MECHANICAL ALLOYING : FAR FROM EQUILIBRIUM PHASE TRANSITIONS ?

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MECHANICAL ALLOYING : FAR FROM EQUILIBRIUM PHASE TRANSITIONS ?

G. Martin, E. Gaffet

To cite this version:

G. Martin, E. Gaffet. MECHANICAL ALLOYING : FAR FROM EQUILIBRIUM PHASE TRANSI- TIONS ?. Journal de Physique Colloques, 1990, 51 (C4), pp.C4-71-C4-77. �10.1051/jphyscol:1990408�.

�jpa-00230768�

MECHANICAL ALLOYING : FAR FROM EQUILIBRIUM PHASE TRANSITIONS ?

G. MARTIN and E. GAFFET*

Centre dlEtudes Nucl6aires de Saclay, DTM/SRMP, F-91191 Gif sur Yvette Fedex, France

CNRS-CECM, 15, Rue Georges Urbain, F-94407 Vitry sur Seine Cedex, France

Un compose en cours de broyage subit en parallble une succession de d6formations (qui le dbsordonnent) et un recuit thermique. I1 acquiert dans ces conditions une structure stationnaire.Cette situation rappelle celle des alliages sous irradiation pour lesquels une thermodynamique des systbmes forcbs est en cours de dbveloppement.

Apr&s une breve presentation de cette dernibre, on montre comment l'appliquer au cas du broyage : le premier diagrame expdrimental d'equilibre dynamique entre cristal et amorphe, en broyage mecanique est presente.

Abstract In the course of ball milling, a compound undergoes repeated shearing in parallel to thermal annealing, and acquires a steady-state structure. This is reminiscent of alloys under irradiation for which thermodynamics of forced systems is under development. After a brief presentation thereof, we show how it may be applied to ball milling.

The first experimentally determined diagram for the crystal-amorphous phase dynamical equilibrium under ball milling is presented.

The recent development of high energy ball milling techniques for preparing alloys with unusual compositions or crystallographic structure, raises many interesting questions with fundamental interest /l/ : in particular is there a phenomenology capable of predicting which milling conditions to select for achieving an a priori chosen structure and/or microstructure ?

Some experimental work has been done along this line, either by performing milling at two distinct temperatures or with distinct devices /2-

6/.

Amorphization by ball milling is a good topic to address for such a discussion, since it has been widely studied. The various mechanisms proposed for ball milling amorphization (BMA), have up to now been ruled out by experiment :

-

^BMA is not a mere enhancement of amorphization by solid state interdiffusion : indeed, VZr which is not a fast diffusing system can be amorphized by BM /7/. Moreover, a negative heat of mixing is not a prerequisite for BMA which was observed in pure Si /8/, in AgCu /2/ or WCu /9a/, SiSn, SiZn /9b/.

-

the amorphous structure can be reached either by mixing pure elements or by milling an equilibrium compound or a mixture of such compounds, with the same compositions : BMA is therefore not driven by a decrease of free energy /10/.

On the other hand, it is well accepted that amorphization results in compounds with large negative mixing enthalpies, when the local chemical order is brought too far away from its thermal equilibrium value /11-14/.

This argument may be of broader applicability, e.g. work for systems with large size effects, with positive mixing enthalpy as well /IS/. For the sake of clarity let us assume that amorphization results from imposing to the crystalline structure a steady nonequilibrium degree of order. The questions then are : can we predict the degree and type of ordering to result from

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1990408

COLLOQUE DE PHYSIQUE

given BM c o n d i t i o n s ? ; how t o d e f i n e t h e BM c o n d i t i o n s , i . e . t h e c o n t r o l parameters of BM ?

