INTERNAL FRICTION CAUSED BY THE INTRINSIC PROPERTIES OF DISLOCATIONS

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INTERNAL FRICTION CAUSED BY THE INTRINSIC PROPERTIES OF DISLOCATIONS

Gilbert Fantozzi, I. Ritchie

To cite this version:

Gilbert Fantozzi, I. Ritchie. INTERNAL FRICTION CAUSED BY THE INTRINSIC PROP- ERTIES OF DISLOCATIONS. Journal de Physique Colloques, 1981, 42 (C5), pp.C5-3-C5-23.

�10.1051/jphyscol:1981501�. �jpa-00220957�

JOURNAL DE PHYSIQUE

CoZZoque C5, suppZ6ment au nO1O, Tome 42, cntobre 1981 page C5-3

INTERNAL FRICTION CAUSED

BY

THE INTRINSIC PROPERTIES OF DISLOCATIONS

G. Fantozzi and I.G. ~ i t c h i e *

INSA, 69621 ViZZeurbanne, France

* A . E. C.L. -W.lV.R. E. ,?inma

,

Canada

Abstract.- Relaxation phenocena a t t r i b u t a b l e to tne i n t r i n s i c p r ~ p e r t i e s of ciislocations a r e revieved. The principal t h e o r e t i c a l rodels For the i n t r i n s i c c;islocations relaxations and the Snoek-KiSster relaxation a r e presented in o u t l i n e . %cent important experinental r e s u l t s , zainly on f.c.c., h.c.2. and b.c.c. metals, are exaslined and compared with the theoretical y e d i c t i o n s .

i.

Introduction.- In 1949, Bordoni ( I ) observed an internal Friction ( I F ) peak i n f . c . c . metals which could only be a t t r i b u t e d t o d i s l o c a t i o r ; ~ and was associated with double-kink generation (DKG) by Seecer

( 2 ) .

From the relaxation enthal py of 3ordoni peaks, estimates of the Peierls s t r e s s can be obtained. The r e l a t i v e l y high value found f o r the T.c.cls has persuaded several authors t h a t the 3ordoni peaks should not be a t t r i b u t e d t o

GKG.

The objective of t h i s paper i s t o review the e x p e r i ~ e n t a l properties of the Bordoni relaxation

(BR)

in the f . c . c 1 s together

w i t h

t h e i r a n a l o y e s i n other s t r u c - t u r e s , and t o compare them w i t h theoretical predictions. In the f . c . c l s the situation seecs c l e a r and in the b . c . c l s we can report the resolution of a long standing contro- versy about the r o l e played by

il

i n t e r s t i t i a l s i n the IF sr;ectra of deformed

sam-

ples. However, in the h . c . p l s and b . c . c B s some contradictions s t i l l e x i s t .

2. Theoretical Aspects.- Several models f o r the

3R

have been proposed and t h e i r e s s e n t i a l c h a r a c t e r i s t i c s a r e reviewed i n d e t a i l elsewhere

( 2 ) .

9nly two of the51 a r e generally retained t o explain experimental data on the

BR : DKG

and geometrical kink migration (GKM). In t h e b . c . c l s , the IF spectra of deforr,ied samples of Mo,

bl

and a-Fe a r e markedly d i f f e r e n t from those of sanples of

V , piby

Ta and hydrogen charged a-Fe. This difference, which until recently has been the subject of a contro- versy,is a t t r i b u t a b l e t o the presence of

H

i n t e r s t i t i a l s with some dislocation core mobility giving r i s e t o Snoek-ICi6ster (S-l:) peaks. According t o some authors

(4,5),

a t the atomic level, t h e S-#(H) relaxation i s due t o the roodification of t h e DKG and

GKN

processes by the core nobile i n t e r s t i t i a l s . Thus, i t i s i ~ p o r t a n t t o outline the ri~odels

O F

the S-X relaxation a s well.

2.1 The DKG nocie1.- The Seeger-Par6 theory (2,6) gives a good description of t h i s model. Consider a dislocation segment ( 1 ) parallel t o a Peierls valley ( f i g . 1 ) . A t

OK,

the Peierls s t r e s s

(o )

i s necessary t o displace i t . Pit

T > 0,

under the combined influence of thermal fluctuations and the applied s t r e s s P

(a,.), DKG

can occur. The IF due t o

DM6

a t t a i n s i t s naximum when the inposed frequency

(P)

i s of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981501

C5-4 JOURNAL DE PHYSIQUE

'the sane o r d e r o f magnitude as t h e frequency

(v)

o f DKG :

P E ~ E R L S VALLEY. v =

vR

exp (-2 l J d k T ) (I

1

- - - - - -

where 2Wk = f o r n a t i o n ener- (=I

- - -

gy o f a k i n k p a i r , and vQ i s

I L L -

\

^fb t h e eicjenfrequency o f t h e d i s -

-

l o c a t i o n l i n e .

A ( 0 ) B

I n Seeger's model, t h e seg- ment can be i n e i t h e r o f two c o n f i g u r a t i o n s (a) o r ( c ) . But w i t h o = 9, c o n f i g u r a t i o n

U = O ( c ) has an energy 2 !Ik g r e a t e r than t h a t o f ( a ) (see f i g . 1).

Consequently, t h e occupation p r o b a b i l i t y o f ( c ) i s v e r y s n a l l and no r e l a x a t i o n peak wi 11 be observed. The r e 1 axa- t i o n s t r e n g t h o n l y becomes ob-

(C)

X I * X servable when t h e exchange o f

d i s l o c a t i o n s between t h e two c o n f i g u r a t i o n s i s s i gni f i c a n t F i g . 1 : L e f t : schematic diagram o f a d i s l o c a t i o n ( i . e . i f t h e two c o n f i g u r a t i o n s overcoxing a P e i e r l s b a r r i e r by c r e a t i o n o f a dou- a r e e n e r g e t i c a l l y e q u i v a l e n t ) . b l e - k i n k : f r e e energy o f t h e double-kink as a func- For o # 0, t h e two c o n f i - t i o n o f k i n k s e p a r a t i o n x. g u r a t i o n s can become equal 1 y a) i n i t i a l p o s i t i o n o f t h e l i n e . b) t h e double-kink nrobable when t h e Par6 condi- i s created. c ) t h e k i n k s g l i d e along t h e l i n e . t i o n

a a b l

=

2kdk 121

i s f u l f i l l e d . When oa i s weak, t h i s c o n d i t i o n can o n l y be s a t i s f i e d by t h e i n t e r - n a l s t r e s s (ai).

This t h e o r y accounts f o r t h e p r i f i a r y c h a r a c t e r i s t i c s o f t h e BR (2) b u t f a i l s t o e x p l a i n t h e e x t e n t o f peak broadening, t h e v a r i a t i o n o f peak temperature (TFV,) w i t h microstruc'cural s t a t e and non-1 i near e f f e c t s ( s t r a i n anpl i tude dependen- ce and e f f e c t s o f b i a s s t r e s s ) . 3y i n c l u d i n g k i n k n i g r a t i o n , Engelke ( 7 ) has shown t h a t some o f these secondary f e a t u r e s can be explained. However, Esnouf and Fantozzi (3,;) have proposed a new approach t o t h e c a l c u l a t i o n o f I F caused by DKG. The energy diagram o f a segment l y i n g i n a P e i e r l s v a l l e y i s determined as a f u n c t i o n o f i t s p o s i t i o n For d i f f e r e n t values o f a and R ( f i g . 2). The a c t i v a t i o n volume ( v c ) and energy (Ec) f o r double-kink n u c l e a t i o n depend o n l y on o :

vm a = const.

