DISLOCATION RELAXATION PEAKS IN MOLYBDENUM

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DISLOCATION RELAXATION PEAKS IN MOLYBDENUM

R. Grau, H. Schultz

To cite this version:

R. Grau, H. Schultz. DISLOCATION RELAXATION PEAKS IN MOLYBDENUM. Journal de

Physique Colloques, 1981, 42 (C5), pp.C5-49-C5-54. �10.1051/jphyscol:1981506�. �jpa-00220962�

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DISLOCATION RELAXATION

P E A K S I N

MOLYBDENUM

R . Grau and H. Schultz

Max-PZanck-lnstitut fiir MetaZZforschung, Institut fiir Physik, Heisenbergstr.1, 0-7000 Stuttgart 2 and Institut fiir Theoretische und Angewandte Physik der Universitat Stuttgart, F. R. G.

A b s t r a c t . - I n h i a h p u r i t y molybdenum s i n s l e c r y s t a l s measurements of t h e damping and modulus a r e r e p o r t e d i n t h e t e m o e r a t u r e r a n g e of t h e a- and y - r e l a x a t i o n . A c t i v a t i o n volumes of t h e a-subpeaks were d e t e r m i n e d from t h e a m p l i t u d e dependence of t h e I n t e r n a l F r i c -

t i o n . The r e s u l t s c l e a r l y s u p p o r t t h e e x p l a n a t i o n o f t h e a - r e l a x a - t i o n i n t e r m s of k i n k p a i r f r o m a t i o n i n 7 1 ° - d i s l o c a t i o n s and d i f - f u s i o n of d i f f e r e n t t y p e s of g e o m e t r i c a l k i n k s i n s c r e ~ d d i s l o c a - t i o n s . Deformation i n d u c e d p o i n t d e f e c t s i n t e r a c t w i t h t h e s e d i s - l o c a t i o n segments g i v i n g r i s e t o t h e 6 - r e l a x a t i o n . Some c h a r a c - t e r i s t i c s of t h e y-peak ( k i n k p a i r f o r m a t i o n on screw d i s l o c a - t i o n s ) a r e d i s c u s s e d .

1 . I n t r o d u c t i o n . - I n t e r n a l F r i c t i o n ( I F o r Q - I ) i s f a r more complex i n b . c . c . m e t a l s t h a n i n f . c . c . m e t a l s due t o t h e s p e c i a l c o r e s t r u c t u r e of screw d i s l o c a t i o n s i n t h e b . c . c . l a t t i c e / I / and t h e h i g h s e n s i t i v i t y f o r i n t e r s t i t i a l i m p u r i t i e s . I n o u r group t h e problem h a s been approached by two complementary s e t s of e x p e r i m e n t s . S y s t e m a t i c doping of niobium and t a n t a l u m e l u c i d a t e d t h e i n f l u e n c e of hydrogen and oxygen o n t o t h e damping s p e c t r a / 2 , 3 / . The p r e s e n t work f o c u s e s on t h e i n t r i n s i c b a r r i e r s t o d i s - l o c a t i o n motion u s i n s h i g h p u r i t y molybdenum. The measurement of "secon- d a r y f e a t u r e s " , e s p e c i a l l y t h e a m p l i t u d e dependence of t h e damping peaks d e l i v e r s a d e c i s i v e t e s t of t h e s u g g e s t e d models / 4 / .

2 . E x p e r i m e n t a l P r o c e d u r e . - The e x p e r i m e n t s have been c a r r i e d o u t i n a t o r s i o n pendulum i n t h e t e m p e r a t u r e r a n g e between 1C) K and 700 K . To de- t e r m i n e a c t i v a t i o n p a r a m e t e r s t h e r e s o n a n t f r e q u e n c y was changed by a f a c t o r of 50 i n t h e r a n g e between 0 . 4 Hz and 26 H z . I n d i f f e r e n t h i g h p u r i t y molybdenum s i n g l e c r y s t a l s ( r e s i d u a l r e s i s t a n c e r a t i o RRR=40000) t h e i n f l u e n c e of t h e c r y s t a l l o g r a p h i c o r i e n t a t i o n of t h e sample, t h e amount and t e m p e r a t u r e of d e f o r m a t i o n and t h e a g i n g t r e a t m e n t on I F have been i n v e s t i g a t e d . A l l damping s p e c t r a were r e c o r d e d a s a f u n c t i o n o f t e m p e r a t u r e and s t r a i n a m p l i t u d e A ( A b e i n g between 5 x 1 0 - ~ and ~ x I o - ~ ) u s i n g a method o f measurement d e s c r i b e d e l s e w h e r e / 5 / .

