F.E. Walker- A Comparison of the Classical and a Modern Theory of Detonation

8/3/2019 F.E. Walker- A Comparison of the Classical and a Modern Theory of Detonation

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JOURNAL DE PHYSIQUE IVColloque C4, supplkment au Journal de Physique 111, Volume 5, mai 1995A Comparison of the Classical and a Modern Theory of DetonationF.E. WalkerInterplay, Danville, California94526, U.S.A.

ABSTRACTA q u i t e complete expos i t ion of what has been ca l le d t hec l a s s i c a l t he o ry o f d e t o n at i on i s g iv en i n t h e S c i e n t i f i cAmerican o f May 1987 by W.C . Davis. However, Davis s t a t e si n h i s r e p o r t t h a t , " In s p i t e o f t h e v a r i e t y o f modern a p p l i -ca t ion s o f exp losives , de tona t ion sc ience has no t y e treached matur i ty . . .," and, " Sc ie n ti st s who study explo-s i on s a r e spur red on by be ing con s ta nt ly reminded t h a t th e

c u r r e n t d e t o n at i o n t h e o r y i s incomplete. " I n t h i s paper acomparison i s made between th e c l a s s i c a l the ory as exppundedby Davis and a more modern theory based on the concepts that:( 1 ) The energy i n th e very narrow shock o r de ton a t ion f r on ti high1y nonergodi c , and thermal equi l ibr ium, p a r t ic u la r l ybetween th e t r an s l a t io na l and vi br a t i on a l energy modes, doesn ot e x i s t i n t he f r on t ; ( 2 ) No r e a l i s t i c t em pe ra tu re c a n beasc r ibe d t o t h i s very narrow zone; and ( 3 ) A physica l regu-l a t o r which cons t r a ins shock and de tona t ion v e l oc i t i e s i s d i -r e c t l y r e l a t e d t o t h e v i b r a t o r y v e l o c i t i e s o f t h e atoms o f t h eshocked mater ia ls .The paper includes a sh or t h i s to r i c a l summary, a s t a t e -

ment o f some c r uc ia l de f i c i enc ie s i n th e c l a s s i ca l t heory ,and it conta ins the presenta t ion and discuss ion of a numbero f exper iments and mathematical arguments fav or in g th e a l t e r -na t i ve theory. Among th es e a r e exper imental obs erva t ion s madei n th e 1960s and 1970s and cont inuing t o th e present . Propos-a l s o f t r ibochemica l o r mechan ical bond f r a c t u r e i n shockf r o n ts i n explos ives were made a s e a r l y as 1938, and theya pp ea re d o c c a si o n a ll y i n l a t e r y e a rs , b u t t h e y were o f t e nignored. Fi na l ly , r e s u l t s f rom more rece nt exper iments andca lcu la t io ns a r e summarized, which appear t o suppor t fo rce fu l lyt h e a l t e r n a t i v e t he or y.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1995419
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JOURNAL DE PHYSIQUE IV

