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ORIGIN OF THE LOW FREQUENCY INTERNAL FRICTION BACKGROUND IN PURE METALS AND
DILUTE SOLID SOLUTIONS
J. Baur, M. Bujard, W. Benoit
To cite this version:
J. Baur, M. Bujard, W. Benoit. ORIGIN OF THE LOW FREQUENCY INTERNAL FRICTION BACKGROUND IN PURE METALS AND DILUTE SOLID SOLUTIONS. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-239-C10-242. �10.1051/jphyscol:19851054�. �jpa-00225438�
ORIGIN OF THE LOW FREQUENCY INTERNAL FRICTION BACKGROUND IN PURE METALS AND DILUTE SOLID SOLUTIONS
J . BAUR, M. BUJARD AND W . BENOIT
Institut de GBnie Atomique, Institut Federal Suisse.de
~ ~ ~ h n o l o g i e , PJG3-Ecublens, CH-1015 Lausanne, Switzerland
R6sum6 - Nous B t u d i o n s l e fond de F.I. basse frCquence d t 6 c h a n t i l l o n s d l o r contenant de f a i b l e s c o n c e n t r a t i o n s de Pt. Les mesures systBmatiques en f o n c t i o n de l a frgquence e t de l ' a m p l i t u d e montrent que l e fond de F.I. dG aux d i s l o c a t i o n s ne p e u t B t r e e x p l i q u 6 p a r des processus de r e l a x a t i o n . A b s t r a c t - We s t u d y t h e I.F. background a t low frequency o f g o l d samples c o n t a i n i n g low c o n c e n t r a t i o n s o f Pt. Systematic measurements o f I.F. as a f u n c t i o n o f frequency and s t r a i n a m p l i t u d e show t h a t t h e I.F. background due t o d i s l o c a t i o n s cannot be e x p l a i n e d by r e l a x a t i o n processes.
I. I n t r o d u c t i o n
D i s l o c a t i o n motion c o n t r i b u t e s s i g n i f i c a n t l y t o t h e i n t e r n a l f r i c t i o n (I.F.) o f metals. T h i s c o n t r i b u t i o n i s commonly i n t e r p r e t e d by t h e Granato-Lucke ,model [I ]
( h e n c e f o r t h : GL model), which c o n s i d e r s t h e d i s l o c a t i o n as a v i s c o u s l y damped s t r i n g p i n n e d a t i t s e x t r e m i t i e s . The GL model was s u c e s s f u l l y v e r i f i e d i n t h e MHz frequency range by A l e r s and Thompson, who observed t h e p r e d i c t e d behavior o f t h e u l t r a s o n i c a t t e n u a t i o n as a f u n c t i o n o f frequency [z]. Moreover, t h e magnitude o f t h e v i s c o u s f r i c t i o n c o n s t a n t t h a t t h e y determined from t h e i r experiments i s i n good agreement w i t h t h e t h e o r e t i c a l v a l u e c a l c u l a t e d by L e i b f r i e d i n a model o f phonon s c a t t e r i n g by d i s l o c a t i o n s [3]. Furthermore, i n t h e low frequency range, t h e p r e d i c t e d e v o l u t i o n o f t h e I.F. and t h e modulus d e f e c t o f a sample under i r r a - d i a t i o n has been l a r g e l y observed [4, 51. F o l l o w i n g these b e a u t i f u l v e r i f i c a t i o n s , t h e GL model has been e x t e n s i v e l y used f o r i n t e r p r e t a t i o n o f e x p e r i m e n t a l obser- v a t i o n s i n a l l frequency ranges.