3 . E x p e r i m e n t a l R e s u l t s . - The damping peaks w i l l be d i s c u s s e d i n t h e nomenclature of Chambers / 6 / u s i n p t h e symbols a ,

6,

and y a c c o r d i n g t o

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981506

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C5-50 JOURNAL DE PHYSIQUE

different temperature ranges and interpretations viven below.

The&mping spectra obtained after low temperature deformation (curve I, € = I % at 200K) and after high temperature deformation (curve 2,

&=I% at 475K) are shown in figure 1 . Curve 1 is enhanced by a relative scaling factor of 2.5 to obtain comparable peak heiqhts. It can be seen, that (i) the y-peak is significantly increased by low temperature deformation, and (ii) the relative heiqhts of the low temperature parts of the a-relaxation are enhanced by low temverature deformation, whereas the main process at 115 K (a ) is increased by high temperature deformation.

1

The a-peak appears here as a shoulder of the a-relaxation located between 110 K and 250 K. This process disappeared after annealing at 600 K (fig.2a, curve 2) and the a-peak reached a stable configuration showing a pronounced 4-fold substructure. The corresponding modules curves (fig.2b) reveal that the aging treatment does not affect the over- all dislocation mobility below room temperature. This confirms that no dislocation pinning by interstitials like nitrogen, oxygen or carbon took place and, therefore, the annealing effects must be caused by deformation induced point defects or by a dislocation rearrangement.

In different b.c.c. metals the a-relaxation is composed of several processes (5,9,2). Any conclusive interpretation of the single process in terms of the suggested models requires a separation of the subpeaks.

However, deconvolution is only useful if it is unique and allows to obtain distinct characteristics of the subpeaks. In figure 3 the decomposed a-relaxation is shown at two frequencies. The subpeaks are symmetrical in a 0-I vs. 1/T plot. This assumntion is fullfilled if processes with symmetrically distributed relaxation times contribute to the a-relaxation

i s / -

Figure 4 shows the a-relaxation at different strain amplitudes.

The observed amplitude dependence belonos just to the relaxation processes observed at low amplitudes. Even the a-peak substructure is re- flected in the amplitude dependent part of the damping (fig.4, below).

The subpeak al is more separated from a2 at higher amplitudes (compare fig. 4 above and below)

.

Activation volumes are calculated from the temperature shift of each subpeak through a variation of the applied strain amplitude. De- tails of the evaluation procedure and further results will be published.

The activation parameters for the a-relaxation in the [100]-orientated crystal are presented in table 1 using a Schmid factor for the torsional stress of 0.58.

The y-relaxation has been associated with the basic mechanism con- trolling the macroscopic flow in b.c.c. metals at low temperatures /6,7/.

Because of the high puritv of our crystals we were able to observe the

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ture on the damping spectrum. Curve 1 is enhanced by a relative

scaling factor of 2.5

.

crystal orientation:[l

I l l

frequency f = 25 Hz 1: &=I% tension at 203 K

+0.2% torsion at 290K 2: € = I % tension at 475 K +O. 2% torsion at 475K

Fig. 2a: Annealing be- haviour after low temperature deformation.

1: as deformed, last deformation 0.2% torsion 2: annealed for about

15 min at 600 K

Pig. 2b: Modulus curves

( G - £ 2 ) corresponding to

the damping curves of fig. 2a.

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C5-52 JOURNAL DE PHYSIQUE

Fig. 3: (above to the left) Decomposition of the a-peak into 4 subpeaks at two measurement frequencies.

above: f = 18.5 Hz below: f = 0.4 Hz

I I

low temperature deformation.

50 100 150

-

^{T [ K I} crystal orientation: [I001

Fig. 5: (above to the right) The y-relaxation compared to a single Debye peak.

..

measurement points

-

damping background subtracted Gil

103

t

2

1

o 1 I I I I

50 100

-

150 ^TCKl 200

--

Debye peak

-

- , . ,. . , .

