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  • 8/3/2019 K.S. Vecchio, Li-Hsing Yu and M.A. Meyers- Shock Synthesis of Silicides- I. Experimentation and Microstructural Evol

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    ~ Pergamon Acta m etall , mater. Vo l. 42, No. 3, pp. 7 01-714, 1994Cop yright 1994 ElsevierScienceLt dPrinted in Gre at B ritain. All rights reserved0956-7151/94 $6.00 + 0.00

    S H O C K S Y N T H E S I S O F S I L IC I D E S - -I .E X P E R IM E N T A T I O N A N D M I C R O S T R U C T U R A L

    E V O L U T I O NK. S. V ECC HIO, LI-HSING YU and M. A. M EYERS

    De partm ent of Ap plied Mechanics and Eng ineering Sciences, University of California, San Diego,La Jol la, CA 92093-0411, U.S.A.(Rece i ved 1 6 S ep t em b er 1 9 9 2; in rev ised f o r m 2 3 Ju l y 1 9 9 3 )

    Ab stra ct--N iob ium and m olybd enum si l icides were synthesized by the passage of high-ampli tude shockwaves through elemental powder mixtures. These shock waves were generated by planar paral lel impactof explosively-accelerated f lyer plates on m om entum -trapped capsules containing the powders. Recoveryof the specimens revealed unreacted, part ial ly-reacted , and ful ly-reacted regions, in accord w ith shockenergy levels experienced by the po wder. Electron microscopy was employed to character ize the part ial ly -and ful ly-reacted regions for the Mo-Si and Nb-Si systems, and revealed only equil ibrium phases.Selected-area and convergent be am electron diffract ion com bined with X -ray microanalysis verif ied thecrystal s t ructure and composi t ions of the reacted products . Diffusion couples between Nb and Si werefabricated for the purp ose of measuring stat ic diffusion rates and determining the phases produ ced undernon-shock condit ion. Comparison of these non-shock diffusion resul ts with the shock synthesis resul tsindicates that a new m echanism is responsible fo r the prod uct ion o f the NbSi2 and MoSi2 phases und ershock com pression. A t the local level the react ion can b e rat ional ized, for example, in the N b-S i systemunder shock compression, through the product ion of a l iquid-phase react ion product (NbSi2) at theNb -part icle/Si- l iqu id interface, the forma tion of spherical nodules (~ 2/ zm diameter) o f this productthrough interfacial tension, and their subsequent solidification.

    1. INTRODUCTIONS h o c k - i n d u c e d r e a c t i o n s ( o r s h o c k s y n t h e s i s ) h a v eb e e n s t u d i e d s i n c e t h e 1 9 60 s b u t a r e s t i ll p o o r l yu n d e r s t o o d , p a r t l y d u e t o t h e f a c t t h a t t h e r e a c t i o nk i n e t i c s a r e v e r y f a s t m a k i n g e x p e r i m e n t a l a n a l y s i s o ft h e r e a c t i o n d i f f i c u l t . S h o c k - i n d u c e d r e a c t i o n s a r eq u i t e d i s t i n c t f r o m s h o c k - i n d u c e d p h a s e t r a n s f o r m -a t i o n s , s u ch a s t h e s y n t h e s is o f d i a m o n d f r o m g r a p h -i t e w h i c h i s a d i f f u s i o n le s s p h a s e t r a n s f o r m a t i o n .S h o c k - i n d u c e d r e a c t io n s a l s o d i f fe r f r o m d e t o n a t i o n sb e c a u s e o n l y c o n d e n s e d p r o d u c t s a r e f o rm e d , i n t h ef o r m e r . S h o c k s y n t h e s i s i s c l o s e l y r e l a t e d t o c o m b u s -t i o n s y n t h e s i s , a n d o c c u r s i n t h e s a m e s y s t e m s t h a tu n d e r g o e x o t h e r m i c g a s l e s s c o m b u s t i o n r e a c t i o n s .Th e t h e r m i t e r e a c t i o n ( Fe 2 0 3 + 2 A1 - - * 2 Fe + A 1 2 0 3) isp r o t o t y p i c a l o f t h i s c l a s s o f r e a c ti o n s . T h e f i rs t r e p o r to f t h e s e s h o c k - i n d u c e d r e a c t i o n s is d u e t o B a t s a n o ve t a l . [ 1 ] . T h i s i n i t i a l d i s c o v e r y w a s f o l l o w e d b ya c t i v i t y i n J a p a n [2, 3] a n d t h e U S S R [ 4 - 8 ] . I n t h eU . S . , t h e p i o n e e ri n g w o r k o f G r a h a m a n d c o - w o r k e r s[ 9 - 1 1 ] w a s f o l l o w e d b y i n v e s t i g a t i o n s b y V r e e l a n da n d c o - w o r k e r s [1 2 , 1 3 ] , H o r i e e t a l . [ 1 4 , 1 5 ] ,B o s l o u g h [ 1 6] , T h a d h a n i a n d c o - w o r k e r s [ 17 , 1 8 ] , a n dY u e t a l . [19, 20].

    S h o c k - w a v e p r o p a g a t i o n t h r o u g h m a t e r i a l s g e n e r -a t e s s i g n i f i c a n t s t r u c t u r a l c h a n g e s ; t h e s e e f fe c t s h a v eb e e n t h e o b j e c t o f e x t e n s i v e s t u d i e s , t h a t w e r e i n -i t i a t e d w i t h t h e M a n h a t t a n p r o j e c t in t h e 1 9 4 0 's a n dc o n t i n u e t o t h i s d a y . A n a l y t i c a l i n v e s t i g a t i o n s

    c o u p l e d w i t h e x p e r i m e n t a l s t u d i e s h a v e y i e l d e dm e c h a n i s m s r a t i o n a l i z in g t h e p r o d u c t i o n o f d i s lo -c a t i o n s a n d p o i n t d e f e c ts d u e t o s h o c k - w a v e p a s s a g et h r o u g h s o l i d m a t e r i a l s . T h e f i rs t m e c h a n i s m w a sp r o p o s e d b y S m i t h [2 1] , f o l l o w e d b Y H o r n b o g e n [ 22 ]a n d l a t e r m o d i f i e d b y M e y e r s [ 23 ], a n d W e e r t m a n[ 2 4 ]. T h e e f fe c ts o f s h o c k - w a v e p a s s a g e t h r o u g hp o r o u s ( p o w d e r ) m a t e r i a l s a r e c o n s i d e r a b l y m o r ec o m p l e x , b e c a u s e i n t e n s e a n d n o n - u n i f o r m p l a s t i cd e f o r m a t i o n i s c o u p l e d w i t h t h e s h o c k - w a v e e f f e c t s .T h u s , t h e p a r t i c l e i n t e r i o r s e x p e r i e n c e p r i m a r i l y t h ee f f e c t s o f s h o c k w a v e s , w h i l e t h e s u r f a c e s u n d e r g oi n t e n s e p l a s ti c d e f o r m a t i o n w h i c h c a n o f t e n r e s u l t i ni n t e r f a c i a l m e l t i n g . T h i s l o c a l i z e d m e l t i n g l e a d s t o t h eb o n d i n g o f t h e p o w d e r , a n d t h i s g a v e r i se to t h er e s e ar c h f ie l d o f s h o c k - w a v e c o m p a c t i o n . Q u a n t i t a t-b e , p r e d ic t iv e m o d e l s h a v e b e e n d e v e l o p e d b yG o u r d i n [ 2 5 ] a n d S c h w a r z e t a l . [26].

    S h o c k s y n t h e s is o f c o m p o u n d s f r o m p o w d e r s i st r i g g e r e d b y th e e x t r a o r d i n a r i l y h i g h e n e r g y d e p o -s i t i o n r a t e a t t h e s u r f a c e s o f t h e p o w d e r s , t h e r e b yc h a n g i n g t h e i r c o n f i g u r a t i o n , f o r c i n g t h e m i n c l o s ec o n t a c t , a c t i v a t i n g t h e m b y i n t r o d u c i n g l a r g e d e n -s i ti e s o f d e f e c t s, a n d h e a t i n g t h e m c l o s e to o r e v e na b o v e t h e i r m e l t i n g t e m p e r a t u r e s [ 8 - 1 1 ]. S o m e f u n d a -m e n t a l q u e s t i o n s r e g a r d i n g t h e s e r e a c t i o n s r e m a i nu n a n s w e r e d . P r o m i n e n t a m o n g t h e m a r e t h e f o l l o w -i n g : ( 1 ) H o w c a n t h e e x t r a o r d i n a r i l y h ig h r e a c t i o nr a t es e n c o u n t e r e d i n s h o c k c o m p r e s s i o n b e e x p l a i n e d ?

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    7 0 2 V ECCH IO e t a l . : S H O C K S Y N T H E SI S O F S I L I C I D E S - - I( 2) A r e t h e p h a s e s f o r m e d u n d e r s h o c k - s y n th e s i sc o n d i t i o n s u n i q u e a n d / o r n o n - e q u i l i b r i u m ?T h i s p a p e r ( i n c o n j u n c t i o n w i t h i t s c o m p a n i o np a p e r [2 7 ] ) p re se n t s e x p e r im e n ta l r e su l t s c o u p le dw i th c h a ra c t e r i z a t io n a n d a n a ly s i s o f tw o me ta l s il i-c id e s fo rme d b y sh o c k sy n th e s i s d i r e c t e d a t p ro v id in ga n a n sw e r t o t h e se q u e s t io n s . I t i s sh o w n th a t t h em e c h a n i s m o f s h o c k - i n d u c e d r e a c t i o n i s q u i t e d i ff e r-e n t t h a n c o n v e n t i o n a l s o l i d - s t a t e r e a c t i o n m e c h a n -i sms fo r t h e s i l i c id e s . Th e h ig h th e rma l g ra d ie n t si m p a r t e d b y t h e e ff ec t o f s h o c k c o m p r e s s i o n , c o m -b in e d w i th th e h ig h p re ssu re s a n d ma te r i a l f l u x ,e n a b l e a r e a c t i o n m e c h a n i s m u n i q u e t o s h o c k c o m -p re ss io n ; h o w e v e r , o n ly e q u i l ib r iu m p h a s e s a n ds t ru c tu re s w e re fo u n d fo r t h e sy s t e ms in v e s t ig a t e d .

