C.T. White, D.H. Robertson and D.W. Brenner- Dissociative phase transitions from hypervelocity...

8/3/2019 C.T. White, D.H. Robertson and D.W. Brenner- Dissociative phase transitions from hypervelocity impacts

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Physica A 188 (1992) 357-366North-Holland P f l Y S I C A

Dissociat ive phase transit ions from hypervelocityimpact sC . T . W h i t e , D . H . R o b e r t s o n a n d D . W . B r e n n e rNava l Research Labora t ory , W ash i ng ton , D C 20375-5000, US A

Molecular dynamics simulations are used to study hypervelocity impacts of an ultrathinflyer plate with a semi-infinite two-dimensional mo de l diatom ic molecular sol id. Thesehypervelocity imp acts are show n to produ ce a d issociative phase transition from a mo lecularto a close-packed solid in the target material. Although this close-packed phase persists forless than 10 picoseconds and is confined to a do m ain les s than 10 nanom eters wide itnevertheless behaves in a manner consistent with continuum theory.

1 . I n t r o d u c t i o nA w i d e v a r i e t y o f l a b o r a t o r y m e t h o d s h a v e b e e n d e v e l o p e d t o la u n c h f l ye r

p l a t e s , m i c r o p r o j e c t i l e s , p e l l e t s , a n d f r a g m e n t s a t h y p e r v e l o c i t i e s . T h e s e m e t h -o d s i n c l u d e t h e u s e o f : f i b e r - c o u p l e d o p t i c a l p u l s e s to a c c e l e r a t e 5 ~ m t h i ck A 1t a r g e t s t o v e l o c i ti e s i n e x c e s s o f 3 k m / s [ 1] ; h i g h - e x p l o s i v e s t h a t c a n l a u n c h0 . 1 5 m m t h ic k s t a in l e ss - s te e l p l at e s at v el o ci ti e s b e t w e e n 6 t o 7 k m / s [ 2];p l a s m a a c c e l e r a t o r s t h a t l a u n c h 3 0 0 m i c r o n d i a m e t e r g l a s s b e a d s a t v e l o c i ti e su p t o 1 0 k m / s [ 3] ; m u l t i s ta g e g a s - d y n a m i c la u n c h e r s t h a t c a n a c c e l e r a t e 1 . 0 m mt h i c k T i a l l o y p l a t e s t o v e l o c i t i e s o v e r 1 0 k m / s [ 4 ]; a n d e l e c t r i c g u n s t h a t l a u n c h0 . 3 m m t h i c k p l a s t i c p l a te s a t v e l o c i ti e s in e x c e s s o f 1 5 k m / s [ 5] .

T h e s e h y p e r v e l o c i ty p r o j e c t i l e s - w h e n i m p a c t e d o n s t a t io n a r y t a r g e t s - ca nb e u s e d t o s t u d y a b r o a d r a n g e o f b a s ic an d a p p l ie d p r o b l e m s . E x a m p l e se n c o m p a s s s t u d i e s o f t h e b e h a v i o r o f m a t t e r u n d e r e x t r e m e c o n d it io n s [ 6 ],s i m u l a t i o n s o f m e t e o r i m p a c t - i n c lu d i n g m a n - m a d e s p a c e d e b r is - o n s a te l l it es h i e l d s ( f o r r e c e n t w o r k , s e e e .g . p a p e r s , p r e s e n t e d i n r e f . [ 7 ]) , i n v e s t i g a t io n so f v e r y h i g h p r e s s u r e p h a s e t r a n s i t io n s [ 8] , s t u d i e s o f t h e c o n d i t i o n s n e c e s s a r yt o i n i ti a t e d e t o n a t i o n s [ 9] , a n d t h e e x p l o r a t i o n o f p o t e n t i a l h ig h p r e s s u r ep r o c e s s i n g r o u t e s t o n o v e l m a t e r i a ls s u c h as " h e x a g o n a l d i a m o n d " [10 ] ( l o n -s d a l e i t e ) o r i g i n a l l y d i s c o v e r e d i n g r a n u l a r f o r m i n m e t e o r i t e s .

B e c a u s e o f th e s h o r t t i m e s i n v o l v e d , m o l e c u l a r d y n a m i c s ( M D ) s i m u l a ti o n sp r o v i d e a p o t e n t i a ll y p o w e r f u l p r o b e o f p r o c e s se s o c c u r ri n g d u r i n g t h e v e r ye a r l y s t ag e s o f h y p e r v e l o c i t y im p a c t s . I n a d d i t i o n , t h e s e m e t h o d s c a n b e u s e d0378-4371/92/$05.00 19 92 - Elsevier Science Publishers B.V. All rights reserved


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358 C . T . W h i t e e t a l . / P h a s e tr a n si ti o ns f r o m h y p e r v e l o c i t y i m p a c t st o d i r e c tl y s i m u l a t e t h e h y p e r v e l o c i t y i m p a c t o f n a n o m e t e r p a r ti c le s a t s u r f a c e sa n d h e n c e , f o r e x a m p l e , t o s t u d y t h e p i t t i n g a n d c o r r o s i v e e f f e c t s o f c o l l i s i o n so f s u c h p a r t i c l e s w i t h o r b i t a l v e h i c l e s . H o w e v e r , w i t h t h e e x c e p t i o n o f H o l i a n ' ss t u d i e s o f a s p h e r e o f 6 8 3 p a r t i c l e s s t r i k i n g a r e c t a n g u l a r p l a t e c o n t a i n i n g 8 0 0 0a t o m s [ 1 1 ] , l i t t l e a t t e n t i o n h a s b e e n g i v e n t o u s i n g M D s i m u l a t i o n s t o s t u d yh y p e r v e l o c i t y i m p a c ts .