,

;:.::.; ...;;. .:

I,:, ,.. ^/ ,.. ,

,,<.<::;-.. ;:' -:(:.,:

,,., , Fig. 4: Amplitude dependence of

.... . the a-relaxation, sample

annealed 1/2 hour at 7 0 0 K after

frequency f = 1 4 Hz AQ-I

xloL

5

-

the strain am~litudes increase by an amount of AA = 2.9~10-' respectively

A = 6.8~10-6 for curve 7 A = 1 . 8 ~ 1 0 - ~ for curve 1

below: Amplitude dependent part of the a-relaxation

(difference between

curve 5 and 1 from above).

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T a b l e 1 : A c t i v a t i o n p a r a m e t e r s f o r t h e a - s u b p e a k s . The a p p l i e d s t r e s s a m p l i t u d e s Oa a r e q i v e n i n u n i t s o f t h e s h e a r modulus G , t h e a c t i v a t i o n volumes v i n u n i t s of t h e B u r g e r s v e c t o r b .

-

^.--- - ~1 1.

-

C 1 ~ . 1 _ . - _ 2

a 3 a4

y-peak u n d i s t u r b e d by i n t e r s t i t i a l atoms. A pronounced peak i s p r e s e n t i n t h e a s deformed specimen s t a t e ( f i g . 2 ) . F i g u r e 5 shows t h e y-peak compared t o a s i n g l e Debye peak w i t h a c t i v a t i o n p a r a m e t e r s 'H = 1.09 e V , fY=3x101 l / s ( c r y s t a l o r i e n t a t i o n : [ I 11

1) ,

a f t e r s u b t r a c t i o n o f a n ex-

0

p o n e n t i a l damping b a c k g r o u n d . The peak s h a p e f i t s t o a r e l a x a t i o n which i s c a u s e d by a s p e c t r u m of r e l a x a t i o n t i m e s d i s t r i b u t e d a c c o r d i n g t o a G a u s s i a n f u n c t i o n ( s e e / l o / ) , a l t h o u g h t h e h i g h t e m p e r a t u r e peak s i d e i s somewhat l o w e r e d a g a i n s t t h e Debye peak due t o t h e a n n e a l i n g o f t h e peak d u r i n g warmup. The c a l c u l a t e d G a u s s i a n p a r a m e t e r s a r e t e m p e r a t u r e d e p e n d e n t and amount t o 1 . 0

-

1 . 6

.

The a m p l i t u d e dependence of t h e s ~ e c t r u m a b o v e room t e m p e r a t u r e h a s b e e n measured i n d e t a i l , i t s e v a l u a t i o n and i n t e r p r e t a t i o n i s s t i l l i n p r o g r e s s .

4. D i s c u s s i o n . - I n t h e f o l l o w i n g we s h a l l d i s c u s s t h e o b s e r v e d r e l a x a - t i o n p r o c e s s e s i n t e r m s of t h e l j i n k P a i r r o r m a t i o n (KPF) and t h e D i f f u - s i o n of g e o m e t r i c a l X i n k s (KD) i n c l u d i n a p o s s i b l e i n t e r a c t i o n s w i t h p o i n t d e f e c t s . I n t h e s t a b l e s p e c i m e n s t a t e 2 ( f i g . 2 , c u r v e 2 ) i n t r i n - s i c p o i n t d e f e c t s a r e a n n e a l e d o u t a n d u n i q u e r e s u l t s a r e o b t a i n e d f o r 3 of t h e 4 s u b p e a k s i n d e p e n d e n t o f t h e c o n s i d e r e d s a m p l e . The a1 p r o c e s s e x h i b i t s a s t r o n g l y s t r e s s d e p e n d e n t a c t i v a t i o n volume. The n u m e r i c a l v a l u e s a r e s m a l l compared t o b 2 L ( L i s t h e f r e e d i s l o c a t i o n l e n g t h ) b u t c o n s i d e r a b l y l a r g e r t h a n o n e a t o m i c volume ( t a b l e 1 ) . T h e s e f e a t u r e s a r e o n l y a c c o u n t e d f o r by t h e KPF model / 1 1 / . F u r t h e r m o r e , i n t h e KPF model a b r o a d e n i n g of t h e damping peak w i t h r e s p e c t t o a Debye peak i s e x p e c t e d d u e t o a d i s t r i b u t i o n o f d i s l o c a t i o n l e n g t h s and i n t e r n a l s t r e s s e s . A t h i g h e x t e r n a l stresses 5 a t h e P a r & c o n d i t i o n /12/ w i l l be m e t by a growing number of d i s l o c a t i o n s e g m e n t s o f c e r t a i n l e n g t h s , e n h a n c i n g t h e peak a n d r e d u c i n g i t s w i d t h . T h i s i s o b s e r v e d f o r a l a s e x p l a i n e d i n t h e p r e v i o u s s e c t i o n ( f i g . 4 ) . The s u b p e a k a l i s i n c r e a s e d by h i g h t e m p e r a t u r e d e f o r m a t i o n , t h e specimen s t a t e i n which t a n g l e s of

