Peaking Effect, Experiments and Theory

Recent observat ions on the peaking e f f e c t i n Cu are repor ted which mainly show t h a t 1) the peaking i s independent o f frequency i n the range 2.102 t o 5.10' Hz, 2) the peak h e i g h t i s a f u n c t i o n o f the i n i t i a l i n t e r n a l f r i c t i o n background which a1 lows a q u a n t i t a t i v e d e s c r i p t i o n o f the amplitude dependence, 3 ) no d i f f u s i o n mechanism i s invo lved i n the i n i t i a l increase o f i n t e r n a l f r i c t i o n , 4) the peaking e f f e c t i s present i n s i n g l e c r y s t a l S . Ear l y f i nd ings concerning the dependence o f peaking wi t h the t o t a l number o f defects created i n the l a t t i c e and the inverse r e l a t i o n between peak t ime and p inn ing r a t e are confirmed. A l l these features are c o r r e c t l y described by a phenomenological model developed by us ing l a t t i c e dynamics ca lcu la t ions , i .e. a d i s l o c a t i o n moves against a constant f o r c e independent o f v e l o c i t y , i ns tead o f the e l a s t i c a l s t r i n g l i k e behaviour. 1 . In t roduct ion. A f t e r Simpson and Sosin (1) had repor ted the existence o f the peaking e f f e c t (P.E.) a g rea t number o f studies, both experimental and t h e o r e t i c a l , have been publ ished (2 t o 10). Most o f the experimental work has confirmed t h a t P.E. i s present i n the frequency range 200-600 Hz i n p o l y c r y s t a l l i n e samples o f Cu, A1 and Ag. Recently however i t was found t h a t i n c o n t r a d i c t i o n w i t h models p r e d i c t i o n and w i t h e a r l i e r observat ions P.E. was a lso present a t 40 KHz (11). The aim o f t h i s work i s t o present the r e s u l t s o f a systematic study o f P.E. i n po ly and s i n g l e c r y s t a l l i n e samples o f Cu v i b r a t i n g i n the KHz frequency range, i n p a r t i c u l a r on the amp1 i tude and frequency dependences o f P.E., on the d i f fus ion mechanisms involved i n the P.E. and on the condi t ions t o observe P.E. i n s i n g l e c r y s t a l s . These r e s u l t s w i l l be then compared w i t h a phenomenological model based on a l a t t i c e dynamics approach. 2. Experimental.Two types o f experimental set-up were used. I n the f i r s t one the sample i s a r o d 60 mm Tong and 4 mm i n diameter v i b r a t i n g l o n g i t u d i n a l l y a t about 40 KHz and the i r r a d i a t i o n source i s the bremsstrahlung y r a d i a t i o n obtained by bombarding an A1 t a r g e t w i t h 25 MeV e lect rons, the energy o f the y spectrum thus obtained was centered about 6 MeV (11). I n the second i n s t a l l a t i o n samples 4 mm i n width, 15 t o 25 mm i n leng th and 0.1 t o 0.25 mn i n thickness v i b r a t i n g i n the f l e x u r a l mode i n the range 1 KHz t o 20 KHz were used. The i r r a d i a t i o n i s done w i t h e lect rons o f 1.5 MeV from a Van de Graaf f Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981543 C5-296 JOURNAL DE PHYSIQUE acce le ra to r (14) . I n both cases the mate r ia l was 5N Cu from Uni ted Mineral and Chemical Corpora t ion , USA. S ing le c r y s t a l s were grown by the Bridgeman technique i n a g raph i te c r u c i b l e . Before i r r a d i a t i o n the samples were annealed f o r 6 hrs a t 800°C, a t r e a t ment o f 10 mn a t 500°c was done between i r r a d i a t i o n s . The i r r a d i a t i o n temperature was 350K under an e l e c t r o n f l u x o f 2.1013 el/cm2 sec. 3. Results.Figures l a and l b show respec t i ve ly the peak height , Q$~/Q;', and the corresponding i n i t i a l value, Q;' , as a f u n c t i o n o f frequency. Inc lud ing i n f i g l a the r e s u l t s a t 40 KHz (11) where QiiX/Qil = 2 and a t 200 Hz-600 Hz (2) (7) where the peak h e i g h t i s i n the range 1.1-2.0, one f i n d s t h a t i f a c o r r e l a t i o n e x i s t s between peak he igh t and frequency i t i s n o t a simple one. F igure l b suggests t h a t the r e l a t i o n between Q; ' and frequency i s the rec ip roca l o f f i g . l a and there fo re the peak h e i g h t i s i n v e r s e l y p ropor t iona l t o the i n i t i a l i n t e r n a l f r i c t i o n background as shown i n f i g . 2 which ind ica tes t h a t the r e s u l t s are described by the r e l a t i o n A Q-l /Q;' = l + MAX Qi' w i t h A = 5.10-". It i s t o be noted t h a t a comparison can on ly be establ ished between F ig . 1 : a) Peak he igh t QiiX/Qil and b ) I n i t i a l background Q; ' vs frequency a t E = 7.10-'. 25A 0:~~/0; I Slope A = 5 10.' F ig . 2: Peak h e i g h t QikX/Qo1 V S q u a l i t y f a c t o r Q. f o r d i f f e r e n t samples. experiments a t the same i r r a d i a t i o n temperature and s t r a i n amplitude. The in f luence o f the s t r a i n ampli tude on the P.E. i s shown i n f i g . 3 . The s h i f t o f the maximum towards longer times confirms previous observat ions i n the sub-KHz range (6). I n t h i s case the i n i t i a l background shows a s l i g h t amplitude dependence even f o r the smal ler values o f E (<10e7) . 24 Q-l,o-~ Polycrystal The values o f peak he igh t and i n i t i a l backf = 13.7 KHZ ground taken from f i g . 3 are found t o obey T = 350K the r e l a t i o n