I n t h i s p a p e r w e r e p o r t r e s u l ts o f a s e r ie s o f M D s i m u l a t i o n s o f t h eh y p e r v e l o c i t y i m p a c t o f a n a n o m e t e r t h i c k p l a t e w i t h a m o d e l t w o - d i m e n s i o n a ld i a t o m i c m o l e c u l a r s o li d . F o r t h e r a n g e o f h y p e r v e l o c i t y i m p a c t s s tu d i e d( 1 0 - 2 0 k m / s ) e v e n t h i s u l t r a th i n p l a te i s f o u n d t o h a v e s u f f ic i en t m o m e n t u m t oi n d u c e a p o l y m o r p h i c ( d i s s o c i a t i v e ) p h a s e t r a n s i t i o n f r o m a m o l e c u l a r t o ac l o s e - p a c k e d s o l i d i n t h e t a r g e t m a t e r i a l . A l t h o u g h t h e c l o s e - p a c k e d p h a s ep e r s i s t s f o r l e s s t h a n 1 0 p i c o s e c o n d s a n d i s c o n f i n e d t o a d o m a i n l e s s t h a n 1 0n a n o m e t e r s w i d e , i t b e h a v e s i n a m a n n e r c o n s i s t e n t w i t h c o n t i n u u m t h e o r y .W e d e s c r i b e t h e m o d e l u s e d i n t h e s e s t u d i e s i n t h e n e x t s e c t i o n . T h e n i ns e c t i o n 3 t h e r e s u l t s a r e r e p o r t e d a n d d i s c u s s e d . F i n a l l y , s e c t i o n 4 p r o v i d e s as u m m a r y a n d c o n c l u d i n g r e m a r k s .2 . M o d e l

T h e 2 D m o d e l u s e d t o o b t a i n t h e r e s u l t s r e p o r t e d i n t h e n e x t s e c t i o n h a sb e e n i n t r o d u c e d i n a n e a r l i e r w o r k [ 1 2 ] . T h i s m o d e l i s b a s e d o n e m p i r i c a l b o n do r d e r p o t e n t i a l s p a t t e r n e d a f t e r t h o s e u s e d b y T e r s o f f [ 1 3 ] t o d e s c r i b e S i b u tt a i l o r e d h e r e t o t r e a t a d i a t o m i c m o l e c u l a r s o l i d . W i t h i n t h i s a p p r o a c h t h e t o t a lp o t e n t i a l e n e r g y o f a c o l l e c t i o n o f N i d e n t i c a l a t o m s i s r e p r e s e n t e d a s

N NV= ~'~ ~ ' , {fc(ri j ) [ V R ( r ij ) - B i Y A ( r O ) ] + V , , d w ( r i j ) } , (1 )

i j > i

w h e r e t h e p a r a m e t e r s a n d f u n c t i o n s u s e d i n t h i s e x p r e s s i o n a r e g i v e n i n t a b l e I .T h e m o l e c u l a r b o n d i n g p o r t io n o f th e p o t e n t i a l c o ns is ts o f a r e p u ls i v e , V R ( r ) ,a n d a t t ra c t i v e , V A (r ) , t e r m , b o t h m o d e l e d b y e x p o n e n t i a ls , w h i l e a L e n n a r d -J o n e s p o t e n t i a l , V v dw , i s u s e d t o d e s c r i b e t h e w e a k l o n g - r a n g e d v a n d e r W a a l si n t e r a c t i o n . T h i s L e n n a r d - J o n e s p o t e n t i a l i s t r u n c a t e d n o t o n l y a t l a r g e d i s -t a n c e s b u t a l so a t b o n d i n g s e p a r a t i o n s t o a l l o w f o r c o v a le n t b o n d i n g . T h e b o n do r d e r f u n c t i o n , / }i j ~ l ( B # + B i i) , e n t e r i n g e q . ( 1 ) i n t r o d u c e s m a n y - b o d y e f -f e c t s i n t o t h e p o t e n t i a l b y m o d i f y i n g V a ( r ) a c c o r d i n g t o t h e l o c al b o n d i n ge n v i r o n m e n t . T h e s e m a n y - b o d y e f f e ct s a r is e f r o m t h e h i d d e n e l e c tr o n i c de -g r e e s o f f r e e d o m t h a t a r e n o t t r e a t e d e x p l i c it ly i n t h e m o d e l . F o r a n i s o l a t e dd i a t o m i c m o l e c u l e / ? ~ i s u n i t y a n d t h e p o t e n t i a l r e d u c e s t o a g e n e r a l i z e d M o r s ef u n c t i o n f a m i l i a r i n t h e d e s c r i p t i o n o f d i a t o m i c b o n d i n g ( s e e e .g . r e f . [ 1 4 ] ). F o r


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C. T. White et al. / Phase transitions fro m hypervelocity impacts 35 9

T a b l e IT h e c o m p o n e n t s a n d p a r a m e t e r s u s e d i n e q . ( 1 ) . I n th e s i m u l a ti o n s ea c h a t o m w a s a s s u m e d t oh a v e t h e m a s s o f N .