C

n - 3 / 4 m = 4

K i n e t i c t h e o r y i s used t o c a l c u l a t e t h e d i s l o c a t i o n n o t i o n . The v a r i a t i o n o f t h e f r a c t i o n (nil o f d i s l o c a t i o n s l y i n g i n "Lie i - t h v a l l e y i s g i v e n by :

where t h e jump frequency from v a l l e y i t o iil i s

ri

,i+l = vR exp(-Ei ,i+l/kT) and Ei ,i+l e t c a r e as s p e c i f i e d i n F i g . 2:~he numerical s o l u t i o n o f t h e F i g . 2 : P o t e n t i a l Energy o f t h e d i s l o c a - above system, f o r an o s c i l l a t i n g ap- t i o n segment as a f u n c t i o n o f t h e number p l i e d s t r e s s , a l l o w s c a l c u l a t i o n o f

o f double-kinks. t h e area swept-out by t h e d i s l o c a t i o n

and hence t h e I F . A l l o f t h e characte- r i s t i c s o f t h e 3R a r e e x p l a i n e d by t h i s model, w i t h o u t t a k i n s i n t o account k i n k m i g r a t i o n . By o b t a i n i n g an e f f e c t i v e d i s l o c a t i o n m o b i l i t y f o r 3x6, Schl i p f and Schindlmayr ( 9 ) have obtained s i n i l a r r e s u l t s .

2.1.1 Peak h e i g h t . - For a p o p u l a t i o n o f equal segments,when t h e Pare condi- t i o n i s f u l f i l l e d , t h e i n t e n s i t y o f t h e "o v a r i e s as in w i t h n = 1 f o r s h o r t segments and n 2 f o r l o n g segr,~ents. For d i s t r i b u t i o n s o f R and oi, t h e peak h e i g h t v a r i e s as R2 f o r s h o r t serjments. !*en t h e Pare c o n d i t i o n i s i I O t s a t i s f i e d , t h e v a r i a t i o n o f peak h e i g h t i s v e r y pronounced. The exponent 2 shows t h a t t h e area swept-out by t h e segaent i s c o n t r o l l e d by t h e l i n e t e n s i o n (EL). I n a d d i t i o n , t h e r e l a x a t i o n s t r e n g t h decreases wit11 v i b r a t i o n frequency.

2.1.2

-.-

TH depends upon oi and R ( f i g . 3). It i s o n l y weakly dependent on R f o r a d i s t r i b u t i o n i n R o n l y , b u t changes s i g n i f i c a n t l y f o r d i s -

1

t r i b u t i o n s o f b o t h R and

a i .

These r e s u l t s show t h a t t h e v a r i a t i o n o f t h e pre-exponen- t i a l f a c t o r (yo) o f t h e r e l a - x a t i o n t i m e w i t h R i s given by : ^{T~ %} Rp (0 < p < 2 ) .

o The a c t i v a t i o n energy i s near

Ec (oil.

Fig.3 : V a r i a t i o n w i t h mean d e v i a t i o n i n i n t e r n a l

s t r e s s f o r d i f f e r e n t mean n o r n a l i z e d l e n g t h s Lb (LA

=

L/a) :

C5-6 JOURNAL DE PHYSIQUE

a) of the relative peak height b) of the peak temperature Ti!

(8).

2.1.3 Broadening .?actcr .- Distribution of

To

and/cr the activation energy cause peak broadening. I t can be up t o four tines -the factor for a ijebye peak. Fur- thermore, the high temperature part of the peak (aue to the longest segments) i s more developed than the r e s t of the peak.

2.1.4

Nan-1 inear effects .- The model predicts iaportant non-1 inear effects.

'!hen ai i s too snall t o s a t i s f y 'the Pare condi- tion, the peak can s t i l l develop and pass througli a maximun as the applied s t r e s s (oscillating or s t a t i c bias) increases ( f i g . 4 ) . ?!oreover, the peak s h i f t s t o lower teinperature and broadens with increasing a,. Sieilarly, the relaxation strength presents a maximm as a function

01'

ai (Fig. 3). The increase in peak height i s due to the F a r k o n d i t i on, the decrease resul t s fro^:

the reduction of swept-out area when the nunber of double-kinks increases.

Fig.

4 . :

Variation of peak height and temperature

Ti,

as a Func- tion OF aa (for L'

=

7 and a.

₁ = 0 )

(8).

2 . 2

The

GIG1

;i.lr:odel.- Geometrical kinks moving a l o n ~ close-paeked directions can be ther~lal

1

y activated over .the second order Peierl s barriers giving r i s e t o

- - - ^* . . .

an I F $ieiio;aenon as Soc~i?

by

Brails-

v a l l e

ford (10) ai~d IYithrich (11). An applied

----.----..--- ,.----.---.-.. - - -

stress csuses

GI3 ((-Fig. 5)

given

by :

---- --

-

.--

---- .---

-

---.-. --.---.

-

⁷

Y D

-

= 0 8 - b i n n

a t ^i; a,v

²

^k

^{1 5 1}

Fig. 5

:

Geor.letrica1 kink ii~otion on a

n =

Zk/kT

= vd b- 3 exp ( -

WH/kT) dislocation making an angle

Y

with a where

=

v d

=

Debye

close-packed di recti

OQ

. frec;uenc:l,

W

M

= l:ir,!<

-;ic;ratisn enercy

and nk t h e nurlber o f geometrical k i n k s per u n i t length.

S o l u t i o n o f t h e above equation y i e l d s t h e relaxa.:ion s t r e n g t h ( A ) and tiix

( T ) o f t h e I F peak :

, ,

1-1 i s -the shear codulus and A t h e d i s l o c a L i o n d e n s i t y . The RL dependence o i i s due t o bc'iiaviour analogous t o a s t r e t c h e d s t r i n g behaviour ( 3 ) .

The

GK4 model can account f o r ;lost o 3 h e 3X c h a r z c t e r i s t i c s

.

D i s t r i b u t i o n s o f R and Y! ( F i g . 5 ) l e a d t o

broaden in^

o f % 1.5. This i s due t o d i s t r i b u t i o i ~ o:

T b u t n o t t h e a c t i v a t i o n energy ( u n l i k e DKG). P.noLher i s p o r t a n t p r e d i c t i o n i s t h a t r0 (1 15 4 /v ) :or

GK!

i s cm orders o f magnitude h i g h e r than

$

⁽⁵ 132/v0) Tor DW. U n l i k e D i S , a we1 1-&Pined s t r e s s l e v e l i s n o t r e ~ u i r e d t o observe a decrease i n A when s t r e s s ( o >

:in

^Y) induces a p i l e - u p o f geometrical k i n k s .