    2 . E X P E R I M E N T A L P R O C E D U R E ST w o e l e m e n t a l p o w d e r m i x t u r e s w e r e u s e d i n t h i s

    i n v e s t i g a t i o n : N b - S i a n d M o - S i . T h e p o w d e r s , p r o -d u c e d b y C E R A C , h a d i r r e g u l a r sh a p e s , a n d s iz ess m a l le r t h a n 4 4 # m ( - 3 2 5 m e s h ) . T h e p u r i t y l ev el sw e r e 9 9 .9 % f o r N b , M o a n d S i. T h e p o w d e r s w e r em i x e d i n t h e p r o p o r t i o n s t o p r o v i d e , u p o n r e a c t i o n ,th e in t e rme ta l l i c c o mp o u n d s N b Si2 a n d Mo Si2 , fo re a c h sy s t e m re sp e c t iv e ly . Th e se p o w d e rs w e re e n c a p -s u l a t e d u n d e r c o n t r o l l e d a r g o n a t m o s p h e r e i n s t a i n -l ess s t ee l c a p su le s ( i n t e rn a l d ime n s io n s o f 1 5 m md i a m e t e r a n d 5 m m h e ig h t ). T h e s e c a p s u l e s w e r es u b j e c te d t o s h o c k c o m p r e s s i o n i n a S a w a o k a f i x tu r e ;th is f ix ture is descr ibed in de ta i l e lsewhere [e .g . 28] ;t h e sy s t e m (c ro ss - se c t io n ) i s sh o w n in F ig . 1 . Ea c hsy s t e m c o n ta in s 1 2 c a p su le s ; fo u r se c t io n e d c a p su le sa re sh o w n in t h i s f i g u re . A f ly e r p l a t e i s a c c e l e ra t e dd o w n w a r d s b y a n e x p l o s iv e s y s t e m c o n s is t i n g o f ama in c h a rg e (PBX 9 4 0 4 e x p lo s iv e ) i n i t i a t e d s imu l -t a n e o u s ly a lo n g i t s t o p su r fa c e b y a n e x p lo s iv e l e n sc o n s i s t i n g o f tw o e x p lo s iv e s w i th d if f e re n t d e to n a t io nv e lo c it i es . I mp a c t v e lo c i t ie s o f 1 .2 a n d 1 .9 k m /s w e rea c h i ev e d b y v a r y i n g t h e q u a n t i t y a n d t y p e o f e x p l o -s iv e a c c e l e ra t in g th e f l y e r p l a t e . Sh o c k e x p e r ime n t sw e r e c o n d u c t e d o n c a p s u l es a t r o o m t e m p e r a t u r e a n do th e r s p re h e a t e d to 7 7 3 K .T h e h i g h - t e m p e r a t u r e s h o c k f i x t u r e i s s h o w n i nF i g . l ( b ) . T h e c a p s u l e s a n d m o m e n t u m t r a p s a r eh e a t e d in a d i sc a rd a b le fu rn a c e , w i th t h e e x p lo s iv esy s t e m a t a sa fe d i s t a n c e . Wh e n th e t e mp e ra tu rere a c h e s th e d e s i r e d v a lu e , t h e fu rn a c e to p i s r e mo v e da n d th e e x p lo s iv e a sse mb ly , t o g e th e r w i th t h e f l y e rp l a t e , ro l l d o w n a 4 i n c lin e d r a m p u n t i l t h e y a rep r o p e r l y p o s i t i o n e d a b o v e t h e c a p s u l e ; t h e s y s t e m isth e n e l e c t r ic a l ly d e to n a te d . So le n o id 1 e n su re d r e -mo te a c t iv a t io n a n d e n a b le d th e f ly e r p l a t e / e x p lo s iv esy s t e m to ro l l d o w n a t t h e d e s i r e d t ime . In c a se o fmis f i r e o r a n y o th e r u n e x p e c te d e v e n t , t h e e x p lo s iv es y s t e m c o u l d b e w i t h d r a w n f r o m a b o v e t h e f u r n a c eb y t h e a c t i v a t i o n o f s o l e n o i d 2 .

    A f t e r sh o c k p ro c e ss in g , t h e sp e c ime n c a p su le s w e res e c ti o n e d a n d a n a l y z e d b y s c a n n i n g a n d t r a n s m i s s i o ne l e c t r o n m i c r o s c o p y . S c a n n i n g e l e c t r o n m i c r o s c o p y

    ( S E M ) w a s c o n d u c t e d o n a C a m b r i d g e $ 3 6 0 e le c t ro nm i c r o s c o p e e q u i p p e d w i t h a L I N K A n a l y t i ca l e n er g yd i sp e r si v e X - r a y s p e c t r o m e t e r ( E D S ) . C o m p o s i t i o n a lm e a s u r e m e n t s o f i nd i v i d u al p h a s e s w e r e c o n d u c t e du s i n g t h e Z A F c o r r e c t i o n p r o c e d u r e w i t h u n r e a c t e dp o w d e r r e g io n s u se d fo r s t a n d a rd s . S in c e th e sh o c ke x p e r ime n t i s v e ry r a p id , a n d th e r e su l t a n t t h e rma le x c u rs io n sh o r t l i v e d , t h e u n re a c t e d p o w d e r r e g io n sw e r e c o n s i d e r e d c h e m i c a l l y u n c h a n g e d a n d s u b -se q u e n t ly u se d a s p u re e l e me n ta l s t a n d a rd s . S t a n -d a r d l e s s q u a n t i f i c a t i o n w a s a l s o c o n d u c t e d o n b o t ht h e u n r e a c t e d p o w d e r s , a n d t h e r e a c t i o n p r o d u c t s ,( a )E le c t r i c a l ly -d e to n a te d H ig h -sp e e db l as t ir . . . . " . . . .

    Thin rf lyer 112 stecapsulhold i tsampl

    (b )Capsuleconta inerI ~ L D e t o n a t o r

    omentum t rap \E x p l o s i v e ~

    Solenoid 1 \

    ' T~rack ~ F~Yter\ \\ Hea t ing uni t

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    Solenoid 2

    We ig h t

    Fig. 1. Schematic illustration of planar impact (Sawaoka)system: (a) room temperature fixture, (b) elevated tempera-ture shock fixture.

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    V E C C H I O e t a l . : S H O C K S Y N T H E S I S O F S I L I C I D E S - - I 7 03a n d t h e r e s u l t s w e r e c o n s i s t e n t w i t h t h e s t a n d a r d s -b a s e d q u a n t i f i c a t i o n r e s u l t s .

    S t a t i c r e a c t i o n e x p e r i m e n t s ( i . e . n o n - s h o c k e x p e r -i m e n t s ) w e r e c o n d u c t e d b y a n n e a l i n g N b - - S i d i f f u s i o nc o u p l e s f o r d i f f e r e n t t i m e s a t 1 2 0 0 C a n d r e c o v e r i n gt h e s p e c i m e n s f o r o b s e r v a t i o n . T h e i d e n t i f i c a t i o no f r e a c t i o n p r o d u c t s a n d t h e i r t h i c k n e s s e s i n t h e s ed i f f u s io n c o u p l e s w a s e s t a b l i s h e d b y S E M a n dq u a n t i t a t iv e E D S X - r a y m i c r o a n a l y s i s u s i n g t h es p e c i m e n r e g i o n s w e l l a w a y f r o m t h e i n t e r f a c e a sp u r e e l e m e n t al s t a n d a r d s .

    T r a n s m i s s i o n e l e c t ro n m i c r o s c o p y ( T E M ) w a s c a r -r i e d o u t in a P h i l ip s C M 3 0 e l e c t r o n m i c r o s c o p ee q u i p p e d w i t h a L I N K A n a l y t i c a l A N 1 0 8 5 u l t r a - th i nw i n d o w ( U T W ) e n e r g y d i s p e rs i v e X - r a y s p e c t r o m e t e r( E D S ) s y s t e m . T h e T E M w o r k w a s c o n d u c t e d a t a na c c e l e r a t i n g v o l t a g e o f 3 00 k V , w i t h t h e e x c e p t i o n o fb o t h t h e X - r a y m i c r o a n a l y s i s a n d c o n v e r g e n t b e a me l e c tr o n d i f f ra c t i o n w o r k w h i c h w e r e e a c h c o n d u c t e da t 100 kV .T h e p r e s s u r e a n d t e m p e r a t u r e s i n d u c e d b y s h o c kw a v e s i n t h e c a p s u l e s w e r e o b t a i n e d f r o m c o m p u t e r

    s i m u la t io n s , c o n d u c te d b y N o r w o o d a n d G r a h a m[ 2 9 ] . T w o - d i m e n s i o n a l e f f e c t s a r e v e r y i m p o r t a n ts i n c e t h e s h o c k w a v e s t r a v e l f a s t e r i n t h e c a p s u l e t h a ni n t h e p o w d e r . T h u s , t h e s h o c k w a v e s e n t e r t h ec a p s u l e s l a t e r a l l y , a s w e l l a s a t t h e i r t o p s u r f a c e ,g e n e r a t in g h i g h l y in h o m o g e n e o u s p r e s s u re a n d t e m -p e r a t u r e r e g i m e s . T h i s i n h o m o g e n e i t y i n b o t h p r e s s -u r e s a n d t e m p e r a t u r e s w a s r e a d i l y a p p a r e n t w i t h i nt h e r e c o v e r e d c a p s u l e s , a n d w a s a c t u a l l y a h i g h l yu s e f u l e f fe c t s in c e i t e n a b l e d t h e a n a l y s i s o f u n r e a c t e d ,p a r t i a l l y - r e a c t e d , a n d f u l l y - r e a c t e d r e g i o n s w i t h i n t h es a m e s p e c i m e n .