D o = 5 . 0 e VV R ( r = e x p [ - - a ~ ( r - - r e ) ] S : 1 . 8a = 2 . 7 A 1

VA(F ) = S D ~ 1 e x p [ - a 2 X/2 7S ( r - r e ) ] r ~ = 1G = 5 . 0

B # = ( I + G Z f c ( % ) e x p [ m ( % - r , k ) ] ) " m = 2 . 2 5 , ~ - 1k~ . j n = 0 .5/ 1 ,f ~ ( r ) = ~ { l + c o s [ ~ r ( r - 2 ) ] } , 2 ~ < r < 3 ~ = 5 . 0 1 0 - 3 e V

[0 , 3 ~< r c r = 2 .98 8 A0 , r < 1 . 7 5 P0 = 0 . 4 7 2 7 e V ~P o + r [ P ~ + r ( P 2 + r P 3 ) ] , 1 .7 5 ~< r < 2 . 9 1 P l = - 0 . 6 9 9 6 e V A

V v d w ( r ) = / 4 ~ [ ( t r / r ) ~ 2 - ( g / r ) 6 ] ' 2 . 9 1 ~< r < 7 . 3 2 P2 = 0 . 3 3 6 4 e V A '~ 0 , 7 . 3 2 ~ r P 3 = - 0 . 0 5 2 0 e V , ~

m o r e h i g h ly c o o r d i n a t e d s t ru c t u r e s/ ~ i j is n o l o n g e r u n i ty , b u t r a t h e r d e c r e a s e sw i t h t h e i n c r e as i n g n u m b e r a n d s t r e n g t h o f c o m p e t i n g b o n d s t h e a t o m s i a n d jf o r m . T h i s d e c r e a s e i n / ~ i j r e f le c t s t h e f i n it e n u m b e r o f v a l e n c e e l e c t r o n s t h e s ea t o m s h a v e a v a i l a b l e f o r b o n d i n g . I f t h e c o u p l i n g G e n t e r i n g / ~i j d e f i n e d i nt a b l e I is s m a l l , t h e n t h e s t r e n g t h o f t h e b o n d b e t w e e n t h e s e t w o a t o m s is n o tr a p i d l y r e d u c e d b y t h e s e o t h e r c o m p e t i n g b o n d s a n d t h e p o t e n t i a l w ill f a v o rh i g h l y c o o r d i n a t e d m e t a l li c sy s t e m s . H o w e v e r , i f G i s l a r g e , t h e n t h e p o t e n t i a lw i l l f a v o r l o w - c o o r d i n a t e d s t r u c t u r e s w i t h a f e w s t r o n g b o n d s a s i n a m o l e c u l a rs o l i d .

H e r e i n G is c h o s e n t o f a v o r a v a l e n c e o f o n e , i n s u r in g t h a t w i t h o u t t h e v a nd e r W a a l s b o n d i n g t e r m , V v d w , t h e g r o u n d s t a te a t z e r o t e m p e r a t u r e a n dp r e s s u r e is a c o ll e c t io n o f 1 N i n d e p e n d e n t d i a t o m i c m o l e c u l e s. F o r t h ep a r a m e t e r s g i v e n in ta b l e I , e a c h o f t h e s e d i a t o m i c m o l e c u l e s h a s a b i n d i n ge n e r g y o f 5 e V a n d a v i b r a t i o n a l f r e q u e n c y o f 1 6 82 c m - 1 a t a n e q u i l i b r iu m b o n dd i s t a n c e o f 1 . 0 , ~ , a ll s im i l a r t o m o l e c u l a r o x y g e n . I n c l u s i o n o f Vvdw c a u s e s t h i ss y s t e m t o c o n d e n s e i n t o a d i a t o m i c m o l e c u l a r s o l i d w h i c h i n t w o d i m e n s i o n sh a s a c r y s t a l li n e b i n d i n g e n e r g y o f 0 . 0 4 e V p e r m o l e c u l e , a d i s ta n c e o f c lo s e s ta p p r o a c h b e t w e e n a t o m s i n n e a r e s t - n e i g h b o r m o l e c u l e s o f 3 .3 , ~, a n d a so li d -s t a te s p e e d o f so u n d o f 1 . 9 k m / s , a ll w e ll w i t h in p h y s ic a l n o r m s . F u r t h e rp r o p e r t i e s o f t hi s m o d e l - i n c l u d i n g i ts s h o ck H u g o n i o t - a r e p r e s e n t e d el se -w h e r e [ 1 2 ] .


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360 C. T. Wh i te et a l . / Phase transi tions f ro m hyperveloci ty impacts3 . R e s u l t s a n d d is c u s s i o n

