ANELASTIC RELAXATION OF METALLIC GLASSES

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ANELASTIC RELAXATION OF METALLIC GLASSES

E. Woldt, H. Neuhäuser

To cite this version:

E. Woldt, H. Neuhäuser. ANELASTIC RELAXATION OF METALLIC GLASSES. Journal de

Physique Colloques, 1980, 41 (C8), pp.C8-846-C8-849. �10.1051/jphyscol:19808208�. �jpa-00220313�

JOURNAL DE PHYSIQUE Colloque C6, suppldment nu n08, Tome 41, aou't 1980, pageC8-846

ANELASTIC RELAXATION O F METALLIC GLASSES

E . Woldt and H . Meuhzuser

I n s t i t u t . A fiir Physik, Technische Universitiit, 0-3300 Braunschweig, Germany ( F R C I .

1. I n t r o d u c t i o n

M e t a l l i c glasses produced by extremely r a p i d quench- i n g o f t h e m e l t e x h i b i t a metastable s t r u c t u r e from thermodynamical p r i n c i p l e s /I/. The f r o z e n - i n l i q u i d s t r u c t u r e may be considered t o c o n t a i n excess o r f r e e volume /2,3,4/ which i s b e l i e v e d t o p l a y an important r o l e i n t h e mechanisms o f deformation o f the glassy m a t e r i a l /5,6,7/. The f r e e volume a l s o appears t o be i n v o l v e d i n s t r u c t u r a l r e l a x a t i o n s upon anneal ing/8,9/ and perhaps i n t h e embrittlement a f t e r annealing a t temperatures f a r below c r y s t a l l i - z a t i o n /10,11/.

I n t h i s work conventional s t r e s s r e l a x a t i o n e x p e r i - ments i n t e n s i o n ( s i m i l a r t o /12,13/) have beer1 per- formed t o examine t h e s t a b i l i t y o f t h e glassy s t r u c - t u r e under l o a d as w e l l as t h e e f f e c t o f s l i g h t an- nealing. From measurements o f t h e temperature and s t r e s s dependence o f a n e l a s t i c s t r e s s r e l a x a t i o n an attempt i s made t o estimate t h e shape o f t h e spec- trum o f a c t i v a t i o n energies f o r s t r u c t u r a l r e l a x a - t i o n s o f the Metglas 2826A.

2. Experimental D e t a i l s

M e t a l l i c glass r i b b o n s o f type 2826A (Fe32Ni36Cr14- P12B6, A l l i e d Chemical) w i t h p o l i s h e d edges ( w i d t h 2.25 mm, thickness 50 pm, f r e e l e n g t h 30 mm) were clamped i n t o f l a t g r i p s h e l d i n a s p e c i a l j i g f o r mounting (and demounting) f o r t e n s i l e t e s t s i n t h e I n s t r o n machine equipped w i t h a l o a d measuring de- v i c e o f increased s e n s i t i v i t y (maximum l o a d 500 N, r e s o l u t i o n

5

5 mN). The machine c o u l d be c o n t r o l l e d by a microprocessor system which a l s o provided a f i r s t e v a l u a t i o n o f t h e raw data ( a p p r o p r i a t e ave- r a g i n g of l o a d readings i n adapted i n t e r v d l s ) . Load r e l a x a t i o n P ( t ) was recorded w i t h e l e c t r i c a l l y sup- pressed zero l o a d l e v e l a t h i g h s e n s i t i v i t y a f t e r l o a d i n g w i t h a cross-head speed o f 0.01 cm/min t o d i f f e r e n t l o a d l e v e l s , a f t e r repeated loading/unloa- d i n g c y c l e s w i t h v a r i o u s w a i t i n g times a t zero load, as w e l l as a t several temperatures between -94 and +61 OC. Samples were used i n t h e asquenched condi-

t i o n as w e l l as a f t e r annealing treatments i n A r atmosphere f o r 20 h a t temperatures o f 80, 120, 160, and 200 OC.

The measured r e l a x a t i o n curves were evaluated by f i t t i n g t h e r e l a t i o n

(1) P = P, + T p i exp(-t/zi)

which w i l l be j u s t i f i e d below as a s i m p l i f i e d ap- proach t o t h e continuous spectrum o f r e l a x a t i o n times 'tactually present. Combining t h e g r a p h i c a l method o f /14/ w i t h a computer o p t i m i z a t i o n , 4 r e -

l a x a t i o n times

ri

were found t o be s u f f i c i e n t t o ap- proximate t h e curves i n t h e i n t e r v a l 1 5 t ( s ) 5 1 0 3 w i t h i n an accuracy o f

dnP

- 3 % . Eventual c o r r e c -

t i o n s f o r machine c h a r a c t e r i s t i c s , t h e r m o e l a s t i c e f f e c t and temperature f l u c t u a t i o n s were checked.