    3 . E X P E R I M E N T A L R E S U L T S A N D D I S C U S S I O N3 . 1 . S h o c k r e c o v e r y e x p e r i m e n t s

    F i g u r e 2 s h o w s r e a c t i o n m a p s o f t h e c r o s s - s e c t i o n sf o r th e r e c o v e r ed c a p su l e s f o r th e N b - S i a n d M o - S is a m p l e s ; f u l l y - r e a c t e d , p a r t i a l l y - r e a c t e d , a n d u n r e -a c t e d r e g i o n s a r e e v i d e n t. U p o n r e c o v e r y , t h e s p e c i -m e n s w e r e c o n s i d e r a b l y c ra c k e d , a n d p o r t i o n s o f t h es p e c i m e n s w e r e l o s t d u r i n g s e c t i o n i n g .

    [ ] Unr eac te~ S H O C K W A V E[] Partially r e a c t e d | Fully reacted ~[~

    impucl Velocity 1.9 km /s al Rmnn Temp .

    Impact Velocity 1.2 kmls at Room Temp.

    I'~ u . r ~c t ~ S H O C K W A V E[ ] P a r t ia l l y eacted |[ ] F u l l y e a c t e d

    Impact V elocity 1.9 km /s ul Ro ,m Tem p.

    lmlmct Velocity 1.2 k mls al Room Temp.

    aImpact Velocily 1.2 kmls at 500 (3 b Impact Velocity 1.2 km/s at 5000 C

    Fig. 2. Ma ps showing fully-reacted, part ial ly-re acted, and u nreacted regions for (a) NI~ Si system and (b)Mo-Si system. Impact velocity and temperature marked below each plot . Black regions representfully-reacted, hatched regions-partially-reacted, dotted region-unreacted, and white represents voidsand/or cracks .

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    704 VECCHIO et al . : SHOCK SYNTHESIS OF SILICIDES---I3 . 1 .1 . S c a n n i n g e l e c t ro n m i c r o s c o p y a n d m i c r o -

    ana ly s i s . Backscattered electron micrographs of apolished section of the Nb-Si sample shocked atroom temperature and low velocity (1.2km/s) areshown in Fig. 3. Figure 3(a) shows the unreacted butcompacted region taken from near the top of thecapsule. Figure 3(b) shows the transition regionbetween unreacted and partially-reacted material,with the reacted mater ial being the small gray nodulesidentified as NbSi2 (Nb-38 wt% Si via X-ray micro-

    analysis); the identifi cation of the crystal structure ofthis phase will be discussed in detail later. Figure 3(c)shows the partially-reacted region which made up themajority of the sample and consisted of Nb particlessurr ounde d by a reaction layer of NbSi2 nodules andembedded within a two-phase matrix of NbSi2 nod-ules and silicon. Figure 3(d) shows the transitionregion from the partially-reacted to fully-reactedmaterial located near the bottom of the capsule.Within this transi tion region an additional interfacial

    Fig. 3. Backscattered electron micrographs of (a) the unreacted but compacted region taken from nearthe top of the capsule, (b) the transition region between unreacted and partially-reacted material, withthe reacted material being the small gray nodules identified as NbSi2, (c) the partially-reacted region whichmakes up the majority of the sample and consists of Nb particles surrounded by a reaction layer of NbSi2nodules and embedded within a two-phase matrix of NbSi2 nodules and silicon, (d) the transition regionfrom the partially-reacted to fully-reacted material located near the bottom of the capsule; within thistransition region an addition interfacial reaction product could be observed as shown in (e) which wasidentified by X-ray microanalysis as NbsSi3.

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    V E C C H I O et aL: S H O C K S Y N T H E SI S O F S I L I C I D E S - - I 7 05r e a c t i o n p r o d u c t c o u l d b e o b s e r v e d a s s h o w n i nF ig . 3 (e ) wh ic h wa s i d e n t i f i e d b y X- ra y m ic ro a n a ly s i sa s N b s Si 3 ( N b - 1 5 w t % S i) . S o m e N b sS i3 r e a c t i o np r o d u c t c o u l d b e f o u n d b e t w e e n t h e N b S i2 p h a s e a n dth e Nb p a r t i c l e s wi th in t h e p a r t i a l l y - r e a c t e d r e g io n ;h o w e v e r , t h e t h i c k n e ss o f t h e Nb sSi3 la y e r , i n t h i sr e g io n , n e v e r e x c e e d e d 1 0 0 n m . In t h e t r a n s i t i o nre g io n , t h e Nb sS i 3 l a y e r e x c e e d e d 1 # m in t h i c k n e ss .In t h e u n re a c t e d r e g io n , t h e n io b iu m p a r t i c l e s r e t a inth e i r o r ig in a l p o wd e r c o n f ig u ra t i o n ( i . e . u n d e fo rm e d ,i r r e g u l a r ly sh a p e d p a r t i c l e s ) , wh e re a s t h e s i l i c o n p a r -t ic le s h a v e b e e n d e f o r m e d a n d c o m p a c t e d a r o u n d t h e

    Fig. 4. Backscattered electron micrographs of the micro-structure of (a) the partially-reacted region in the lowvelocity (1.2 km/s) and elevated temperature (773 K) sh ockexperim ent, (b, c) the partially-reacted region of the speci-men shocked at higher velocity (1.9 km/s) and room tem-perature.

    n io b iu m p a r t i c l e s . F ig u re 4 (a ) sh o ws a b a c k sc a t t e re de l e c tr o n m i c r o g r a p h o f th e m i c r o s t r u c t u r e o f t hep a r t i a l l y - r e a c t e d r e g io n i n t h e l o w v e lo c i t y (1 .2 k m /s )a n d e l e v a t e d t e m p e ra tu re (7 73 K) sh o c k e x p e r im e n t .Th e m o s t n o t a b l e f e a tu re t h a t d i f f e re n t i a t e s t h i ss a m p l e f r o m t h e r o o m t e m p e r a t u r e , l o w v e l o c i t ye x p e r im e n t i s t h e s i g n i f i c a n t ly i n c re a se d a m o u n t o fr e a c te d p r o d u c t N b S i 2. C o m p a r i s o n b e t w e e n F i g . 3 (c )a n d F ig . 4 (a ) i n d i c a t e s t h a t a g re a t e r v o lu m e f r a c t i o no f Nb S i2 w a s fo rm e d a s a r e su l t o f c a p su l e p re h e a t i n g .Th i s i s e x p e c t e d s in c e a h ig h e r t e m p e ra tu re wi l l b ea c h i e v e d i n t h e c a p su l e a s a r e su l t o f th e sh o c k , p lu sp re h e a t i n g , a n d t h e c a p su l e wi ll r e m a in h o t t e r fo r alo n g e r t im e fo l l o win g th e sh o c k s in c e t h e sh o c kf ix tu re i s n o l o n g e r a n e f f i c i e n t q u e n c h in g m e d iu m .

    F ig u re 4 (b , c ) sh o w th e p a r t i a l l y - r e a c t e d r e g io n o fth e sp e c im e n sh o c k e d a t h ig h e r v e lo c i t y (1.9 k m /s )a n d r o o m t e m p e r a t u r e . I n t h i s s a m p l e l e s s n o d u l a rNb S% wa s o b se rv e d ; h o we v e r , a s i g n i f ic a n t a m o u n t o fNb S i2 wa s a l so fo u n d p re se n t a s a l a m e l l a r e u t e c t i cs t ru c tu re wi th in t h e s i l i c o n r i c h m a t r i x , a s sh o wn inF ig . 4 (c ) . Un d e r t h e se sh o c k c o n d i t i o n s , t h e m o l t e ns i l ic o n m a t r i x b e c o m e s e n r i c h e d wi th n io b iu m , a n dsubsequent ly so l id i f ies a t 1300C v ia a eu tec t ic reac-t i o n b e tw e e n S i a n d Nb S i 2. A sm a l l a m o u n t o f t h ise u t e c t i c r e a c t i o n wa s e v id e n t i n t h e o th e r two Nb - -S isa m p le s ; h o we v e r , i n t h o se sa m p le s t h e v o lu m e f r a c -t i o n w a s v e r y i n si g n if i ca n t c o m p a r e d t o t h e a m o u n to f n o d u l a r N b S i 2 t h a t w a s f o u n d .