However, some d i s c r e p a n c i e s appeared i n t h e low frequency range between t h e GL p r e d i c t i o n s and t h e e x p e r i m e n t a l observations. As p o i n t e d o u t by A l e r s and Thompson, t h e v a l u e o f t h e v i s c o u s damping c o n s t a n t c a l c u l a t e d from MHz experiments l e a d s t o very low values of I.F. a t low f r e q u e n c i e s [z]. Thus, t h e observed magnitude o f I.F. a t low frequency cannot be e x p l a i n e d by t h e GL model. F u r t h e r - more, t h i s model p r e d i c t s a monotonic decrease o f I.F. as a f u n c t i o n o f p o i n t d e f e c t c o n c e n t r a t i o n . Simpson e t al., however, observed an i n i t i a l i n c r e a s e o f t h e I.F. o f Cu d u r i n g an i r r a d i a t i o n experiment [6]. T h i s i n i t i a l i n c r e a s e o f I.F. as a f u n c t i o n o f p o i n t d e f e c t c o n c e n t r a t i o n , - i.e. i r r a d i a t i o n time, i s known as t h e peaking e f f e c t , and was l a t e r observed i n Mg, Ag and A1 [7]. The peaking e f f e c t was n o t o n l y observed d u r i n g i r r a d i a t i o n experiments, b u t a l s o by quenching, as a f u n c t i o n o f vacancy c o n c e n t r a t i o n , i n Cu [ 8 ] and r e c e n t l y i n CuZnAl [9]. I t was a l s o measured as a f u n c t i o n o f i m p u r i t y c o n c e n t r a t i o n i n g o l d based d i l u t e s o l i d s o l u t i o n s [ l o ] . Thus, t h e peaking e f f e c t seems t o be a g e n e r a l f e a t u r e o f t h e i n t e r a c t i o n s between d i s l o c a t i o n s and p o i n t d e f e c t s . However, i t cannot be des- c r i b e d by t h e GL model.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851054
C10-240 JOURNAL DE PHYSIQUE
To overcome t h e s e d i f f i c u l t i e s , Simpson and S o s i n i n t r o d u c e i n t h e GL model an a d d i t i o n a l v i s c o u s f r i c t i o n term due t o p o i n t d e f e c t dragging by d i s l o c a t i o n s [ll]. The h i g h I.F. v a l u e observed a t low frequency as w e l l as t h e peaking e f f e c t c o u l d , then, be explained. However, even m o d i f i e d , t h e GL model d e s c r i b e s a r e l a x a t i o n , and thus, a frequency dependent I.F. Therefore, i t cannot e x p l a i n t h e f a c t t h a t , a t low frequency, t h e observed I.F. i s more o r l e s s frequency inde- pendent [I 21.
I n t h i s work, we want t o show t h a t a v i s c o u s l y damped s t r i n g equation, on which t h e GL model i s based, i s n o t s u i t a b l e t o d e s c r i b e t h e I.F. background o f metals.
To t h i s end, we s t u d y t h e I.F. o f d i l y t e s o l i d o l u t i o n s o f P t i n Au as a f u n c t i o n B
o f s t r a i n a m p l i t u d e i n t h e range 10- t o 2.10- , frequency i n t h e range 0.3 t o 3 kHz, and i m p u r i t y c o n c e n t r a t i o n . Two d i f f e r e n t m i c r o s t r u c t u r a l s t a t e s , l e a d i n g t o a low and a h i g h I.F. background, a r e measured.
11. E x p e r i m e n t a l R e s u l t s
The experiments a r e performed on g o l d samples o f p u r i t y 99.9999 L a l l o y e d w i t h v a r i o u s c o n c e n t r a t i o n s o f P t (0 - 1000 ppm). The sam l e has t h e form o f a c a n t i - l e v e r beam notched i n t h e m i d d l e o f i t s f r e e end ~157. T h i s shape g r e a t l y reduces p a r a s i t i c i n t e r a c t i o n s w i t h t h e clamps [14], and t h u s improves t h e measurement accuracy and r e p r o d u c i b i l i t y . To p e r f o r m measurements a t d i f f e r e n t temperatures, t h e sample i s mounted i n a c l o s e d c y c l e c r y o g e n i c r e f r i g e r a t o r which a l l o w s t h e measurement o f I.F. i n t h e range 20 K t o 340 K. The I.F. i s measured u s i n g wave form a n a l y s i s o f t h e resonant v i b r a t i o n f r e e decay [15]. T h i s technique e l i m i n a t e s d i s t u r b a n c e s due t o c a s u a l p a r a s i t i c v i b r a t i o n s and g i v e s a weak measurement d i s - p e r s i o n , even a t low s t r a i n amplitudes 1161.
a) Low I.F. background
To i n d u c e a l o w I.F. background, t h e samples a r e deformed 5 ?A by r o l l i n g a t room temperature. They a r e t h e n s t r a i n e d 0.1 L a t 20 K t o u n p i n t h e d i s l o c a t i o n s from p o i n t d e f e c t s . A f t e r a n n e a l i n g a t room temperature, t h e samples show, b e s i d e t h e B o r d o n i peaks, a low I.F. background due t o s h o r t d i s l o c a t i o n segments.