In t h e course of BM, a compound undergoes simultaneous atomic mixing by shear and t h e r m a l l y a c t i v a t e d d i f f u s i o n t o lower energy c o n f i g u r a t i o n s . This i s r e m i n i s c e n t of compounds under heavy p a r t i c l e i r r a d i a t i o n , f o r which a s o p h i s t i c a t e d phenomenology i s being developed /16/. A f t e r a b r i e f survey t h e r e o f , we show how t o apply t h i s t e c h n i q u e t o BM and show p r e l i m i n a r y r e s u l t s t o i l l u s t r a t e t h e procedure.

An AxBy compound s u b j e c t e d t o s t e a d y s h e a r i n g may b e viewed a s an ordered a l l o y where atoms exchange s u b l a t t i c e by two d i s t i n c t mechanisms a c t i n g i n p a r a l l e l : one c o n s i s t s of thermally a c t i v a t e d jumps of atoms, t h e second i s d r i v e n by s h e a r i n g and i n d u c e s d i s o r d e r / 1 7 / . The d e t a i l e d mechanism by which such d i s o r d e r i s f o r c e d i n t o t h e compound i s not c l e a r . The t h e r m a l l y a c t i v a t e d jumps, when a c t i n g i n t h e absence of f o r c e d jumps d r i v e t h e compound t o i t s e q u i l i b r i u m c o n f i g u r a t i o n , d e f i n e d a t a mesoscopic s c a l e by an o r d e r parameter ( e . g . t h e occupancy C i , i

-+

^{1, S ,} of t h e S

s u b l a t t i c e s forming t h e c r y s t a l ) . I f we d e s c r i b e t h e thermodynamics of t h e compound i n t h e Bragg Williams approximation, s i m p l e i n t e r a t o m i c bond c o u n t i n g y i e l d s a s p e c i f i c f r e e energy f u n c t i o n f (C) ( t h e v e c t o r C h a s components C i ) which g i v e s t h e t h e r m a l e q u i l i b r i u m p r o b a b i l i t y of t h e c o n f i g u r a t i o n C a s :

P (C) = Z-1 exp

- p 6

^{f ( c )} (1)

with

p

^{= l/kgT, Z} t h e p a r t i t i o n f u n c t i o n , A t h e number of l a t t i c e s i t e s i n t h e compound. A t t h e a t o m i s t i c l e v e l , t h i s i m p l i e s t h a t t h e t h e r m a l l y a c t i v a t e d atomic jumps occur i n such a way a s t o e x p l o r e t h e c o n f i g u r a t i o n C with a p r o b a b i l i t y given by ( 1 ) . A simple way of b u i l d i n g a k i n e t i c model with t h e l a t t e r p r o p e r t y i s t o assume t h a t t h e a c t i v a t i o n energy b a r r i e r f o r an AB i n t e r c h a n g e among two neighbouring s i t e s i s a l i n e a r f u n c t i o n of t h e binding energy of t h e p a i r t o t h e s e s i t e s .

If we e v a l u a t e t h e l a t t e r energy by bond counting t o t h e same degree of s o p h i s t i c a t i o n a s used f o r c a l c u l a t i n g f ( C ) , it i s found t h a t P ( C ) a s given by e q . (1) i s t h e s t e a d y s t a t e s o l u t i o n of t h e master equation governing t h e p r o b a b i l i t y o f a c o n f i g u r a t i o n C i n t h e compound undergoing t h e r m a l l y a c t i v a t e d atomic jumps only / 1 6 / :

t h

where, WC+C,is t h e t r a n s i t i o n r a t e from c o n f i g u r a t i o n C t o C' under t h e a c t i o n of t h e r m a l l y a c t i v a t e d jumps only. When forced jumps a c t i n p a r a l l e l t o t h e former, t h e t r a n s i t i o n r a t e s

wth

i n eq. ( 2 ) must be r e p l a c e d by

where ~f s t a n d s f o r t h e forced jumps. The l a t t e r occurs with a frequency not r e l a t e d t o t h e l o c a l c o n f i g u r a t i o n . I t may be shown /16/ t h a t t h e s t e a d y s t a t e s o l u t i o n of e q . ( 2 ) with W given by ( 3 ) w r i t e s :

