POINT DEFECT - DISLOCATION INTERACTION IN MgO

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POINT DEFECT - DISLOCATION INTERACTION IN

MgO

M. Gabbay, C. Esnouf, A. Vincent, Gilbert Fantozzi

To cite this version:

M. Gabbay, C. Esnouf, A. Vincent, Gilbert Fantozzi.

POINT DEFECT - DISLOCATION

page c5-289

POINT DEFECT

-

DISLOCATION INTERACTION IN MgO

M.

Gabbay,

C. Esnouf, A .

Vincent and

G. F a n t o z z i

Groupe drEtudes de M6taZZurgie Physique e t Physique des Matgriaux, E.R.A. 463 I.N.S.A., B&. 502

-

69621 ViZZeurbanne Cedex, France

Abstract

.-

Amsl i tude Dependent Internal Friction has been measured from

77

K

t o 593 K i n FlgO s i n g l e c r y s t a l s p l a s t i c a l l y deformed a t room tenperatu-

r e . Experiiioental r e s u l t s have been tested

w i t h

several theoretical nodels of

dislocation breakaway. A re1 iable value

of

interaction energy (0.5 eV) i s

deduced fro111 the aodel of Teutonico, Granato and LGcke,

b u t

only a p a r t i a l

agreement between expericnental r e s u l t s and the model i s obtained. For t h a t

reason, a nulnerical analysis of therrlonechanical breakaway has been under-

taken.

1.

Introduction.-

Different behaviours of riobile dislocations in MgO

single

c r y s t a l s p l a s t i c a l l y deformed a t Room Temperature (R.T.) have been presented i n pre-

vious papers

111,

[ z ] . Among these aspects, one of the most important i s the high

sensivity of Internal Friction ( I F . ) t o annealing; f o r treatments above RT., the

level of the

IF.

spectrum decreases very quickly a s annealing temperature increases.

Such a reduction of IF. has been already explained by pinning of dislocations with

migrating point defects. In our l a s t paper

[3],

we t r i e d t o apply

-

i n order t o

determine binding energy between pinning point defects and dislocations

-

the c l a s s i

-

ca1 theoretical models (reviewed by Perez e t a l .

L41)

(such as the models of Granato

and Lucke r 5 L Saul and Bauer

161,

Friedel

[ 7 ] ;

Teutonico, Granato and LGclte

(TGL.)

[8]).

For the most p a r t , these models did not f i t correctly our r e s u l t s along

the whole temperature range; besides, the d i f f e r e n t values of dislocation-point

defect i n t e r a c t i o n energy

U,,

deduced from the few measurements consistent with

these models, seemed t o be unreliable except f o r the model of

TGL

(Uo

= 0.5

eV)

.

New experiments have been performed f o r the present paper and ngw the theo-

r e t i c a l models have been t r i e d on computed local internal f r i c t i o n data. However

none of those models f i t exactly experimental r e s u l t s . About the

TGL

mode1,partial

agreement i s obtained i n the low temperature range. This f a c t could be due to the

thermal breakaway of other species of pinning points activated i n t h e higher p a r t of

temperature range. Moreover these two temperature parts seem t o overlap one anotner

making more complex the dissociation of these various processes and t h e i r undestan-

di ng

.

For t h i s reason, numerical analysis of tnermomechanica~ breakaway has been

undertaken involving various parameters such a s i n t e r a c t i o n energy

U o ,

average loop

length, number of pinning points. Amplitude dependent Internal Friction

_Qt,

i s c a l -

culated as a function of s t r e s s

0

f o r a given temperature. Such a calculation i s

C5-290 JOURNAL DE PHYSIQUE

obtained from the s t a t i s t i c a l depinning and repinning of a dislocation along which several pinning points a r e non regularly located. Depinning and repinning energies, f o r each pinning point a r e determined from the energy diagram considering disloca- tion-point defect binding energy, tension l i n e and s t r e s s work. Then,the r e s u l t s of t h a t numerical analysis a r e compared t o experimental measurements.

2.- Experimental r e s u l t s

.-

Detailed experimental conditions have been described elsewhere 13

1.

Experimental r e s u l t s a r e presented using t h e real

Local

m AHL Amplitude aependent Internal Friction

AHL

corresponding t o the s t r a i n amplitude E .

AHL

i s deduced from amplitude dependent Internal Friction

AH

(experimentally measured) by the Lazan's method

(9

(

leading t o the to1 lowing r e l a t i o n :

For example, Figure 1 shows the large difference between

AH

and

1,

.

'

' c : .105

AHL

plotted versus E. For each an-

1 5 nealing temperature (293 K , 366

K ,

429 K, 5 2 1 K, 543 K ) , a s e t of

_AHL

Fig. 1 : Difference between measured

_AH

( E ) curves a r e plotted f o r measure- and computed

AHL

by Lazan's method. ments performed between 77K and the

-

annealing temperature. Two of these s e t s of curves are presented i n Figu- res 2 and 3 respectively f o r the annealing temperatures 293 K and 593 K. Thermal activation of depin- ning, already observable on Figures 2 and 3 , i s p a r t i c u l a r l y pointed out by the plot of

AHL

versus tempera- t u r e a t constant s t r a i n amplitude E

presented on Figure 4 . Such

AHL

( T )

curves a r e obtained from data of Figure 2.