The I.F. i s measured as a f u n c t i o n o f s t r a i n a m p l i t u d e a t 200 K and 290 K and a t f r e q u e n c i e s v a r y i n g between 0.3 and 3 kHz. A t b o t h temperatures and a t a l l t h e measured frequencies, t h e b e h a v i o r o f I.F. as a f u n c t i o n o f s t r a i n a m p l i t u d e i s t h e same. The I.F. depends l i n e a r l y on t h e s t r a i n a m p l i t u d e as shown i n F i g u r e 1 i n t h e case o f p u r e gold. The l i n e a r dependence i s c h a r a c t e r i z e d by two'parameters, t h e i n t e r c e p t and t h e slope, t h a t have d i f f e r e n t b e h a v i o r s as a f u n c t i o n o f frequency and temperature.
The i n t e r c e p t depends l i n e a r l y on temperature and e x h i b i t s a peak as a f u n c t i o n o f frequency, as shown i n F i g u r e 2. T h i s r e l a x a t i o n peak as w e l l as i t s l i n e a r dependence on temperature a r e c o m p l e t e l y e x p l a i n e d by t h e t h e r m o e l a s t i c e f f e c t due
Fig. 1 - I . F . as a function o f s t r a i n amplitude F i g . 2 - I n t e r c e p t o f the curve - I.F. vs s t r a i n i n Au 6N deformed 5 % by r o l l i n g . Temperature: - as a function of frequency a t 200 K and 290 K 200 K . Frequency: 980 Hz. Sample thickness: 0.45 i n Au 6N (same sample .as i n Fig. 1 ) . The s o l i d
mm. l i n e s represent t h e thermoelastic e f f e c t a t both
temperatures.
beam and t o t h e h i g h P o i s s o n ' s r a t i o o f g o l d , t h e modulus i n v o l v e d i n t h e f l e x u r a l v i b r a t i o n is 1.6 t i m e s g r e a t e r t h a n t h e Young's modulus. The t h e o r e t i c a l c u r v e s a r e drawn on F i g u r e 2. Thus, t h e I.F. background due t o d i s l o c a t i o n s i s z e r o when t h e s t r a i n a m p l i t u d e g o e s t o z e r o .
The s l o p e o f t h e l i n e a r dependence o f I.F. on s t r a i n a m p l i t u d e is d u e t o i n t e r - a c t i o n s between d i s l o c a t i o n s and p o i n t d e f e c t s . I t d e c r e a s e s w i t h i m p u r i t y concen- t r a t i o n , b u t is t e m p e r a t u r e i n d e p e n d e n t i n t h e r a n g e 200 K t o 290 K and f r e q u e n c y i n d e p e n d e n t f o r t h e measured f r e q u e n c i e s .
The f r e q u e n c y i n d e p e n d e n c e o f t h e I.F. due t o d i s l o c a t i o n motion a s w e l l a s i t s s t r i c t dependence on s t r a i n a m p l i t u d e show c l e a r l y t h a t a v i s c o u s l y damped s t r i n g model is n o t s u i t a b l e f o r t h e d e s c r i p t i o n o f t h e low f r e q u e n c y I.F. background.
Fig. 3 - I . F . as a function o f s t r a i n amplitude a t 290 K i n Au + 50 ppm P t
annealed 1 h a t 630 K. The value o f the 9 2 thermoelastic effect (T.E.) i s shown.
b ) High I.F. background
The s a m p l e s a r e r o l l e d 5 % a t room t e m p e r a t u r e and t h e n a n n e a l e d 1 h a t 630 K t o i n d u c e a h i g h I.F. background. S i n c e t h e a n n e a l i n g t e m p e r a t u r e c o r r e s p o n d s t o t h e b e g i n n i n g o f t h e r e c o v e r y s t a g e o f g o l d , l o n g d i s l o c a t i o n s e g m e n t s a r e c r e a t e d i n t h e s a m p l e s .