A

P (C) a e x p

-

^Qcp

cc)

( 4 )

where (+l can be computed numerically, and i s a f u n c t i o n of t h e temperature, t h e entropy of t h e c o n f i g u r a t i o n C, t h e bond e n e r g i e s (but which appear i n a complicated form, not reducable t o t h e i n t e r n a l energy of C ) , and t h e r a t i o

Under such f o r c i n g , t h e more s t a b l e s t r u c t u r e w i l l b e of t y p e S, s i n c e t h e minimum of i s d e e p e r f o r S t h a n f o r L . A diagram f o r t h e d y n a m i c a l e q u i l i b r i u m between s u c h p h a s e s can be c o n s t r u c t e d : i n t h e YO, T p l a n e , r e g i o n s e x i s t where t h e minimum o f (P i s d e e p e r i n t h e S a s compared t o t h e L s t r u c t u r e , o t h e r s where t h e r e v e r s e i s t r u e . Numerical c o m p u t a t i o n of (P y i e l d s t h e boundary between s u c h r e g i o n s . F i g . 2 i s a n example o f a dynamical e q u i l i b r i u m phase diagram s o o b t a i n e d .

F i g . 1 : T y p i c a l shape o f (p (C) a s F i g . 2 : R e s u l t i n g dynamical

computed f o r two a l t e r n a t i v e e q u i l i b r i u m phase diagram. The phase s t r u c t u r e s (L,S) of t h e compound boundary between t h e s t r u c t u r e s S

Ni4Mo ( c f . /16/)

.

and L, i s s h i f t e d by about 100 K

when t h e cascade s i z e ( b ) i n c r e a s e s from 1 t o 100 ( c f . /16/)

..

The p o i n t we s t r e s s i s t h a t Ip i s b y no means a f r e e e n e r g y o f some c o n s t r a i n e d c o n f i g u r a t i o n . The r e a s o n f o r t h i s i s t h a t t h e c o n f i g u r a t i o n s p a c e o f t h e compound i s e x p l o r e d a c c o r d i n g t o a d i f f e r e n t r u l e t h a n i n t h e r m a l e q u i l i b r i u m !

The t h e o r y i s s o p h i s t i c a t e d enough f o r i n c l u d i n g "cascade s i z e

e f f e c t s " : f o r given yo and T v a l u e s , (P i s a f u n c t i o n of t h e number o f f o r c e d jumps which o c c u r s i m u l t a n e o u s l y . i . e . f o r c e d jumps w i t h a g i v e n a v e r a g e f r e q u e n c y may o c c u r by r a r e l a r g e b u r s t s o r f r e q u e n t s m a l l b u r s t s : t h e phase b o u n d a r i e s w i l l b e s h i f t e d a c c o r d i n g l y .

I f we a c c e p t t h e above p i c t u r e f o r a compound under BM, t h e s t e a d y s t a t e c o n f i g u r a t i o n o f t h e compound may be p r e d i c t e d from t h e f u n c t i o n (P i n s t e a d of t h e f r e e energy f . "BM c o n d i t i o n s " e n t e r (P by f o u r p a r a m e t e r s :

-

t h e a l l o y composition

-

t h e t e m p e r a t u r e

-

Y,J : t h e p r e f a c t o r o f t h e r a t i o of t h e frequency o f t h e f o r c e d atomic i n t e r c h a n g e s t o t h a t o f t h e t h @ r m a l l y a c t i v a t e d ones.

-

t h e "cascade s i z e " , i . e . t h e number o f f o r c e d a t o m i c jumps o c c u r i n g

" a t once", i . e . e v e r y t i m e a g r a i n of m a t e r i a l undergoes an impact.

COLLOQUE DE PHYSIQUE

The f i r s t two parameters may ( i n p r i n c i p l e ) be kept c o n s t a n t . The two l a t t e r ones depend i n a complicated way on t h e m i l l i n g machine. We consider b r i e f l y two t y p e s of devices : a v i b r a t i n g frame and a p l a n e t a r y m i l l .