Because o f general d i f f i c u l t i e s t o e s t a b l i s h a w e l l - d e f i n e d s t r e s s s t a t e i n t h e v e r y t h i n sample o f non- u n i f o r m cross s e c t i o n o n l y r e l a t i v e trends o f r e - s u l t s taken from t h e same sample w i l l be evaluated.

3. Results

3.1. Repeated l o a d i n g and s t r e s s r e l a x a t i o n o f as- quenched specimens.

H y s t e r e s i s e f f e c t s observed d u r i n g loading/unloading c y c l e s i n d i c a t e d u r i n g f i r s t l o a d i n g some i r r e v e r - s i b l e deformation and d u r i n g f o l l o w i n g l o a d i n g s an- e l a s t i c deformations most o f which occur i n times s h o r t enough t o be n e a r l y completed d u r i n g t h e load- i n g time. Therefore, t h e apparent Young's modulus E~~~ (Fig. 1 ) c a l c u l a t e d from recorded load, elonga- t i o n and measured cross section, and c o r r e c t e d f o r r e l a x a t i o n s w i t h <>2 s, increases a f t e r t h e f i r s t l o a d i n g and i s s m a l l e r than values determined by dynamic methods (e.g. /15/).

I f t h e l o a d i s k e p t a t i t s maximum value f o r some time t h e w i d t h o f t h e h y s t e r e s i s increases. These a d d i t i o n a l a n e l a s t i c processes a r e examined i n more d e t a i l on l o a d r e l a x a t i o n curves recorded a f t e r stopping t h e machine cross-head a t Po = 150 N f o r tR = 13 min. Repeated l o a d r e l a x a t i o n a f t e r unload- i n g , w a i t i n g a t zero l o a d f o r tw = 34 min and r e -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19808208

number of lood~ng

- , . . . . , - , , . , , . r . , - C

16.

not annealed spec~men o

F i g . 1 Apparent Young's modulus measured on annealed and n o t annealed specimens d u r i n g several successive loadings.

l o a d i n g t o Po showed l e s s r e l a x a t i o n than before.

Results from several c y c l e s o f t h i s k i n d are given i n Fig. 2 where t h e t o t a l l o a d r e l a x a t i o n A P ( t ) =

R Po

-

P ( t R ) a f t e r a time o f tR = 13 min i s p l o t t e d versus t h e number o f r e l a x a t i o n experiments. k l a i t i n g times a t zero l o a d f o r 34 min and 7 d a r e i n d i c a t e d a t the abscissa. Obviously tw., though exceeding tR considerably, i s n o t l o n g enough t o recover t h e r e - l a x a t i o n process completely ( t h i s can be estimated

0 1 (w)wa/t/ng t~me at zero load 0 f i j t i ' 1 7 ' ' f i o t i 3 i 6 in)

v

⁷⁶

v

⁷⁶

v

⁷⁶

v

⁷⁶

v _}

( w ) 34m1n 34m1n 34mm 34mtn 34rnm

t 4 t t

F i g . 3 C o n t r i b u t i o n s t o l o a d r e l a x a t i o n w i t h 4 r e l a - x a t i o n times ( T ~ , . . z 4 ) measured on 2 speci- mens d u r i n g successive loadings a f t e r v a r i o u s w a i t i n g times and annealing treatments a t zero l o a d between loadings, and p l o t t e d i n r e l a t i o n t o t h e c o n t r i b u t i o n s Pi(l.) on f i r s t l o a d i n g i n t h e as-quenched c o n d i t i o n :

i=1: T1=2 s, P1(l. 0 )=0.25 N, P1(l. )=0.25N i=2: T25=9 s, P2(1. A)=0.35 N, P2(1. r)=0.31N i = 3 : T3=80s, P3(1. a)=0.29 N, P3(1. r)=0.26N i = 4 : 'irq*800s, P 4 ( l . v)=0.35 N, P 4 ( l . *)=O.70N t o occur o n l y a f t e r tWe1o9 s ) .