2.3 The S-K r e l a x a t i o n . - S-K(X) r e l a x a t i o n s where X i s an i m p u r i t y i n t e r s - t i t i a l (11) a r e w e l l e s t a b l i s h e d i n t h e I F spectra o f deformed b.c.c1s. A pheno- :menological model proposed by Schoeck (12) has been used w i t h v a r y i n g degrees o f success t o e x p l a i n t h e e x p e r i n e n t a l r e s u l t s . It i s based on t h e dragging o f 1 1 ' s oy s t r i n g l i k e d i s l o c a t i o n segments ( f i g . 6a). The r e l a x a t i o n tirce (T~!,) anci s t r e n g t h (ASK) found using t h i s model f o r a d i l u t e c o n c e n t r a t i o n (Cd) o f 1 1 ' s on t h e d i s l o c a - t i o n s a r e given by :

2 2

-cSK = a kT Lo Cd exp (i-iSK/kT) ; ASK =

6

A Lo 1 7 1

and t h e r e l a x a t i o n e n t h a l p y (HSK) by : tiSK = i-16 ⁺ l-lfd '

I S

I

I n these equations, Lo i s t h e mean segment l e n g t h , H' t h e b i n d i n s u>o, t > r ( D K G ) enthalpy o f t h e 1 1 ' s t o

t h e d i s l o c a t i o n s ,

8 '

0 0 - 0 - 0 0 0

K., 0 - 0 - 0 o O < t h e m i g r a t i o n enthalpy

u>O

x0

^u.0. t<<~,. o f t h e 1 1 ' s a t t h e d i s l o -

0- 0 _ O o o c a t i o n s

( H ~

i s t h e same

0 0 ' 0 -oC

U=O q u a n t i t y i n t h e l a t t i c e )

anci a, B a r e numerical constants. When t h e cores

a = O , t = o a r e saturated, HSK redu-

a b

ces t o H ~ ' . Recently, F i g . 6 : Nodels o f t h e S-K r e l a x a t i o n : a) s t r i n g model. V e r d i n i and Bacci (13) b) double-kink generation i n t h e presence o f core-mobile have developed a m o d i f i - i m p u r i t y i n t e r s t i t i a l s. c a t i o n o f t h e model which

C5-8 JOURNAL DE PHYSIQLJE

takes i n t o account t h e d i s s i p a t i o n associated w i t h bow-out between t h e 1 1 ' s . They B

W'

show t h a t

aSK

becomes dependent on Gd (below s a t u r a t i o n ) and t h a t ?is#= 2H +H

.

Other m o d i f i c a t i o n s have been r e p o r t e d . For exaaple, Miner e t a l . (14) have shown t h a t when t h e occupation p r o b a b i l i t i e s o f t h e p i n n i n g s i t e s a r e more c o r r e c t l y t r e a t e d by Ferrni-Oirac s t a t i s t i c s , tiSK can take on values between H~

+

H~ and 2 H~ t

H"" .

Fror,~ many comparisons o f t h e p r e d i c t i o n s o f Schoeck's codel w i t h e x p e r i - ment, t h e r e i s l i t t l e donbt t h a t several aspects o f t h e nodel a r e c o r r e c t .

Seeger (4) a b b r i b u t e s S-K ( X ) t o DKG i n t h e presence o f core n o b i l e X i n t e r s t i t i a l s ( f i z . 6b). I n t h i s model, w i t h t h e e x c e p t i o n o f t h e numerical cons- t a n t s , equ. 17

1

i s unchanged, w h i l e t h e r e l a x a t i c n e n t h a l p y becomes :

HSK = 2 Hk

+

H

M'

19

I

where 2 tik i s t h e f o r m a t i o n e n t h a l p y o f a k i n k p a i r . E i r t h (5) c o n s i d e r i n g t h e s p e c i a l case o f S-K(H) i n a-Fe, has developed a s i m i l a r nodel f o r t h e case o f near s a t u r a t i o n . He f i n d s

6 112

HSIc = 2 Hk t HM1

-

(vo b /219 110

1

A t t h e s t r e s s l e v e l s normally i n v o l v e d eqns

/

S

I

and

1

13

1

become p r a t i c a l l y iden- t i c a l . However, t h e l a s t t e r n does g i v e an e x p l i c i t dependence on a (and hence ui) which can account F o r t h e broadening o f t h e S-S peaks. The most i m p o r t a n t p o i n t t o e s t a b l i s h i s which o f t h e p r e d i c t i o n s , eqn. 16

1

( o r i t s m o d i f i c a t i o n s ) o r eqn. 19

1

( o r 115 I) cones c l o s e s t t o r e p r e s e n t i n g thei'experimental values o f tiSK.

3. Important Experimental Results.- Our t a s k i n t h i s s e c t i o n i s t o examine t h e i m p o r t a n t experimental r e s u l t s on t h e i n t r i n s i c r e l a x a t i o n s o f d i s l o c a t i o n s i n me- t a l s and t o t r y t o i n t e r p r e t them w i t h the inodels o u t l i n e d i n s e c t i o n 2. Results p u b l i s h e d up t o t h e time o f the Manchester conference (1579) have been reviewed r e c e n t l y ( 3 ) , so we w i l l concentrate m a i n l y on more r e c e n t r e s u l t s .

3 . 1 F.C.C. and H.C.P. metals.- The

ER

i n these metals i s u s u a l l y conposed o f two I F peaks : 6, ( t h e W i b l e t t and Wilks peak) and Bz ( t h e Bordoni peak

.

^{I n}

metals o f o r d i n a r y p u r i t y t h e BR i s n o t observed i n annealed specimens and o n l y appears a f t e r p l a s t i c deformation. I n u l t r a h i g h p u r i t y (UHP) samples, t h e BR i s always observed, even a f t e r r e c r y s t a l l i z a t i o n , b u t depends s t r o n g l y on t h e a p p l i e d s t r e s s . This i s shown on f i g . 7 f o r Pb (15) and on f i g . 8 f o r Ag (16). Thus t h e disappearance o f t h e BR i n non-UHP metals a f t e r r e c r y s t a l l i z a t i o n i s n o t due s o l e l y t o t h e decrease i n A b u t a l s o t o p i n n i n g by i m p u r i t i e s . T h i s shows t h a t t h e BR can o n l y be a t t r i b u t e d t o t h e i n t r i n s i c p r o p e r t i e s o f d i s l o c a t i o n s , i . e . GKM and/or DKG.

F i g . 8 : E v o l u t i o n o f t h e RR d u r i n g r e c r y s - t a l l i s a t i o n a t 20C°C i n GN s i l v e r c o l d - r o l l e d 6% a t 20°C

( %

⁼ 2.5 x : 1,O.n; 2,10mn;

3, 30nn; 4, 60 mn; 5,122mn; 6 , 840mn (16).

F i g . 7 : E v o l u t i o n o f t h e BR i n Pb : 1, unannealed; 2, annealed a t C70K;

3, a t 550K (15).

3.1.1 Deak height.- The peak h e i g h t v a r i e s w i t h i m p u r i t y content, c o n d i t i o n s of p l a s t i c deformation, annealing and i r r a d i a t i o n . This v a r i a t i o n i s l i n k e d t o t h e e v o l u t i o n o f R and i s o f t h e form gr w i t h 1

6

r

&

2.

3.1.2 Peak tenperaSture.- The peak teraperature v a r i e s s l i g h t l y w i t h t h e mi

-

c r o s t r u c t u r a l s t a t e and i s caused e s s e n t i a l l y by a dependence o f T on R ( c k S w i t h s l y i n g between 1 and 4) (3,17). This v a r i a t i o n e x p l a i n s t h e l a r g e d i s p e r s i o n o f the data i n ,Arrhenius p l o t s .

