INFLUENCE OF THE DISLOCATION STRUCTURES ON THE BEHAVIOUR OF MAGNETIC DOMAIN WALLS IN HIGH PURITY IRON

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INFLUENCE OF THE DISLOCATION STRUCTURES

ON THE BEHAVIOUR OF MAGNETIC DOMAIN

WALLS IN HIGH PURITY IRON

B. Astie, J. Degauque

To cite this version:

B. Astie, J. Degauque.

INFLUENCE OF THE DISLOCATION STRUCTURES ON THE

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JOURNAL DE PHYSIQUE

CoZZoque

65,

suppZ6ment au nOIO, Tome

42,

octobre 2981

page

C5-627

INFLUENCE OF THE DISLOCATION STRUCTURES ON THE BEHAVIOUR

O F MAGNETIC

DOMAIN WALLS IN HIGH PURITY IRON

B. A s t i e and J. Degauque

Laboratoire de Physique des SoZides,

I. N .

S.

A.,

Avenue de Ranguei 2,

32077 Toulouse-cedex, France

Abstract.- The i n f l u e n c e o f d i s l o c a t i o n d e n s i t y and arrangement on t h e movement of 90° magnetic domain w a l l s (DW) was i n v e s t i g a t e d by magnetomechanical damping measurements on high p u r i t y p o l y c r i s t a l l i n e i r o n . The d i s l o c a t i o n s t r u c t u r e s c r e a t e d by s t r a i n i n g a t 300 K , 190 K and by s t r a i n i n g a t 77 K a f - t e r p r e s t r a i n i n g a t 300 K were observed by h i g h v o l t a g e (800 KV) t r a n s m i s s i o n e l e c t r o n microscopy (TEM)

.

F o r t h e s t r a i n i n g a t 300 K , t h e e f f e c t i v e i n t e r n a l

s t r e s s Qi and t h e r e c i p r o c a l of t h e maximum magnetomechanical damping l / Q - l M e x h i b i t t h r e e l i n e a r s t a g e s , r e l a t e d t o d i f f e r e n t d i s l o c a t i o n d i s t r i b u t i o n s . The d i s l o c a t i o n s t r u c t u r e s b u i l t by s t r a i n i n g a t 190 K and 77 K i n f l u e n c e d i f f e r e n t l y Ci and l/Q-'. This i s l i n k e d t o t h e more homogeneous d i s t r i b u t i o n of d i s l o c a t i o n s c r e a t e 3 a t low temperatures i n i r o n .

1. I n t r o d u c t i o n . - I n f e r r o m a g n e t i c m a t e r i a l s t h e i n f l u e n c e of d i s l o c a t i o n s on t h e movement of D W ' s h a s been widely s t u d i e d using c o n v e n t i o n a l magnetic measurements i n weak o r i n t e r m e d i a t e f i e l d s [l, 2 , 3

1.

I t h a s been shown t o o t h a t t h e magnetomechani- c a l damping, which a r i s e s from t h e i r r e v e r s i b l e motion o f 90° DW's under an a l t e r n a - t i n g s t r e s s , allows t h e d e t e r m i n a t i o n of t h e e f f e c t i v e i n t e r n a l s t r e s s Q. opposed t o t h e movement o f t h e s e D W ' s . I n p u r e i r o n , f o r i n s t a n c e , a t low l e v e l s of s t r a i n i n g ,

Qi h a s been r e l a t e d t o t h e s t r u c t u r e of d i s l o c a t i o n s [4, 53. Most of t h e s e works ho- wever have been performed w i t h o u t d i r e c t o b s e r v a t i o n of t h e l a t t i c e d e f e c t s i n v o l - ved. F o r t h i s reason we have t r i e d t o c a r r y o u t a more complete s t u d y of t h e i n t e r - a c t i o n between d i s l o c a t i o n s and 90° D W ' s , i n high p u r i t y p o l y c r i s t a l l i n e i r o n . To do t h i s we f i r s t s t r a i n e d t h e i r o n samples i n a range o f s t r a i n l e v e l s and temperatures l a r g e enough t o change markedly t h e d e n s i t y and arrangement o f c r e a t e d d i s l o c a t i o n s . The s t r u c t u r e s of d i s l o c a t i o n s have been then d i r e c t l y checked by high v o l t a g e t r a n s - mission e l e c t r o n microscopy (TEM)

.