H y p e r v e l o c i t y i m p a c t s i m u l a t i o n s a r e i n i t ia t e d b y s l a m m i n g a t h i n f ly e r p l a t ei n t o t h e e d g e o f t h e s e m i - i n f in i t e m o d e l d i a t o m i c m o l e c u l a r c r y s t al in i ti a ll y atr e s t. B o t h t h e f l y e r p l a t e a n d t h e m o l e c u l a r c r y st a l a r e i n it ia l ly t a k e n t o h a v en e a r - z e r o t e m p e r a t u r e a n d p r e s s u r e . T h e d y n a m i c s o f t h e s y s te m r e s u lt in gf r o m t h is h y p e r v e l o c i t y im p a c t is t h e n s t u d i e d b y i n t e g r a t i n g H a m i l t o n i a n ' se q u a t i o n s o f m o t i o n u s in g a N o r d s i e c k p r e d i c t o r - c o r r e c t o r m e t h o d [1 5] .D u r i n g t h e s e s i m u l a t i o n s p e r i o d i c b o u n d a r y c o n d i t i o n s a r e i m p o s e d p e r p e n -d i c u l a r t o t h e d i r e c t i o n o f sh o c k p r o p a g a t i o n . A s e r ie s o f s t u d ie s a r e c a r r i e do u t c o r r e s p o n d i n g t o d i f f e r e n t f ly e r p l a t e v e l o c i t ie s r a n g in g f r o m 1 0 t o 2 0 k m / s .I n a ll t h e s e s i m u l a t i o n s t h e f l y er p l a t e i s f o r m e d f r o m 1 6 l a y e r s o f t h e m o l e c u l a rc r y s t a l .A s e q u e n c e o f sn a p s h o t s f o r t h e s i m u l a t i o n b e g u n w i t h t h e 1 5 k m / s v e l o c i t yp l a t e i s s h o w n i n fi g. 1 . A t 0 . 8 p s ( f ig . l a ) o n l y a s i n g l e c o m p r e s s i o n a l s h o c kw a v e is v i si b le . A c r o s s t h is s h o c k f r o n t t h e d i a t o m i c m o l e c u l a r s o l id ( D M S )t r a n s f o r m s d i r e c t l y t o a c lo s e - p a c k e d s o li d ( C P S ) . A l t h o u g h t h e d e n s i t y o f t h isC P S , P c e s , i s a p p r o x i m a t e l y 2 .4 t i m e s l a r g e r t h a n t h e d e n s i t y o f t h e D M S ,P DM S, t h e a v e r a g e n e a r e s t - n e i g h b o r i n t e r a t o m i c s e p a r a t i o n i n th i s p h a s e , d NN ,is a c t u a l l y 2 0 % l a r g e r d u e t o a n i n c r e a s e in t h e in t e r a t o m i c c o o r d i n a t i o n . T h e s ep r o p e r t i e s o f t h e C P S m a k e t h is D M S t o C P S t r a n s i ti o n s i m i l ar t o th ed i s s o c ia t i v e t r a n s i ti o n r e p o r t e d i n d i a t o m i c m o l e c u l a r s o l id s o f io d i n e [1 6] a n db r o m i n e [ 17 ] . T h i s t r a n s i t i o n o c c u r s a t 2 1 G P a i n I 2 a n d 8 1 G P a i n B r 2 l e a d i n gt o a n i n c r e a s e i n t h e o v e r a l l r e l a t i v e d e n s i t y , P C e s / P D M s , o f 1 . 7 f o r 12 an d 2 . 3f o r B r 2 , a n d a n i n c r e a s e i n KNNo f a r o u n d 1 5 % f o r b o t h m a t e ri a ls .

A t 1 .6 p s (f ig . l b ) a s e c o n d l e a d i n g c o m p r e s s i o n a l s h o c k w a v e h a s a p p e a r e di n th e 1 5 k m / s s i m u l a t i o n . A c r o s s t h i s n e w f r o n t t h e d i a t o m i c m o l e c u l e s a r ec o m p r e s s e d a n d r o t a t e d f r o m t h e i r i n i t i a l p o s i t i o n s i n t h e u n d i s t u r b e d c r y s t a lb u t r e t a i n t h e i r m o l e c u l a r i d e n t i t y . O n c e t h i s s e c o n d s h o c k f r o n t i s c l e a r l yv i s i b l e i t r a p i d l y s e p a r a t e s f r o m t h e d i s s o s c i a t i v e f r o n t a s c a n b e s e e n b yc o m p a r i n g f i g . l b . t o f i g . l c . A l t h o u g h b o t h t h e c o m p r e s s i o n a l a n d d i s s o c i a t i v es h o c k f r o n t s p r o p a g a t e a t v e l o c it i e s i n e x c e ss o f t h e s p e e d o f s o u n d i n t h eu n d i s t u r b e d c r y s ta l , t h e v e l o c i t y o f t h e d i s s o c i at i v e f r o n t r a p i d l y d e c r e a s e s f r o mm o r e t h a n 1 2 k m / s a t 0 . 5 p s t o c lo s e t o 3 k m / s a t 2 . 4 p s . I n c o n t r a s t, t h ev e l o c i t y o f t h e l e a d i n g c o m p r e s s i o n a l s h o c k r e m a i n s p i n n e d c l o s e t o 1 2 k m / s s ol o n g a s t h e d i s s o c i a t i v e f r o n t e x i s t s , o n l y b e g i n n i n g t o g r a d u a l l y s l o w a f t e r t h eC P S d i s a p p e a r s . A s t h e d i s s o c ia t iv e f r o n t sl o w s t h e a c c o m p a n y i n g d i s so c i a t iv ez o n e a l s o n a r r o w s a s t h i s r e g i o n i s c o n s u m e d b y t h e r a r e f a c t i o n w a v e f r o mb e h i n d ( fi g . 1 a - d ) . F i g s. 1 a n d 2 s h o w t h a t a s th e p a r t i c l e f lo w v e l o c i t y , U p ce s,b e h i n d t h e d i s so c i a t iv e f r o n t a p p r o a c h e s 3 k m / s ( fi g. 2 ) th i s f r o n t a l s o b e g in s t os m e a r w i t h t h e m a t e r i a l b e h i n d b e g i n n i n g t o e n t e r t h e m i x e d p h a s e r e g i o n b y


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C .T . W hite et al . / P hase transitions fr om hypervelocity impacts 361~ Q ~e~mQ~

, @ t , ~ . , . , ~ . ~ . o . , . l ' ~ o , . . o o . . . o , . . . . . . . . . . o . ( a ) ~ * . - o ~ O =

* ~ . ~ . * . . . %, , . ' ~ . ~~~ l~J~ .~~ ' , ~o ,~? , , ,

" . . . ' ~ ' . . . " . ~ . ' ~ . . . n L , ' ~ ' ~ ' ~ ~ ~ ~

. , , " ~ . " . " s . ~. ~ - " u l ~ :~ . . ~ . ~ ~ " "~'. ~ ; ~ ' ~ t ~~ ~ 4 e w~cmm4 ~ ~ 4 ~ ~ v ~ - - ~ " ~ ~ ~ - ~ l T ~" ~, . . , ~ , . ' _ ~ . ' - . - - , ~ ~ . . . ~ ~ t . ~ ~ - " , ~

F i g . 1 . S n a p s h o t s o f t h e s i m u l a ti o n s b e g u n w i t h t h e 1 5 k m / s f ly e r p l a t e a t : ( a ) 0 . 8 ; ( b ) 1 . 6 ; ( c ) 2 . 4 ;( d ) 3 . 2 ; a n d ( e ) 4 . 0 p s a f t e r t h e i m p a c t . T h e s h o c k w a v e s a r e p r o p a g a t i n g f r o m l e f t t o r i g h t .