    Th i s r e su l t su g g e s t s t h a t t h e t e m p e ra tu re t h ro u g h -o u t t h e m o l t e n S i e x c e e d e d th e m e l t i n g t e m p e ra tu reo f t h e Nb Si2 p h a se (~ 1 9 4 0 C) c a u s in g t h e n o d u la rNb S i2 t o d i s so lv e i n S i a n d t o su b s e q u e n t ly r e so l i d ifyt h r o u g h t h e e u t e c ti c r e ac t io n . I n c o n t r o v e r t i b le p r o o fth a t s i l ic o n wa s m o l t e n i n t h e p a r t ia l l y - r e a c t e d r e g io no f e v e n t h e l o w v e l o c it y , r o o m t e m p e r a t u r e e x p e r-im e n t i s p ro v id e d b y t h e o b se rv a t i o n o f a f i n e e u t e c t ics t ru c tu re o f l a m e l l a r N b S i 2 a n d S i . Th i s e u t e c t i cs t r u c t u r e f o r m e d l a s t a s t h e m o l t e n , N b - e n r i c h e dsi l icon so lid if ied . Th e h ighe r shock energ ies achievedin t h e 1 .9 k m /s sa m p le r e su l t i n s i g n i f ic a n t ly h ig h e rt e m p e ra tu re s wi th in t h e p o wd e rs . A g re a t e r f r a c t i o no f t h i s sh o c k e n e rg y i s d e p o s i t e d i n t h e s i li c o n p o w d e rc o m p a r e d t o t h e N b p o w d e r a s e v i d e n c e d b y t h ec o n s id e ra b l e p l a s t i c d e fo rm a t io n o f t h e s il i c o n p a r -t ic le s i n t h e u n re a c t e d r e g io n , a n d t h e e x t r e m e ly h ig ht e m p e ra tu re a c h i e v e d i n t h e m o l t e n s i l i c o n i n t h ep a r t i a l l y - r e a c t e d r e g io n . In a d d i t i o n , t h e h ig h e r sh o c ke n e rg y i s l ik e ly t o r e su l t i n i n c re a se d t u rb u l e n c e i n t h em o l t e n S i wh ic h wi l l a i d i n h o m o g e n iz in g t h e m e l t( i . e . d i s so lv e t h e Nb S i2 n o d u le s ) t h ro u g h a s t i r r i n ga c t i o n . C le a r ly , t h e r e a c t i o n m e c h a n i sm a sso c i a t e dw i t h t h e f o r m a t i o n o f t h e n o d u l a r N b S % i s di s ti n c tf ro m th e e u t e c t i c r e a c t i o n o b se rv e d i n F ig . 4 (b , c ).

    C o m p a r i s o n o f t h e l o w v e l o c it y (1 .2 k m / s ), e l e v a t edt e m p e r a t u r e ( 7 7 3 K ) e x p e r i m e n t w i t h t h e r o o m t e m -p e ra tu re , h ig h v e lo c i t y (1 .9 k m /s ) e x p e r im e n t r e v e a l sse v e ra l i n t e re s t i n g o b se rv a t i o n s r e g a rd in g t h e n a tu rea n d e x t e n t o f t ~ s h o c k r e a c ti o n . F i r s t, t h e e x te n t o fr e a c t io n ( i. e. t h e a m o u n t o f r e a c ti o n p r o d u c t f o r m e d )

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    706 VECCHIO e t a l . : S H O C K S Y N T H E S I S O F S I L I C I D E S - - Iw a s g r e a t e r f o r t h e l o w v e l o c i t y ( 1 .2 k m / s ) , e l e v a t e dt e m p e r a t u r e e x p e r i m e n t t h a n t h e h i g h v e l o c i t y( 1 .9 k m / s ) e x p e r i m e n t , e v e n t h o u g h t h e h i g h v e l o c i t ye x p e r i m e n t c r e a t e s a h i g h e r t e m p e r a t u r e w i t h i n t h ec a p s u l e c o m p a r e d t o t h e l o w v e l o c i t y , e l e v a t e d te m -p e r a t u r e e x p e r i m e n t a f t e r t h e p r e h e a t t e m p e r a t u r e i sa d d e d t o t h e c a l c u l a t e d t e m p e r a t u r e s ( as b a s e d o n t h ec a l c u l a ti o n s o f N o r w o o d a n d G r a h a m [2 9] a l sos h o w n a s F i g . 2 i n t h e c o m p a n i o n p a p e r t o t h is w o r k[ 27 ]) . T h e p r e h e a t i n g i s m o r e e f f e c ti v e f o r p r o m o t i n gt h e r e a c t i o n b e c a u s e t h e t e m p e r a t u r e i s u n i f o r mt h r o u g h o u t t h e p o w d e r s , h e a ti n g u p b o t h t h e N b a n dS i p a r t i c l e s r e l a t i v e l y e v e n l y , w h e r e a s t h e - s h o c k e n -e r g y ( i .e . h e a t ) i s p r e f e r e n t i a l l y d e p o s i t e d i n t h e s o f t e rS i p a r t i c l e s . A s s u c h , a l a r g e r f r a c t i o n o f s h o c k e n e r g yc a n c o n t r i b u t e t o t h e r e a c t i o n i n t h e p r e h e a t e ds a m p l e , r a t h e r t h a n h e a t i n g o f th e p o w d e r s i n t h eh i g h v e l o c i ty e x p e r im e n t . S e c o n d l y , th e m o r p h o l o g yo f t h e N b S i 2 p h a s e d i f f e r s b e t w e e n t h e h i g h v e l o c i t ye x p e r i m e n t a n d t h e e l e v a t e d te m p e r a t u r e e x p e r i m e n t .I n t h e h i g h v e l o c i t y e x p e r i m e n t t h e N b S i 2 e x i s tsb o t h a s a l a m e l l a r e u t e c t i c s t r u c t u r e w i t h i n t h e S ir e g i o n s , a s w e l l a s n o d u l e s a l o n g t h e N b - S i i n t e r f a c e .I n c o n t r a s t , t h e N b S i 2 p h a s e e x i s t s a s n o d u l e s

    s u r r o u n d i n g a t h i c k l a y e r o f N b S i2 w h i c h e n c a p s u -l a t e s t h e N b p a r t i c l e s , a s s h o w n i n F i g . 4 ( a ). S i n c e t h ep r e h e a t i n g r a is e s t h e t e m p e r a t u r e o f b o t h t h e p o w -d e r s a n d t h e w h o l e f i x t u r e i t s e l f , t h e c o o l i n g r a t e i nt h i s e x p e r i m e n t i s c o n s i d e r a b l y l o w e r t h a n i n e it h e r o ft h e o t h e r t w o ( lo w v e l o c i t y - r o o m t e m p e r a t u r e a n dh i g h v e l o c i t y - r o o m t e m p e r a t u r e ) e x p e r i m e n t s. T h em o r p h o l o g y o f t h e t h i c k N b S i 2 r e a c t i o n l a y e r s u r -r o u n d i n g t h e N b p a r t i c l e s s u g g e s t s t h a t t h i sl a y e r : ( 1 ) f o r m s t h r o u g h s o l i d - s t a t e d i f f u s io n ,( 2 ) o c c u r s s u b s e q u e n t t o t h e n o d u l e r e a c t i o n m e c h -a n i s m , a n d ( 3 ) i s n o t d i r e c t l y a s s o c i a t e d w i t h s h o c k -w a v e p a s s a g e .

    B a c k s c a t t e r e d e le c t r o n m i c r o g r a p h s o f a p o l i s h e ds e c ti o n o f t h e M o - - S i s a m p l e s h o c k e d a t r o o m t e m -p e r a t u r e a n d l o w v e l o c i t y (1 . 2 k m / s ) a r e s h o w n i nF i g . 5 . A n a l y s i s o f t h e o t h e r t w o M o - S i s a m p l e s w i lln o t b e p r e s e n t e d h e r e , b u t e x a m i n a t i o n o f t h e s es a m p l e s r e v e a l e d s t r u c t u r e s s i m i l a r t o t h e c o r r e s p o n d -i n g N b - S i s a m p l e s . F i g u r e 5 ( a ) s h o w s t h e u n r e a c t e db u t c o m p a c t e d r e g i o n t a k e n f r o m n e a r t h e t o p o f t h ec a p s u l e . F i g u r e 5 ( b ) s h o w s t h e t r a n s i t i o n r e g i o nb e t w e e n u n r e a c t e d a n d p a r t i a l ly - r e a c t e d m a t e r i a l,w i t h t h e r e a c t e d m a t e r i a l b e i n g th e s m a l l g r a y n o d u l e s

    Fig. 5. Backscattered electron micrographs of a polished section of the Mo-Si sample shocked at roomtemp erature and low velocity (1.2 km/s), (a) the unreacted but com pacted region taken from n ear the topof the capsule, (b) the transi t ion region between unreacted and p art ial ly-reac tedma terial , with the reactedma terial being the small gray nodules identified as M oSi2, (c) the p art ial ly-reacte d region which m ade upthe ma jor i ty of the sample and consi sted o f M o p ar t ic les sur rounded by a react ion layer of MoSi2 nodulesand embedded within a two-phase matrix of MoSi2 nodules an d si licon; in m any instances, the entire M opar t ic le has been reacted to form the M oSi2 phase, as ind icated by an arrow in (c); (d) shows the transi t ionregion from the pa rt ial ly-reac ted to ful ly-reacted m aterial located near the bo ttom of the capsule.