INTRODUCTIONThe e a r l y h i s t o r y o f t h e s t ud y o f t h e deton at ion of ex-plosives was reviewed by W . C . Davis i n th e May 1987 i s s u e o fth e S ci en t i f i c American--from th e sy nthes i s and deton at ion o fn i t r og ly ce r i n by Ascanio Sobrero i n 1846 through the develop-ment of the ZND th eo ry by Yakov Zel' dov ich , John von Neumann,and Werner Doering. He discusse d th e pio nee rin g a na ly si s doneby David Chapman and m i l e Jouguet t h a t l e d t o th e C - J theory ,from which most modern th e o r e t i c a l st u d ie s have been deri ved .The concepts inc luded i n th e ZND model provided usefblhypotheses a s to how de ton at i on i s s t ructured and main ta ined .According t o t h e model, a shock wave propaga tes i n t o t h e unre-acted explosive and compresses it in s t an t l y . This compress ion,modeled a s a pi s to n moving ag ai ns t th e explos ive , p rovidesenough h e at t o i n i t i a t e c he mic al r e a c t i o n s ( i n t he rm al e q u i l i -brium) behind th e shock fr o n t which re le as e t h e exp losive en-erg y. This chemical energy produces th e high tempe rature andpr es su re which mainta in th e deton at ion. The expansion of th er e a c t i o n s ' g a s es p ro v id e s t h e f o r c e s t h a t a r e o bse rv ed a s t h eus e fu l work, o r t h e d es t ruc t iv e power, o f t he h igh exp losive .From th i s th eor y, a r a t h e r complex formalism with t h eas so ci at ed mathematics was developed. Davis described th i sformali sm, a s shown gra phi ca l ly i n F ig . 1. B r i e f l y , a p l o t o fa l l p o s s i b le p r e s s u r e v a l u e s i n a shocked m a t e r i a l ( t h e m ate r-i a l behind a shock wave) f o r a l l pos s ib l e va lues o f t he shockv e l o c i t y i n t h e m a te r ia l i s ca l l ed a Hugoniot curve ( a ) . A l lt h e p o s s i b le s t a t e s ( p r e s s u r e and m a t e r i a l v e l o c i t y ) o f ashocked mater ia l for a giv en shock-wave ve lo c it y can be dep icte di n t he Hugon io t-curve coord ina t e system a s a s t r a ig h t l i n e , aRayleigh l i n e , whose s lop e i s pro por t ion al t o th e shock-wavev e l o c i t y . The f i n a l s t a t e o f a m a t e r i a l u nd er t h e i n f lu e n c eo f a shock wave with a g i ve n v e l o c i t y i s shown g r a p h i c a l l y a st h e p o i n t a t which i t s H ugoniot c ur ve i n t e r s e c t s t h e s p e c i f i cR ay le ig h l i n e , a s s ee n i n F ig . l ( a ) .The C - J theory main ta inst h a t t h e po in t a t which theRayle igh l ine i s t a ng e n t t ot h e Hugoniot f o r th e com-p l e t e l y r e a c t e d e x p l o s i v e

( t h e C - J p o i n t ) s p e c i f i e s tth e s t a t e from which th e efre ac t i on products expand t o gdo work. Th is po in t al so ndetermines the detonat ionv e l o c i t y ( D ) from the s lopeo f t h e R ay le ig h l i n e , a ss ee n i n Fig. l ( b ) . The ZND Materialvelocity--,theory requi res Hugonio t Figure 1. The Hugoniot and Rayleigh curvesc ur ve s f o r t h e p a r t i a l l y which represent the C-J and ZND models.r eac t ed exp los ive , as w e l l


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a s fo r t h e un react ed and comple te ly reac t ed ma te r i a l . Theexplos ive w i l l be a t a h i g h er p r e ss u r e i n i t s unreacted (1)and p a r t i a l l y r e a c t e d ( 2 ) s t a t e s , a s s een i n F ig. l ( c ) . Ah ighe r de tonat ion ve l oc i ty ( a s t e e pe r Rayle igh l i n e ) deno tes a" s t rong" de tonat ion , a s s een i n F ig . l ( d ) . I n some ca se s , atemporary s ta te ( 3 ) i s pos s ib l e i n which t he Hugoniot cu rvel i e s above the curve f o r t h e complet ely reac t ed exp los ive.Th is s t a t e descr ibe s a "weak" d etonat io n, which can reach af i n a l s t a t e ( W ) t h a t has a l ower ma te r i a l ve lo c i t y and p re s s -u r e t h an i n t h e C - 3 s t a t e .

This i s a macroscopic th eor y t h a t can be modeled wit hhydrodynamic and thermodynamic algorithms, b u t it den ie s t hei mp or ta nc e o r e ven t h e n e c e s s i t y f o r k i n e t i c i n p u t s , and itprovides no he l pfu l mic roscopic in s i gh ts . A s Davi s s t a t e s(Ref. l ) , " In sp i t e o f t he va r i e t y o f modern app l i c a t ions o fexplos ives , de ton a t ion sc ience has no t reached matur i ty . . .,and, "S c i en t i s t s who s tudy explos ions a r e spurred on by be ingcons t an t ly reminded th a t t he cu r ren t de tona t ion theory i sincomplete . "