We show i n a companion paper /18/ t h a t , f o r a v i b r a t i n g frame with a s i n g l e b a l l i n t h e c o n t a i n e r , assuming t h a t t h e whole k i n e t i c energy a t t h e impact of t h e b a l l with t h e c o n t a i n e r i s t r a n s f e r r e d t o t h e powder, t h e energy p e r impact s c a l e s with :

where m i s t h e mass of t h e b a l l , A and O r e s p e c t i v e l y t h e amplitude and p u l s a t i o n of t h e frame v i b r a t i o n . The impacts occur with a frequency of t h e o r d e r g/2WA ( g = g r a v i t y c o n s t a n t ) , s o t h a t t h e mechanical power i n j e c t e d i n t o t h e powder s c a l e s with :

M i l l i n g c o n d i t i o n s i n such a device a r e c h a r a c t e r i z e d by t h e r o t a t i o n speed of t h e d i s c

(a),

t h a t of t h e c o n t a i n e r r e l a t i v e t o d i s c ( W ) , t h e mass ( m ) , size and number of b a l l s , t h e r a d i u s of t h e d i s c ( R ) and of t h e c o n t a i n e r ( r ) , t h e amount of m a t t e r t o be m i l l e d .

Simple c a l c u l a t i o n shows t h a t depending on t h e r e l a t i v e v a l u e s of t h e r o t a t i o n f r e q u e n c i e s

(@/a)

and of t h e r a d i i ( r / R ) two extreme regimes may be achieved : e i t h e r t h e b a l l r o l l s on t h e i n n e r s u r f a c e of t h e c o n t a i n e r o r i t escapes and knocks an o p p o s i t e p o r t i o n of t h e s u r f a c e . I n b o t h c a s e s , t h e energy t r a n s f e r e d t o a s p e c i f i c a r e a s c a l e s with

ma2

and t h e frequency of occurence of such e v e n t s s c a l e s with a . The power i n j e c t e d mechanically t o t h e m a t e r i a l t h e r e f o r e s c a l e s with :

P = m12 Q2 o (5c)

where l2 i s a c h a r a c t e r i s t i c a r e a of t h e o r d e r o r r R f o r t h e r o l l i n g o r impact regime r e s p e c t i v e l y .

For making t h e c o n n e c t i o n with t h e t h e o r e t i c a l g u i d e p r e s e n t e d i n s e c t i o n 2, it i s reasonnable t o assume t h a t t h e frequency of f o r c e d jumps

(and a s a consequence 'yo i n cp) s c a l e s with' P . Indeed most of t h e power 8' i s d i s s i p a t e d i n t o h e a t , a small f r a c t i o n (= 10 % ) is i n j e c t e d i n t o t h e l a t t i c e i n t h e form of vacancies o r a n t i s i t e d e f e c t s /19/.

Dynamical e q u i l i b r i u m phase diagrams should t h e r e f o r e be looked f o r i n t h e '8 @ T plane.The r o l e of o i s more s u b t i l e : f o r a given P, decreasing O i m p l i e s t h a t t h e "damage" o c c u r s by l a r g e r b u r s t s ( l a r g e r T*cascades" a s i n t r o d u c e d i n s e c t i o n 2)

.

In t h e '8 8 T diagram, t h e b o u n d a r i e s of t h e s t a b i l i t y f i e l d s of phases should be O dependant.

