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EVALUATION OF ANELASTIC EVIDENCE FOR
INTERSTITIAL SOLUTE BINDING IN BCC METALS
J. Cost, J. Stanley
To cite this version:
EVALUATION OF ANELASTIC EVIDENCE FOR INTERSTITIAL SOLUTE BINDING IN BCC METALS
J.R. COST AND J.T. STANLEY'
Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, N.M. 87545, U.S.A.
'Mechanical and Aerospace Engineering Department, Arizona State University, Tempe, Arizona 85287, U.S.A.
~ L s u m L - Une nouvel le technique d'analyse directe d e s spectres TDSA) a et6 appl iauee aux resul t a t s cruciaux de frottement int6rieur et de trainage mkchanique invoquis d a n s la controverse sur l'existance d'une agglomiration d e s intersti t i e l s dans les mitaux rifractaires. On trouve que, pour les concentrat ions de s o l u t h s intersti tiels relativement ilevies, une part ie de l"6largissement du pic de Snoek est due a d e s relaxations distinctes de la relaxation principale. Ce resultat renforce l'idge d'une interaction de s o l u t 6 s aui conduit a la formation d'amas d'interstitiels.
Abstract- A Direct Spectrum A n a l y s i s (DSA) technique h a s been applied to key internal friction a n d elastic after-effect data which are involved in the controversv over the existance of interstitial clustering in the refractory metals. It is found that at relatively high interstitial solute concentrations some of the Snoek peak broadening is due to relaxations that are distinct f r o m the main relaxation. T h i s finding s u p p o r t s the view that interstitial s o l u t e s have an interaction that produces clusters of interstitials.
I- INTRODUCTION
In 1 9 5 5 P o w e r s /l/ published internal friction data showing that the oxygen Snoek peak is broadened asymmetrically a s the oxygen solute concentration increases. In 1956 P o w e r s and Doyle /2/ suggested that the broadened peak could be considered to be the sum of two single relaxation peaks; the main peak w a s assumed to be the regular Snoek peak due to single oxygen a t o m s and the smaller high-temperature peak w a s due to stress-induced reorientation of closely associated pairs of oxygen a t o m s (bound-pair model).-Later P o w e r s and Doyle /3/ published r e s u l t s of a more extensive investigation using elastic after-effect measurements which confirmed the bound-pair model and gave a value of roughly 0.09 ev for the binding enthalpy of oxygen atoms.
T h i s work o f P o w e r s a n d Doyle has had a profound influence on our ideas about interstitial s o l i d s o l u t i o n s and many other investigators have f o u n d similar results in various bcc metals. N o w however, Welter et a1 /4/ have published new results for the Ta-0 system w h i c h they claim s h o w that the oxygen Snoek peak is symmetrically broadened a s the oxygen concentration is increased and that there is n o specific'evidence f o r the existence of bound-pairs. In view of the importance of t h i s question w e decided to reanalyze the r e s u l t s reported by Weller and b r P o w e r s and Doyle using a newly-developed direct spectrum a n a l y s i s (D%) method which analyzes an internal friction peak to give an estimate of the spectrum of relaxation times (at constant temperature). T h e key reason for using the DSA method is that it d o e s not make a priori a s s u m p t i o n s about the f o r m of the spectrum /5,6/. T h e results of the DSA m e t h o d support the bound-pair model.
11- RESULTS
Ila- INTERNAL F R I C T I O N DATA OF WELLER et a1
W e analyzed Weller's data for s a m p l e s containing 1200, 3400 and 5 9 0 0 appm oxygen. T h e data w e r e taken f r o m h i s Fig. 2 /4/ using a high precision digitizer. T h e same c o r r e c t i o n s u s e d by Weller et a1 /4/ for the variation of frequency a n d
C10-36 JOURNAL
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PHYSIQUErelaxation strength with m e a s u r i n g temperature w e r e applied. Also, a small back- ground correction w a s m a d e , T h e resulting data are shown in Fig. l a s internal friction versus reciprocal temperature.