3.1.5 Broadening f a c t o r . - The peaks a r e g e n e r a l l y

tvo

t o four times broader tnan a Jebye peak, i . e . -r i s d i s t r i b u t e d . They a r e broader f o r small amounts o f p l a s t i c defor;!ation,witl~ t h e increase i n w i d t h ?ore pronounced on t h e h i g h tenpera- t u r e s s i l e s . I n c o n t r a s t , annealing decreases t h e \:id",~s by r e d u c i n ~ t h e h i y h tem- p e r a t u r e sides p r e f e r e n t i a l l y . This asyrr7etry i n t h e r e L u c t i o n O F t i l e w i d t h i s shown by t h e d i f f e r e n c e s i n t h e I F curves f o r s l i g h t l y deformed A1 i n f i g . 9 ( 18)

-

C5-10 JOURNAL DE PHYSIQUE

Fig. 9 : the d i f f e r e n c e 6n

-

6n+l between t h e curve obtained d u r i n g t h e l i n e a r warm- up, n, and t h a t obtained d u r i n s t h e l i n e a r warc-up, n + l

,

a f t e r f l e x u r a l aeformation o f O.2 % a t 83 X ( n = 3, annealing temperature T R = 222 K; n = $, T _R = 24; K; n = 5,

T 2 =

205 K; n = 6 , T - 316 S). The s h o r t arrow

2

-

i n d i c a t e s t h e peak temperature o f _Z2, w h i l e t h e l o n g arrow i n d i c a t e s t h e texpera- t u r e o f t h e oaximum o f 6,

-

6n+l ( 1 8 ) .

3.1.4 Non-Linear E f f e c t s . - When oi i s s i g n i f i c a n t ( a f t e r 1ar:e p l a s t i c defamation), oa has l i t t l e e f f e c t ( f i ~ . 1,;). However, f o r weak oi

A a-lx l o "

I

^{l a}

^I

F i g . 10. : I n t e r n a l f r i c t i o n i n g o l d colci-worked 7 Z a t 23°C : a ) a f t e r d e f o r n a t i o n , b) a f t e r annealing 60 n i n a t 35C°C. O s c i l l a t i n c s t r a i n amplitude : ( 1 ) c m = 4 x 1 0 - ~ ,

( 2 ) I ~ X ~ C - " ( 3 ) 5 ~ 1 3 - ~ ' ( 4 )

~ x I o - ~ . c ) I n t e r n a l f r i c t i o n i n g o l d cold-worked 62 % and a n n e a l e ~ 60 min a t 1GS0C.

( 1 ) = ?x~;-7, ( 2 ) 1 . 5 ~ 1 0 - , ( 3 ) O X ~ O - ~ , ( 4 ) 1 . 5 x 1 0 - ~ (14).

i m p o r t a n t n o n - l i n e a r e f f e c t s are observed ( F i g . I C ) . : t h e r e l a x a t i o n s t r e n g t h de- pends s t r o n g l y on

%

( p e r i o d i c o r s t a t i c ) . S i r i l a r r e s u l t s have been observed by many authors ( 3 ) . The BR i n t e n s i t y increases considerably w i t h the vibra" ~ 1 0 n an- p l i t u d e o r s t a t i c s t r e s s . Moreover, t h e rezoval o f t h e BR d u r i n g recovery o r r e - c r y s t a l l i z a t i o n i s caused by a decrease o-f oi. I n soae cases, t h e peak h e i g h t pas+

ses through a naxir~um as a f u n c t i o n o f t h e s t r a i n amplitude. I n

MQ,

s i y n i i ' i c a n t non- l i n e a r e f f e c t s are observed a f t e r p l a s t i c deformation when o n l y one s l i p system i s a c t i v a t e d (20). As shown i n f i ~ . 11, t h e peak h e i g h t s o f both B1 and S2 pass through a maxieurfi as t h e superimposed b i a s s t r e s s i s increased.

F i g . 11 : V a r i a t i o n s o f t h e peak h e i s h t s o f as a f u n c t i o n o f b i a s s t r e s s

-

⁶ as ) ; 1, o = 0; 2, o =8x10 11; 3,

-5

s

-5 s -4

as = 2x10 11; 4, o s = 5 x 1 0 11; 5, _S = 1 0 11.

6 i and 3; : a f t e r s u b s t r a c t i o n o f t h e back- ground (2C).

3.1.5 Lgw T e ~ p e r a t u r e Modulus Defect.- I n b o t h f . c . c B s and h.c.pls, t h e r e i s a modulus d e f e c t a t ter3peratures lower t h a n t h e 6R. Consequently, SZ?, on a t l e a s t one o f t h e d i s l o c a t i o n types, must be reserved t o e x p l a i n t h i s phenonenon.

3.1.5 D i s l o c a t i o n types.- Seeger (2) proposed t h a t non-screw d i s l o c a t i o n segments ( 1 ' s ) g i v e r i s e t o B1 and screws ( 0 ' s ) g i v e r i s e t o B2, since t h e P e i e r l s energy f o r 0 ' s i s I i i g l i e r than t h a t f o r 1 ' s . T h i s i s supported by obser- v a t i o n s t h a t Bl i s qore s e n s i t i v e t o p i n n i n g by p o i n t d e f e c t s than B2. However, r e c e n t e l e c t r o n nicroscopy s t u d i e s by Lauzier and i i n i e r (21) suFport an e a r l i e r hypothesis o f Thompson and tlolr!es (22),

i

.e.

31 i s associated w i t h 90' and 30' d i s l o c a t i o n s l y i n g along <112> d i r e c t i o n and 52 i s associated w i t h 60° and screw d i s l o c a t i o n s l y i n g a l o n ~ < I 1 9 d i r e c t i o n . The 0 ' s are r e s p o n s i b l e :or t h e h i g h t e o p e r a t u r e component of B2 whereas t h e 6C0 d i s l o c a t i o n s a r e r e s p o n s i b l e f o r t h e low t e c ~ p e r a t u r e co,lponen'i. T h i s hypothesis a1 locrs us t o e x p l a i n t h e v a r i a t i o n of

C5-12 JOURNAL DE PHYSIQUE

the peak tenperature during i r r a d i z t i o n o r annealing (21) an3 also accounts f o r the two peaks

X

and

Y

observed in deformed Ni (23)

:

peak

X

may be the analogue of anci

Y

the analogue of

B1.

Besson (23) proposed t h a t

Y

was caused by dissociated forns of the sane dislocations responsible f o r

X.

The Thonipon and Holmes hypothesis i s more plausible and does not necessitate the assunption of an increase in dissociation with p l a s t i c deforsation. Nevertheless, the r d l e of stac- king f a u l t energy i n the BX remains t o be elucidated. In Wg, Seyed-Reihani (20) has shown t h a t r e s u l t s lead t o a conclusion i n keeping with Thonpson and Holmes hy- pothesis a l s o .

3.1.7 Comment.- Although the

BR

has been observed in several h . c . p l s , only i n

UKP Mg

(26) have 31 and

B2

peaks

w i t h

properties conparable t o those i n t h e f . c . c ' s been reported. We conclude t h a t f . c . c l s and h.c.p's behave s i m i l a r l y ( 3 ) . Iievertheless, f u r t h e r studies on other

UHP

h . c . p l s will be necessary t o confiri3 t h i s point.

