DISLOCATION CORE DIFFUSION AND UNPINNING IN α-Zr

(1)

HAL Id: jpa-00221106

https://hal.archives-ouvertes.fr/jpa-00221106

Submitted on 1 Jan 1981

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

DISLOCATION CORE DIFFUSION AND

UNPINNING IN α-Zr

I. Ritchie, K. Sprungmann

To cite this version:

(2)

JOURNAL DE PHYSIQUE

CoZZoque

CS,

supple'rnent au nOIO, Tome

4 2 ,

octobre

1981

page

C5-427

DISLOCATION CORE DIFFUSION AND UNPINNING

I N

a-Zr

I . G . R i t c h i e and K.W. Sprungmann

Materials Science Branch, Atomic Energy

of

Canada Limited, Whiteshell NucZear

Research Estab Zishment, Pinawa, Manitoba ROE

lLO,

Canada

A b s t r a c t . - The h i g h t e m p e r a t u r e , low f r e q u e n c y , i n t e r n a l f r i c t i o n s p e c t r u m of deformed and a n n e a l e d a-Zr i s dominated a t low s t r a i n a m p l i t u d e s by a peak (P2)

a t

-

600°C (4 Hz). A t h i g h e r s t r a i n a m p l i t u d e s , two new peaks PO (= 480°C)

and P1 (= 530°C) a p p e a r . It i s shown t h a t PO i s d u e t o t h e t h e r m a l l y a s s i s t e d

u n p i n n i n g of d i s l o c a t i o n s from oxygen i n t e r s t i t i a l s w h i l e P1 and P2 a r e due t o t h e l o n g i t u d i n a l and t r a n s v e r s e movements of t h e same d e f e c t s i n t h e d i s l o c a -

t i o n c o r e . P 2 , p r e v i o u s l y a t t r i b u t e d t o grain-boundary r e l a x a t i o n , i s a

Snoek-Ki6ster peak. A b e h a v i o u r a l map of t h e t e m p e r a t u r e - s t r a i n a m p l i t u d e p l a n e

c a n b e c o n s t r u c t e d t o f a c i l i t a t e t h e i n t e r p r e t a t i o n of amplitude-dependent r e -

s u l t s . It i s shown t h a t unpinning c a n b e d i s t i n g u i s h e d from l o n g i t u d i n a l c o r e

d i f f u s i o n , even when b o t h a r e observed a t t h e same t e m p e r a t u r e , p r o v i d e d t h e modulus d e f e c t i s measured t o g e t h e r w i t h t h e i n t e r n a l f r i c t i o n .

1. I n t r o d u c t i o n . - The h i g h t e m p e r a t u r e i n t e r n a l f r i c t i o n (A) spectrum of a-Zr i s domi-

n a t e d by a peak (P2) a t

-

550°C ( 1

.

A p l o t of I n f ( f i s f r e q u e n c y ) v s . r e -

c i p r o c a l peak t e m p e r a t u r e ( l / T ( P ) ) y i e l d s t h e r e l a x a t i o n e n t h a l p y ,

%

= 2.5 eV, and

2

l i m i t i n g r e l a x a t i o n t i m e , r o = 10-l6 S; P i s a b o u t t w i c e a s b r o a d a s a s i m p l e Debye

2

peak"). The h e i g h t of P* (and A t h r o u g h o u t t h e h i g h - t e m p e r a t u r e spectrum) i s reduced

by h e a t t r e a t m e n t s which i n c r e a s e t h e g r a i n s i z e . Hence, i t i s n o t s u r p r i s i n g t h a t

some have a t t r i b u t e d P2 t o grain-boundary r e l a x a t i o n . We have shown (4)

t h a t P c a n n o t b e a s s o c i a t e d w i t h o r d i n a r y g r a i n b o u n d a r i e s a s is t h e c a s e w i t h ₂ s i m i - l a r r e s u l t s on o t h e r p u r e m e t a l s ( 5 ) . T h i s p a p e r o u t l i n e s a d e t a i l e d s t u d y of ampli-

t u d e ( E ) dependence i n t h e v i c i n i t y of P2. The r e s u l t s a r e a t t r i b u t e d t o t h e r m a l l y

a c t i v a t e d u n p i n n i n g of d i s l o c a t i o n s , l o n g i t u d i n a l c o r e d i f f u s i o n and t r a n s v e r s e c o r e

d i f f u s i o n . I n t h e f o l l o w i n g , t h e s e phenomena a r e simply r e f e r r e d t o a s unpinning, LCD

and TCD, r e s p e c t i v e l y .