In order to critically examine the symmetry of the internal friction peak, w e first determined the locus of m i d p o i n t s for various internal friction levels. T h i s l o c u s is indicated by a dashed line in Fig. 1 for the 5 8 0 0 appm sample. It is clear from the deviation of t h i s median line from the vertical that the internal friction peak is not symmetric. T o examine the nature of the asymmetry w e folded the internal friction peak about the peak temperature (determined by the intersection of the median line w i t h the internal friction curve). The two branches clearly did not coincide over the entire 1/T range. Instead, there w a s an appreciablly greater internal friction on the high temperature side. When the low temperature branch w a s subtracted from the high temperature branch, a small internal friction peaK at about 1000./T=2.2 1454 K ) c o u l d be seen. T h i s peak should not be considered to be a good representation of the bound-pair peak because the method of seperating it from the ordinary Snoek peak is rather crude.
Since the data in Fig 1. show evidence for a high temperature peak, it is desirable to analyze the data t o obtain an approximation t o the total spectrum of relaxation times responsible for the peak. T h e DSA method h a s been shown to provide approximations of known input spectra which rep1 icate the position, amp1 i tude, w i d t h , and shape of an original input spectrum with good accuracy and without introducing s p u r i o u s spectral p e a k s /5,6/. T h e DSA of Weller's data gives the histogram of relaxation times shown in
1000 IT^ K - ' Fig. 2 calculated for a temperature of
423.7
K
for the three oxygen concentra- Fig. 1 . Internal friction d a t a tions. T h e major contribution t o the of Weller et a1 /4/ plotted v s spectrum is centered at TIZO.l s regard- reciprocal temperature. less of the oxygen concentration.A
second important contribution is centered at T2$0.3 S for the t w o highest oxrgen concentrations. T h e s e two major components c a n be represented q u i t e well by t w o lognormal distributions of relaxation times. T h e two parameters w h i c h c h a r a c t e r i z e a lognormal distribution, namely the mean relaxation time, T m , a n d the width ,F, are given in T a b l e l for lognormal distributions which best fit the histograms shown in Fig 2. For the sample containing 5 9 0 0 appm oxrgen the small peak at T%2 S m a y be significant since asimilar peak a p p e a r s for Powers'data (see below). However, the small peak at TZ0.01 s is probabally an artifact arising f r o m errors in background subtraction. T h e spectra w e r e calculated assuming a distribution of activation energies and a constant 70=i0-14 S. T h e distribution in activation energies corresponding to the relaxation time distribution are g i v e n ' b ~ the s c a l e s at the top of the figure.
IIb- DATA O F P O W E R S A N D D O Y L E
0.01 0 1 10 r . s ( LOG SCALE) ACTIVATION ENERGY, eV 1 0 1 0 5 1.1 115 1.2 0.01 0 1 1 .o r , s ( LOG SCALE) 0.01 0.1 10 r . s ( L O G SCALE) ACTIVATION ENERGY, eV 1.0 1.05 1 1 1.15 1.2 I I : I I I I I 0.1 10 r , s (LOG SCALE)
Fig. 2. DSA relaxation time (or activation energy) distribution from Weller's data for oxygen concentrations 1200, 3400 and 5900 appm and from
Powers' data for a sample containing 5900 appm. T h e solid c u r v e s s h o w
lognormal d i s t r i b u t i o n s fit to the histograms with parameters T m and B
given in T a b l e 1. T h e vertical dashed lines give the spectral limits imposed on the calculation.
W e a l s o analyzed s o m e o f the elastic after-effect data of Powers and Doyle
/3/ using DSA. Since these m e a s u r e m e n t s were made at lower temperatures than the internal friction m e a s u r e m e n t s the relative concentration of bound pairs is expected to be greater a n d the pair relaxation should show up at smaller oxygen concentrations. We a n a l y z e d the data for a sample containing l900 appm oxygen and found two peaks in the spectrum with mean T values shown in T a b l e 1.
l
.
