r i e u r sont effectuées dans l e Nb-0 e t V-0 ( 0 , 1 à 0,85 a t %), en é t u d i a n t les mêmes é c h a n t i l l o n s pour l e s o s c i l l a - t i o n s autour de 1 Hz e t 1 kHz, pour déterminer précisément l e s paramètres de l a r e l a x a t i o n de Snoek. Avec l'augmentation de l a teneur en oxygène l e s pics de Snoek dans l e Nb-0 e t V - 0 , pour les deux fréquences, sont déplacés à des températures élevées, accompagnées par un élargissement continu e t presque symmetrique. Cet élargissement e s t i n t e r p r ê t é par une d i s t r i b u t i o n continue des temps de r e l a x a t i o n . Pour l e cas de Nb-0, i l e s t montré q u ' e l l e se déduite d'une d i s t r i b u t i o n dans les énergies d ' a c t i v a t i o n . Une analyse d é t a i l l é e dé- montre que l e s p r é d i c t i o n s du modèle de " c l u s t e r i n g " pour l ' i n t e r a c t i o n entre des i n t e r s t i t i e l s se d i s t i n g u e n t considérablement des o b s e r v a t i o n s .

A b s t r a c t - I n t e r n a l f r i c t i o n experiments on Nb-0 and V-0 a l l o y s ( 0 . 1 t o 0.85 a t %) using the same samples f o r o s c i l l a t i o n s a t about 1 Hz and 1 kHz were performed to a c c u r a t e l y determine the Snoek r e l a x a t i o n parameters. With i n - creasing 0 c o n t e n t , the Snoek peaks f o r Nb-0 and V-0 f o r both frequencies are s h i f t e d to higher temperatures accompanied by a continuous and almost sym- m e t r i c broadening. This broadening i s accounted f o r by a continuous d i s t r i b u - t i o n i n r e l a x a t i o n times and i n t h e case o f Nb-0 i t i s shown t o o r i g i n a t e from a d i s t r i b u t i o n i n a c t i v a t i o n energies. A d e t a i l e d a n a l y s i s o f the Nb-0 data demonstrates t h a t the p r e d i c t i o n s o f the c l u s t e r i n g model f o r the i n t e r - s t i t i a l i n t e r a c t i o n deviates s t r o n g l y from the o b s e r v a t i o n s .

I - INTRODUCTION

Controversial experimental r e s u l t s and i n t e r p r e t a t i o n s e x i s t about the a n e l a s t i c r e l a - x a t i o n o f i n t e r s t i t i a l f o r e i g n atoms (IFA) i n group Va b . c . c . metals V, Nb and Ta.

These metals e x h i b i t a r a t h e r high s o l u b i l i t y (up t o about 1 a t %) f o r heavy IFA such as oxygen or n i t r o g e n . I n t e r a c t i o n e f f e c t s are observed at hiqher IFA contents i n measurements o f the Snoek r e l a x a t i o n .

Based on e a r l i e r experiments i t was suggested t h a t i n a d d i t i o n t o i s o l a t e d IFA p a i r s , t r i p l e t s e t c . , i . e . discrete clusters o f them,are also present due to short range interaction o f IFA / 1 - 4 / . This was concluded by decomposing the Snoek peak r e l a x a t i o n as observed e . g . , i n i n t e r n a l f r i c t i o n ( I F ) or mechanical a f t e r e f f e c t experiments i n several d i s c r e t e r e l a x a t i o n peaks/processes. As a consequence o f t h i s c l u s t e r i n g ' model the Snoek peak should e x h i b i t an asymmetrical broadening a t the high tempera- t u r e side o f the peak becoming more pronounced, higher the IFA c o n c e n t r a t i o n i s , but no shift of the peak temperature should occur.

Permanent addresses :

' 'institute of Physics and Chemistry of Metals. Silesian University, Bankowa 12, PL-40007 Katowice, Poland

(21

v 'Indira Ganghi Center for Atomic Research, Kalpakkam, India

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987833

C8-240 JOURNAL DE PHYSIQUE

More r e c e n t I F experiments /5,6/ using h i g h p u r i t y Ta and Nb samples c a r e f u l l y doped w i t h o n l y one species o f IFA (oxygen) showed a synnnetrical broadening and a s h i f t to higher temperatures o f the 0 Snoek peak w i t h i n c r e a s i n g 0 content. This continuous broadening was accounted f o r by a continuous d i s t r i b u t i o n o f r e l a x a t i o n times o r i g i - n a t i n g from a r e p u l s i v e long range i n t e r a c t i o n o f oxygen atoms. A d d i t i o n a l doping w i t h small amounts o f n i t r o g e n caused an asymmetrical broadening o f t h e 0 Snoek peak on i t s h i g h temperature s i d e /7/ i n d i c a t i n g an i n t e r a c t i o n between 0 and N atoms.