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    V E C C H I O e t a l . : SH O C K SY N T H E SI S O F SI L I C I D E S- - I 707i d e n ti f ie d a s M o S i : ( M o - 3 7 w t % S i v i a X - r a y m i c r o -a n a l y s i s ) ; t h e i d e n t i f i c a t i o n o f t h e c r y s t a l s t r u c t u r e o ft h i s p h a s e w i l l b e p r e s e n t e d l a t e r . F i g u r e 5 ( c ) s h o w st h e p a r t i a l ly - r e a c t e d r e g i o n w h i ch m a d e u p t h e m a -j o r i t y o f th e s a m p l e a n d c o n s i s te d o f M o p a r t ic l e ss u r r o u n d e d b y a r e a c t io n l a y e r o f M o S i 2 n o d u l e s a n de m b e d d e d w i t h i n a t w o - p h a s e m a t r i x o f M o S i 2 n o d -u l e s a n d s i li c o n . I n m a n y i n s t a n c e s , th e e n t i r e M op a r t i c l e h a s b e e n r e a c t e d t o f o r m t h e M o S i 2 p h a s e , a si n d i c a t e d b y a n a r r o w i n F i g . 5 (c ). F i g u r e 5 ( d ) s h o w st h e t r a n s i t i o n r e g i o n f r o m t h e p a r t i a l l y - r e a c t e d t of u l ly - r e a c te d m a t e r i a l l o c a te d n e a r t h e b o t t o m o f t h ec a p s u le . N o a d d i t i o n a l i n t e r fa c i a l r e a c t i o n p r o d u c tc o u l d b e o b s e r v e d i n t h i s s a m p l e , u n l i k e t h e N b - S is a m p l e s . I n t h e u n r e a c t e d r e g i o n , t h e M o p a r t i c l e sa p p e a r t o f r a g m e n t a l o n g g r a i n b o u n d a r i e s w i t h in t h ep a r t i c l e s , w h i le t h e s i l ic o n p a r t i c l e s s ee m t o h a v eu n d e r g o n e i n t en s e p l a s t ic d e f o r m a t i o n .

    T h e f u l l y - r e a c te d r e g io n s f o r t h e N b - S i a n d M o - S is a m p l e s w e r e e s s e n t i a l ly id e n t i c a l in t e r m o f m a c r o -s c o p i c m o r p h o l o g y . V o i d s w e r e p r e s e n t th r o u g h o u t ,r e s u l t i n g f r o m e i t h e r s o l i d i f i c a t i o n s h r i n k a g e , g a s e se v o l v e d d u r i n g t h e r e a c t i o n , o r t e n s i l e s t r e s s e s i m -p o s e d o n t h e c o m p a c t p r i o r t o s o l i d i f ic a t i o n . T h ep r e s e n c e o f s p h e r i c a l v o i d s , a s w e l l a s d e n d r i t i cs t r u c t u r e s o b s e r v e d a r e e v i d e n c e o f m e l t i n g a n d

    2 ~ . 18~ b161t 4 " ~ ; ~1 2 !

    8 i6 i4 i

    ~ , . ~ ,,~ : ,,,,~ . , .2 4 6 8 10( keV )20 . . . . . . . . . . . . . . . . . . .18' C161412' r , . j ~ z ,Z10 '8 '6

    4 ' ~

    0 2 4 6 8 10( keV )Fig. 7. (a) Backscattered electron micrograph of the ful ly-reacted region of the Mo-Si capsule which containsprim ari ly MoS i: [ labeled A in this f igure]; (b) shows a typicalEDS spectrum from this phase. A second phase [labeled Bin (a)] had a com posit ion close to M osSi3, but alsocontain ed small amounts of Fe, Cr and N i, as shown in theEDS spectrum of (c) .

    Fig. 6. Backscattered electron microg raphs o f fully-reactedregions of the N b-S i capsules tested at (a) elevated tempera-ture (773 K) a nd (b) high velocity (1.9km /s) and roomtemperature . Microvoids are marked by ar rows and severa ldifferent phases are present marked A, B, C and D in (a) .

    r e - s o l i d if i c a t i o n . F i g u r e 6 ( a ) a n d ( b ) s h o w t h e m i c r o -s t r u c t u r e i n t h e f u l l y - r e a c t e d r e g i o n s o f t h e N b - S ic a p s u l e s t e s t e d a t e l e v a t e d t e m p e r a t u r e ( 7 7 3 K ) a n dh i g h v e l o c i t y (1 . 9 k m / s ) , r e s p e c t iv e l y ; t h e m i c r o v o i d sa r e m a r k e d b y a r r o w s a n d s e v e r a l d i f f e re n t p h a s e s a r ep r e s e n t . E n e r g y d i s p e r s i v e X - r a y a n a l y s i s o f th e s ed i s t i n c t p h a s e s [ m a r k e d A , B , C a n d D i n F i g . 6( a ) f o re x a m p l e ] r e v e a l s F e , N i a n d C r p e a k s , i n a d d i t i o n t od i f f e r ences i n t he r e l a t i ve i n t ens i t i e s o f t he muchl a r g e r N b a n d S i p e a k s . T h e p r e s e n ce o f F e , N i a n dC r i s e v i d e n c e f o r m e l t i n g o f t h e c a p s u l e ( w h i c h i ss t a i n le s s s t e e l) a n d s u b s e q u e n t c o n t a m i n a t i o n o f s p e c-i m e n . T h i s i s a p o s t - s h o c k e f f e ct , si n c e t h e r e w o u l d b en o t i m e f o r d i f fu s i o n o f th e s e e l e m e n t s d u r i n g s h o c k -w a v e p a s s a g e . T h e p h a s e s w h i c h c o n t a i n e d t h e F e , C ra n d N i t o v a r y i n g a m o u n t s a l s o h a d a n o v e r a l l N b - S ir a t i o c l o s e t o t h e c o m p o s i t i o n o f N b s S i 3. F i g u r e 7 ( a )s h o w s t h e f u l l y - r e a c t e d r e g i o n o f t h e M o - S i c a p s u l e

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    708 VECCHIO et al . : S HOC K S YNT HES IS O F S I L I C I D E S - - Iw h i c h c o n t a i n s p r i m a r i l y M o S i 2 [ la b e l e d A i n t h i sf ig u r e ]; F i g . 7 ( b ) s h o w s a t y p i c a l E D S s p e c t r u m f r o mt h i s p h a s e . A s e c o n d p h a s e [ l a b e l e d B i n F i g . 7 ( a ) ]h a d a c o m p o s i t i o n c l o s e t o M o s S i 3 , b u t a l s o c o n -t a i n e d s m a l l a m o u n t s o f F e , C r a n d N i , a s sh o w n i nt h e E D S s p e c t r u m o f F i g . 7 (c ). T h i s r e s u l t , in c o n -j u n c t i o n w i t h s i m i l a r f i nd i n g s fo r t h e N b - S i s y s te ms u g g e s t t h a t t h e N b s S i3 a n d M o s S i a p h a s e s h a v e ag r e a t e r s o lu b i l it y f o r F e , C r , a n d N i c o m p a r e d t o t h ec o r r e s p o n d i n g d i s i li c i d e p h a s e s .

    3 . 1 .2 . T r a n s m i s s i o n e l e c t ro n m i c r o s c o p y a n dd i f f rac t i on ana ly s i s . F i g u r e 8 s h o w s t r a n s m i s s i o n e l e c -t r o n m i c r o g r a p h s o f t h e p a r t i a ll y - r e a c t e d r e g i o n o ft h e l o w i m p a c t v e l oc i ty , r o o m t e m p e r a t u r e N b - S i

    Fig. 8. Transmission electron micrographs of the part ial ly-reacted region of the low veloci ty , room temperature N b-Sisample. (a, b) reveal the structure of the nodules an d o f thesurrounding si l icon matrix. The si l icon surrounding thesereacted regions generally shows an an nealed structure witha profusion of annealing twins. (c) Electron diffractionpattern from twins in (b).

    Fig. 9. [0001] zone axis CBED patte rn ob tained from theN b S i2 nodules, (a) shows the zero -order Laue lay er patter nwhich possesses 6 m m projec tion diffraction symmetry, (b)shows the whole pattern revealing only 6-fold rotationalsymmetry; no mirror planes exist in this pattern, and (c)shows an enlarged view of the black rectangle outl ining asmall por t ion of the second -order Lau e r ing in (b).s a m p l e . F i g u r e 8 ( a ) a n d ( b ) r e v e a l th e s t r u c t u r e o f th en o d u l e s a n d o f t h e s u r r o u n d i n g s i li c o n m a t r i x . T h eN b S i 2 n o d u l e s a r e m o n o c r y s t a l li n e , a p p r o x . 1 - 2 # mi n d i a m e t e r, a n d h a v e f a ce t s. T h e y d o n o t s h o w a n ym a r k e d i n t e r n a l s t r u c t u r e , s u c h a s d i s lo c a t i o n s , s ta c k -i n g f a u l t s, o r t w i n s . T h e s i l i c o n s u r r o u n d i n g t h e s er e a c t e d r e g i o n s g e n e r a l l y s h o w s a n a n n e a l e d s t r u c t u r ew i t h a p r o f u s i o n o f a n n e a l i n g t w i n s , a s s h o w n i nF i g . 8 ( b ) . A f ew s i l i con r eg i on s exh i b i t a mi c r o -c r y s t a l l i n e s t r u c t u r e . T h e s e r e g i o n s w e r e e i t h e rs u b j e c t e d t o i n t e n s e p l a s t i c d e f o r m a t i o n a n d r e c r y s -t a l l iz e d ( s t a t ic a l l y o r d y n a m i c a l l y ) o r w e r e m o l t e na n d r a p i d l y r e - s o l i d i fi e d . T h i s m i c r o s t r u c t u r e i s ins t a r k c o n t r a s t w i t h t h e p r e v i o u s s i l i c o n r e g i o n s[ F i g . 8 (b ) ] w h i c h s u g g e s t e d m e l t i n g f o l l o w e d b y s l o wr e - so l i d i f i ca t i on .