2 . 4 p s ( f ig . l c ) , w h i c h i s c le a r l y p r e s e n t a t 3 . 2 p s ( f ig . l d ) j u s t p r i o r t o t h ec o m p l e t e d i s a p p e a r a n c e o f t h e d i s so c i a ti v e z o n e .A d i s s o c ia t iv e p h a s e t o g e t h e r w i t h a n a c c o m p a n y i n g s p li t s h o c k w a v e s u c h a ss h o w n i n f i g . l b i s a l s o p r e s e n t i n a l l t h e o t h e r s i m u l a t i o n s b e g u n w i t h f l y e rp l a t e v e l o c it ie s b e t w e e n 1 0 a n d 2 0 k m / s . H o w e v e r , t h e i n d u c t i o n t i m e f o r th ea p p e a r a n c e o f th e l e a d i n g c o m p r e s s i o n a l w a v e v a r ie s , w i th th i s w a v e a p p e a r i n ga l m o s t i m m e d i a t e l y i n t h e 1 0 k m / s s i m u l a t i o n b u t t a k i n g p r o g re s s i v e ly l o n g e rt o a p p e a r a s th e i n i t ia l i m p a c t p l a t e v e l o c i t y is i n c r e a s e d . A l t h o u g h t h ea p p e a r a n c e o f t h e l e a d i n g c o m p r e s s i o n a l w a v e i s d e l a y e d f o r h i g h e r i m p a c tp l a t e v e l o c i t i e s , o n c e f o r m e d t h i s f r o n t a l w a y s e x h i b i t s a v e l o c i t y c l o s e t o b u ts l i g h t l y l e s s t h a n 1 2 k m / s , p r o v i d e d t h e d i s s o c i a t i v e r e g i o n r e m a i n s w e l l


6/10

36 2 C.T . Wh i t e e t a l . / Ph a se t ra n s i ti o n s f ro m h y p e rv e lo c i t y im p a c t s

, a ,- ,

"'."~.~....: " : : 2 . : .

. . , . , . * .

2 . . . . I . . . . I . . . . I . . . . i . . . .0 0 .5 1 1 .5 2 2 .5

T i m e ( p s )Fi g . 2 . Sc a t t e r p l o t o f UpcPs 3 . 0 A b e h i n d t h e d i ss o c i a t i v e f r o n t f o r t h e h y p e r v e l o c i t y i m p a c ts i m u l a t i o n b e g u n w i t h t h e 1 5 k m / s f l y er p la t e .

d e f i n e d . I n a d d i t i o n , i n a l l s i m u l a t i o n s , o n l y a f t e r t h e p a r t i c l e fl o w v e l o c i t yb e h i n d t h e d i s s o c i a t iv e f r o n t s lo w s to n e a r 3 k m / s , d o e s t h e d i s s o c ia t iv e z o n eb e g i n t o l o s e it s i d e n t i t y . T h e s e g e n e r a l p r o p e r t i e s o f t h e s e h y p e r v e l o c i t yi m p a c t s i m u l a t i o n s a s w e l l a s t h e e x p l i c i t b e h a v i o r s h o w n i n fi g. 1 a r e a l lc o n s i s t e n t w i t h c o n t i n u u m t h e o r y a s w e n o w s h o w .

M o r e t h a n 3 5 y e a r s a g o t h e f ir st s h o c k - i n d u c e d p o l y m o r p h i c p h a s e t r a n s i t i o nw a s o b s e r v e d [1 8]. A n i m p o r t a n t p r o p e r t y o f th e s e p h a s e t r a n s i t i o n s - p r e d ic -t e d f r o m c o n t i n u u m t h e o r y [ 8 , 19 , 2 0] a n d o b s e r v e d e x p e r i m e n t a l l y [ 19 ] - is t h ea s s o c i a t e d c o m p r e s s i o n a l s h o c k w a v e s p l it ti n g t h a t m a y o c c u r . I f s p li t c o m p r e s -s i o n a l s h o c k w a v e s a r e p r e s e n t , t h e n c o n t i n u u m t h e o r y p r e d i c t s [2 0] th a t t h el e a d i n g s h o c k f r o n t s t a r t s t h e m a t e r i a l f l o w i n g , b r i n g i n g i t t o t h e p o i n t o ft r a n s i t i o n , w h i l e t h e t r a n s i t i o n o c c u r s a c r o s s t h e s e c o n d c o m p r e s s i o n a l s h o c kf r o n t . A s p l i t s h o c k w a v e w i t h t h e t r a n s i t i o n o c c u r r i n g a c r o s s t h e s e c o n d f r o n ti s j u s t w h a t i s o b s e r v e d i n f i g s . l b a n d l c .T h e c o n t i n u u m t h e o r y o f p l a n a r s h o c k w a v e s a l so p r e d i c t s [2 0] t h a t a s h o c kw a v e p r o p a g a t e s i n to a m e d i u m ( a s su m e d a t r e st a n d c h a r a c t e r i z e d b y ap r e s s u r e P 0 a n d a sp e c i f ic v o l u m e V 0) w i t h a v e l o c i t y D g i v e n b y

D = ( 1 - V / V o ) l U p , ( 2 )w h e r e t h e p a r t i c l e f lo w v e l o c i t y b e h i n d t h is s h o c k f r o n t , U p , is g iv e n b y