Such an i n f l u e n c e o f t r a c e s o f n i t r o g e n atoms

-

apparently being present i n most samples used i n e a r l i e r experiments

-

on t h e oxygen Snoek peak was r e c e n t l y concluded by Gibala from a r e - i n s p e c t i o n o f h i s own and o t h e r i n v e s t i g a t i o n s /8/.

To throw more l i g h t on t h e p r o p e r t i e s o f IFA i n t e r a c t i o n i n b.c.c. metals,we a p p l i e d a new experimental technique which g r e a t l y extends t h e frequency (and temperature) range o f I F measurement t o be c a r r i e d o u t on the same sample and opens t h e p o s s i b i l - i t y t o determine the r e l a x a t i o n parameters w i t h h i g h p r e c i s i o n and consequently a l s o t h e i r p o s s i b l e v a r i a t i o n w i t h IFA concentration. I n e a r l i e r experiments /9/ on Nb and Ta doped w i t h low concentrations o f IFA,mechanical a f t e r e f f e c t measurements were combined w i t h I F experiments ( c o v e r i n g a range i n r e l a x a t i o n time o f -103). The advan- tage o f t h e method i n t h i s paper i s t h a t the same measuring technique, namely I F , i s employed t o cover a s i m i l a r l y wide range i n T ( o r frequencies) and t h a t t h e mean r e - l a x a t i o n parameters ( i m p o r t a n t whenever a spectrum o f T i s i n v o l v e d ! ) can be obtained from a simple a n a l y s i s o f t h e peak temperatures. On Nb-0 more 0 concentrations (0.1 t o 0.8 a t % ) are i n v e s t i g a t e d here than i n our e a r l i e r experiments /9/ and t h e measurements a r e extended t o V-0.

I 1

-

EXPERIMENTAL PROCEDURE

Sample p r e p a r a t i o n .

-

Niobiwn samples w i t h dimensions o f 5 0 x 5 ~ 1 mm were prepared from p o l y c r y s t a l l i n e Nb ribbons. The i n t e r s t i t i a l content was reduced t o low values (H < 1, 0 <lo, N <10 and <5 at.ppm) by r e s i s t a n c e h e a t i n g a t 2470K f o r s e v e r a l hours t i l l a pressure o f 5x10-

Eo

mbar was reached. Oxygen (0.12, 0.2, 0.42, 0.6 and 0.85 a t % ) was introduced by h e a t i n g i n f l o w i n g h i g h p u r i t y oxygen gas. The main m e t a l l i c i m p u r i t y o f t h e s t a r t i n g m a t e r i a l ( s u p p l i e d by Heraeus GmbH) was Ta(O.l%), t h e c o n c e n t r a t i o n o f o t h e r s i s one o r d e r o f magnitude smaller. One sample w i t h 0.7 % 0 was prepared i n a d d i t i o n from u l t r a pure Nb as described i n

/ l o /

(and used e a r l i e r /6,7/) t o examine the p o s s i b l e i n f l u e n c e o f m e t a l l i c i m p u r i t i e s .

P o l y c r y s t a l l i n e vanadiwn wires w i t h 1 mm diameter were prepared from e l e c t r o l y t i c a l l y r e f i n e d V ( m e t a l l i c i m p u r i t i e s : A1 10, C r 5, Cu 5, Mn 5, Ni 3, S i 10 a t ppm) by an- n e a l i n g a t 1770 K i n a s i m i l a r manner as described above f o r t h e Nb ribbons. I n t h i s case, however, t h e r e s i d u a l N c o n t e n t could n o t be reduced below = 0.02 a t . % . Samples w i t h 0.16, 0.19, 0.27, 0.52 and 0.85 a t % 0 were prepared by h e a t i n g a t 1770 K i n f l o w i n g an oxygen gas ( 5 . 1 0 - ~ mbar).

I n b o t h cases,the IFA content was determined by e l e c t r i c a l r e s i s t i v i t y measurements a t t h e doping temperature and a t 300 K (see e.g. /11/).