A n a l y s i s o f t h e 1 oad r e l a x a t i o n curves according t o e q . ( l ) shows t h a t t h e c o n t r i b u t i o n Pi o f each r e l a - x a t i o n t i m e zi f o l l o w s a s i m i l a r course as shbwn i n Fig.2, t h e l o n g e s t t i m e ( z 4 ) c o n t r i b u t i n g t h e major

p a r t . ⁱ

(n) number of relaxot~on (w) watting tlme at zero load

Fig. 2 T o t a l l o a d r e l a x a t i o n a f t e r tR = 13 min mea- sured on several successive l o a d i n g s w i t h v a r i o u s w a i t i n g times a t zero l o a d between.

3.2. Load r e l a x a t i o n on annealed specimens A s i m i l a r procedure o f repeated l o a d r e l a x a t i o n s was performed on specimens annealed stepwise f o r 20 h a t 80, 120, 160, and 200 OC. F i g . 3 gives some r e - s u l t s on two specimens p l o t t e d as r e l a t i v e c o n t r i b u - t i o n s o f t h e processes o f t h e

4

r e l a x a t i o n tinles P i / P i ( f i r s t l o a d i n g ) versus t h e number o f e x p e r i - ments and annealing treatments. Waiting times a t zero l o a d a r e s i m i l a r as i n 3.1.

A f t e r annealing below 160 OC t h e c o n t r i b u t i o n s o f --c4 and l a t e r o f

zj

decrease considerably, w h i l e y2 andYl f i r s t increase, l a t e r a l s o decrease, i . e . t h e l o n g r e l a x a t i o n times s h i f t t o s h o r t e r ones w i t h i n - c r e a s i n g annealing treatment ( r e l a x a t i o n times <1 t o 2 s cannot be measured by t h e l o a d r e l a x a t i o n ex- periment). Young's modulus remains constant d u r i n g these treatments ( F i g . 1).

JOURNAL DE PHYSIQUE

A q u i t e d i f f e r e n t behaviour occurs a f t e r annealing c o r d i n g t o i t s random s t r u c t u r e a r e c h a r a c t e r i z e d by f o r 20 h a t 200 OC. The c o n t r i b u t i o n s of t h e l o n g e s t n o n - s y m e t r i c a l p o t e n t i a l w e l l s . An imposed e x t e r n a l r e l a x a t i o n time ('r4) increases considerably. Simul- l o a d w i l l d i s t u r b the metastable e q u i l i b r i u m and taneously Young's modulus increases d i s t i n c t l y ( F i g . some rearrangements wi 11 occur w i t h n o t a b l e frequen- 1) and t h e m a t e r i a l becomes b r i t t l e : most samples cy. The k i n e t i c s of these processes can be described a f t e r the 200 OC anneal break d u r i n g f i r s t loading. approximately along l i n e s g i v e n e a r l y by Becker /16/

3.3. Temperature dependence o f l o a d r e l a x a t i o n . and l a t e r by Argon /17/ f o r a n e l a s t i c a f t e r e f f e c t s . The dependence o f l o a d r e l a x a t i o n on temperature was ^{A S} the load effect is it can measured i n a l i m i t e d temperature range t o a v o i d be approximated by e q . ( l ) w i t h

s t r u c t u r a l changes a t h i g h e r temperatures. Consider- ('1 Ti ='To exp(AGi/kT)

a b l e d i f f i c u l t i e s were encountered because of tern- ^(OGi = free e n t h a l ~ ~ t h r e s h o l d f o r thermal a c t i v a - p e r a t u r e f l u c t u a t i o n s which d i s t u r b the h i g h l y sensi- tion* To = 11/2V~, 'D = Debye frequency / 5 9 7 / ) and t i v e l o a d measurements considerably. Therefore, o n l y

( 3 ) A N V ' P ' f .

P. = O 0 . - 1

3 measurements a r e shown i n F i g . 4 where no tempera-

'

^{'"gkT 'oQo Ti}

t u r e d r i f t was observed o r where the f l u c t u a t i o n s

w i t h fi = number o f r e l a x i n g regions w i t h f r e e a c t i - c o u l d be c o r r e c t e d s a t i s f a c t o r i l y . I n F i g . 4 t h e con-

v a t i o n e n t h a l p y bGi ( s t r i c t l y speaking fi a l s o con- t r i b u t i o n s t o l o a d r e l a x a t i o n o f t h e zi values a r e

t a i n s an eventual d i s t r i b u t i o n o f vw values f o r d i f -

given The for very short

ferent k i ) , N = total number of relaxing regions, and very l o n g times a r e r a t h e r u n c e r t a i n . l l i t h de- vw = t h e i r mean volume, Vo = specimen volume, Qo =

creasing T the c o n t r i b u t i o n s s h i f t t o l o n g e r r e l a -

specimen c r o s s section, Poo= f i n a l value o f l o a d x a t i o n times as expected f o r a t h e r m a l l y a c t i v a t e d

after relaxing all regions. A is a constant of the mechanism.