    T h e c r y s t a l s t r u c t u r e o f t h e N b S i 2 n o d u l e s w a sd e t e r m i n e d b y c o n v e r g e n t b e a m e l e c tr o n d i f f r ac t io n( C B E D ) a n a l y s i s . F i g u r e 9 s h o w s t h e [ 0 00 1] z o n e a x i sC B E D p a t t e r n o b t a i n e d f r o m t h e N bS i 2 n o d u l e s .F i g u r e 9 ( a ) s h o w s t h e z e r o - o r d e r L a u e l a y e r p a t t e r n

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    V E C C H I O e t a l . : S H O C K S Y N T H E S I S O F S I L I C I D E S - - I 7 09

    Fig. 11. Transm iss ion elect ron micrograp h of the par t ia l ly-r eac ted r eg ion o f t he l ow ve loc ity, r oom t em pera tu re M o ~ isample reveal ing the interna l s t ructure of the M oSi2 nodu lesinclud ing dis locat ions and twins .

    h e r e, d i s p l a y e d o n l y 2 - fo l d w h o l e - p a t t e r n s y m m e t r yc o n s i s t e n t w i t h t h e p o i n t g r o u p 6 2 2 . T h e e s t a b l i s h e dc r y s t a l s t r u c t u r e f o r t h e N b S i 2 p h a s e i s th e C 4 0h e x a g o n a l s t r u c t u r e ( s p a c e g r o u p P 6 2 2 2 a n d p o i n tg r o u p 6 2 2 ) [ 3 0 ] . N o a t t e m p t w a s m a d e h e r e t od e t e r m i n e t h e s p a c e g r o u p o f t h i s p h a s e ; h o w e v e rt h e r e is n o r e a s o n t o s u s p e c t a n y o t h e r s p a c e g r o u p .

    F ig. 10. Transmis s ion elect ron micrograph s of the par t ia l ly-reacted reg ion of the low veloci ty , room tempe rature Mo -S isample, (a) and (b) reveal the s t ructu re of the MoSi 2 nodu lesand the su rrou ndin g s il icon matr ix , respect ively. Th e s i l iconsur round in g these r eac t ed r eg ions gene ra l ly show s a n an -nea l ed s t ruc tu re w i th a p ro fus ion o f annea l ing tw ins .

    w h i c h p o s s e s s e s 6 m m p r o j e c t i o n - d i f f r a c t i o n t s y m -m e t r y . F i g u r e 9 ( b ) s h o w s t h e w h o l e p a t t e r n t r e v e a l -i n g o n l y 6 - fo l d r o t a t i o n a l s y m m e t r y ; n o m i r r o r p l a n e se x i s t i n t h i s p a t t e r n . F i g u r e 9 ( c ) s h o w s a n e n l a r g e dv i e w o f t h e b l a c k r e c t a n g l e o u t l i n i n g a s m a l l p o r t i o no f t h e s e c o n d - o r d e r L a u e r i n g i n F i g . 9 ( b ) . C a r e f u le x a m i n a t i o n o f F i g . 9 ( c ) r e v e a l s t h a t t h e r e f l e c t i o n si n d i c a t e d b y t h e a r r o w s [ ( 7 1 9 1 2 2 ) a n d ( 1 2 1 9 7 2) ]d o n o t m i r r o r t o e a c h o t h e r. T h i s l a c k o f m i r r o rs y m m e t r y r e d uc e s t h e w h o l e p a t t e r n s y m m e t r y f ro m6 m m t o 6 i n t h e [0 0 01 ] z o n e a x i s o r i e n t a t i o n . A s s u c h ,t h e d i f f r a c ti o n g r o u p f o r th i s s y m m e t r y is 6 m r m a n dt h e ~ p o in t g r o u p _ i s 6 2 2 . C B E D a n a l y s i s o f b o t h t h e( 1 1 2 0 ) a n d ( 1 1 0 0 ) t y p e o r i e n t a ti o n s , n o t s h o w n

    tT he t e rm s p ro j ec t ion -d if f r ac tion sym m et ry and w ho le pa t -t e rn sym m et ry have the sam e m ean ings a s i n B ux ton e t a l .[31] . P roject ion-dif f ract ion symmetry corresponds to thesymm etry of the di f f ract ion disks and di ffuse inten si ty wi thindif f ract ion disks of the zero-order Laue layer. W hole pat ternsymmetry refers to the symmetry of the higher-order Lauezone (HOLZ) ref lect ions and HOLZ Kikuchi l ines seen inlow camera length pat terns such as F ig. 9(b) .

    F ig. 12. [001] zone axis CBED pat tern obtained f rom theM o S i2 nodules , (a) shows the zero-order Laue layer pat ternwhich possesses 4 m m project ion-dif f ract ion symm etry, and(b) shows the wh ole-pat tern sym metry reveal ing 4 m m sym-metry as wel l.

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    7 1 0 VECCHI O et a l . : S H O C K S Y N T H E S I S O F S I L I C I D E S - - IF i g u r e s 1 0 a n d 1 1 s h o w t r a n s m i s s i o n e l e c t r o n

    m i c r o g r a p h s o f t h e p a r t i a l l y - r e a c t e d r e g i o n o f t h e l o wi m p a c t v e l o c it y , r o o m t e m p e r a t u r e M o - S i s a m p l e .F i g u r e 1 0 (a ) a n d ( b ) r e v e a l t h e s t r u c t u r e o f t h e M o S i 2n o d u l e s a n d t h e s u r r o u n d i n g s i l i c o n m a t r i x , r e s p e c t -i v e ly . T h e M o S i 2 n o d u l e s a r e m o n o c r y s t a l l i n e , a p -p r o x . l - 2 # m i n d i a m e t e r , a n d h a v e fa c e ts . T h e ys h o w s i g n i f ic a n t i n t e r n a l s t r u c t u r e , i n c l u d i n g d i s l o -c a t i o n s a n d t w i n s , a s s h o w n i n F i g u r e 1 1. T h e s i l ic o ns u r r o u n d i n g t h e se r e a c t e d r e g i o n s g e n e r a l l y s h o w s a na n n e a l e d s t r u c t u r e w i t h a p r o f u s i o n o f a n n e a l i n gt w i n s , a s s h o w n i n F i g . 1 0 ( b ) . T h i s m i c r o s t r u c t u r es u g g e s t e d m e l t i n g f o l l o w e d b y s l o w r e - s o l i d i f i c a t i o n .

    T h e c r y s t al s t r u c t u r e o f t h e M o S i 2 n o d u l e s w a sd e t e r m i n e d b y C B E D a n a l ys i s. F i g u r e 1 2 s h o w s t h e[ 0 0 1 ] z o n e a x i s C B E D p a t t e r n o b t a i n e d f r o m t h e

    M o S i 2 n o d u l e s . F i g u r e 1 2 ( a ) s h o w s t h e z e r o - o r d e rL a u e l a y e r p a t t e r n w h i c h p o s s e ss e s 4 m m p r o j e c t i o n -d i f f r a c t i o n s y m m e t r y ; F i g . 1 2 ( b ) s h o w s t h e w h o l e -p a t t e r n s y m m e t r y r e v e a li n g 4 m m s y m m e t r y a s w e l l.E x a m i n a t i o n o f b o t h t h e [1 00 ] a n d [ 11 0 ] o r i e n t a t i o n s ,n o t s h o w n h e r e, d i s p l a y e d 2 m m w h o l e - p a t t e r n s y m -m e t r i e s . T h e s e s y m m e t r i e s , i n c o n j u n c t i o n w i t h t h e4 m m s y m m e t r y o f t h e [ 0 0 1 ] o r i e n t a t i o n , a r e c o n s i s t -e n t w i t h a p o i n t g r o u p o f 4 / m m m . F r o m t h e w h o l ep a t t e r n s h o w n i n F i g . 1 2 ( b ) t h e c e n t e r i n g o f t h es t r u c t u r e w a s d e t e r m i n e d t o b e b o d y - c e n t e r e d ( I) .S i n ce n o d y n a m i c a l a b s e nc e s c o u l d b e l o c a t e d i n a n yo r i e n t a t i o n s , t h e s p a c e g r o u p w a s d e t e r m i n e d t o b eI 4 / m m m . M o S i 2 h a s b e e n r e p o r t e d t o e x i s t a s t w od i f f e re n t c r y s t a l s t r u c t u r e s , C 4 0 h e x a g o n a l ( f l - M o S i 2 )a b o v e 1 9 00 C a n d a s C 1 l b ( b o d y - c e n t e r e d t e t r a g o n a l

    i ~ i i i j

    1 1 ~ " 1 1 - '2 " 1 T O 1 1 " 2 1 T 4 o~. 2o_!

    00~- 00~- 000 oo2 oo4 1 1 2 _ _ 1 1 21 0 1 0 1 1

    ~ 1 4 - 1 1 "~ ~ 1 0 " ~ 1 2 " 1 1 4 2o_! o=.~2 d

    Fig. 13. (a) [110] microdiffraction pat tern from one side of the twin plan e in a MoSi 2 nodule a nd (b) showsa [111] selected area diffract ion pat te rn (SA DP ) from th e othe r side, (c) shows a composi te S AD P acrossbo th sides of the twin, and (d) shows the indexing of the composi te p at tern. T he sol id circles indicate thefirst variant pa t tern show n in (a) , the ope n circles represent the ref lect ions from the second varian t shownin (b), and a solid circle inside an open circle indicates overlapping reflections.