2. M a t e r i a l . - Measurements of A i n f l e x u r e (f = 4 Hz) by b o t h t h e f r e e decay and con-

s t a n t - ~ t e c h n i q u e s ( 6 ) were c a r r i e d o u t on c o l d - r o l l e d s t r i p of n o m i n a l l y 5N pure Z r .

I n t e r s t i t i a l i m p u r i t y c o n c e n t r a t i o n s (ug/g) were found by a n a l y s i s t o b e : H < 5;

N = 6; and 0 , 17 t o 23. R e s u l t s s i m i l a r t o t h o s e p r e s e n t e d below were o b t a i n e d w i t h

specimens a n n e a l e d f o r a few h o u r s i n t h e t e m p e r a t u r e r a n g e 500 t o 700°C o r v i b r a t i o n - a n n e a l e d o v e r n i g h t (16 h ) a t 400°C i n t h e pendulum(4).

(3)

JOURNAL DE PHYSIQUE

3 . R e s u l t s . - A v s . T, E c o n s t a n t ( f i g u r e 1 ) ( i ) E

5

2 X 1 0 - ~ o n l y

P2

i s o b s e r v e d

( i i ) E > 2 n 1 0 - ~ P2 i s accompanied by PO ( v 48OoC) and P1 ( 2 53O0C) a s shown by t h e

d i f f e r e n c e c u r v e i n f i g u r e 1.

With i n c r e a s i n g E, b o t h P and P s h i f t t o lower T ( a s e x p e c t e d f o r t h e r m a l l y a c t i -

0 1

v a t e d p r o c e s s e s ) w h i l e P2 s h i f t s s l i g h t l y t o h i g h e r T (anomalous b e h a v i o u r ) . A v s . T, E c o n s t a n t ( f i g u r e 2 )

NOYlNAL STRAIN AURITUOE. N

F i g . 1 I n t e r n a l f r i c t i o n v s . t e m p e r a t u r e F i g . 2 I n t e r n a l f r i c t i o n v s . s t r a i n ampli- f o r two c o n s t a n t s t r a i n a m p l i t u d e s . t u d e a t s e l e c t e d c o n s t a n t t e m p e r a t u r e s .

( a ) Region l ( 4 0 0

-

493'C). A peak d e v e l o p s and moves t o l o w e r E a s T i n c r e a s e s .

These c u r v e s a r e s i m i l a r t o t h o s e p r e d i c t e d by t h e B l a i r , H u t c h i s o n and Rogers (BHR)

theory") based on t h e T e u t o n i c o , G r a n a t o and Liicke model(8) of d i s l o c a t i o n unpinning.

An i m p o r t a n t p r e d i c t i o n of t h e BHR t h e o r y i s t h a t t h e modulus d e f e c t (q) a s a f u n c t i o n o f E i s 0 . 5 Ao, i . e . h a l f t h e peak h e i g h t , a t t h e peak p o s i t i o n , and s a t u r a t e s a t

n

= A0 f o r l a r g e E. T h i s i s confirmed e x p e r i m e n t a l l y i n r e g i o n 1 (480°C) a s shown i n f i g u r e 3 . 0 6 .

g

A Y

j

a

094- 4 8 0 - C _ cW- 512.C I . 5 We" t

a

!iOD3-

m -

/

THERMALLY ASSISTED UNPINNING

E

0 0 1 -

*

1 2 3 4 5 6 7 8 9

NOMINALSTRAIN AMPLITUDE. N NOMINAL STRAIN AMPLITUDE. N

F i g . 3 I n t e r n a l f r i c t i o n and modulus d e f e c t a s a f u n c t i o n of s t r a i n a m p l i t u d e a t 480°C

(4)