I n t e r n a l f r i c t i o n measurements

-

The I F measurements were c a r r i e d o u t by u s i n g the same samples i n two d i f f e r e n t types of apparatus. Low frequency measurements i n the range o f 1 t o 15 Hz were c a r r i e d o u t w i t h an automatic, computer c o n t r o l l e d i n v e r t e d t o r s i o n pendulum, high frequency measurements i n t h e kHz range by e x c i t i n g t h e samples t o f l e x u r a l e i g e n v i b r a t i o n s i n t h e fundamental tone. I n t h e pendulum t h e Nb ribbons were mounted i n s p e c i a l g r i p p i n g jaws w i t h wedges, t h e V w i r e s clamped w i t h p i n s . For d e t a i l s o f t h e kHz apparatus see /12/.

I 1 1

-

EXPERIMENTAL RESULTS AND THEIR ANALYSIS

~ x a m ~ i e s .- Figs. 1 and 2 show examples o f I F measurements o f the Snoek peaks obtained f o r r e p r e s e n t a t i v e oxygen concentrations. F i g . 1 i s from a Nb r i b b o n doped w i t h 0.6 a t % 0 o s c i l l a t i n g a t f z 2 . 4 Hz and-0.98 kHz. The s h i f t i n peak temperature i s c l e a r l y demonstrated. For c l a r i t y f 2 vs. T i s shown o n l y f o r the low frequency measurements. F i g . 2 shows t h e r e s u l t s o f s i m i l a r experiments on a V w i r e c o n t a i n i n g 0.52 a t % 0 w i t h o s c i l l a t i o n frequencies o f f ~ 0 . 7 a n d z 2 . 4 kHz.

6 a b of Q - I ( T ) above 0.9 of the maximum value, Q,I ( a f t e r appropriate subtraction of the background with a Debye function containing corrections f o r the expected tempera- t u r e dependence of the relaxation strength

A =

2.9,1 1/T and the measured variation of f 2 with

T

(comp.

/6,9/).

In t h i s f i t t i n g procedure, by means of a numerical, non l i n e a r l e a s t square minimization /13/, Qil, Tm, and t h e e f f e c t i v e activation enthalpy, Hs, a r e used as adjustable parameters.

( i i ) In the second s t e p the same procedure was applied t o t h e t o t a l curves with a s i n g l e Debye peak f o r 0 i n Nb and with two Debye peaks f o r O+N i n V ( i n which always small traces of

N

were present). The r e s u l t of the f i t t i n g s i s demonstrated i n Fig. 3 by a

V

sample containing about 0.02 a t % 0 and 0.02 a t %

N .

( i i i

)

Final ly , i n some cases t e corrected internal f r i c t i o n [ Q - ~ ( T ) T / Q - ~ T was plot- from ( i ) o r ( i i ) and of H from the analysis described below. m1

ted f o r f u r t h e r analysis vs. b l / T + H / k l n ( f ( ~ ) / f , ) ] using the values of Q- and Tm Frequency s h i f t - The mean relaxation parameters H a n d ' r ~ a r e as usual assumed t o obey an Arrhenius equation -c=-c,exp (H/kT) and can therefore be determined from the temperature s h i f t of the

I F

maximum from

Tml

t o Tm2 due to the frequency change from f m l t o fm2 as

H = K ln(fm2/fml)/(1/Tml-1/Tm2)

( l a ) In

^b=

ln(1/2 nfml) - ln(fm2/fml)/(1-Tm1/Tm2) ( l b ) Since the Tm values from evaluation ( i ) agree i n general within the e r r o r l i m i t s (see below) with those from (ii),normally the r e s u l t s of ( i ) are used i n eq. ( l a ) and

(lb).

The peak positions,

T

corresponding t o normalized reference frequencies f m l

= 1

Hz and fm2

= 1

kHz may tEen be calculated from the r e l a t i o n

Tm1,2

⁼

-H/k l n ( 2 nfml,2 T ~ ) . (2

In Fig.4 a r e shown the r e s u l t s f o r the oxygen Snoek peaks i n Nb and V. Plotted a r e

H,

T,

and

T m l ,

Tm2 f o r specimens with various oxygen contents. To determine r e l i a b l y whether

H

and T,vary with oxygen content systematically, the following e r r o r l i m i t s have t o be taken into account. The t o t a l e r r o r i n peak temperature i s estimated t o be

AT =

+

^{0.7 K .}

The e r r o r in f m i s negligibl small (Afm/fm Y With eq. ( l a , b ) i t foylows t h a t

A H =

2 0.01 eV,

LIT,=

2 0.7-10' 5s. Fig. 4 shows t h a t the s l i g h t varia- tions of H and-cmwith 0 content a r e within or close t o these experimental e r r o r s . However, f o r both Nb-0 as well as f o r V-0, the peak temperatures a t both reference frequencies fm exhibit c l e a r l y an increase with 0 content.