2 . Experimental meEo32.- The s t a r t i n g m a t e r i a l i s a c y l i n d r i c a l i n g o t of h i g h p u r i - t y i r o n ( l e s s than 1 w.ppm of i n t e r s t i t i a l i m p u r i t i e s ) . A s h e e t 0,5 mm t h i c k i s

2

o b t a i n e d by c o l d r o l l i n g , t h e n c u t i n t o r e c t a n g l e s (80 x 1 0 mm ) which, a f t e r recrys- t a l l i s a t i o n a t 75OoC, have a uniform g r a i n s i z e o f 0 , s mm. Three s e t s of specimens a r e s t r a i n e d by t e n s i o n a t t h r e e temperatures i n o r d e r t o produce d i f f e r e n t d i s l o c a - t i o n s s u b s t r u c t u r e s . The f i r s t s e t i s s t r a i n e d a t 300 K a t s t r a i n l e v e l s between 0 and 16 %. A f t e r p r e s t r a i n i n g a t 300 K , a t 2 %, 3 % and 4 %, t h e t h r e e specimens of t h e second s e t a r e f u r t h e r s t r a i n e d a t 77 K , a t s m a l l s t r a i n l e v e l s ( < 0 , 3 %) and a t a p p l i e d s t r e s s e s lower than t h e flow s t r e s s . The t h i r d s e t i s d i r e c t l y s t r a i n e d

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C5-628 JOURNAL DE

PHYSIQUE

-4 -1 a t 190 K between 0 and 7 % . I n a l l experiments t h e s t r a i n r a t e i s about 0 , 3 x 1 0 s

The magnetomechanical damping experiments a r e performed a t room temperature, a t a frequency o f 0 . 7 H z on a r e v e r s e d t o r s i o n pendulum. The magnetomechanical damping

-'

i s given by : Qmag

-1 1

AU

Qmag =

-

_{2 n} -

_U

where

hU

r e p r e s e n t s t h e energy l o s s e s a r i s i n g from magnetomechanical h y s t e r e s i s and -1

U t h e maximum e l a s t i c energy by c y c l e . T h i s damping e x h i b i t s a maximum QM when p l o t - t e d as a f u n c t i o n o f t h e s h e a r s t r a i n . This t e c h n i q u e h a s a l r e a d y been d e s c r i b e d elsewhere[6,7]. .rile r e c a l l simply t h a t t h e p o s i t i o n and t h e l e v e l of t h e damping maximum a r e connected t o t h e e f f e c t i v e i n t e r n a l s t r e s s Ui.

The c e n t r a l p a r t o f t h e i n t e r n a l f r i c t i o n specimens a r e observed by h i g h voltage TEM a t 800 KV. T h i s t e c h n i q u e a l l o w s an o b s e r v a t i o n o f d i s l o c a t i o n s u b s t r u c t u r e s which i s comparable t o t h a t of b u l k specimens.

-1

3 . Experimental r e s u l t s

.-

The i n c r e a s e o f 6. and l/QM can be simply r e l a t e d t o t h e d e n s i t y N o f d i s l o c a t i o n s by r e l a t i o n s [ 6 , 7

1

:

-1

G Q A/ N 1/2 (2)

Keh and Weissmann d e r i v e d from TEM experiments a relationship between t h e s t r a i n hardening and N

[

8 1

h

a

=

cc

G b (N1/2 - NO1I2) ( 3 )

where G i s t h e s h e a r modulus, b t h e Burgers v e c t o r o f d i s l o c a t i o n s , No t h e d i s l o c a - t i o n d e n s i t y a t t h e flow s t r e s s . The r e l a t i o n s h i p ( 3 ) h o l d s a s soon a s t h e tempera- t u r e of s t r a i n i n g o f p o l y c r i s t a l l i n e i r o n exceeds 150 K [8,9]. The c o n s t a n t d i n ( 3 ) v a r i e s s l i g h t l y with t h e temperature. With t h e v a l u e s given by Ikeda [ 9 2 u s i n g ap- p l i e d s t r e s s e s d i n s t e a d o f s h e a r s t r e s s e s ( Q = 2 x 1 , we t a k e 6( = 0 , 7 6 a t 300 K and S = 1 , O a t 190 K . Thus t h e r e l a t i o n s h i p between di, and N can b e i n v e s t i g a - t e d by s t u d y i n g t h e i r e v o l u t i o n w i t h

he.