The C - J and ZND t h e o r i e s l e a d t o t h e c o n cl us io n t h a t t h e"cons tant" de tona t ion shock waves observed f o r pa r t ic u la r mate r -i a l s c au se t h e e x p lo s iv e m a t e r i a l t o t u r n i n t o g aseo us pr o d uc t sa t a te mp er at ur e s u f f i c i e n t t o j u s t e x a c t ly p ro vi de t h e c o r r e c tp r e s s u r e t o m ai n ta in t h e c o r r e c t d e t o n a ti o n v e l o c i t y . T her e-fo r e , th e proponents of th es e th eo ri es have developed a numbero f equa tions o f s t a t e (EOS) wi th some ra th e r a r b i t r a r y coe f f i c -i e n t s and pa rameter s t o c a l c u l a t e t he "co r r ec t " t empera tu resand p re s su re s i n t he rea c t io n p roduct s. Two qu i t e r e cen t s t a t e -ments on the f a i l u r e o r inaccuracy of EOSs ar e given and d is-c us se d i n a l a t ? e r s e c t io n .

The p r i nc i pa l pu rpose o f t h i s r ep or t i s t o p re se nt f o rcompar ison a qui te d i f f e r en t theory , o r hypothes i s, which de-s c r i b e s bo th i n i t i a t i o n and d e t o n a t i o n i n a mic ro sc op ic o rmolecula r reg ime, inc lud es new k in e t ic pr i nc ip le s , and g ives aphys i ca l exp lana t ion f o r t h e cons tancy of de tona t ion ve lo c i t i e s .To d i r e c t a t t e n t i o n t o t h e s i g n i f i c a n t a s p e c ts of t h eexper iments and ca lc u l a t io ns to be reviewed i n the fo l lowingsec t io ns , he re a r e t he ba s i c concept s o f t h i s modern theory r

1 . The in i t i a t i o n of explos ive re ac t io n by shock waves i nchemical explosives i s determined by ( a ) th e product ion by th eth e momentum t r an s f e r , she ar , o r energy gradie nt for ces ac ro sst h e s hock f r o n t o f i o n s , f r e e atoms and r a d i c a l s , i n a d d i t i o nt o the rmal ly- ac t iva ted molecules , randomly d i s t r i bu ted wi th i nt h e bulk of th e shocked explos ive ; (b ) th e growth of re ac t i ons i t e s a t t h e p o i n t s w here s u f f i c i e n t numbers o f t h e f r e e ato ms,ra d i ca l s , i on s , and molecu la r fr agmen ts a r e formed t o su s t a i nt h e a p p r o pr i at e i n i t i a t i o n r e ac t i o n s; and ( c ) t h e i n p u t o f ac r i t i c a l quan t i t y o f ene rgy f luence from the shock fo r ce s t ot h e shock-compressed ex pl os iv e t o ena ble a minimum number ofr e a c t io n s i t e s t o r ea ch a s e l f - s u st a i n i ng exothermic reac t ion .(Ref. 2 ) .


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C4-234 JOURNALDE PHYSIQUEIV2 . The ex ceeding ly h igh k i n e t i c energy of momentum tra ns -f e r i n t h e d et on at io n f r o n t i s s u f f i c i e n t t o c au se m as si vef r a c tu r e o f t he c ova l e n t bonds o f th e e xp los ive s m ole c ule s a tand n e ar t h e f r o n t s o t h a t t h e l a r g e m aj or it y o f t h e mo lec ul es

are b rok en , a s i n t h e i n i t i a t i n g s ho ck , t o i n d i v i d u a l a to ms ,r a d i c a l s , m o le c ula r fr a gm e nt s , i on s , a nd the y a r e re a r r ange de x te n s iv e l y. These p a r t i c l e s can t h e n r e a c t i n a bo ut10-'lc t o 10 -l 2 s to provide t h e chemica l energy which dr iv est h e de tona t ion . (Re f. 3 ) .