Peak shape analysis - By the f i t t i n g method ( i i ) , an a c t i v a t i o n enthalpy Hs i s ob- tained which i s i n general smaller than the mean activation enthalpy H determined i n the frequency s h i f t analysis. This indicates t h a t the measured Snoek peaks can be matched t o a symmetrical curve of the Debye type i f i t i s broadened. The f i t t i n g with a (broadened) Debye curve with

Hs <

H can be viewed /14/ as representing a Fuoss-Kirk- wood d i s t r i b u t i o n of the relaxation times with

wh = H/Hs

as the width parameter of

t h e curve. This parameter, corresponding t o the re1 a t i v e width of the curve a t half maximum, i s plotted in Fig.

5

f o r Nb-0 and V-0 a s a function of the 0 content. I t in- creases from wh

= 1

( d i l u t e a l l o y ) up t o values of about 1 , 3 f o r 0.85 a t % 0. Besides, Fig.

5

shows t h a t the low frequency

(1

Hz) Snoek peaks ( a t l e a s t f o r Nb-0) a r e wider than the peaks measured a t

1 kHz.

According t o /14/, in cases of continuous d i s t r i b u t i o n s of relaxation times, i t i s d i f f i c u l t t o distinguish between d i f f e r e n t distributions (lognormal, Fuoss-Ki rkwood, box) except a t the t a i l s of the peak. I f a lognormal d i s t r i b u t i o n i s assumed t o be c l o s e s t t o r e a l i t y , the width parameter

B

characterizing t h i s d i s t r i b u t i o n can be de- duced from the parameter wh by using the tables of Nowick and Berry /14/. The values of

B

determined i n t h i s way a r e presented i n the lower parts of Fig.

5

f o r d i f f e r e n t concentrations.

The r e s u l t s of the peak width analysis of 0 in

V

i n Fig.

5

show a l a r g e r s c a t t e r of

the data f o r the kHz measurements. This a r i s e s from d i f f i c u l t i e s i n separating the

simultaneously present

N

Snoek peak. This i s the main reasbn t h a t we r e s t r i c t e d the

more detailed analysis in the following t o the oxygen Snoek peak in niobium. In Fig.6

C8-242 JOURNAL DE PHYSIQUE

t h e temperature dependence o f t h e spectrum w i d t h parameter B i s p l o t t e d f o r Nb-0 as a f u n c t i o n o f 1/T. Values d e r i v e d from measurements i n t h e t o r s i o n pendulum on Nb-0.6%

0 w i t h s e v e r a l frequencies a r e included. As can be seen, e s p e c i a l l y from t h e data f o r Nb-0.6 % 0, B can be we1 1 approximated by s t r a i g h t l i n e s through t h e o r i g i n , i .e. by B 1/T.

To check t h e symmetry o f t h e oxygen Snoek peak a s i m i l a r procedure as i n /6/ was ap- p l i e d t o t h e p l o t s obtained w i t h method ( i i i ) . The asymmetry was determined from t h e w i d t h s w- and wf o f t h e low(-) and h i g h (+) temperature s i d e o f the peak a t d i f f e r e n t f r a c t i o n s o f t h e peak h e i g h t by i n t r o d u c i n g an asymmetry parameter A = (w+-w-)/

(w++w)/2. Values of Ao.5 and AO.l a r e l i s t e d i n Table 1.

Table 1: Asymmetry A o f t h e 0 Snoek peak i n Nb-0,in %

kHz A0.5 AO. 1

Experiments

0 c o n t e n t ( a t . % ) 0.12 0.4 0.6 0.85

The observed asymmetry i s , i n a l l cases, r a t h e r small. I t depends on frequency and temperature apparently i n a s i m i l a r manner as the broadening and can be almost neglec- t e d a t kHz frequencies. Furthermore, no d e f i n i t e v a r i a t i o n o f t h i s small asymmetry w i t h c o n c e n t r a t i o n can be detected.

C l u s t e r i n g model 0.7%

For a comparison w i t h t h e p r e d i c t i o n s o f t h e c l u s t e r i n g model I F curves were composed from the r e l a x a t i o n parameters (Hl,rwl, A1(T)i H 2 , ~ " 2 , A2(T); HS,r,?, A3(T) f o r s i n g l e s , p a i r s and t r i p l e t s o f oxygen r e c e n t l y presented by Okamo o / 4 f o r Nb-0.7%0.