(b) Region 2 (493

-

580°C). A peak moves s l o w l y t o lower E w i t h i n c r e a s i n g T. Its

h e i g h t a f t e r s u b t r a c t i o n of t h e low E background remains a p p r o x i m a t e l y c o n s t a n f . A l -

though s i m i l a r i n s h a p e t o t h e peak i n r e g i o n l , q/A i n r e g i o n 2 i s s i g n i f i c a n t l y

0

g r e a t e r t h a n 0.5 a s shown i n f i g u r e 3. A p l o t of T v s . E a t t h e peak i s a s t r a i g h t

l i n e . Its i n t e r c e p t a t z e r o E i m p l i e s a r e l a x a t i o n e n t h a l p y f o r P1 of 1 . 8 6 eV. A t 493OC t h e c u r v e i s made up of two peaks b e c a u s e of o v e r l a p p i n g r e g i o n 1 and r e g i o n 2 b e h a v i o u r .

( c ) Region 3 (590

-

650°C). A peak moves back, anomalously, t o h i g h e r E w i t h i n c r e a s -

i n g T.

The complex behaviour i n r e g i o n s 2(P ) and 3(P ) i s s i m i l a r t o t h e behaviour pre-

1 2

d i c t e d t h e o r e t i c a l l y f o r LCD and TCD. Liicke and ~ c h l i p f " ) were t h e f i r s t t o show

t h a t b o t h LCD and TCD g i v e

rise

t o r e l a x a t i o n peaks. Subsequently, t h e i r model f o r

a n ensemble of double-loops was t h o r o u g h l y i n v e s t i g a t e d by ~ i n k l e r - ~ n i e w e k ' " ) . 4. Comparison of Theory and Experiment.- Unpinning. Comparison of t h e BHR t h e o r y f o r

v e r y l o n g segments w i t h t h e c u r v e s of r e g i o n 1 (P ) y i e l d s e s t i m a t e s of t h e b i n d i n g

0

energy (U ) and l o o p - l e n g t h (R): U = 1.47 e V and IL = 2000 b (b i s t h e Burgers vec-

0 0

t o r ) . T h e r e i s e v i d e n c e t h a t U. f o r i m p u r i t y i n t e r s t i t i a l s i n t h e h . c . p . t r a n s i t i o n 3

m e t a l s c a n b e as h i g h a s vb3/6(11) (p i s t h e s h e a r modulus). For U-Zr, ub 16

= 1.55 eV, s o t h a t PO i s c o n s i s t e n t w i t h unpinning from a n i m p u r i t y i n t e r s t i t i a l .

Core D i f f u s i o n . LCD i s s i m i l a r t o unpinning. A c r i t i c a l s t r e s s (oc) p l a y s a r o l e

s i m i l a r t o t h e unpinning s t r e s s ( a u ) . Once oc i s exceeded, t h e r e i s a n i n c r e a s e i n

t h e f r e e d i s l o c a t i o n - l e n g t h . Thus, i t i s n o t s u r p r i s i n g t h a t t h e s h a p e s of t h e c u r v e s f o r A v s . E a r e s i m i l a r i n r e g i o n 1 and r e g i o n 2. LCD is governed by a r e l a x a t i o n t i m e

(r

) g i v e n by (10) L T

_L

= 1 2 / j ~ L ( ~ 2

+

a 2 ) ] ; u2 = u2b2R3/ ( 4 ~ ~ k ~ ) [ l 1 i s t h e mean l o o p - l e n g t h , DL i s t h e LCD c o e f f i c i e n t , a i s t h e a p p l i e d s t r e s s (a = REE

i n f l e x u r e e x p e r i m e n t s ; E is Young's modulus and R i s t h e o r i e n t a t i o n f a c t o r ) ,

2 .

TIL = 0.5 pb is t h e l i n e t e n s i o n , and k i s Boltzmann's c o n s t a n t . The e x p r e s s i o n s f o r

A and r, a r e complex(lO) b u t e a s i l y e v a l u a t e d n u m e r i c a l l y . We have c a l c u l a t e d A and q

f o r homogeneous s t r a i n and f o r t h e s t r a i n d i s t r i b u t i o n i n o u r s p e c i m e n s c 6 ) . The c a l - c u l a t e d r e s u l t s a g r e e q u a l i t a t i v e l y w i t h t h e e x p e r i m e n t a l r e s u l t s f o r r e g i o n 2(P ) .