3.1.8 Interpretation.- Only the

DKG

model accounts f o r a l l of the experimen- t a l c h a r a c t e r i s t i c s of the

32

as can be seen fron a d i r e c t conparison of sections 2.1.1. t o 2.1.<.. w i t h sections 3.1.1. t o 3.1.4. Nevertheless, the value of a ob-

4

P

tained fror?, the relaxation enthalpy of the

BR

-

^10-

p) i s considerably grea- t e r than t h a t predicted from p l a s t i c behaviour and so, the

DXG

node1 f o r the

ER

i s s t i l l contested (3,17). Two r e l a t i v e l y new types of experirient a l s o support the

CXU

model. F i r s t l y , neasurexents of ultrasonic attenuation a t very low

temperatures

de:.ionstrate

GKFl

(24)

:

the attenuation decreases as the bias s t r e s s increases ( f i g . 12). This " s t i f f e n i n g " phenonenon i s due t o the pile-up of geometrical kinks

in response t o the bias

- .

_a

-

_•

s t r e s s (25). In the tenpe-

\ 0 \ a

r a t u r e range of the

ER,

4 K 1 9 ~ 55K 105K

4

1 5 1 ~

dislocation segoents sur-

nount the P e i e r l s b a r r i e r s and the attenuation in-

- _creases

_{w i t h}

bias s t r e s s

Fig. 12

:

Variation of attenuation versus s t r e s s a t ( f i g . 12). So.2e d i f f e r e n t d i f f e r e n t t e s t i n g temperatures in A1 ( 2 4 ) . r e s u l t s were reported re- cently (26)

b u t

remain t o be confir~ied. Secondly, a thermal l:f activated microdefor~iation stage (3,27) associa- ted with the

9k

has been observed i n A1 , Au and

Mg

( f i g . 13) tosether with a va- r i a t i o n i n t h e a n e l a s t i c l i m i t (27).

A

q u a n t i t a t i v e analysis of these r e s u l t s y i e l d s an activation energy of

%

0 . 1 eV and a voluae of %1OC

b3

e n t i r e l y in keeping with the

DKG

model ( 2 7 ) .

In conclusion, the experisjental r e s u l t s strongly support the existence of a

Peierls-Nabarro s t r e s s in the f.c.c and h.c.p metal of t o p.

Fig. 13

:

?licrodeforr4iation (an6 derivative curve) as a function of temperature f o r a 6N gold sam- ple, deforned

0.7 %

in torsion a t

,7-\

10

K

and annealed a t 150 K

:

( a )

with a s t a t i c s t r e s s

a =

5x10

-4

, ( b ) a f t e r suppression of the s t r e s s a t 10

K ( 3 ) .

0 020 40 80 80 lo0 0 50 100

r e s u l t s f o r a deformed s i n g l e c r y s t a l of Ta (33) a r e shown i n f i g .

15

where the IFS i s resolved i n t o

7

compo- nent peaks with only one of them a t t r i b u t e d (by the authors) t o 3.2 B.C.C. Heta1s.- The i n t r i n s i c dislocations relaxations i n the b . c . c l s a r e of special i n t e r e s t because the mobilities of y s and 0 ' s a r e such t h a t the analogue of the Bordoni relaxation i s s p l i t i n t o two well-separated peaks (28,29)

:

a low temperature peak associated with

DKG

(L) and a peak a t a much higher tercpera- t u r e associated with DkS ( 0 ) . Moreover, geometrical kinks on 0 ' s a r e expected t o be r a t h e r abrupt ( e f f e c t i v e l y high second order Peierls b a r r i e r s (33)) so t h a t

GKF4

( 0 ) should f a l l i n t c a tenperature range close t o t h a t f o r

^DKG

(I). As in the case o f the .F.c.cls,

GR4

(I) i s expected t o occur a t very low temperatures

( < 4 K)

and manifest i t s e l f as a modulus defect a t the lowest temperatures investigated.

These expectations seem t o be realized

i n

Ho,

fJ

and a-Fe as typified by t h e IFS of a deformed s i n g l e crystal o f Mo (31,32) in f i g . 14. In c o n t r a s t , i n

V ,

Nb

and Ta ( a l s o a-Fe + H ) the IFS i s characteri-

t h e i n t r i n s i c disloca-

100 200 300 400 500 600 T ( K )

tion processes discus-

sed above; t h e others Fig.

14 :

Internal f r i c t i o n spectrum of a deformed crystal a r e a t t r i b u t e d t o the of Mo. P l a s t i c a l l y strained 1

%

a t 200

K

+ a small additio- interactions of dislo- nnal p l a s t i c s t r a i n i n torsion a t 295

K

(31). cations with 1 1 ' s .

Q-'

~ 1 0 ~ Molybdenum

-

ci t 1001

RRR = 7357 T

zed by a l a r g e r number

of peaks. Typical re-

JOURNAL DE PHYSIQUE

SNOEK-KOSTER RELAXATION

S.K.P.

71 7'2

Most of the differen- ces between the f.c.cls and b.c.ci s can be t r a - ced t o the strong interactions between residual 11's (H,

N ,

0 o r

C

atoms) with the dislocations in b.c.c1s. In f a c t , these i n t e r a c t i o n s can lead t o diametri- c a l l y opposed changes i n properties, e.g.

Fig. 15: Internal f r i c t i o n spectrum of a deformed single crys- hardening through t a l of Ta. Deformation history

:

3.1

%

t e n s i l e s t r a i n a t the interactions of 375K + 0.5

%

t e n s i l e s t r a i n a t 200K +. a small additional plas- 11's with 1 ' s and t i c s t r a i n i n torsion a t 295K (33). softening through

t h e i r interactions with 0 ' s ( s e e review by Pink and Arsenault ( 3 4 ) ) . The presence of t r a c e amounts of H in deformed

V ,

Nb and Ta samples has led t o a controversy over the i n t e r p r e t a - tion of the IFS i n these metals which has been resolved recently.

3.2.1

A

Controversy Resolved.- The IFS of deformed

V ,

Nb or Ta i s general- l y characterized by a group of relaxations i n the range 120-200K ( e - g . f i g . 15) l a - belled

or

by most workers (35,36). However, a peak labelled

6 ,

a t even lower tem- peratures, i s observed i n some samples (35,37). As suggested by Bruner ( 3 8 ) , the Rome school (35,37). has argued t h a t

a

requires the presence of both

H

and d i s - locations and t h a t

S

can be a t t r i b u t e d t o i n t r i n s i c dislocation processes. This i n t e r p r e t a t i o n was contested by the S t u t t g a r t School who studied samples with consi- derably lower I1 concentrations and observed neither

6

nor any indication of d i s - location movement below

a,

leading them t o a t t r i b u t e

a

t o i n t r i n s i c dislocation processes. Nevertheless, over the l a s t few years, evidence t h a t a involved H began t o accumulate

:

notably from Shibata e t a l . (39) and Mizubayashi e t a l . (40) f o r V , Ferron e t a l . ( 4 1 ) , Kuramochi e t a l . (42) and Verdini and Bacci (43) f o r Nb and Rodrian (33) f o r Ta. Yet, no explanation f o r the absence of

6

i n samples with lower I1 ( p a r t i c u l a r l y 0) contents was offered. More recently, work on UHP Nb (31, 44, 45) has demonstrated t h a t a involves H and t h a t the major component can be a t t r i b u t e d t o an S-K(H) relaxation (43). In the highest purity samples

(CH

<< 1

a t . p.p.m,

Co <

5 a t . p.p.m), the work a t S t u t t g a r t (31, 44, 45) has shown

t h a t another peak appears below a ( % 70 K a s shown i n f i g . 16). B u t , i n order t o

completely s e t t l e the controversy, i t i s necessary t o show t h a t the 70 K peak i s

equivalent t o

6.