For t h i s reason, a new p l a n e t a r y m i l l was b u i l t a t CECM-Vitry allowing t h e independant adjustement of a and

a

^{(R = 75 mm; r = 20 mm;}

a

^{I 700 rpm;}

101 1200 rpm. Such a device allows t o i n j e c t a mechanical power of some 1 0 - ~ eV/at.sec /20/ i n t h e m a t e r i a l being m i l l e d . A s d i s c u s s e d elsewhere /21/ t h e above f i g u r e i s t y p i c a l of what i s o b t a i n e d with i r r a d i a t i o n by p r o t o n s o r a p a r t i c l e s i n a Van de Graaf a c c e l e r a t o r . Phase changes a r e known t o be induced by such i r r a d i a t i o n (Fig. 3 ) .

e-Yande Graaf Ion Implantation

Nuclear Reacmn HYEM

Reported effece of irradiation on phase stability

F i g . 3 : S p e c i f i c power i n j e c t e d i n m a t e r i a l s , under t y p i c a l mechanical s t r a i n i n g o r i r r a d i a t i n g c o n d i t i o n s ( a f t e r r e f . / 2 1 / ) .

4

-

FIRST EXAMPLE OF A DYNAMICAL EOUILIBRIUM PHASE DIAGRAM UNDER B A U M I L L I N G

Following t h e above i d e a s a s y s t e m a t i c s e a r c h f o r m i l l i n g c o n d i t i o n s which promote amorphization i n a N i l o Z r 7 compound were i n v e s t i g a t e d . Indeed amorphizing t h i s composition was found t o be very s e n s i t i v e t o t h e m i l l i n g c o n d i t i o n s / S / . The p l a n e t a r y m i l l j u s t d e s c r i b e d was used : c o n t a i n e r s (hardened s t e e l ) were loaded, under d r i e d A r atmosphere, with -10 g of N i l o Z r 7 i n t h e form of melt spun ribbons; t h e c r y s t a l s t r u c t u r e of t h e ribbon was c o n t r o l l e d by X ray d i f f r a c t i o n . The c o n t a i n e r was t h e n s e a l e d with an 0 r i n g . The c o n t a i n e r s were f i l l e d with 5 b a l l s 15 mm i n diameter.

The p l a n e t a r y m i l l was o p e r a t e d a t v a r i o u s v a l u e s of and 0, a l l o t h e r parameters kept c o n s t a n t . The temperature however was n o t c o n t r o l l e d , but ranged from 30 t o 50 ' C . A f t e r m i l l i n g , f o r 35 t o 40 hours, t h e powder was c h a r a c t e r i z e d by X Ray d i f f r a c t i o n , (CoKff r a d i a t i o n ) ; t h e XRD p a t t e r n s were analyzed using t h e "ABF" r o u t i n e / 5 , 8 , 2 2 / . The m i l l i n g time was shown i n /5/

t o be s u f f i c i e n t t o reach a s t e a d y s t r u c t u r e f o r m i l l i n g c o n d i t i o n s t y p i c a l of t h o s e used h e r e .

R[rprn)

t ^,

^\

^.

tncreasing power

800 ^'\\/

\

F i g . 4 : A p o r t i o n of t h e dynamical e q u i l i b r i u m diagram of t h e amorphous phase i n N i l o Z r 7 under p l a n e t a r y BM :

f u l l y amorphized compound

0 steady mixture of c r y s t a l l i n e and amorphous phases

COLLOQUE DE PHYSIQUE

Fig. 4 summarizes the results. Filled circles imply a single amorphous phase, while half filled circles point to a mixture of amorphous and crystalline phases, in a steady amount.

A narrow domain of amorphization is clearly visible. It seems that amorphization proceeds below a certain power input (boundary (l)) and above a minimum energy per impact ((2)). It may be that if the former is too high, too much heating occurs. A minimum energy per impact requirement may be imposed by the yield stress of the particles.

Further data are necessary to fully define the amorphization domain in the Q, w, T space.

Building of phenomenology of phase stabilization by ball milling raises three types of difficulties :

1. identifying the atomistic processes by which mixing occurs at the atomic level.

2. relating the frequency of such processes to the milling conditions

3. predicting the most stable steady-state crystallographic structure in the presence of such processes.

As summarized in this paper, step 3 is being achieved with some sophistication, step 2 is still at a very nalve level and step 1 is almost untouched.