3 . The e ne rgy i n the ve ry nar row shock o r de tona t ion f r o n ti s nonergodic , and the rmal equi l ib r iu m, pa r t ic u l a r ly betweent h e t r a n s l a t i o n a l an d v i b r a t i o n a l e ne rg y modes, d oe s n o t e x i s ti n t h e f r o n t . No r e a l i s t i c t em p er a tu r e c an be a s c r i b e d t ot h i s zone (Ref 4 ) .4. A phys ic a l r e g u l a to r c ons t r a ins t he shock a nd de tona t ionv e l o c i t i e s , and t h i s r e g u l a t o r i s d i r e c t l y r e l a t e d t o t h e v i br a-t o r y v e l o c i t i e s o f t h e ato ms o f t h e s hocked m a t e r i a l ( Re f. 5 ) .T h i s c on cep t o f d e t e m i n i n g en er gy r e l e a s e r a t e s o r r e a c t i o nra t e s through a none qu i lib rium p roc e ss ba se d on th e r e l a t iv ev i b r a t i o n v e l o c i t i e s o f t h e atom p a i r s an d g ro up s i n vo l ve d ,

i s des igna ted as p h y si c al k i n e t i c s .A summary of comparisons of t h e c l a s s i c a l and t h e modernthe o ry i s g iv en i n T ab le 1 t o a s s i s t i n t h e e lu ci da t i on o f t h ed i f f e r e n c e s a s t h e y a r e p r e s en t ed i n t h e f ol lo w in g d i s cu s s io n .

EARLY SIGNIFICANT CLASSICAL STUDIESDisc ussion o f s e ve r a l e a r ly e xpe rime nt s and th e o re t i c a la na lyse s may a i d i n under s t a nding th e de pa r tu r e s o f th e newthe or y from what have been c a l l e d th e c l a s s i c a l s t ud ie s i ns hoc k i n i t i a t i o n an d d e t o n a ti o n . Campbell e t a l . (R e f . 6 ) con-duc ted some e lab ora te exper iments i n th e e a r l y 1960s on thei n i t i a t i o n t o d e tona t ion o f homogeneous (n i t romethane) andheterogeneous (Ref . 7 ) (PBX-9404, a pl as ti c- bo nd ed HMX) explo-s i ve s . Ana lys is o f the e xpe r im e nt s i n which n it r om e tha ne (NM)was i n i t i a t e d w i th shoc ks o f a bout 8 GPa and du ra ti on s o fabout l p l e d t h e e xp er im en te rs t o t h e c on cl us i on t h a t t h eshock wave compressed t h e NM; the compression heated the NM t osome va lue a t which s ig n i f i ca n t the rmal r ea c t io n began; and,a f t e r a n i n d u c t io n p e r i o d , t h e d e t o n a t i o n wave o r i g i n a t e d a tt h e NM f a c e f i r s t impacted, t r av el ed through t h e compressedl i q u i d o v e r t ak i n g t h e s ho ck f r o n t , a nd c on ti nu ed i n t o t h e un-shocked mat e r i a l . The en t i r e proces s was cons ide red t o be athermal equ i l i br i um proces s . The ac t iv at i o n energy presumedwas about 59 kcal/mole, as i n low tem per atu re thermal decom-p o s i t i o n .

The a n a l y s i s o f h et er og en eo u s i n i t i a t i o n w a s n o t s oe a s i l y r e a c he d , b ec au se t h e b ul k t e m pe r at u re i n a n e x p l o s iv es ho ck ed s t r o n g l y enough t o c a u s e i n i t i a t i o n t o d e t o n a t io n w a sb e l i e ve d n o t t o b e n e a r l y h i g h enough t o pr od uc e s u f f i c i e n t


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Table 1. CompariC l a s s i c a l T h e o r y

s o ns o f t h e C l a s s i c a l a n d th e Modern Theor ie sModern Theoryo n cep t s , P r in c ip lesand Observat ions

The s h oc k a c t s a s a p i s t o n ,co mpress ion h ea t in g , eq u i l i -b r ium thermal decomposi t ion ,A r rh en iu s k in e t i c s , t he rmod y-namic determinat ion and con tro lo f d e t o n a t i o n v e l o c i t y , manyd i f f e r e n t e q ua t i on s - of - s ta t er e q u i r e d .