-1

S_training a t 300

5.-

Ui and l / Q M show, f o r t h e s t r a i n hardening between 0 and

2 1 0 , 3 da~/mm

,

t h r e e l i n e a r s t a g e s corresponding t o ( F i g . 1, 2 ) : 0

4 A d

( 2 , s daN/mm2 f o r s t a g e I 2.5<

b 6 <

5.5 da.N/mm2 f o r s t a g e 11 2 5 , 5 < b 6 < 10.3 daN/mrn f o r s t a g e I11 The maximum r a t e of v a r i a t i o n i s i n s t a g e 11. S t r a i n i n g - ~ - ~ ~ - A f t e r p r e s t r a i n i n g i n s t a g e I1 a t 300 K , t h e s m a l l s t r a i - -1

n i n g s a t 77 K induce a d e c r e a s e of bi and 1 / e x c e p t f o r ~ ~

e300K

= 4 % +t77K= 0.3 %

where t h e a p p l i e d s t r e s s exceeds t h e flow s t r e s s .

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AmidaN/mm2l

FLg.

3,4

:

cL

and

11%'

an

6unetLom

o d

A C

at

I90 K.

Fig.

1,2

:

ci

and I/&'

a.4 &~v~&ovl.s

06 Aoat

300 K

and

300 K

+ 77 K. 2

%

+

0.10%[8)

;

3 %

+

0.70 %

( v )

;

4 %

+

0.1 %

(+) ;

2 %

+

0.20 %

(01 ;

3 %

t 0 . 1 5

%

( A 1 ;

4 %

+ 0 . 3 %

( 0 1 . 2 0 0 . - " ' I I I 1 ; . 4 . I n t e r p r e t a t i o n . - The v a r i a t i o n s of

ci

and l / Q i l c a n b e r e l a t e d t o t h e e v o l u t i o n of

f

l

d i s l o c a t i o n d e n s i t y and s u b s t r u c t u r e s . 15- -10-

"E

d

$05- S t a g e I _ - ~ ; - O ~ - K . - F o r s t r a i n l e v e l s lower than 2 % a very h i g h hardening r a t e i s observed on t h e s t r e s s s t r a i n curve ( F i g . 5 ) . T h i s s t a g e i s c h a r a c t e r i z e d by a s t r u c t u r e o f mixed i s o l a t e d d i s l o c a t i o n s d i s t r i b u t e d i n a r a t h e r homogeneous f a s h i o n . A t a s t r a i n l e v e l of a- b o u t 1.5 % some t a n g l e s appear ( F i g . 6 a ) . I ~ I ' I

_I

./.

_'

-

- 0 L 1 , I J I

L

.

I , , I These i s o l a t e d d i s l o c a t i o n s i n c r e a s e markedly "0 5 10 15

E i%l Ci and l/p;l, a c t i n g i n t h e same way on the

0 1 2 3 4 5

~u~doN/rnm?l o₀ ~ ₁, l ₂, , ₃, l ₄, , ,₅ l

- . .

fLg.5

:

S z t u . 6

A ~ L U M CWLVE UZ m o b i l i t y and t h e range of displacement of 90°

300 K .

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C5-630 J O U R N A t DE PHYSIQUE s u l t s

16,

73.