o r d e r o f 1 depending on t h e exact n a t u r e o f t h e a t o -

4. Discussion mic rearrangement which occurs i n each r e l a x i n g r e -

F~~~ t h e trends observed d u r i n g repeated l o a d r e l a - gion and produces some e l o n g a t i o n of t h e specimen x a t i o n on as-quenched and annealed m e t a l l i c g l a s s /I7/ orland some decrease of i t s l o a d c a r r y i n g cross specimens we can o b t a i n some conclusions r e g a r d i n g s e c t i o n /16/.

t h e s t a b i l i t y and s t r u c t u r a l r e l a x a t i o n s o f the ma- The range o f r e l a x a t i o n times o r a c t i v a t i o n energies terial on loading and on slight annealing treatments. obtained from one l o a d r e l a x a t i o n experiment i s l i m i - The observed tendencies o f h y s t e r e s i s loops, appa- ted: 2 L x i ( s ) k 850 o r a t T = 300 K 0.79 s B i ( e V ) g r e n t Young's modulus, and repeated l o a d 0.95 (assuming v~ = 9 . 6 ' 1 0 ~ ~ s'l). From F i g . 4 and (,-f. /12/) on as-quenched samples show a temporal eqs. ('1 * ( 3 ) we estimate the spectrum H = asymmetry of the r e l a x a t i o n processes. his suggests f(AG)/N of r e g i o n s w i t h f r e e a c t i v a t i o n e n t h a l p ~ ~6 t h a t t h e atomic p o s i t i o n s i n t h e m e t a l l i c glass ac- Fig. 5 f o r T = 300 and 334 K, assuming a c o n t i n u -

A

p,

^[NI ous spectrum which does n o t change i n t h e small tem-

1 5 . + p e r a t u r e i n t e r v a l , and assuming t h e same t o t a l num-

.

^x\

-

T=300K

P,: ^150N

%

= 150 N

---

T = 334 K

10. \ \ x---\

( e v - l )

0 5.

0 1.

i---l

\ \ ^--I _\ ^{1 I}

\ ^{+ \ \} \

179K

\ ' 3 0 0 ~

\

'

^{+ \}

;>334 K \

\ \ _\ \

\ \ ^{\ 'x} \

2

i

' j j ' 5 ' jO 20 50 1

Fig. 4 C o n t r i b u t i o n s t o l o a d r e l a x a t i o n w i t h 4 r e l a - 0.7 08 0.9 10 1.1 A G C e V l xation times measured (after several l o a d i n g s F i g . 5 Frequency spectrum of a c t i v a t i o n enthal p i e s a t room temperature) on t h e same specimen a t f o r r e l a x a t i o n processes d e r i v e d from mea- temperatures o f T = 179, 300, and 334 K. surements a t 300 and 334 K ( F i g . 4 ) .

ber N o f processes ( t h e l a t t e r assumption i s n o t v a l i d f o r t h e measurement a t 179 K, t h e r e f o r e i t s spectrum cannot be i n c o r p o r a t e d i n t o F i g . 5 ) . The spectra a r e q u a l i t a t i v e l y s i m i l a r t o those d e t e r - mined by Argon and Kuo /18/ from creep t e s t s a t h i g h e r temperatures f o r several o t h e r metal glasses (AlCuZr, CuZr, PdSi) and i n d i c a t e t h a t r e l a x a t i o n s i t e s w i t h h i g h AG, i . e . l o n g 7 a r e much more f r e - quent than those w i t h s h o r t 7 .

The concept o f f r e e volume i n m e t a l l i c glasses sug- gests t h a t r e g i o n s w i t h r e l a t i v e l y l a r g e f r e e volume should p e r m i t atomic rearrangements w i t h small a c t i - v a t i o n energy ( s h o r t 'C), those w i t h small f r e e vo- 1 ume should correspond t o rearrangements w i t h 1 ong

z

values ( c f . / 5 / ) .