Systematic experimental data would be of great help for establishing steps 1 and 2.

Acknowledgments : Enlightening discussions with P. Bellon, F. Haider,

H. Bakker are gratefully acknowledged, as well as the technical contributions of J.Bigot and A.Dezellus for alloy ribbons preparation, and of A.Quivy for the achievment of XRD patterns.

REFERENCES

/l/ For a pionnering work : BENJAMIN, J.S., Sci. Amer.

a

(1976) 40 For a recent conference : "New materials by mechanical alloying", Eds Artz, E. and Schultz, L., DGM, FRG, 1989

/2/ RICHARDS, T.G., JOHARI, G.P., Phil. Mag. 3 (1988) 4 4 5

/3/ WEEBER, A.W., HAAG, W. J., WESTER, A. J., BAKKER, H. J. Less Common Met.

;L4a (1988) 119

/4/ CALKA, A. and RADLINSKI, A.P., Mat. Sci. Eng. (1989) 131 /S/ GAFFET, E., Mat. Sci. Eng. U (1989) 185

/6/ ECKERT, J., SCHULTZ, L., HELLSTERN, E., URBAN, K., J.A.P. 64 (1988) 3224

/7/ WEEBER, A.W. and BAKKER, H., 2 . fiir Chem. Phys. N.F. (1988) 221 /8/ GAFFET, E. and HARMELIN, M., J. Less Comm. Met.,

m

(1990) 210 /9a/ GAFFET, E. and LOUISON, C., this issue.

b GAFFET, E. and HARMELIN, M., this issue.

/10/ PETRICH, R.R. and SCHWARZ, R.B., J. Less Comm. Met. (1988) 171

/12/ LUZZI, D.E. and M E S H I I , M., R e s . Mechanics 21. ( 1 9 8 7 ) 2 0 7

/13/ MASSOBRIO, C . , P O N T I K I S V. and MARTIN, G . , P h y s . R e v . L e t . 6;! ( 1 9 8 9 ) 1 1 4 2

/ 1 4 / HSIEH, H. and Y I P , S., P h y S . R e v . B 32 ( 1 9 8 9 ) 7 4 7 6

/15/ JOHNSON, W.C. and FECHT, H . J . , J . L e s s Common M e t . l.45 ( 1 9 8 8 ) 6 3 EGAMI, T . and WASEDA, Y., J. N o n C r y s t . S o l i d s 64 ( 1 9 8 4 ) 113

/ 1 6 / BELLON, P . , MARTIN, G., P h y s . R e v . B 3 ( 1 9 8 9 ) 2 4 0 3 ; M a t . R e s . Soc.

S y m p . P r o c .

m

( 1 9 8 9 ) 15

HAIDER, F., BELLON, P . , DOAN,N.V., MARTIN, G . , P ~ o c . ICFRM-4, K y o t o , 1 9 8 9

/ 1 7 / KOCH, C.C., JANG, J . S . C . , LU, P . Y . , DMG C o n f e r e n c e , H i r s c h a u , pp. 1 0 1 /18/ CHEN, Y., LE H A Z I F , R . , MARTIN, G . , t h i s i s s u e

/ 1 9 / MECKING, H. and E S T R I N , Y . , S c r i p t a M e t . ( 1 9 8 0 ) 815

/ 2 0 / We a s s u m e t h a t t h e e n e r g y of an i m p a c t i s shared b y a s i n g l e l a y e r of p o w d e r p a r t i c l e s i n a n area scaled b y t h e b a l l r a d i u s .

/ 2 1 / MARTIN, G . , A n n . C h i m . F r . h ( 1 9 8 1 ) 4 6

/ 2 2 / ANTONIADIS, A., BERRUYER, J. AND FILHOL, A . , I n s t . L a u e L a n g e v i n I n t e r n a l R e p o r t ( 1 9 8 8 ) 8 7 A N 2 2 T .