S t a g e

_---

I1 a t 300 _-

_---

K and 300

_---

K

+

77 K.- For s t r a i n l e v e l s between 2 % and 6 % a li- n e a r hardening r a t e o c c u r s (Fig. 5 ) and an inhomogeneous 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 s appears (Fig. 6 b ) . This new d i s t r i b u t i o n , w i t h d e n s i f y i n g t a n g l e s s e p a r a t e d by low d e n s i t y r e g i o n s o f s i z e 3 t o 4 r m a t t h e end o f s t a g e 11, d e c r e a s e s more c l e a r l y t h e long range i r r e v e r s i b l e displacements o f 90° DW's i n comparison w i t h i s o l a t e d d i s l o - c a t i o n s . The r e s p e c t i v e p a r t s o f t a n g l e s and i s o l a t e d d i s l o c a t i o n s on t h e p i n n i n g of 90- D W ' s can be s t u d i e d u s i n g t h e low temperature s t r a i n i n g r e s u l t s . B y s t r a i n i n g a t 77 K , a t s t r e s s e s lower t h a n theflow s t r e s s , t h e d e n s i t y o f edge and mixed segments i n s i d e t h e t a n g l e s d e c r e a s e s , w h i l e t h e d e n s i t y o f screw d i p o l e s i n c r e a s e s (Fig.6d) [lo1 This d e c r e a s e o f the p i n n i n g s t r e n g t h due t o the m o d i f i c a t i o n o f arrangement o f t a n g l e s i s more e f f e c t i v e on t h e i r r e v e r s i b l e motion of the 90° DW's than the

increa-

s e due t o the higher screw d e n s i t y .

d e f

: DhLoccction n&utLuotuha

an

nhown by

TEM

o b n m v a t i o n b . a : 7.5

%

l30OKl

_;

_b

_:

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Stage I11 a t 300 K.- The hardening r a t e d e c r e a s e s a t s t r a i n l e v e l s h i g h e r than 6 % (Fig. 5) and t h e t a n g l e s tend t o form a c e l l u l a r s t r u c t u r e made o f h i g h d e n s i t y d i s l o c a t i o n w a l l s 0 . 1 t o 0.2

p m

t h i c k , s e p a r a t i n g r e g i o n s ( o f a s i z e o f 2 t o 3 @ o f

- 1 very low d i s l o c a t i o n d e n s i t y (Fig. 6 c ) . The lower r a t e of i n c r e a s e of Ui and l / Q M compared w i t h s t a g e I1 i s c o n s i s t e n t w i t h t h e lowering o f t h e i n c r e a s e r a t e o f t h e i n t e r n a l s t r e s s s u g g e s t e d by t h e s t r e s s - s t r a i n curve.

S t r a i n i n g a t 1 9 _ ~ - ~ . - A t 190 K t h e p l a s t i c i t y of i r o n i s c o n t r o l l e d by t h e mobi- l i t y of screw d i s l o c a t i o n s . I n comparison with s t r a i n i n g a t 300 K , t h e t r e n d towards t h e b u i l d i n g of t a n g l e s d e c r e a s e s and t h e d i s t r i b u t i o n of d i s l o c a t i o n s i s very homogeneous, a s p r e v i o u s l y r e p o r t e d

18,

91. We observed t h e same bahaviour up t o a s t r a i n l e v e l of around 6 % ( F i g . 6 e ) . D i f f u s e t a n g l e s appear only a t h i g h e r s t r a i n l e v e l s

-

1

( F i g . 6 f ) . The uniforme r a t e o f v a r i a t i o n o f T~ and l / Q M with bCS can b e e x p l a i n e d t h e r e f o r e by t h e almost i n v a r i a b l e arrangement o f screw d i s l o c a t i o n s whatever t h e i r d e n s i t y .

Compar_ls_?-b_e_peen th_e_-e_f_fe_~:s_-of d i f f e r e n t @:Aocation substrug_tgge_g.- The i n - f l u e n c e of t h e d i f f e r e n t d i s l o c a t i o n s u b s t r u c t u r e s c r e a t e d i n s t a g e I1 a t 300 K on one hand and a t 190 K on t h e o t h e r hand, on t h e behaviour of 90° D W ' s , can b e com- p a r e d , u s i n g t h e v a l u e s of d. given above : t h e s l o p e of CTi 300 ( i n s t a g e I1 a t