In an attempt t o do t h i s , Maul (45) repeated measurement on sam-

p l e s doped w i t h 0 and H (Co = 800

-

1000 a t , p.p.m and CH = 20

-

30 a t . p.p.m).

The r e s u l t s a r e shown i n F i g . 17 and compared d i r e c t l y w i t h 6 (35).

It i s c l e a r t h a t i n doped Nb t h e r e i s a peak % 30 0 which i s Nb 7011 e q u i v a l e n t t o 6. A sug-

7 8 9 10 C.< 5 atpprn

F 3 1.5 kHz T -20K

gested e x p l a n a t i o n o f these r e s u l t s l i e s i n t h e t r a p p i n g o f m o b i l e H a t immobile 0 ( o r N) so t h a t t h e number o f H atoms a v a i l a b l e t o deco- r a t e t h e d i s l o c a t i o n s i s reduced, a1 lowing t h e i n - t r i n s i c mechanisms t o be revealed i n l e s s pure samples (44, 45). However, F i g . 16 : I n t e r n a l f r i c t i o n o f a s i n g l e c r y s t a l o f Nb we do n o t regard t h e equi- a f t e r a thorough degassing (CH << 1 a t . p.p.m) and de- valence o f t h e 30 K ( 6 )

f o r m a t i o n a t 20 K (45). and 70 K peaks as having

been demonstrated conclu- s i v e l y . Since 6 i s ob-

1

served o n l y i n t h e presen- ce o f s i g n i f i c a n t q u a n t i -

0

-

t i e s o f 0 ( o r N), we

-

X

i=l suggest t h a t 6 i s pre-

dominantly GKM ( 0 ) and 0.5

-

t h a t DKG ( l ) , which i s predominant i n t h e 70 K peak, i s pinned-out. T h i s i s supported by f o u r t y -

,

/ pes o f o b s e r v a t i o n : i)

0 - I I I

-

0 100 200 300 a s h i f t as l a r g e as 70 K

f (K)

-

t o 30 K i s n o t observed F i g . 17 : I n t e r n a l f r i c t i o n i n a doped Nb s i n g l e c r y s - i n c o n t r o l l e d p i n n i n g ex- t a l (Co = 800

-

1000 a t . p.p.m)

.

^1, a f t e r deformation 2 periments, where t h e a f t e r H charging t o CH = 20-30 a t . p.p.m; 3, r e s u l t s s h i f t f o r an e q u i v a l e n t o f Mazzolai and Nuovo (35,45). r e d u c t i o n i n peak h e i g h t

i s o n l y 5-6 K (35,3);

i i ) t h e r e l a x a t i o n parameters of 6 a r e more c o n s i s t e n t w i t h GKM ( 0 ) than DKG ( 1 ) ( s e c t i o n 3.2.4); i i i ) r e s u l t s on thoroughly outgassed V (40) appear t o e x h i b i t b o t h

~ 5 - 1 6 JOURNAL DE PHYSIQUE

peaks i n t h e same spectrum, w h i l e t h e h i g h e r temperature peak i s absent i n samples outgassed t o a l e s s e r e x t e n t ; i v ) a ( a t t r i b u t e d t o DKG

(1)

^{i n cc} -Fe)cannot be gene- r a t e d i n t h e presence o f o n l y % 2 0 a t . p.p.m o f C o r N (46).

3.2.2 S-K (H) Peaks.- I t i s i n t e r e s t i n g t o examine t h e p r e d i c t i o n s o f t h e models o u t l i n e d i n s e c t i o n 2-3 f o r t h e case o f t h e S-K (H) i n a-Fe : i ) because i t i s t h e most thoroughly i n v e s t i g a t e d S-K (H) and ii) because i t i s s i m i l a r i n most respects t o t h e S-K (H) ( l a b e l l e d a) i n V, Nb and Ta. To check t h e v a l i d i t y o f eqns 18

1

and 19

1

we must compare t h e experimental values o f HSK ( r a n g i n g from 0.11 t o 0.33 eV) (47-50) w i t h ~ ~

+

^{H ~ '} ( and 2 H k ( l ) 1

+

^H". Fmm s t u d i e s of peak a i n Fe, 2 Hk

(I)

i s i n t h e range 0.04 t o 0.06 eV (48, 50, 51), w h i l e t h e most probable value o f H

B (L)

i s 0.61 eV (52). Whether we take HM' = HM ( f o l l o w i n g Seeger ( 4 ) ) o r H ~ H 12 ( f o l l o w i n g H i r t h ( 5 ) ) , since t h e values o f H~ curren- M ' ~ t l y advocated by v a r i o u s reviewers l i e i n t h e range 0.042 t o 0.069 eV (53,54), no combination o f t h e data seems t o be c o n s i s t e n t w i t h e i t h e r t h e Schoeck model, eqn.

181, o r t h e Seeger o r H i r t h models, eqn. 191, unless t h e lower bound o f HSK (found i n a s e r i e s o f magnetic a f t e r - e f f e c t s t u d i e s o n l y ) i s compared w i t h t h e upper bound o f 2 Hk

(I) +

HM' as p o i n t e d o u t by KC e t a l . (49). We suggest t h a t t h i s v e r y unsa- t i s f a c t o r y s i t u a t i o n a r i s e s because 2 Hk

(I)

i s e f f e c t i v e l y increased i n t h e p r e - sence o f H. This i s c o n s i s t e n t w i t h t h e v i e w p o i n t expressed by H i r t h (5) who a t t r i - butes t h e S-K (H) i n Fe t o a combination o f hardened 1 ' s and softened 0 ' s .

3.2.3 C l a s s i f i c a t i o n o f t h e I F Peaks.- From t h e above, i t i s c l e a r t h a t the l a b e l l i n g o f t h e peaks i n t h e IFS o f a deformed b.c.c. has become confusing.

We propose t h a t t h e l a b e l l i n g should be m o d i f i e d i n t h e manner shown i n t a b l e 1 t o r e t a i n as much o f the t r a d i t i o n n a l c l a s s i f i c a t i o n scheme (3) as p o s s i b l e , y e t t o r e f l e c t t h e mechanisms involved, r a t h e r than simply t h e temperature ranges i n which the peaks occur.

3.2.4 Other Recent Experimental Results.- From f i g . 14, i t i s c l e a r t h a t i n UHP deformed b.c.c's t h e IFS c o n s i s t s o f a low temperature group o f peaks and a h i g h temperature peak. The low temperature group i s g e n e r a l l y a t t r i b u t e d t o one o r b o t h o f t h e a l ( 0 ) and a processes; t h e h i g h temperautre peak i s a t t r i b u - t e d t o t h e y process. I n t h e f o l l o w i n g , we r e f e r t o them p i m p l y as al/a and y r e s p e c t i v e l y . Evidence f o r t h e presence o f a t l e a s t two d i s c r e t e r e l a x a t i o n s i n a ' l a c o n s i s t s o f t h e marked asymmetry o r shoulder which appears on t h e low tempe- r a t u r e s i d e o f t h e peak and a corresponding step i n t h e modulus curve. Four such steps have been r e p o r t e d f o r t h e lowest temperature peak i n V ( 4 0 ) . T h i s i s sirni- l a r t o t h e stepped modulus curves associated w i t h t h e BR ( 3 ) .

a ) R e l a x a t i o n Parameters.- A c t i v a t i o n parameters from t h e peak s h i f t o f a ' l a w i t h frequency f a l l i n t o two groups : f o r V (37), Nb (43,55) and Ta (35) t h e a c t i - v a t i o n energy f a l l s i n t h e range 0.012 t o 0.047 eV and t h e pre-exponential f a c t o r f a l l s i n t o t h e range t o 2 x 1 0 - ~ s ; f o r Mo (3,32),

W

(3) and a-Fe (51,46), t h e

e q u i v a l e n t ranges a r e 0.04 t o 0.29 eV and 1 . 4 x 1 0 - ' ~ t o 5x10-1°s. The f i r s t set, i .e. t h e o l d 6 peaks, seems t o be c o n s i s t e n t w i t h GKM ( 0 ) ; w h i l e t h e second s e t seems t o be more c o n s i s t e n t w i t h DKG

(I).