1 TCD g i v e s r i s e t o a s u p e r - p o s i t i o n of e l e m e n t a r y r e l a x a t i o n p r o c e s s e s ( l O ) i n

q u a l i t a t i v e agreement w i t h P2. The e f f e c t i v e r e l a x a t i o n t i m e (T ) i s g i v e n by

T

where q i s t h e d e f e c t d i s t a n c e from t h e double-loop c e n t r e and DT is t h e TCD c o e f f i -

c i e n t . I f , up t o t h e g i v e n a m p l i t u d e , t h e l o n g i t u d i n a l d i s t r i b u t i o n i s ' f r o z e n - i n '

(q f i x e d ) , t h e n t h e peak i s €-independent up t o t h a t a m p l i t u d e . However, i f a t a

h i g h e r E , l o n g i t u d i n a l r e l a x a t i o n becomes p o s s i b l e , t h e TCD peak w i l l show weak E-de-

2

-

pendence t h r o u g h (l-q /fi2) i n q u a l i t a t i v e agreement w i t h P _2'

We assume t h a t t h e same d e f e c t s c a u s e PO and t h e P /P complex. Then, i d e n t i f y -

(5)

C5-430 JOURNAL DE PHYSIQUE

i n g P2 (HR = 2.5 eV, T, = 1 0 - l 6 S ) w i t h TCD and t a k i n g = 2000 b , DT = 210 exp

(-2.5 eV/kT). S i m i l a r l y , i d e n t i f y i n g P1

(HR

= 1 . 8 6 eV) w i t h LCD, we f i n d DL = 1570

exp (-1.86 e V / k ~ ) . Thus LCD i s much f a s t e r t h a n TCD a s e x p e c t e d i n t u i t i v e l y . Also,

t h e p r e d i c t e d v a r i a t i o n of T(P ) w i t h E when t h e r e i s l o n g i t u d i n a l m o b i l i t y ( l O ) , can 2

show a n i n c r e a s e w i t h E i n t h e unexpected s e n s e observed i n r e g i o n 3 .

A comparison of r e g i o n 2(P ) r e s u l t s and t h e o r y i s shown i n f i g u r e 4. The ex-

1

,c?

/X -THEORY ADAPTED TO FLEXURE

1

C

8 o 5-

U

PENDULUM

'

/

0 . X NORWLIZED EXPERIMEWAL

1 ----

THEORY HOMOOENEOUS STRAIN

-

THEORY ADAPTED X1 FLEXURE PENWLUM

o X NORMALIZED EXPERIMENTAL RESULTS _l FITTED AT THE PEAK POSITION

@ /C X X RESULTS FTTED AT T M PEAK POSITION I

0 1 2 3 4 5 6 7 8 9 NOMINAL STRAIN bMPL1TUDE.N NOMINAL STRAIN AMPLITUDE. N

F i g . 4 Comparison o f t h e o r e t i c a l and e x p e r i m e n t a l c u r v e s f i t t e d a t t h e peak p o s i t i o n .

p e r i m e n t a l v a l u e s were m u l t i p l i e d by c o n s t a n t f a c t o r s t o f o r c e a f i t a t t h e peak p o s i - t i o n . T h i s is e q u i v a l e n t t o f i x i n g AE' (A i s t h e d i s l o c a t i o n d e n s i t y ) and R. A t t h e h i g h e s t E v a l u e s , t h e a d a p t e d t h e o r y i s i n good agreement w i t h t h e r e s u l t s f o r b o t h A and Q . A t t h e l o w e s t E v a l u e s t h e f i t i s poor. T h i s i s caused by comparing t h e over- s i m p l i f i e d double-loop t h e o r y w i t h r e s u l t s f o r m u l t i - p i n c o n f i g u r a t i o n s . I n s u c h a c a s e , a c i s v e r y s h a r p l y d e f i n e d , a c c o u n t i n g f o r t h e a l m o s t s t e p - l i k e i n c r e a s e i n A o b s e r v e d e x p e r i m e n t a l l y .