The change o f l o a d r e l a x a t i o n curves w i t h repeated l o a d i n g (as-quenched specimens) i n d i c a t e s t h a t on f i r s t l o a d i n g some " i r r e v e r s i b l e " ( i n t h e times o f measurement) rearrangements have occurred. During f u r t h e r l o a d i n g s a c e r t a i n e q u i l i b r i u m between r e - arrangements and recovery o f the d i f f e r e n t r e l a x a - t i o n processes i s approached which i s determined by t h e r e l a t i o n between l o a d i n g and w a i t i n g times.

The behaviour a f t e r s l i g h t annealing treatments ( 6 160 OC) (no change i n t h e apparent modulus, F i g . 1, however, a change i n t h e c o n t r i b u t i o n s P i ( ~ i ) , F i g . 3) would mean i n t h e p i c t u r e above t h a t d u r i n g t h i s treatment small f r e e volumes segregate t o l a r - ger ones remaining t h e same i n t o t a l . From eq. (3) and t h e n o r m a l i z i n g c o n d i t i o n we can estimate t h e t o t a l r e l a x i n g volume t o be i n t h e o r d e r o f Nvw

=

nm3 = 0.3 %o Yo ( n e g l e c t i n g t h e small c o n t r i - b u t i o n w i t h < 2 s). Eqs.(l),(3) a r e v a l i d i f vw i s smaller o r i n t h e o r d e r o f t h e mean f r e e volume per atom ( ~ 0 . 3 vatom /19/).

During annealing a t 200 OC, on t h e o t h e r hand, t h e modulus increases d e f i n i t e l y (Fig.1) and some f r e e volume disappears ( c f . increase o f d e n s i t y

P

by an- n e a l i n g o f several o t h e r s i m i l a r glasses /20/). Fur- t h e r , t h e increase o f the c o n t r i b u t i o n o f z4 c o u l d i n d i c a t e t h a t new small f r e e volumes have been pro- duced, perhaps by decomposition o f l a r g e ones o r by f i l l i n g them up w i t h some d i f f u s i n g atom species.

Both e f f e c t s c o u l d e x p l a i n t h e tendency t o e m b r i t t - lement

/lo,

11/ which commences a f t e r t h i s annealing treatment. A s i m i l a r d e s t r u c t i o n o f f r e e volume a f t e r annealing f o r h 2 h a t 250 ^OC has been observed r e c e n t l y by X-ray d i f f r a c t i o n /8/, cf. a l s o /4/.

I n summary, from a n e l a s t i c s t r e s s r e l a x a t i o n mea- surements on Metglas 2826A i n the as-quenched and

s l i g h t l y annealed c o n d i t i o n we f i n d the f o l l o w i n g r e s u l t s and conclusions which may be o f i n t e r e s t f o r p r a c t i c a l a p p l i c a t i o n s o f these m a t e r i a l s : ( 1 ) The metastable s t r u c t u r e w i t h asymmetrical po- t e n t i a l w e l l s f o r atomic rearrangements g i v e s r i s e t o an i n h e r e n t temporal asymmetry o f a n e l a s t i c r e l a - x a t i o n processes. Therefore t h e whole preloading h i s t o r y e n t e r s i n t o t h e r e s u l t s o f any experiment.

T h i s makes i t d i f f i c u l t t o o b t a i n r e p r o d u c i b l e r e - s u l t s f o r mechanical p r o p e r t i e s .

( 2 ) The apparent Young's modulus seems t o increase a f t e r f i r s t l o a d i n g o f t h e m a t e r i a l . P o s s i b l y some f r e e volume i s removed permanently from t h e as- quenched s t r u c t u r e by t h i s f i r s t 'loading.

( 3 ) S l i g h t annealing treatments w i t h temperatures up t o 160 OC (20 h) change t h e s t r u c t u r e s l i g h t l y ; i n t h i s temperature i n t e r v a l f r e e volume seems t o segregate i n t o l a r g e r u n i t s , b u t s t i l l remains i n t h e sample which keeps i t s d u c t i l i t y .

( 4 ) Annealing f o r 20 h a t 200 OC, however, increases Young's modulus and produces a tendency f o r e m b r i t t - lement. Probably some l a r g e f r e e volume disappears and some decomposes i n t o many small f r e e volumes o r i s f i l l e d up by a d i f f u s i n g atom species.

Acknowledgements. F i n a n c i a l support by t h e Deutsche Forschungsgemeinschaft i s g r a t e f u l l y acknowledged.

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