-1

300 K ) i s h i g h e r than t h a t o f Q 190 whereas ( l / Q ) 360 i n c r e a s e s more slowly

,,>

t h a n ( I / Q M ~ I a s f u n c t i o n o f

AG

a t 300 K. T h i s discrepancy can b e e x p l a i n e d 190 K

when c o n s i d e r i n g t h e c o n c l u s i o n s o f t h e model o f Smlth and Birchak, which h a s been used h e r e t o c a l c u l a t e b . [4]. According t o t h i s model, t h e l o s s e s 4 U M a t t h e magnetomechanical damping maximum must vary a s 6 . . This t h e o r e t i c a l r e s u l t i s c o n s i s - t e n t w i t h t h e v a r i a t i o n s o f h U M observed f o r t h e s t r a i n i n g s i n t h e s t a g e I1 a t 3 0 0 K ,

b u t n o t f o r t h e s t r a i n i n g s a t 190 K . For experiments a t 190 K,

A

UEf h a s lower v a l u e s t h a n t h o s e observed f o r experiments a t 300 K , and i s p r a c t i c a l l y independent o f t h e s t r a i n l e v e l , which shows t h a t t h e s t r a i n i n g i n c r e a s e s very l i t t l e t h e number of pin- n i n g c e n t e r s of 90" D W ' s . So t h e u s u a l model o f t h e magnctomechanical h y s t e r e s i s , which a s s o c i a t e s t h e d e c r e a s i n g m o b i l i t y of 90' D W ' s t o t h e d e c r e a s e o f magnetome- c h a n i c a l damping, i s perhaps n o t n e c e s s a r i l y s u i t e d t o a l l d i s t r i b u t i o n s o f i n t e r n a l s t r e s s e s . Indeed i f r e l a t i v e l y s t r o n g p i n n i n g c e n t e r s a c t s i m i l a r l y on qi and

-1

l/QN

,

" s o f t e r " pinning c e n t e r s , d i s t r i b u t e d more uniformly, seem t o modify t h e mobi- l i t y o f DW's more t h a n t h e range of displacements of D W ' s a t t h e magnetomechanical damping maximum.

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JOURNAL DE PHYSIQUE

The more homogeneous s t r u c t u r e o f screw d i s l o c a t i o n s b u i l t by s t r a i n i n g a t 190K d e c r e a s e s t h e m o b i l i t y o f 90° DW's l e s s t h a n t h e s u b s t r u c t u r e b u i l t i n s t a g e I1 a t 300 K ; on t h e o t h e r hand

Qil

d e c r e a s e s more. T h i s b e h a v i o u r i s a t t r i b u t e d t o t h e i n c r e a s e o f t h e a v e r a g e l e v e l o f t h e e f f e c t i v e i n t e r n a l s t r e s s w i t h o u t a n o t a b l e change o f t h e d e n s i t y o f p i n n i n g c e n t r e s of 90" D W ' s .

R e f e r e n c e s .

-

[

1 2 H . TRAUBLE, Modern Problem d e r M e t a l l p h y s i k , v o l . 2 , S p r i n g e r V e r l a g (1966)

[2) H . BILGER, Phys. S t a t . S o l . ,

18,

207 (1966)

[3] K. LUBITZ, J. Appl. P h y s . ,

4,

5 1 (1974) and

16,

87 (1978)

[4] J . DEGAGQUE, B . ASTIE, L.P. KUBIN, J. Appl. P h y s . , E , 2140 (1979)

[ 5 3 B . ASTIE, J. DEGAUQUE, J . L . PORTESEIL, R. VERGNE, P r o c e e d i n g s o f I n t e r m a g .

1981 ( t o b e p u b l i s h e d )

L6] J . DEGAUQUE, B. ASTIE, L.P. KUBIN, P h y s . S t a t . S o l . ( a ) ,

2,

493 (1978) C7) J. DEGACQUE, T h e s i s , Univ. P a u l S a b a t i e r , Toulouse (1977)

c8] A.S. KEH, S. WEISSMANN, E l e c t r o n Microscopy and t h e S t r e n g t h o f C r y s t a l s ,

I n t e r s c i e n c e P u b l i s h e r s , New-York (1963)