The T v a r i a t i o n of t h e A v s . E p e a k s i n r e g i o n 2(P ) i s shown i n f i g u r e 5. Lim-

1

700 , I , , , , , , ,

1 I

X EXPERIMENTK RESULTS R '2,377 I

j

0 EXPERIMENWC RESULTS R.1

I 3 --.THEORY NOMCGENEOUS STRAlN

! !, ----IHEORV ADIPTED m FLEXWE PENOM 600 I F i g . 5 Comparison of t h e o r e t i c a l and e x p e r i -

i

m e n t a l r e s u l t s f o r t h e p o s i t i o n of t h e A v s . E

_

peaks i n r e g i o n 2(P1) of f i g u r e 2 .

---___

4 0 0

EFFECTIVE SiRAlN mPLITUOE XIO'

i t i n g v a l u e s of R = 1 and R = 2 / ( 3 ~ ) a r e assumed and t h e r e s u l t s compared w i t h t h o s e

c a l c u l a t e d . C o n s i d e r i n g t h e u n c e r t a i n t i e s i n t h e p a r a m e t e r s and t h e l i m i t a t i o n s of t h e t h e o r e t i c a l model, f i g u r e 5 shows e x c e l l e n t agreement between t h e o r y and e x p e r i - ment.

The e x p e r i m e n t a l r e s u l t s i n f i g u r e 3 s u g g e s t t h a t n / A O c a n b e u s e ? t o d i s t i n -

(6)

c a l c u l a t e d r a t i o s f o r q/AO w i t h t h o s e found e x p e r i m e n t a l l y a s t a b u l a t e d below shows good agreement.

Temp. "C q/Ao CALC. a/Ao EXPT. Mechanism

480 0.50 0.50 Unpinning

512 0.58

531 0.60 LCD

550 0.70 0.67

5. Map of t h e T-E Plane.- I n t h e BHR t h e o r y , t h e unpinning b o u n d a r i e s i n t h e l'-E p l a n e

a r e e a s i l y c a l c u l a t e d ( 7 ) . Also, t h e b o u n d a r i e s of ' i n s t a n t a n e o u s ' c o r e d i f f u s i o n ,

2 w.cL = 1 and w-rT = 1 c a n be c a l c u l a t e d . These b o u n d a r i e s and t h e e x p e r i m e n t a l r e -

s u l t s a r e shown i n f i g u r e 6. The arrow i n d i c a t e s t h e r a n g e of E covered experimen-

t a l l y . With t h e a i d of t h i s map, a l l of t h e complex and a p p a r e n t l y anomalous r e s u l t s

i n f i g u r e s 1 and 2 a r e e a s i l y i n t e r p r e t e d .

F i g . 6 B e h a v i o u r a l map of t h e T-E p l a n e .

m bm 100 L I X ) -0 IOm

T U I E R L T W I , X I

I f t h e root-mean-square v i b r a t i o n a m p l i t u d e exceeds a _{C '} d e f e c t r e d i s t r i b u t i o n

w i l l proceed, w i t h a t i m e c o n s t a n t T ~ a t t e m p e r a t u r e s much lower t h a n T(P1). , This

s u g g e s t s a n experiment t o confirm t h e i n t e r p r e t a t i o n s of PO and P g i v e n above. It

1

i s a d e m o n s t r a t i o n t h a t e i t h e r unpinning o r LCD can be observed a t t h e same tempera-

t u r e , depending upon t h e o b s e r v a t i o n time. Another specimen was used and t h e r e s u l t s

a r e g i v e n i n f i g u r e 7. The f u l l c u r v e s (rl/AO = 0.49) t r a c e d i n < 10 s a r e due t o un-

F i g . 7 Deolonstration of unpinning ( f u l l

c u r v e s ) and l o n g i t u d i n a l c o r e d i f f u s i o n

(7)

C5-432 JOURNAL DE PHYSIQUE

p i n n i n g . The broken c u r v e s (n/A0 = 0.77) o b t a i n e d by t h e c o n s t a n t - E method (90 S

v i b r a t i o n a t each s t e p i n c r e a s e i n E ) a r e d u e t o LCD. These r e s u l t s a l s o d e m o n s t r a t e t h a t t h e d e f e c t s i n v o l v e d i n PO and P a r e i n d e e d t h e same. ₁