Up = V ( v o - v ) ( p - p o ) , ( 3 )


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C .T . W hi te et a l . / P hase t ransit ions f rom hyperveloci ty impacts 363w i t h V t h e s p e c i fi c v o l u m e a n d P t h e p r e s s u r e o f t h e s h o c k e d m a t e r i a l . T h e s er e s u lt s a r e d e r i v e d f r o m t h e R a n k i n e - H u g o n i o t r e l a ti o n s (s e e e . g. r e f . [2 1 ]) b ya s s u m i n g t h a t t h e s e r e l a t i o n s c a n b e a p p l i e d a s j u m p b o u n d a r y c o n d i t i o n sa c r o s s t h e s h o c k f r o n t . I n v i e w o f t h e s h a r p s h o c k f r o n t s d e p i c t e d i n fig . 1 , t h isa s s u m p t i o n s h o u l d b e q u i te g o o d . T h e r e f o r e , b e c a u s e t h e l e a d in g s h o c k f r o n tc a r r i e s t h e p r e s s u r e , P T , a n d s p e c if ic v o l u m e , VT , o f t h e p h a s e t r a n s i t i o n , i t sv e l o c i t y f r o m e q s . ( 2 ) a n d ( 3 ) is g i v e n b y D , = V o ~ / ( P T - P o ) / ( V o - V x ) , a n dh e n c e i s p r e d i c t e d a s p i n n e d a t a c o n s t a n t v a l u e d e t e r m i n e d b y t h e p r o p e r t i e so f t h e p h a s e t r a n s i t io n a n d t h e u n d i s t u r b e d m o l e c u l a r c r y s ta l . In a d d i t i o n , t h es e c o n d f r o n t c a n o n l y e x i s t as a s h o c k f r o n t s o lo n g a s t h e p a r t i c le f lo w v e l o c i t yb e h i n d t h is f r o n t e x c e e d s t h e p a r t i c le f l o w v e l o c i t y i n t h e l e a d i n g c o m p r e s s i o n a lz o n e , U p 1. B u t f r o m e q . ( 3 ) , u m = ~ /(V ~ - V T ) ( P T - P o ) an d h en ce U p , i s a l s o ac o n s t a n t d e t e r m i n e d b y t h e p r o p e r t i e s o f t h e p h a se t r a n si ti o n a n d t h e i ni ti als t at e . C o n t i n u u m t h e o r y t h e r e f o r e e x p la i n s w h y w h e n t w o s h o c k w a v e s a r ep r e s e n t i n t h e s y s t e m - r e g a r d l e s s o f t h e i m p a c t p l a t e v e l o c i t y - t h e f ir st s h o c kis a l w a y s o b s e r v e d t o p r o p a g a t e a t a n e a r c o n s t a n t v e l o c i t y D , , w h i l e t h es e c o n d a l w a y s b e g i n s t o f r a g m e n t a s t h e p a r t i c l e v e l o c i t y b e h i n d t h is f r o n ta p p r o a c h e s a f ix e d v a l u e u . E l s e w h e r e w e h a v e s h o w n [ 12 ] t h a t f o r t h ep r e s e n t m o d e l : VT = 4 .5 A g / a t o m ; P 1 - - 0 . 8 1 3 e V / A g ; V , - - 6 . 1 4 A ' / a t o m ; a n dP0 ~ 0 . 0 0 e V / A 2 ; r e s u lt s w h i c h i m p l y t h a t D l = 1 1 . 5 k m / s a n d Up, ~ 3 . 0 k m / s .T h e s e p r e d i c t i o n s d i f fe r n o m o r e t h a n 5 % f r o m t h e c o r r e s p o n d i n g n e a r -c o n s t a n t v a l u e s o f D 1 a n d U p, o b s e r v e d i n a ll t h e s e f l y e r p l a t e s i m u l a t i o n sc o n f i r m i n g t h e c o n s i s te n c y o f th e c o n t i n u u m i n t e r p r e t a ti o n .

T h e s e r e s u l ts a r e a l so c o n s i s t e n t w i t h t h e in c r e a s in g l y d e l a y e d a p p e a r a n c e o ft h e l e a d i n g c o m p r e s s i o n a l w a v e o b s e r v e d w i t h i n c re a s i n g fl y e r i m p a c t p l a t ev e l o c i t ie s . S p e c i f ic a l ly , s o l o n g a s t h e v e l o c i t y o f t h e c l o s e - p a c k e d f r o n t D c p se x c e e d s D , , o n l y a s i n g l e s h o c k w a v e w i l l b e p r e s e n t w i t h t h e p h a s e t r a n s i t i o no c c u r r i n g a c r o s s t h i s f r o n t . H o w e v e r , e q . ( 2 ) i m p l i e s t h a t a s t h e p a r t i c l e f l o wv e l o c i t y in t h e c l o s e - p a c k e d r e g i o n , U pc ~s d e c r e a s e s , s o t o o w i ll D(.ps , to t h ep o i n t t h a t D c p s = D ~. T h e l e a d i n g c o m p r e s s i o n a l f r o n t w i ll t h e n b e e m i t t e da n d t h e s h o c k w a v e s w i ll s p l it as d e p i c t e d i n f ig . l b . T h e r e f o r e , c o n s i s t e n t w i t ht h e d a t a , t h e t i m e i t t a k e s f o r t h e s h o c k w a v e s t o s pl it s h o u l d l e n g t h e n w i t hi n c r e a s i n g i n i ti a l f ly e r p l a t e v e l o c i t i e s , b e c a u s e t h e s e h i g h e r i n i ti a l v e l o c i t i e s w i llr e s u l t i n h i g h e r e a r l i e r v a l u e s o f U p c p s .A l t h o u g h t h e t i m e i t t a k e s f o r t h e s h o c k w a v e s t o s p l i t w i l l i n c r e a s e w i t hi n c r e a s i n g f l y e r p la t e v e l o c i t ie s , t h e c o n d i t i o n D c p s = D 1 t o g e t h e r w i t h e q s . ( 2 )a n d ( 3 ) i m p l y t h a t w h e n t h e s p l i tt i n g f ir s t o c c u r s U pc ~s w i ll a l w a y s b e g i v e n b y

u 2 = (1 - V c e s / V o ) D , , ( 4 )w h e r e V cp s is t h e v o l u m e i n t h e c l o s e - p a c k e d r e g i o n . T o a r r i v e a t t hi s r e su l t t h e