The c a l c u l a t e d curves f o r 1 Hz and 1 kHz were normalized i n peak heights, p l o t t e d as Q - ~ / Q - ~ vs. 1/T and analysed i n t h e same way as our experimental curves. The r e s u l t s are ayso l i s t e d i n Tab. 1 ( r i g h t s i d e ) . I t can be seen t h a t the c l u s t e r i n g model pre- d i c t s much s t r o n g e r asymmetry.of t h e Snoek peaks than i s e x p e r i m e n t a l l y observed.

I V SUMMARY AND CONCLUSIONS

Combination o f I F experiments a t Hz and kHz frequencies a l l o w s t o determine t h e mean r e l a x a t i o n parameters w i t h h i g h p r e c i s i o n .

For Nb w i t h 0.1 a t % oxygen, values f o r H (1.148 eV) and r w = ( 2 . 9 ~ 1 0 - ' ~ s ) agree w e l l w i t h e a r l i e r p u b l i s h e d data o b t a i n e d from I F and mechanical a f t e r e f f e c t experiments /9/. With i n c r e a s i n g 0 content, t h e Snoek peak temperature f o r 1 Hz and 1 kHz i s sys- t e m a t i c a l l y s h i f t e d t o h i g h e r temperatures f o r Nb-0 as w e l l as f o r V-0. This s h i f t may o r i g i n a t e from small v a r i a t i o n s o f H and/or .rm w i t h 0 content. However, i n s p i t e o f t h e h i g h p r e c i s i o n o f measurements t h e two c o n t r i b u t i o n s cannot be separated c l e a r l y .

The Nb-0, V-0 Snoek peaks a r e c o n t i n u o u s l y and r a t h e r symmetrically broadened. The assumed continuous d i s t r i b u t i o n o f r e l a x a t i o n times becomes w i d e r w i t h i n c r e a s i n g 0 content. I n Nb-0 t h e parameter B c h a r a c t e r i z i n g t h e s p e c t r a l w i d t h of t h e assumed l o p normal d i s t r i b u t i o n , i s found t o be p r o p o r t i o n a l t o 1/T, which i n d i c a t e s t h a t t h e dis- t r i b u t i o n o f r e l a x a t i o n times o r i g i n a t e s ( p r i m a r i l y ) from a d i s t r i b u t i o n i n t h e a c t i - v a t i o n e n t h a l p i e s /14/ and n o t i n t h e preexponential f a c t o r .

The d e t a i l e d a n a l y s i s o f t h e Nb-0 Snoek peak shows t h a t t h e broadening i s r a t h e r s m - m e t r i c and markedly s m a l l e r than corresponding curves c a l c u l a t e d according t o t h e c l u s t e r i n g model. Since a l l t h e r e s u l t s presented here c o n f i r m t h e e a r l i e r observa- t i o n s /5,6/ o f a s h i f t i n peak temperature and a continuous and almost symmetrical broadening o f t h e Snoek peak w i t h i n c r e a s i n g IFA c o n c e n t r a t i o n and cannot be brought i n t o agreement w i t h the p r e d i c t i o n s o f t h e c l u s t e r i n g model, d i f f e r e n t p h y s i c a l models f o r the IFA i n t e r a c t i o n i n b.c.c. metals have t o be developed. Such models based on the assumption of l o n g range i n t e r a c t i o n s o f IFA, i n c l u d i n g t h e r e c e n t l y p r o ~ o s e d model o f Dattagupta e t a l . /15,16/, are under c o n s i d e r a t i o n and w i l l be discussed i n

F i g . 1

-

^{I F} and f vs. T i n Nb- 2 F i g . 2

-

I F and f vs. T i n V-0.5at%O 2 0.6at%0 a t Hz and kHz frequencies. a t Hz and kHz frequencies.

Rahn f o r t h e i r t e c h n i c a l assistance, and Miss H. Rau f o r h e r t y p i n g assistance.

REFERENCES

/1/ R.W. Powers and M.V. Doyle, J.Appl.Phys. 30, 514 (1958).

/2/ R. Gibala and C. Wert, Acta M e t a l l . 14, 1 m 5 and 1105 (1966).

/3/ S.N. Tewari and d.R. Cost, ICIFUAS-57 0. Lenz and K. Lucke eds. ), p . 330, Springer Verl ag, B e r l i n (1975).