Fig.

2

: After p l a s t i c deformation a t 293K, variations of AHL versus E a t

t u r e s . a : 77K, b : 105K, c : 133K, d : 1931(, e : 2461<, f : 425K, g : 523K. F i g . 4 : A f t e r p l a s t i c deformation, v a r i a t i o n s o f AHL versus T a t v a r i o u s s t r a i n a m p l i t u d e s . a : 5 . 1 0 - ~ , b :10c5, c : 1 . 5 . 1 0 - ~ , d : 2 . 1 0 - ~ , e : 2.5.10m5, f : 3 . 1 0 - ~ . D i s c u s s i o n : A l l t h e e x p e r i m e n t a l r e s u l t s show o b v i o u s l y t h a t t h e r m a l a c t i v a t i o n i s a l r e a d y o p e r a t i v e a t 77K. So, o n l y t h e r m a l l y a c t i v a t e d models Rave been t e s t e d . F o r i n s t a n c e t h e model developped by Saul and 3auer l e a d s t o t h e f o l l o w i n g expres- s i o n f o r

nHL.

AHL =

no

( 1 + w / k ~ ) e x p

[-

U,/XT) where o i s t h e r e s o l v e d shear s t r e s s a c t i n g on a d i s l o c a t i o n v i s t h e a c t i v a t i o n volume A, i s t h e r e l a x a t i o n s t r e n g t h f a c t o r . T h i s r e l a t i o n i s a v a i l a b l e f o r e a r l y s t a t e s o f d e p i n n i n g . i . e . f o r t h e case where t h e f r a c t i o n o f unpinned l o o p s . f ( t ) i s v e r y s m a l l ( f ( t ) << 1 ) and f o r

l

h i g h t e m p e r a t u r e ( o v c< k T ) . Then,

aH

i s e x p e c t e d t o v a r y e x p o n e n t i a l l y w i t h

-

T '

E x p e r i m e n t a l r e s u l t s f i t o n l y p a r t i a l l y t h i s model ; th e v a l u e o f i n t e r a c t i o n energy U. deduced f r o m t h i s p a r t i a l agreement i s t o o s m a l l ( 0 . 1 eV) c o m p a r a t i v e l y t o t h e t e m p e r a t u r e range a l o n g which thermal a c t i v a t i o n i s o p e r a t i v e .

C5-292 JOURNAL DE PHYSIQUE

with

U.

interaction energy

a,,,

mechanical depinning s t r e s s .

Along the temperature range where the

TGL

model

10 i s v a l i d , such

U

a r e l a t i o n allows us t o expect a l i n e a r variation of s t r a i n amplitude

E (E = -)

E

as a function of

T ~ /

f o r a given level of

~ A,,L.

Besides, a c r i t i c a l temperature

Tc can be determined by the intercept of t h i s s t r a i g h t variation w i t h temperature

axis i .e. f o r zero s t r e s s . The mathematical development of t h i s model

[9

1

links

such a c r i t i c a l temperature

Tc

t o interaction energy

U.

with the following

r e l a t i o n

:

U,

-

23

k

Tc

Figure 5 shows variation of experi-

mental s t r a i n amplitude

E

versus

T " ~

f o r a given level of internal f r i c t i o n

AHL

(10-l) and f o r d i f f e r e n t annealing

s t a t e s . Only along the low temperature

part,experimental data seem t o be consis-

t e n t

w i t h

t h e predicted r e s u l t s of the mo-

del

.

R1 1 these extrapolated s t r a i g h t l i n e s

determine an approximated c r i t i c a l Tempera

t u r e

Tc

of 250K which leads, using the

preceeding re1 a t i o n , t o an i n t e r a c t i o n

energy

U.

=

0.5 eV. About the high tem-

perature p a r t , the TSL model i s no more

v e r i f i e d . This deviation could be due e i -

t h e r t o the interaction of dislocations

with another type of pinning point, o r t o

the f a c t t h a t the

TGL.

model i s no more

Fig. 5

:

Variation of

E

versus

T

valid in t h i s temperature range.

3

f o r the same level of ~ ~ ~ ( 1 0 -

)

and f o r

-

various annealing s t a t e s . a

:

293K,

b :

366K, c

:

429K, d

:

521K,

e

:

5931:.

In order t o get a more extensive analysis of these experi~ilental results,

a

numerical analysis of internal f r i c t i o n

bH

due t o dislocation breakaway has been

undertaken extending a study developed by Vincent e t a l . 1111.

1 ~ 1 1 1 1 1 ~

L

,

L

, l , l , I , l

l o o p and t h e o t h e r p i n n i n g p o i n b

l

a r e r e g u l a r l y spaced.