^{I t} w i l l be i n t e r e s t i n g t o see how t h e r e l a x a t i o n parameters o f t h e r e c e n t l y discovered 70 K peak i n Nb and t h e 57 i n V compare w i t h those o f t h e o l d 6 peaks.

TABLE 1

CLASSIFICATION SCHEME FOR THE I F PEAKS I N DEFORMED BCC METALS

.

R e l a x a t i o n parameters so f a r obtained f o r t h e y peaks i n Nb (56), Ta (33), Mo(32) W(3), a-Fe (46,57,58) a r e a l l e n t i r e l y c o n s i s t e n t w i t h DKG ( 0 ) . The y peak narrowness and i n s t a b i l i t y i s taken i n t o account by a model proposed by AstiC (58). I n t h i s model. t h e O's move by thermal a c t i v a t i o n i n t h e i n t e r n a l s t r e s s f i e l d and t h e d i s l o c a t i o n segments change from an i n i t i a l s t r a i g h t p o s i t i o n

towards a bowed-out position. During t h i s motion, t h e screw p a r t o f t h e d i s l o c a t i o n decreases and t h e y peak disappears. This model gives a good d e s c r i p t i o n o f t h e y behaviour i n b.c.cls.

NEW LABEL a' ( 1 )

a; ( 0 )

1

^{a l / a}

a i i = 1,2,3

Y ( i

Bi

(1)

fii ( @ I S-K' (X), S-K' ( X , l ) S-K (X), S-K (X,O) (X = H, 0, N o r C)

B,(X) 2 BY(x) PROCESS

INTRINSIC

1

^GKM

⁽¹⁾

DISLOCATION GKM ( 0 )

LOW TEMP. DKG (1)

INTRINSIC

DISLOCATION DKG (0)

1

HIGH TEMP.

INTRINSIC INTERACTION EXTRINSIC INTERACTION CORE-MOBILITY

EXTRINSIC INTERACTION IMMOBILE PINS

OLD LABEL1S) a'

a ' a2 a (Mo, W, Fe) 6 (V, Nb, Ta) 57 K (V) 70 K (Nb)

Y. Y1 Y2

B ~ , i = 1 , 2, 3

a (V, Nb, Ta) C.W.P.

S-K 'i

'i

C5- 18 JOURNAL DE PHYSIQUE

b) Conditions of P l a s t i c deformation.- Studies of the amount and temperatu- r e of p l a s t i c deformation on the a ' / a and y peaks, p a r t i c u l a r l y i n Mo (32,59),

W

(77) and a-Fe (58, 60) indicate t h a t a major component of a ' l a i s due t o 1 ' s and t h a t

y

i s due t o 0 ' s . In a-Fe the e n t i r e a ' / a complex i s a t t r i b u t e d t o

DKG

(1) ( 6 0 ) , which suggests t h a t the apparent s t r u c t u r e of a ' l a i s due t o the presence of several types of t s with nearly equal mobilities.

c ) Effects of Impurities.- In a-Fe, the interaction of 11's (other than H ) w i t h 1 ' s gives r i s e t o 6, (60,61). Similar peaks a r e expected i n t h e other

b . c . c l s but i n

V , Nb

and Ta they a r e probably inhibited by t h e i n t e r a c t i o n s of 0 (or

N ) w i t h

residual

H,

o r masked by the

S-K ( H )

relaxation. Extra interaction peaks a r e observed i n the r e s u l t s of Rieu

(59)

on single c r y s t a l s of Mo and

W .

Of these, the peak labelled B2 by t h e author i s a t t r i b u t e d t o the i n t e r a c t i o n of dislocations w i t h unspecified impurities. In Nb (62) and Ta ( f i g . 1 5 ) , the two components yl and y2 t h a t a r e candidates f o r

DKG ( 8 )

behave d i f f e r e n t l y

i n

the presence of 11's. I t has been reported t h a t i n Nb

yl

requires the presence of 0 (62), whereas in Ta, y2 requires the presence of 0 (33). In Fe, By (60, 61) seems t o require the presence of

C

( o r N). I t i s probable, t h a t i n a l l the b . c . c l s of suf- f i c i e n t l y high p u r i t y

y

i s a symmetric s i n g l e peak ( s e e f i g .

14

f o r Mo). In subs- t i t u t i o n n a l Fe a l l o y s , Asti& (58) has observed two peaks c a l l e d yI and y I I

( f i g . 18)

:

yI appears around 230 K and y I I a t about 320 K. For d i l u t e a l l o y s ,

yI

and

yII

appear together whereas f o r concentrated alloys only

y I

appears.

The behaviour of these two peaks i s q u i t e similar t o t h e

y

peak in pure iron.

Fig. 18

:

Internal f r i c t i o n spectra of Fe-Ti alloys predeformed 5 % a t 300 K

then deformed a t 120 K

:

influence of T i concentration (58).

The

YI

peak i s associated t o

DKG

on softened 0 ' s and the activation enthalpy measured from IF experiments i s i n good agreement w i t h the values deduced from p l a s t i c i t y behaviour

(58).

The yII peak i s due t o DKG on normal 0 ' s .

d ) Effects of I r r a d i a t i o n . - Low temperature, low dose i r r a d i a t i o n s of prede- formed b . c . c l s produce similar changes t o the IFS a s low temperature deformation.

Both create i n t r i n s i c point defects which i n t e r a c t with the dislocations and give r i s e t o interaction peaks analogous t o the Hasiguti peaks i n the f . c . c l s

( 3 ) .

The most detailed study of a deformed and i r r a d i a t e d b.c.c. i s the study of a-Fe re- ported by the Grenoble group (46, 60, 61). The evolution of the IFS a f t e r 20K

electron i r r a d i a t i o n i s shown i n f i g . 19 and the r e s u l t s of

fflxlos

experiments comparing the l ow

SPECTRULI AFTER ANNEAL AT I 77 K 2 1 5 0 K

3 18OK

temperature i r r a d i a t i o n w i t h

4 220K

s 2 6 0 K

deformation a r e summarized i n

f i g . 20. Generation of i n t r i n - s i c point defects a t low tem- peratures suppresses a 1 / a and generates

B1.