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    VECCHIO et al . : SHOCK SYNTHESIS OF SILICIDES--I 711ct-MoSi2) below 1900C [32]. Boettinger e t a l . [33]have reported that pure MoSi2 exists only as the C1 lbstructure, and that the C40 is only metastable at hightemperatures as a result of other solutes stabilizingthis phase. In addition, they point out that in rapidliquid quenching operations, such as plasma-spray-ing, and we propose here for the conditions of thisreaction mechanism, that "the formation of ametastabl e MoSi2 C40 phase can occur directly fromthe melt if the undercooling takes the melt below themetastable melting point of the C40 phase. Thismelting point may be only a few degrees Ceiciusbelow the melting point of the Gl l b phase." TheMoSi 2 phase observed here is consistent with the lowtemperature tetragonal phase (C1 lb) suggesting thateither this phase formed via solid-state below 1900C,

    in contradiction to the mechanism being proposedherein, or was formed from the liquid state (consist-ent with the mechanism proposed here) first as thehigh-temperature C40 structure which subsequentlytransformed during cooling to the low-temperatureC 11 b phase.

    Mitchell e t a l . [34] have examined the (C40) hexag-onal-to- (C 11 b) tetragonal tran sform atio n of MoSi2 inplasma-sprayed processing in which the MoSi 2 phasestarts to f orm in the liquid state. Their results indicatethat a hexagonal-to-tetragonal phase transformati ondoes occur in their experiments even for the veryrapid solidification rates of the plasma-spr ay process-ing. During the transformation the stacking ischanged from ABC in the hexagonal phase to AB inthe tetragonal phase, and three different stacking

    0 2 0 0 Z l 3 1 - 1 0 i 0 3 2 00o o o o

    2~o 1 io ooo ~1o ~2~

    200 10 - 3 110 01 - 3 020 O o o o

    dFig. 14. (a) [001] selected area diffraction pattern from one side of the twin plane in a MoSi2 nodule and(b) shows a [331] selected area diffraction pattern from the other side, (c) shows a composite SADP acrossboth sides of the twin, and (d) shows the indexing of the composite pattern. The solid circles indicate thefirst variant pattern shown in (a), the open circles represent the reflections from the second variant shownin (b), and a solid circle inside an open circle indicates overlapping reflections.

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    7 1 2 VECCHIO et a l . : S H O C K S Y N T H E S I S O F S I L I C I D E S - - Iv a r i a n t s a re p o ss ib l e wi th in a g iv e n h e x a g o n a l g ra in :A B , B C a n d C A . I f tw o d i f f er e n t v a r i a n t s f o r m w i t h i na g iv e n g ra in t h e y wi l l p o sse ss a twin r e l a t i o n sh ipwi th e a c h o th e r . Mi t c h e l l e t a l . [3 4 ] su g g e s t t h a t t h e i ro b s e r v a t i o n o f { l l 0 } t w i n s i n t h e t e t r a g o n a l M o S i 2p h a s e i s a d i r e c t c o n s e q u e n c e o f t h e h e x a g o n a l - t o -t e t r a g o n a l p h a s e t r a n s f o r m a t i o n . F i g u r e 1 1 s h o w s an o d u l e o f M o S i 2 c o n t a i n i n g a t w i n ; e a c h M o S i 2n o d u l e e x a m i n e d , w h e n s u i t a b l y o r i e n t e d , d i s p l a y e dtwin s . F ig u re 1 3 (a ) sh o ws a [ l l 0 ] m ic ro d i f f r a c t i o np a t t e rn f ro m o n e s id e o f t h e twin p l a n e a n d F ig . 1 3 (b)sh o w s a [ l 1 ] se l e ct e d a re a d i f f r a c t i o n p a t t e rn(SADP) f ro m th e o th e r s i d e . F ig u re 1 3 (c ) sh o ws ac o m p o s i t e S A D P a c r o s s b o t h s i d e s o f t h e tw i n , a n dF ig . 1 3 (d ) sh o ws th e i n d e x in g o f t h e c o m p o s i t ep a t t e rn ; t h e twin b o u n d a ry i s p a ra l l e l t o (1 1 0 ) wh ic hi s c o m m o n t o b o t h s i d e s o f t h e t w i n , a n d t h e ( 0 04 )p l a n e o f o n e v a r i a n t i s p a ra l l e l t o t h e (1 12 ) p l a n e o ft h e o t h e r . T h e c r y s t a l l o g r a p h i c n a t u r e o f t h e tw i n w a sfu r th e r a n a ly z e d b y t i l t i n g o n e v a r i a n t i n to t h e [0 0 1 ]o r i e n t a t i o n , sh o wn in F ig . 1 4 (a ) , a n d t h e o th e r v a r i -a n t wa s o r i e n t e d a lo n g th e [3 3 1 ] a x i s [F ig . 1 4 (b ) ] .F i g u r e 1 4 (c ) s h o w s t h e c o m b i n e d S A D P t a k e n a c r o s sth e twin i n t h i s o r i e n t a t i o n , a n d F ig . 1 4 (d ) sh o ws th ein d e x in g o f_ F ig . 1 4 (c ) . Th e twin b o u n d a ry i s s t i l lp a r a ll e l t o ( 11 0) a n d c o m m o n t o b o t h v a r i a n t s , w h i le(1 30 ) o f o n e v a r i a n t i s p a ra l l e l t o (0 1 3) o f t h e o th e r .Th e se r e su l t s a r e c o n s i s t e n t wi th t h e a n a ly s i s o fMi t c h e l l e t a l . [34 ] a n d su g g e s t h e re t h a t t h e n o d u le so f M o Si 2 we re fo rm e d f ro m th e l i q u id s t a t e , so l id i f ie da s h e x a g o n a l , f l - M o S i z w h i c h s u b s e q u e n t l y t r a n s -fo rm e d to t h e l o w- t e m p e ra tu re , t e t r a g o n a l , ~ t -Mo Si2 .In a d d i t i o n , t h e se r e su lt s a r e c o n s i s t e n t wi th t h e p h a see q u i l i b r i a d i sc u sse d b y Bo e t t i n g e r e t a l . [33] forMo Si2, p a r t i c u l a r ly wi th r e g a rd t o t h e C 4 0 to C 1 lbp o l y m o r p h i c t r a n s fo r m a t i o n .3 . 2. S t a t i c s y n t h e s i s ( d i ff u s io n c o u p l e ) e x p e r i m e n t s

    T h e m o r p h o l o g i e s o f th e p a r t i a l ly - r e a c t e d r e g i o n si n t h e N b - S i a n d M o - S i s y s t e m s h a v e u n i q u e f e at u r e st h a t a r e i n d ic a t iv e o f t h e m e c h a n i s m s o p e r a t i n g . T h ep r o f u s e p r e s e n c e o f N b S i 2 a n d M o S i z n o d u l e s a t t h eN b - S i a n d M o - S i i nt e rf a c es , an d , m o r e i m p o r t a n t l y ,i n t e r sp e r se d i n t h e s i l i c o n a re a u n iq u e a sp e c t o fs h o c k - i n d u c e d c h e m i c a l r e a c t i o n s . I n o r d e r t o b o t hc o m p a r e r e a c t i o n m e c h a n i s m s a n d a s se s s th e k i n e ti c so f r e a c t io n u n d e r c o n v e n t i o n a l h e a t t r e a t m e n t , i n t h eso l id s ta t e , p i e c e s o f n io b iu m a n d s i l ic o n we re p o l -i sh e d f l a t , c l a m p e d to g e th e r , a n d t h e n e n c a p su l a t e d .Th e se d i f fu s io n c o u p le s we re a n n e a l e d a t 1 2 0 0 C fo rd i f f e re n t t im e s , se c t i o n e d , a n d a n a ly z e d . F ig u re 1 5 (a )sh o ws ty p i c a l r e a c t i o n l a y e r s t h a t fo rm e d a s a r e su l to f so l i d - s t a t e d i f fu s io n ( i n t h i s e x a m p le t h e c o u p lewa s a n n e a l e d a t 1 2 0 0 C fo r 2 h ). Th e i n t e rd i f fu s io nre su l t e d i n t h e fo rm a t io n o f a t h i c k l a y e r o f NbS i2,a d j a c e n t t o t h e s i l i c o n sa m p le , fo l l o w e d b y a l a m e l l a re u t e c t i c s t ru c tu re o f Nb sS i3 i n Nb S i2 , g ro w in g f ro m al a y e r o f N b s S i 3 a d j a c e n t t o t h e p u r e N b s a m p l e. T h e s er e a c t i o n p r o d u c t s a n d m o r p h o l o g i e s a r e c o n s i s t e n ta n d p r e d i c t a b l e f r o m t h e N b - S i p h a s e d i a g r a m . T h e

    th i c k n e sse s o f t h e p ro d u c t l a y e r s ( e x c lu d in g t h e e u te c -t ic r e g i o n ) a s a f u n c t i o n o f t i m e f o r e a c h o f t h ed i f fu s io n c o u p le s f a b r i c a t e d a re p lo t t e d i n F ig . 1 5 (b ) .Th e d a t a c a n b e e a s i ly r a t io n a l i z e d i n t e rm s o f as im p le d i f fu s io n e q u a t io n

    x = k ~ (1 )wh e re x i s t h e t h i c k n e ss o f t h e r e a c t i o n l a y e r , D i sthe d i f fusion coeff ic ien t , t i s the t ime , and k i s ap a r a m e t e r t h a t i s a f u n c t i o n o f t h e g e o m e t r y , p h a s e sfo rm e d , e t c . Th e a c t i v a t i o n e n e rg y fo r d i f fu s io n fo rth e se m a te r i a l s v a r i e s f ro m 2 0 0 to 4 0 0 k J /m o l . T a k in ga we ig h t e d a v e ra g e ( a m o n g th e a v a i l a b l e d a t a )b e twe e n th e a c t i v a t i o n e n e rg i e s fo r se l f -d i f fu s io no f s i l ic o n a n d n io b iu m , a v a lu e o f 3 5 0 k J / t o o l i so b t a i n e d . H e n c e