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36 4 C.T . W hi t e e t a l . / P has e tr ansi tions f r o m hyper ve loc i t y impac t sc l o s e - p a c k e d r e g i o n w a s a s s u m e d e f f e c t iv e l y i n c o m p r e s s i b l e , w h i c h i s c o n s is -t e n t w i t h t h e m o d e l H u g o n i o t [ 1 2 ] . T h i s H u g o n i o t a l s o s h o w s t h a tVcp s ~ 2 . 3 5 A 2 / a t o m a n d h e n c e e q . ( 4 ) i m p li e s t h a t u 2 ~ 7 . 1 k m / s .T o t e s t e q . ( 4 ) , w e h a v e c a l c u l a t e d U p cp s a s a fu n c t i o n o f ti m e a t ~ 3 . 0 Ab e h i n d t h e c l o s e -p a c k e d f r o n t a v e r a g e d o v e r a 3 . 0 ~ w i d e st ri p , f o r t h es i m u l a t i o n b e g u n w i t h t h e 1 5 k m / s f l y e r p l a t e i m p a c t . T h e r e s u l ts a r e s h o w n i nf i g . 2 a s a s c a t t e r p l o t . T h i s d a t a s u g g e s t t h a t f r o m 0 . 5 t o 1 . 5 p s , U p c p s ( t ) =at + b, w h e r e t h e c o e f f i c i e n ts a a n d b a r e d e t e r m i n e d f r o m a le a s t sq u a r e s f i t o ft h is d a t a a n d a r e g i v e n b y : a = - 2 . 8 k m / ( p s s ); a n d b = 8 .2 k m / s . N e x t , u s i n gt h i s r e s u l t a n d a s s u m i n g e q . ( 4 ) i s v a l i d , s h o w s t h a t i f t h e s h o c k w a v e s s p l it a tt i m e t o, t h e n t h e i r s e p a r a t i o n X s ( t ) a t a l a t e r t i m e t i s g i v e n b y : X s ( t ) = [ a ( V c p s /V0 - 1 ) ~ ] [ ( t - t 0 )2 / 2 ] , w h i ch i mp l i e s t h a t t o = t - [2 (X s/a) (Vcps /V o - 1) ] 1/2.U s i n g t h is e x p r e s s i o n f o r t 0 a n d t h e o b s e r v e d X s ( t ) f r o m 0 . 5 t o 1 .5 ps , w e t h e nc a l c u l a t e a r a n g e o f t o 's a n d a v e r a g e t o o b t a i n {o ~ 0 . 5 1 p s #1 w i t h a 9 5 %c o n f i d e n c e i n t e r v a l o f - + 0. 04 p s . F i n a l l y , s u b s t i t u t i n g i 0 i n t o t h e l e a s t s q u a r e s f itr e l a t i o n f o r U pc ps(t ) y ie l d s u 2 ~ 6 . 8 k m / s , w h i c h i s c l o s e t o t h e 7 . 1 k m / so b t a i n e d b e f o r e . T h i s l e v el o f a g r e e m e n t f u r t h e r c o n f i rm s t h e c o n s i s te n c y o ft h e s i m u l a t e d r e s u l t s w i t h t h e c o n t i n u u m t h e o r y .

4 . S u m m aryI n c o n c l u s i o n , i n th i s p a p e r w e h a v e r e p o r t e d t h e r e s u l ts o f a s e r ie s o f M D

s i m u l a t i o n s o f h y p e r v e l o c i t y i m p a c t s o f a n u l t r a - th i n p l a t e w i t h a m o d e ld i a t o m i c m o l e c u l a r s o li d . A t t h e s e h i g h i m p a c t v e l o c i ti e s e v e n t h i s u l tr a - t h inp l a t e i s f o u n d a b l e t o i n d u c e a d i s s o c i a t i v e p h a s e t r a n s i t i o n t o a c l o s e - p a c k e ds o l i d w i t h a c c o m p a n y i n g c o m p l e x b e h a v i o r s u c h a s s h o c k w a v e s p l i t t i n g .A l t h o u g h t h is c l o s e - p a c k e d p h a s e p e r s is t s f o r le ss t h a n 1 0 p s a n d i s c o n f i n e d t oa d o m a i n l e ss t h a n 1 0 n m w i d e i t s ti ll b e h a v e s i n a m a n n e r c o n s i s t e n t w i t hc o n t i n u u m t h e o r y .