After an- nealing i n stage I11 of t h e recovery of e l e c t r i c a l r e s i s - t i v i t y , the dislocations which give r i s e t o a ' / a a r e

o SO 100

cleaned of t h e i r i n t r i n s i c

point defects and

a 1 / a

reap- Fig. 19

:

Evolution of the internal f r i c t i o n spec- pears. By following changes t r u m of deformed and electron i r r a d i a t e d (20 K) i n the relaxation i n t e n s i t y a-Fe during successive anneals (60,61). and peak temperature of a ' / a

and B1 during anneal i ng , stages s i m i l a r t o those observed i n t h e recovery of r e s i s t i v i t y can be observed, allowing the IFS t o be used as a sensitive tool in the study of radiation damage.

In

Nb

and Ta, i t i s apparent t h a t the interaction of t r a c e s of H with vacancies leads t o f u r t h e r complications (33,45).

Effects of i r r a d i a t i o n on y have not been studied in any d e t a i l .

A

second interaction peak, By, i s observed a t temperatures j u s t below y i n a-Fe (46).

I t i s a t t r i b u t e d t o the dragging of a s e l f - i n t e r s t i t i a l - t y p e defect by geometrical kinks on 0 ' s .

e ) Low Temperature Modulus Defect.- Changes i n the dynamic e l a s t i c moduli a t very low temperatures have been reported in

V ( <

6K) (401,Nb

(<

15K) (45), Ta

(<

209 (33) and a-Fe

(<

4K) (60). These r e s u l t s are generally attributed t o a 1 ( 1 ) ( i .e.

GKM(1) )..However, i n Fe there i s some evidence t h a t

GKMaO)

may be involved as well (60).

C5-20 JOURNAL DE PHYSIQUE

f ) Effects of Oscillation Amplitude and Bias Stresses.- In the Nb single c r y s t a l s ( 4 2 ) , a l / a increases i n i n t e n s i t y with increasing s t r a i n amplitude.

In a-Fe, s t r a i n ampli-

o;l

.lo3

tude dependence occurs

r e s u l t s a r e e n t i r e l y Fig. 20

:

Evolution of the a l / a + B1 complex in defor- consistent with

DKG

(I) med a-Fe following electron i r r a d i a t i o n o r supplemen- and

DKG (0)

respectively.

t a r y cold-work a t

77 K

(60,61) o r a f t e r neutron i r r a d i a - Increasing s t r a i n am-

t i o n a t

77 K

(46). plitude causes the inten-

s i t y o f

y

i n Nb t o increase (62) and bias

8.10~

s t r e s s e s increase the

PO

high temperature back-

ground. These r e s u l t s a r e analogous t o those reported f o r the Bordoni relaxation ( 3 ) .

g) Microdeformation. -

Microdeformation stages

0 BOO I W Tx 0 roo zW TI 0 a s o ,.

associated w i t h a l / a

2

I

0 .

( a ) (b) ( c ) (see f i g . 21) and

y

Fig. 21

:

( a )

IF

peaks a 1 / a and 8, in Fe a f t e r 2

%

(58'65) have been

deformation a t RT. (b) Microdeformation cycle

: AB,

loa- ted recently. The results ding t o os

=

6 x l 0 - ~

; BC

heating under s t r e s s ;

C D ,

coo- obtained using a torsion ling under s t r e s s ; DE,unloading; EF, recovery without pendulum technique can s t r e s s ; ( c ) Derivative curves of the a 1 / a stage

:

be summarized a s follows

1

os

=

3 x l 0 - ~ ~ ; 2 os

=

6 x 1 0 - ~ ~ (64).

i)

the activation volume associated with

a

i s

i n the range 10 t o 100b3

0 100 150 200 250 300 350

T( 10 ^%

50 b3 f o r

y.

These

-

^a-F*

_{4 4}

_{+ d ' ~ a*&}

/-

,

i

/" \.

i \

\.

;

I'

..- -

ELLCTROMS

i

-

ⁱ I _UW

TENP,

-. --__

a t 5 x 1 0 - ~ even a t 4K and increases with i ncrea- sing temperature (61,63).

Recent studies of the

s t r a i n amp1 i tude depen-

dence associated

w i t h

a l / a and

y

in M o s i n -

g l e c r y s t a l s (32) y i e l d

activation volumes of

30-150

b

3 f o r the major

component of

a l / a

and

i n keeping w i t h DKG

(b;

ii) a s u b s t r u c t u r e corresponding t o a' i s observed b u t has n o t been analysed i n d e t a i l ; i i i ) t h e recovery stage (ar) (see f i g . 20) ( b ) ) i n t h e absence o f s t r e s s i s always a t a lower temperature than stage a; i v ) a micro- deformation stage i s a l s o associated w i t h 6, b u t i t s c h a r a c t e r i s t i c s are such t h a t i t i s n o t amenable t o t h e same t y p e o f a n a l y s i s used i n t h e case o f stage a;

and v ) t h e stage associated w i t h

Y

(58,65) can be c o r r e l a t e d w i t h t h e z e r o - p o i n t - d r i f t o f t h e pendulum i n conventional s t u d i e s o f t h e I F peak y and t h e r e s u l t s c o n f i r m t h a t 0 ' s a r e r e s p o n s i b l e f o r b o t h t h e microdeformation stage and peak y.

Furthermore, t h e model proposed by A s t i e e t a l . (65) (see 3.2.4. a) can a l s o descri- be t h e y microdeformation i n b.c.cls.

The I F peaks a ' l a and y ( a t

=

1 Hz) a r e i l l u s t r a t e d s c h e m a t i c a l l y ( t o g e t h e r w i t h t h e S-K (H) peaks) i n f i g . 22. I n Mo, W and a-Fe, a l / a c o n t a i n s a major component due t o DKG

(I),

whereas i n V , Nb and Ta c o n t a i n i n g s i g n i f i c a n t amounts o' b o t h H and 0 ( o r N) i t seems t h a t DKG

(I)

i s pinned-out and a ' / a ( p r e v i o u s l y 6) i s pre- dominant1 y due t o GKM ( 0 )

.

However, i n UHP Nb a major component o f a ' l a i s a t t r i b u t e d t o DKG

(I).

I n V, Nb. Ta and a-Fe t h e r e i s a good evidence t h a t a l ( l ) occurs below t h e l o w e s t temperatures y e t i n v e s t i g a t e d .

F i g . 22 : Shematic diagram showing t h e r e l a t i v e p o s i t i o n s and shaped o f t h e a l / a and y peaks a t about 1 Hz i n u l t r a h i g h p u r i t y b.c.c.

t r a n s i t i o n metal.

'b' ', _*

0 100 200 300 4W 5 M T I K I

Although no one b.c.c. has been s t u d i e d t o t h e e x t e n t t h a t a l l t h e primary and secondary c h a r a c t e r i s t i c s o f t h e

BR

(3) have been confirmed f o r b o t h a l / a and y; each o f t h e c h a r a c t e r i s t i c s i s e x h i b i t e d by one o r more o f t h e b.c.c. metals taken as a group. Now, t h e r e can be 1 i t t l e donbt t h a t a ' / a and y taken t o g e t h e r c o n t a i n t h e analogue o f t h e

BR

i n t h e f.c.cls.

Acknowledgements.- The authors wish t o thank P r o f . H. Schultz,

P .

Groh, C. M i n i e r , M. Koiwa and Dr. C. Esnouf, J. Lauzier, L.B. Magalas who k i n d l y made r e s u l t s o f t h e i r groups' i n v e s t i g a t i o n s a v a i l a b l e p r i o r t o p u b l i c a t i o n .

C5-22 JOURNAL DE PHYSIQUE

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