6. D i s c u s s i o n . - I f D i s t h e b u l k - d i f f u s i o n c o e f f i c i e n t f o r t h e s p e c i e s of d e f e c t i n - B

v o l v e d , i t i s e x p e c t e d , i n t u i t i v e l y , t h a t DL > DT = DB. S i n c e DT is v e r y c l o s e t o t h e d i f f u s i o n c o e f f i c i e n t f o r oxygen i n u - ~ r " ~ ) o v e r t h e T r a n g e of PO, PI and P2,

we i d e n t i f y t h e d e f e c t s i n v o l v e d a s oxygen i n t e r s t i t i a l s . Liicke and ~ c h l i p f have

argued t h a t D _Land DT s h o u l d be comparable and t h a t t h e TCD boundary i n f i g u r e 6

s h o u l d b e a t lower t e m p e r a t u r e s t h a n t h e LCD boundary. T h i s i s i n c o n s i s t e n t w i t h o u r

r e s u l t s . The TCD peak (Pg) c a n b e subsumed i n t o t h e c l a s s of peaks a t t r i b u t e d t o t h e

Snoek-KGster (13-14) r e l a x a t i o n . Our t r e a t m e n t o f P i s c o n s i s t e n t w i t h r e c e n t models

o f t h e Snoek-K6ster r e l a x a t i o n , p r o v i d e d t h a t t h e e n t h a l p y of double-kink f o r m a t i o n is

n e g l i g i b l e compared w i t h t h e e n t h a l p y of TCD.

F i n a l l y , i t s h o u l d b e n o t e d t h a t t h r e e peaks s i m i l a r t o PO, P and P have been

1 2

o b s e r v e d i n ~ i l v e r ' ' ~ ) . Core r e d i s t r i b u t i o n of i m p u r i t y i n t e r s t i t i a l s a p p e a r s t o b e a g e n e r a l phenomenon which c o n t r i b u t e s peaks t o t h e low f r e q u e n c y , i n t e r n a l f r i c t i o n s p e c t r a o f ' deformed m e t a l s .

REFERENCES

1. W . J . B r a t i n a and W.C. Winegard, T r a n s . ATME ( J o u r n a l of M e t a l s )

206

(1956) 186.

2. K. Bungardt and H. P r e i s e n d a n z , Z . M e t a l l k d e

51

(1460) 280.

3. J.L. Gacougnolle, T h e s i s , P o i t i e r s , F r a n c e , 1974.

4. I . G . R i t c h i e and K.W. Sprungmann, Atomic Energy of Canada Limited R e p o r t ,

AECL-6810 (1981).

5. J. Woirgard, P h i l . Mag.

2

(1976) 623.

6. K.W. Sprungmann and I.G. R i t c h i e , Atomic Energy of Canada Limited R e p o r t ,

AECL-6438 (1980).

7 . D.G. B l a i r , T.S. Hutchison and D.H. Rogers, Can. J. Phys,

49

(1971) 633.

8. L.J. T e u t o n i c o , A.V. Granato and K. Liicke, J . Appl. Phys.

35

(1964) 220.

9 . K. Liicke and J. S c h l i p f , P r o c . Conf. on The 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 , Atomic Energy Research E s t a b l i s h m e n t R e p o r t , AERE-R-5944

1

(1968) p. 118.

1 0 . W. Winkler-Gniewek, T h e s i s , Aachen, 1973.

11. W.R. Tyson, Can. Met. Quart.

6

(1967) 301.

12. I . G . R i t c h i e and A. A t r e n s , J . Nucl. Mater.

67

(1977) 254.

1 3 . A. Seeger, Phys. S t a t . S o l . ( a )

55

(1979) 457.

1 4 . J . P . H i r t h , Met. T r a n s . M e t . Soc. AWE

G

(1980) 861.

15. A. R i v i h r e , J . P . A m i r a u l t and J. Woirgard, P r o c . ICIFUAS 6, Ed. by R.R. H a s i g u t i