F i g . 6 : C o n f i g u r a t i o n o f a pinned d i s l o c a t i o n

A r e l i a b l e value f o r i n t e r a c t i o n energy U. (0.5 eV) i s choosen and t h e n , a c t i v a t i o n energies f o r depinning UD and r e p i n n i n g UR f o r each p i n n i n g p o i n t are computed essuming t h a t t h e d i s l o c a t i o n depinning s t a r t s from t h e l a r g e s t l o o p and continues one p o i n t a t a time. U,, U, a r e computed by t h e r e l a t i o n s (1) ,(2):

where : A and B a r e c o e f f i c i e n t s depending upon several parameters which d e t e r - mine the d i s l o c a t i o n c o n f i g u r a t i o n o D : mechanical s t r e s s f o r depinning

uR : r e p i n n i n g s t r e s s .

Both o f these stresses depend upon t h e number o f each p i n n i n g p o i n t . The r e l a t i o n s (1) and ( 2 ) a r e v a l i d f o r U < oD and a

>

oR.

The r a t e t h e o r y allows

t o compute t h e area swept by d i s l o c a t i o n s and consequently t h e s t r a i n - s t r e s s c y c l e from which AH i s deduced.

F i g u r e 7 shows t h e f i r s t r e s u l t s o f t h i s c a l c u l a t i o n ; t h e a p p l i e d s t r e s s amplitude a i s p l o t t e d versus T~~~

a t constant l e v e l o f A!!. The main para- meters a r e given h e r e a f t e r :

-

number o f p i n n i n g p o i n t s N = 9

-

c e n t r a l l o o p l e n g t h L = lOOb ( b :

Burger ' S v e c t o r )

- r a t i o L11 = 2.

Along t h e main p a r t o f t h e temperature range a l i n e a r p l o t i s obtatned. Such a 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 r e l a - t i o n s (1) and ( 2 ) . Indeed, f o r an i n t e r - F i g . 7 :

a/u

versus T ~ a t constant / ~ n a l f r i c t i o n l e v e l , t h e depinned f r a c -

A~ t i o n ( i .e. t h e depinning p r o b a b i l i t y )

i s almost constant; thus we have :

CS-294 JOURNAL DE PHYSIQUE

Furthermore t h e diagrams o f energy

NdF"!:d

presented on F i g u r e Sa, b c o n f i r m t h a t i n t h e low temperature range,

• a * • 0) t h e t h e r m a l l y a c t i v a t e d depinning

o f the f i r s t p i n n i n g p o i n t i s s u f f i -

c3

@

0

c i e n t t o i n i t i a t e t h e mechanical breakaway o f t h e whole d i s l o c a t i o n . F i g . 8 : Diagrams o f energy f o r various Along t h e h i g h temperature p a r t stresses. Figrrre 8c shows t h a t successive

t h e r m a l l y a c t i v a t e d depinnings a r e

l/

necessary t o t r i g g e r t h e whole breakaway. Then, t h e l i n e a r i t y o f the TGL law cr (T 2) i s n a t u r a l l y no more expected i n these c o n d i t i o n s . T h i s 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 conclusion o f Teutonic0 e t a l . 112). Therefore, t h i s work shows t h a t the analy- s i s o f t h e experimental r e s u l t s according t o t h e TGL model has t o be conftrmed. I n o r d e r t o f i t b e t t e r the experimental c o n d i t i o n s , we must complete o u r c a l c u l a t i o n i n p a r t i c u l a r i n c l u d i n g a d i s t r i b u t i o n o f d i f f e r e n t parameters ( l o o p l e n g t h s f o r example).

References

(l] GABBAY, N., ESROUF, C., FAITOZZT, G. J. Phys. L e t t e r s , 39, L-271, 1478.

[ 2 ] FAFITOZZI, G., GA88AY, M., I n t e r n a l F r i c t i o n and U1 t r a s o n i c A t t e n u a t i o n

.I'n

S o l i d s , E d i t o r C.C. Smith, Pergamon Press, Oxford, 1980, p. 395.

( 3 ) GABBAY, N . , FANTOZZI, G., 2" dorkshop on " I n t e r a c t i o n between O i s l o c a t i o n s and Defects i n Oxides" S t - D i d i e r au blont d'Or, Sept. 1980, t o be published i n J. Phys.

[ 4 ] PEREZ, J., PEGUIN, P., FAblTOZZT, G., GOSIX, ?.F., Ann. Phys. 5, 303-352, 1970. [ 5 ] GRANATO, A.V., LUCKE, K., J. Appl. Phys., 27, 533, 1956.

[6] SAUL, R.E., BAUER, C.L., J. Appl. Plqys., 39, 3, 1469, 1963.

[7]

FRIEDEL, J., Conference Teddington, Rfddlesex, 410, 1963.

[ a ]

TEUTONICO, L.J., SRANATO, A., LUCKE, K., J. Appl. Phys., 35, 220, 1954.

[

91 FANTOZZI, S., These Lyon, 1971.

[l11

VINCENT, A., PEREZ, J., P h i l . i'lag. A, 40, 3, 377-397.