--
T a b l e 1 Comparison of r e s u l t s obtained by DSA for various s a m p l e s Data Ref.t
I
I l 4 I I l 1 lC10-38 JOURNAL
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PHYSIQUE111. DISCUSSION
Our a n a l y s i s of the internal friction data of Weller et a1 s h o w s that the spectral distribution of relaxation times agrees quite well with the distribution obtained f r o m the older d a t a of P o w e r s for similar oxrgen concentrations. At small oxygen concentrations a narrow (approximately lognormal) distribution of relaxation times is observed. A s the concentration of oxygen increases, a shoulder appears on the high relaxation time side (or equivalently the high energy side) of the original distribution. T h i s shoulder can be treated a s a second lognormal distribution of relaxation times. A t still higher concentrations of oxygen a third lognormal distribution of relaxation t i m e s a p p e a r s at longer relaxation times. T h e general pattern is in agreement w i t h P o w e r s bound-pair model w i t h the modification that the two discrete r e l a x a t i o n s d u e t o single oxygen a t o m s and pairs of oxrgen a t o m s are replaced by two lognormal distributions of relaxation times. Physically such a modification a p p e a r s r e a s o n a b l e s i n c e the lognormal distributions are very narrow and t h u s barely distinguishable f r o m discrete relaxations. Since the distributions are s o narrow w e will d i s c u s s the s p e c t r a a s though they composed of one, two or three single relaxation times. which are taken a s the mean relaxation t i m e s of the corresponding lognormal distribution.
It
is
n o t e w o r t h y that the first relaxation which is attributed to single oxygen a t o m s does not change position or w i d t h w i t h increasing oxrgen concentration. However, the second r e l a x a t i o n , k h i c h is attributed to oxygen pairs, s h i f t s to lower relaxation times a n d increases in w i d t h a s the oxygen concentration increases. T h i s behavior might be e x p l a i n e d by the superposition of a peak due to triplets or higher-order g r o u p s of oxygen atoms. A c c o r d i n g to the law of m a s s action t.te magnitude of the peak d u e to oxygen pairs should be proportional to the square of the magnitude of the peak due to single oxygen atoms. T h i s relationship is not obeyed for the W e l l e r d a t a ; the pair peak in the 5900 appm sample is too large relative t o the pair peak in the 3 4 0 0 appm sample. A possible explanation for the discrepancy is the presence of a substantial contribution from oxygen triplets or higher-order g r o u p s to the peak attributed to the pairs in the 5900 appm sample. Or it m a y be that because of the close proximity of the two relaxations the DSA method does not give a r e l i a b l e estimate of the r e l a t i v e m a g n i t u d e 5 of the two peaks.T h e third distribution of relaxation t i m e s is centered at a mean relaxation time which c o r r e s p o n d s well with the position of the oxygen-nitrogen interaction peak found by P o w e r s a n d Doyle / 3 / . T h e A r r h e n i u s equation given by P o w e r s and Doyle predicts a relaxation time of 1.2 s at 423.7 K . T h u s t h i s peak may be due t o residual nitrogen in the samples.
P o w e r s and Doyle's model for the association of oxrgen a t o m s in tantalum w a s derived primarily f r o m elastic after-effect measurements rather than internal friction measurements. A s shown in T2b:e 1 . the separation between the Snoek peak and the pair peak is greater f o r the elastic after-effect data than for the internal friction data. T h e relaxation t i m e s for these two peaks calculated from P o w e r s and Doyle's equations are; 5 9 s and 361 s at 349.9 K . 0.10 s and 0.35 s at 423.7 K .
These times agree well w i t h the mean relaxation times determined by the DSA method for the three different s e t s of data.
REFERENCES
/l/ Powers,
R.
W., A c t a Met.,3
,1955) 135./2/ Powers, R. W. a n d Doyle, M. V., A c t a Met.
4
(19565 233. /3/ Powers,R.
W . and Doyle,M.
V . , Trans. Met. Soc. A I M E ,215
(1959) 655.
/4/ Weller,