-- 0.226 0 150 0.087

2 . 8 ~ 1 0 ' ~ 3 . 0 ~ 1 0 ~ ~ - 6 . 7 ~ 1 0 ~

0.075 1 7 . 4 ~ 1 0 ~ ~ v = c o n s t . = I b3

~ X I O - ~ G 1 2 5 b3

-

v = c o n s t . = 4 b3

1 ~ l o - ~ ~

89 b 3

-

~ X I O - ~ G 40 b3

-

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C5-54 JOURNAL DE PHYSIQUE

preferably 71°-dislocations are dominant in the dislocation structure /13/. We therefore attribute the subpeak al to the KPF in 7l0-dislocations. The subpeaks ci3 and a4 are enhanced by low temperature deformation. They exhibit similar activation energies and stress independent activation volumes which amount to the order of one atomic volume. This is expected for a dislocation motion via KD /I/. Due to the special s y m metry of screw dislocations in the b.c.c. lattice the existence of different types of kinks in screw dislocations is conceivable /I/ even though as yet unconfirmed by experimental results. We attribute the subpeaks a3 and c ~ q to the diffusion of two different t y m screw dislocations, most likely the kinks :K and

KI

(in the notation of ref.1) with lowest formation energy. A distribution of diffusion lengths leads to overlapping distributions of the relaxation times for both processes and may account for the unequal preexponential factors fo stated in table 1 (this will be further outlined in /5/). The y-peak is a symmetrical relaxation peak with a temperature dependent broadening relative to a single Debye peak. This is a necessary feature if the KPF mechanis~? is adequate. If one attributes the y-peak to the KPF in screw dislocations all dislocation segments become mobile at the y-peak temperature allowing for an irreversible rearrangement of the dislocation network. This may cause the disappearance of the y-peak after annealing above the peak temperature which at least in the present case cannot be explained as pinning by interstitial atoms. The 6-peak in our opinion is due to an interaction of deformation induced point defects with dislocation segments intrinsically relaxing in the temperature range of the a-relaxation. By the disappearance of those point defects the dislocations are freed and the relaxation strength transferes into the ^ci- peak. Such an interaction peak may also be situated above the y-peak

(fig.2) as previously reported for iron /14/.

References.

--

/I/ A. Seeger, C. Wiithrich, Nuovo Cimento 33B (1976), 33 /2/ U. Rodrian, H. Schultz, this c o n f e r e n c e

/3/ M. Maul, H. Schultz, this conference

/4/ G. Fantozzi, W. Benoit, C. Esnouf, J. Perez, Ann.Phys.Fr.4,7,(1979) /5/ R. Grau, H. Schultz, to be published

/6/ R.H. Chambers, Physical Acoustics, Vol. IIIA, Ed. W.P. Mason (Academic Press, New York, (1966), p. 123

/7/ A. Seeger, B. S e s t ~ k , Scripta !let.

5 ,

375 (1971)

/8/ G. Knoblauch, W. Benoit, H. Schultz, Scripta Met., 9, (3975),657 /9/ R. Klam, H. Schultz, H.E. Schaefer, Acta Met.

2 ,

(i979), 205 /lo/ A.S. Nowick, B.S. Berry, Academic Press, New York (1972) /11/ A. Seeger, Phil. Mag. 1, 651 (1956)

/12/ V.K. Par$, J. appl. ~ h y s .

2 ,

332 (1961)

/13/ A. Luft, L. Kaun, phys. stat. sol.

3,

781 (1970)

/14/ V. Hivert, P. Groh, P. Moser, W. Frank, phys. stat. sol.

42,

511, ( 1 977)