    I A 1x = KD~o(e - O/Rrt)2 . (2 )B y g r o u p i n g t h e t w o u n k n o w n p a r a m e t e r s k a n d

    D~ a n d f i t t i n g e q u a t io n (2) t o t h e e x p e r im e n ta l r e su l t so f F ig . 1 5 (b ), i t i s p o ss ib l e t o p re d i c t r e a c t i o n l a y e rt h ic k n e s se s a s a f u n c t i o n o f t i m e f o r b o t h N b s S i 3 a n dNb Si 2 . Th e se p re d i c t e d t h i c k n e sse s , fo r a r a n g e o ft e m p e ra tu re s b e lo w th e m e l t i n g p o in t o f s il i co n , a r ep lo t t e d i n F ig . 1 5 (c ). Th e e f f ec t o f t e m p e r a tu re o n t h ep ro d u c t l a y e r t h i c k n e ss i s v e ry sm a l l , i n t h e sc a l e o fF ig . 1 5 (c ). Th e u se fu ln e ss o f t h i s p lo t i s t h a t i t e n a b l e sc o m p a r i s o n o f t h e a m o u n t o f e x p e ct e d r e a c ti o np r o d u c t o n t h e t i m e s c al e o f t he s h o c k e x p e ri m e n t s.Th e p re d i c t e d r e a c t i o n l a y e r th i c k n e sse s , fo r a tim e o f5 p s ( m a x i m u m d u r a t i o n o f s tr e ss p ul s e w i t h i nsh o c k e d sp e c im e n s) a n d a t e m p e ra tu re o f 1 67 3 K [ th em a x i m u m a d m i s s ib l e t e m p e r a t u r e f o r s o l id - s ta t ep r o c e s s ( th e m e l t i n g t e m p e r a t u r e o f s i l i c o n =1 6 87 K ) ] a re 1 0 -7 a n d 1 0 -9 / t i n fo r N b S i 2 a n d Nb sS i3 ,r e sp e c t i v e ly . Un d e r sh o c k c o m p re ss io n , t h e r e a c t i o nf r o n t a d v a n c e s b y a d i m e n s i o n o n t h e o r d e r o f t h er a d i u s o f t h e n o d u l e s ( ~ 1 # m ) w i t h in t h i s s a m e t i m esp a n (5 /~s ) . Th u s , t h e r e a c t i o n r a t e s u n d e r sh o c kc o m p r e s s i o n a r e 1 0 7 -1 0 9 t i m e s h i g h e r t h a n u n d e rs t a t i c , so l i d - so l i d c o n d i t i o n s .3 .3 . P r o p o s e d r e a c t io n m e c h a n i s m

    Th e a n a ly s i s o f t h e p a r t i a l ly - r e a c t e d r e g io n s i n t h eN b - S i a n d M o - S i s h o c k e x p e r i m e n t s r e v e a l e d t h ed e t a il e d n a t u r e o f t h e r e a c ti o n s e q u e n c e a n d m e c h a n -i s m s ( f o r t h e s a k e o f b r e v i t y o n l y t h e N b - S i s y s t e mwi ll b e d i sc u sse d b e lo w , h o w e v e r t h i s a n a ly s i s a p p l i e se q u a l l y w e ll t o t h e M o - S i s y s te m ) . A t h e r m o d y n a m i ct r e a t m e n t o f t h e r e ac t i o n m e c h a n i s m p r o p o s e d b e l o wi s g i v e n i n a c o m p a n i o n p a p e r [ 2 7 ] . T h e p r e p o n d e r -a n c e o f sm a l l Nb S i2 p a r t ic l e s su r r o u n d e d b y s i l i co n ,a s we ll a s t h e e x i s t e n c e o f Nb S iz p a r t i c le s a t t a c h e d t oth e n io b iu m p a r t i c l e s (F ig s 3 a n d 4 ) a re e v id e n c e fo ra r e a c t i o n m e c h a n i s m i n w h i c h t h e N b S i 2 o r M o S i :p a r t i c l e s a re c o n t in u o u s ly b e in g g e n e ra t e d a t t h ein t e r f a c e a n d e j e c t e d i n to t h e (m o l t e n ) s i l i c o n . Th u s ,n o p e r m a n e n t d i f f u s io n b a r r i er t h a t w o u l d s l o w d o w nt h e r e a c t i o n p r o c e s s i s f o r m e d , a n d r e a c t i o n c a np ro c e e d a t a c o n s t a n t r a t e u n t i l t h e e n t i r e m e ta l

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    VECCHIO et al.: SHOCK SYNTHESIS OF SILICIDES---I 713

    b7 0

    o 6 0"~ 5 0~ 4 0~ 3 0-r.~ 2 0

    o o

    ftf N b S i/ 0 2/ o/ e/

    N b S i~ . S 3 0)o I i I

    0 2 0 40 60 8 0 1 0 0H o l d i n g T i m e ( h o u r )

    1 2 0

    C~ O ] i 0 0 0 . 1 4 0 0 o c

    ~ -~ o ~ ., . . . . . . . . . . . .-7 -6 - s -4 -3 -2 -1 0 1

    H o l d i n g T i m e ( L o g S e c . )Fig. 15. (a) Backscattered electron micrograph of typicalreaction layers that formed as a result of solid-state diffusion(in this example the couple was annealed at 1200C for 2 h).The interdiffusion resulted in the formation of a thick layerof NbSi2, adjacent to the silicon sample, followed by alamellar eutectic structure of NbsSi3 n NbSi2, growing froma layer of NbsSi3 adjacent to the pure Nb sample. (b) a plotof the measured thicknesses of the product layers (excludingthe eutectic region) as a function of time for each of thediffusion couples fabricated, the dashed and solid linesrepresent best fit curves. (c) is a plot of the predictedthicknesses, based on equation (2), for a range of tempera-tures below the melting point of silicon.

    (Nb o r Mo) or silicon is consumed. The shock-in-duced reaction is initiated along the solidmetal-molten Si interface. After reaction has pro-ceeded to a certain extent, surface (interfacial) forcesbecome dominant, and the liquid reaction productagglomerates, forming a spherule. At this point,

    reactio n kinetics are drastically decreased, due to thereducti on in the Nb -S i interfacial area, and solidifica-tion of the disilicide sphere starts. As the spheresolidifies, new nuclei form al ong the N b- Si interface.The new nuclei grow, agglomerate in to spheres whenthey reach a critical size, and thereby form ne ighbor-ing spheres. As these neighboring spheres solidify,they exert forces on the first sphere, expelling it intothe molten silicon, and thus exposing fresh surfaces.This reaction process can continue unimpeded, untilthe reactants are consumed. In addition, turbulentflow of the liquid silicon under shock can alsocontribute to the detachment of the spherules fromthe interface. The companion paper (Part II; [27])presents this mechanism in detail.

    4. CONCLUSIONS1. It was possible to successfully initiate and prop-agate shock-induced reactions for the two systems

    investigated (Nb-Si and Mo-Si), and the extent ofreaction was found to increase with shock energy,shock temperature, and the energy of reaction.

    2. The following qualitative statements can bemade: (a) as the heat of reaction increases, the shockpressure/temperature necessary for full reaction de-creases, and (b) the extent of shock-i nduced reactionincreases with shock energy, at a constant tempera-ture, and with temperature, at a constant shockenergy.

    3. Electron microscopy observations reveal thatthe main reaction product in the partially-reactedregions is the disilicide formed from the mol ten stateas spherules with radii of approx. 1-2/zm. Thesespherules are formed at the metal- Si interface and areexpelled into the silicon.

    4. There is clear indicatio n that silicon melting isa prerequisite for shock-induced reactions.

    5. The kinetics in static solid-state reactions wereestablished and found to be lower, by ~ 108 com-pared to the kinetics in shock compression.

    6. A reaction mechan ism und er shock com-pression for the metal- Si interface is proposed involv-ing the dissolution of Nb or Mo into molten Si,producing the molten intermetallic, with its sub-sequent spheroidization, solidification, and expulsioninto the surrounding liquid silicon melt. In thisreaction mechanism a fresh solid (Nb or Mo)-liquid(Si) interface is continuously maintained, enabling ahigh reaction rate.A c k n o w l e d g e m e n t s - - T h i s research was supported byNational Science Foundation Grant DMR 8713258(Materials Processing Initiative), and by McDonnell-Douglas Research Laboratory. We thank the supportprovided by Dr B. McDonald (NSF) and by Drs C.Whitsett and P. Meschter (MDRL). The help of Dr N. N.Thadhani and of the Center of Explosives TechnologyResearch (New Mexico Institute of Mining and Technology)Field Laboratory technicians in the execution of theexperiments is gratefully acknowledged.

    AMM42/3--1

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