F i g u r e 3 shows t h e t y p i c a l dependence o f I.F. on s t r a i n a m p l i t u d e a f t e r t h i s t r e a t m e n t . The I.F. is v e r y h i g h f o r s t r a i n a m p l i t u d e s g r e a t e r t h a n 2 * 1 0 - ~ , and i s more o r less a m p l i t u d e i n d e p e n d e n t . B u t , f o r s m a l l e r s t r a i n a m p l i t u d e s , a s h a r p d e c r e a s e o f I.F. is o b s e r v e d . A t t h e l o w e s t measured a m p l i t u d e , t h e I.F. d r o p s t o
F i g . 4 - I.F. as a function of Pt concentration Fig. 5 - I.F. as a function o f frequency a f t e r a f t e r substracting t h e thermoelastlc e f f e c t substracting t h e thermoelastlc effect (T.E.) f o r (T.E.) for %old samples annealed 1 h a t 640 K. Au + 000 ppm P t annealed 1 h a t 650 K. S t r a i n :
S t r a i n 5-10-
.
Temperature: 290 K. 25.10-
.
Temperature: 290 K.C10-242 JOURNAL DE PHYSIQUE
t h e v a l u e o f t h e t h e r m o e l a s t i c e f f e c t c a l c u l a t e d as i n s e c t i o n a). Thus, even i n t h e case o f h i g h I.F. background, t h e I.F. due t o d i s l o c a t i o n motion i s zero when t h e s t r a i n amplitude i s s m a l l e r t h a n about T h i s behavior i s s i m i l a r t o t h a t o f t h e peaking e f f e c t observed d u r i n g i r r a d i a t i o n , which disappears a t low s t r a i n amplitudes [18]. As i n t h e case o f i r r a d i a t i o n experiments, we observe a peaking e f f e c t as a f u n c t i o n o f t h e i m p u r i t y c o n c e n t r a t i o n . T h i s i s shown i n F i g u r e 4. (Note t h e q u a n t i t a t i v e d i f f e r e n c e between F i g u r e s 3 and 4 due t o a s l i g h t l y d i f f e r e n t t h e r m a l t r e a t m e n t ) .
F i g u r e 5 shows t h e I.F. background due t o d i s l o c a t i o n motion, i.e. - a f t e r sub- s t r a c t i n g t h e t h e r m o e l a s t i c e f f e c t , as a f u n c t i o n o f frequency i n t h e range 300 Hz t o 2500 Hz. Again, as f o r t h e low I.F. background, t h e I.F. due t o d i s l o c a t i o n s i s frequency independent.
111. Conclusion
The I.F. background measured i n d i l u t e s o l i d s o l u t i o n s o f P t i n Au, i s due t o two c o n t r i b u t i o n s : t h e t h e r m o e l a s t i c e f f e c t and t h e i n t e r a c t i o n s between d i s l o - c a t i o n s and p o i n t defects. The l a t t e r c o n t r i b u t i o n i s shown t o be frequency i n - dependent i n b o t h t h e m i c r o s t r u c t u r a l s t a t e s we s t u d i e d . T h i s f e a t u r e shows c l e a r l y t h a t a v i s c o u s f r i c t i o n term cannot be r e s p o n s i b l e o f t h e I.F. background measured a t low frequency. Depending on ,the m i c r o s t r u c t u r a l s t a t e , t h e I.F. decreases w i t h i m p u r i t y c o n c e n t r a t i o n i n t h e case o f s h o r t d i s l o c a t i o n segments, and shows a peaking e f f e c t f o r l o n g d i s l o c a t i o n segments. However, i n b o t h s t a t e s t h e I.F. due t o d i s l o c a t i o n motion i s e s s e n t i a l l y s t r a i n amplitude dependent so t h a t a t v e r y low amplitudes i t vanishes. T h i s main f e a t u r e o f t h e i n t e r a c t i o n s between d i s l o c a t i o n s and p o i n t d e f e c t s suggests t h a t a s l i d i n g f r i c t i o n term s h o u l d be i n c l u d e d i n t h e d e s c r i p t i o n o f these i n t e r a c t i o n s , i n s t e a d o f t h e c l a s s i c a l viscous term. T h i s s l i d i n g f r i c t i o n c o u l d be a t t r i b u t e d t o l a t t i c e f r i c t i o n [19], b u t more p r o b a b l y t o d i s l o c a t i o n m o t i o n i n an a r r a y o f weak obstacles. Our i n t e r p r e t a t i o n i s t h a t t h e I.F. background, as w e l l as t h e peaking e f f e c t , can be e x p l a i n e d b y t h e h y s t e r e t i c motion o f d i s l o c a t i o n s through an a r r a y o f weak b u t l o n g range i n t e r a c t i n g obstacles.
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