/4/ M.A. Okamoto, Acta m e t a l l . 31, 1169 (1983).

/5/ M.Weller, J.X.Zhang, G.Y .LiTT.S.K@ and J.Dieh1, Acta M e t a l l . 29, 1055 (1981).

/6/ M.Weller, J.X.Zhang, K.Schulze, T.S.KG and J.Dieh1, J.de Physique 42C5-817 (1981).

/7/ M.Wel l e r , J,.Diehl

,

G.Horz, R.Mann and K.Schulze, J.de Physique 3 , 7 1 0 - 4 7 (1985).

/8/ R. Gibala, J. de Physique 46, C10-43 (1985).

/9/ M.Weller, G.Y.Li, J.X.Zhanc T.S.KG and J.Dieh1, Acta M e t a l l . 29, 1047 (1981).

/ l o /

K. Schulze, E. G r a l l a t h and M. Weller, Z e i t s c h r . Metallkde. 7 2 T 4 3 9 (1981).

/11/ G. Horz, Z e i t s c h r . Metallkde. 61, 371 (1970).

/12/ M. W e l l e r and E. T'orok, t h i s conference.

/13/ G. Haneczok, Proc. I 1 P o l i s h Conference " A n e l a s t i c Relaxations and Magnetic A f t e r - E f f e c t s i n S o l i d s " , RENIOM-78, S i l e s i a n U n i v e r s i t y Press., Katowice, 1979, p.87 ( i n P o l i s h ) .

/14/ A.S.Nowick and B.S.Berry, A n e l a s t i c Relaxation i n C r y s t a l l i n e S o l i d s , Academic Press, New York, 1972.

/ 1 5 7 S.Dattagupta, R.Balakrishnan and R.Ranganathan, J .Phys .F. :Met.Phys.IZ-,1345 (1982).

/16/ S.Dattagupta, J.Phys.F. Met.Phys.

3,

1363 (1982).

2 0 6 280 360 4 4 8 5 2 8 688 68% 7 6

T I K I

F i g . 3

-

Numerical f i t t i n g o f I F and background vs. T f o r V w i t h 0.02at%O and 0.02at% N. Points represent measured data.

*

-

N

4 ,

5 -

* m

.m,

- _-

⁰

'a '2

m

T I K 1 T I K 1

e

-

. m 1

-z 2.

* _{m .}

L-, -?

m 19.

* 01'

5'.

m

0 . 2 N

b "

0 . N

2-

m .

f .

0.67 HZ

!'::

^{246 kHz}

: - - . / - - <

. 2.4 HZ!?.

. , . ;

. :

. , 0.98 kHz

. .

. . . .

. .

.\

. ..

: .

. . , '\

. i . .

. . i

. . ; !,

: .. . : .

. . , :

. . . ,

. ;

.

. . .

i . . . . . . . _{> :} . l

Ier5.L

, ,& ^\.-.,:

T W . 2

320 400 480 560 6 4 0

. . . .

. . 7%

. . . . . .

. . c

i

^,::?

.

, . . ^" -,

.

. . . 7.

.

.

. .

- . . . _. . . : . . . _. . ^{r I ,}

j'

'.

c

,ma. , \.-Am-.

-

3 0 0 3BB 4 6 0 5 4 0 6 2 0 700 780

C8-244 JOURNAL

DE

PHYSIQUE

-

V)

-

5' L E

re

²

0

TmX2

-

_Y ^{428 566}

*s -

^{424 5LO}

L20 536

0 0.2 0.L 0.6 0.8 1

oxygen concentration I a t % 1

Fig. 4 - Relaxation parameters

H, T,,

and i n

'Nb-0

and

V-0

a s a f u n c t i o n o f oxygen concentration. Also shown

Il

,m a r e d a t a from r e f . /5/ on

Nb-0.

A 1 kHz

1 0

p;pl

0 L

0 2 I,'

0 0 0 5 1

oxygen concentration [at%]

A 1 kHz

am

1.0 0.L

0.2 /

ku

0 0 oxygen concentration 0.5 lat % 1 1

Fig. 5 - Width parameter

wb

and

6

( f o r lognormal d i s t r i b u t i o n ) f o r

Nb-0

and

V-0

a s a function of oxygen concentration.

( 8

d a t a from r e f .

/5/).

Fig.

6

- vs.

1 / T

f o r

Nb-0

c o n t a i n i n g d i f f e r e n t amounts

oxygen.