T h e s e s i m u l a t i o n s a l s o s h o w t h a t h y p e r v e l o c i t y i m p a c t s s u f fi c ie n t to i n d u c e al o c a l d is s o c i at i v e t r a n s it i o n s h o u l d a l s o b e c a p a b l e o f c a u si n g a g o o d d e a l o fc h e m i s t r y th r o u g h r e a r r a n g e m e n t o f t h e a t o m s i n t h e d is s o c ia t i v e z o n e . A l -t h o u g h n o t r e a d i l y a p p a r e n t i n f ig . 2 , b e c a u s e o n l y o n e t y p e o f a t o m i s p r e s e n ta n d h e n c e o n l y t r a n s f e r r e a c t io n s a r e a l l o w e d , t h is r e a r r a n g e m e n t l e a d s t o th ef o r m a t i o n o f p r o d u c t m o l e c u l e s i n t h e r a r e f a c t i o n r e g i o n b e h i n d t h e d i s s oc i a -

~ A l t h o u g h t h is r e s ul t i m p l i e s t h a t t h e l e a d i n g c o m p r e s s i o n a l w a v e i s a c t ua l ly a l r e a d y p r e s e n t i nf ig . l a , i t a l s o s h o w s a t 0 . 8 p s t h i s f r o n t i s s ti ll t o o n e a r t o t h e d i s s o c i a ti v e f r o n t t o b e s e e n w i t h t h er e s o l u t i o n o f f ig . l a .


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c .T . W hi te et a l . / P hase t ransit ions f rom hyperveloci ty imp acts 365tive front that are composed of atoms which were not mates in ei ther the targetmaterial or the flyer plate. The question of chemistry induced by hypervelocityimp act s- including the re la t ionship of this i ssue to quest ions involving thebeginn ing of de t ona t i on- i s cur rent ly under fu r the r inves tiga tion us ing morecomplex models describing a material with more than one type of atom.

AcknowledgmentsThis work was support in part by the Office of Naval Research (ONR)

throug h the Naval Research La borator y and through the ONR Physics Divi-sion. Computat ional support was provided in par t by a grant of computerresources f rom the Naval Research Laboratory. One of us (DHR) acknowl-edges a NRC /NR L Postdoctora l Research Associa teship.

R e f e r e n c e s[1] W.M. Trott and K.D. Meeks, in: Shock Compression Condensed Matter-1989, S.C.Schmidt, J.N. Johnson and L.W. Davis, eds. (North-Holland, Amsterdam, 1990) p. 997.[2] S.P. Marsh, R.G. McQueen and T.H. Tan, in: Shock Compression in Condensed Mat te r-1989, S.C. Schmidt, J.N. Johnson and L.W. Davis, eds. (North-Holland, Amsterdam, 1990)

p. 985.[3] H. Tamura, K. Ueda, A.B. Sawaoka and E.B. Ingenbergs, in: Shock Compression InCondensed Mat te r- 1989, S.C. Schmidt, J.N. Johnson and L.W. Davis, eds. (North-Holland,Amsterdam, 1990) p. 993.[4] L.C. Chhabildas, Bull. Am. Phys. Soc. 36 (1991) 1819.[5] J.E. Osher, H.H. Chau, G.R. Gathers and R.C. Weingart, in: Shock Compression inCondensed Mat te r- 1989, S.C. Schmidt, J.N. Johnson and L.W. Davis, eds. (North-Holland,Amsterdam, 1990) p. 963.[6] H.B. Radousky, W.J. Nellis, M. Ross, D.C. Hamilton and A.C. Mitchell, Phys. Rev. Lett. 57(1986) 2419.[7] 1991 APS Topical Conference on Shock Compression of Condensed Matter, Session DF1,Bull. Am. Phys. Soc. 36 (1991) 1885.[8] G.E. Duvall and R.A. Graham, Rev. Mod. Phys. 49 (1977) 523.[9] J.J. Dick, R.N. Mulford, W.J. Spencer, D.R. Petit, E. Garcia and D.C. Shaw, J. Appl. Phys.70 (1991) 3572.[10] D.J. Erskine and W.J. Nellis, Nature 349 (1991) 317.[11] B.L. Holian, Phys. Rev. A 36 (1987) 3943.[12] D.H. Robertson, D.W. Brenner and C.T. White, Phys. Rev. Lett. 67 (1991) 3132.[13] J. Tersoff, Phys. Rev. Lett. 56 (1986) 632; Phys. Rev. B 37 (1988) 6991.[14] J.N. Murrell, S. Carter, S.C. Farantos, E Huxley and A.J.C. Varandas, Molecular PotentialEnergy Functions (Wiley, Chichester, 1984) p. 4.[15] C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations (Prentice-Hall, Englewood Cliffs, 1971) p. 148.[16] K. Takemura, S. Minomura, O. Shimomura, Y. Fujii and J.D. Axe, Phys. Rev. B 26 (1982)998.


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36 6 C.T . Wh i t e e t a l . / Ph a se t ra n s i ti o n s . f ro m h y p e rv e lo c i t y im p a c t s

[17] Y . Fu j i i , K . Hase , Y . Ohi sh i , H. Fu j ih i sa , N. Hamaya , K . Takemura , O. Sh imomura , T .Kikegaw a , Y . Am em iya and T . Ma t sush i t a , Phys. Rev . Le t t . 63 (1989) 536 .[18] S. Minshall , Phys. Rev. 98 (1955) 271.[19] D. Bancrof t , E .L. Peterson and S. Minshal l , J . Appl . Phys. 27 (1956) 291.[20] Ya .B . Ze l ' do v ich and Yu .P . Ra ize r , Physi cs o f Shockw aves and High Tem pera tu re H ydro-dynamic Phen om ena , vo l s . 1 and 2 (Academ ic Pre ss , N ew York , 1967) vo l . 1 , 13 ; vo l . 2 , 19.[21] M. R oss , Encyc loped ia o f Physi cs , R .G. Le rne r and G.L . T r igg , eds . (Ad di son-W esley ,Lon don , 1981) p . 924 .

Date post:	06-Apr-2018
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C.T. White, D.H. Robertson and D.W. Brenner- Dissociative phase transitions from hypervelocity...

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