T heory C on cept S hock en erg y ca r r i e d i n v e rynarrow zone by momentum tr a n s -f e r , v e r y h ig h e n er g y g r a d i e n tfo rce s cau se mech anica l f r a c -t u r e o f c o v a l e n t b on ds , p h y s i c a lk i n e t i c s , d e t on a t io n v e l o c i t ydetermined and con tr o l le d bya ve ra ge r e l a t i v e v i b r a t i o n a lv e l o c i t i e s o f atom p a i r s o r i nmo lecu la r f r ag men t s , eq u a t io n s -o f - s t a t e n o t v a l i d .Corresponds well with mechani-c a l f r a c t u r e c o n ce p t a nd r ea c -t i o n r a t e s o bs e rv ed . V ery d i f -f e r e n t f ro m A r r he n iu s k i n e t i c s .M e ch an ic al f r a c t u r e o f c o v a l e n tb onds i n s ho ck f r o n t l e a d s t oh o t s p o t s , c r i t i c a l e n er gyf l u en c e re q u ir e d f o r i n i t i a t i o n .E xp la i ne d by d i f f e r e n t f r a c t i o n sof thermal and shock inpu t .

No g oo d ex p lan a t io n . Eyr ing SS t a r v a t i o n K i n e t i c s

Shock a c t s a s p i s t o n fo r com-p r e s s i o n he a t i n g , r e q u l r e s v a r -i o u s c o n c e p ts o f t h e r m a l h e at -i n g t o fo rm h o t s p o t s .No good ex pl an at io n.

S h o c k I n i t i a t i o nof HeterogeneousExplosivesD i f fe r e nc e s i nS e n s i t i v i t y i n V ar io usS e n s i t i v i t y T es t s

Time t o I n i t i a t i o n o fNM a t Low ShockP ressu resA cce le ra t io n o f S h o ckFront with Non-I n i t i a t i n g Shocks

No good ex pl an at io n,V i o l a t i o n o f t h eo r y. E x pl a in e d by p h y s i c a l k i n e t i c s .

No good expl an at io n, M e ch an ic al f r a c t u r e o f bon ds i na nd n e a r t h e s h oc k f r o n t .No good ex pl an at io n. I n i t i a t i o n t o D etona-t i o n b y F ree -Rad ica lGrad ien t

The h igh ene rgy g r ad ie n t fo rmssho ck wave w hich i n i t i a t e sd e t o n a t i o n .Explained by massive mechanicalb o n d sc i s s io n .

No good ex pl an at io n. BTNEA ExperimentNo ex pl an at io n;v i o l a t i o n o f t h e or y. In c reased D e to n a t io nV e l o c i t y o f NM + DETA E a s i l y e x p l a i n e d by p h y s i c a lk i n e t i c s , a n d it i s c a l c u l a t e dac cu ra te ly f rom Hugonio t dat aand em pir ica l fo rmulae .

C o r ro b o ra t io n o f massiv ebond sciss ion .M e ch an ic a l s c i s s i o no f Bonds i n P l a s t i c sR.Graham, e t a l .No good ex pl an at io n.

C o r ro b o ra t io n o f massiv e. bond sciss ion .No good expl an at io n. Shock-Induced Chem-i s t r y , R . Graham e t a1Very l i t t l e h el p. Unders tand ing o fMicro scop ic P ro cesse s P r o v i d e s r a t i o n a l e x p l a n a t i o n s .No good ex pl an at io n. I s o m e r P a i r s D i f f e ri n T he rm al o r ShockS e n s i t i v i t y

I t i s p ro b ab le t h a t t h ey w ouldd i f f e r , s in ce o ne d eco mpo s it ioni s t h e r m a l , a nd t h e o t h e r i s bymechan ical bond f ra ct u r e .

D i f f i c u l t e x p l a n a ti o n . D e t on a t io na t Low V e lo c i ty D i f f e r e n t k i n e t i c r a t e due t ol o w er l e v e l o f bond f r a c t u r e a tl ow er i n i t i a t i o n p r e ss u r e.Wi th b es t eq u a t io n -o f - s t a t e ,c a l c u l a t i on i n e r r o r by 1 4 .5 5 C alcu la t ed D e to n a t io nV elo c i ty o f E25(PETN/Paraffins75/25)

Cal cu l a te d by Hugoniot valu esand empi r ica l fo rmula wi t h in0.5%.Note: There a r e s t i l l que st i ons abou t how to ex p la in deflagration-to-detonation t r a n s f e r(DDT) and how to determine th e te mperatu re i n a shock f r on t . The modern theoryp ro p oses t emp e ra tu res o f ab o u t 1 0 ,0 00 to 3 0 ,0 0 0 K v ersu s 3 ,0 0 0 to 5 ,0 0 0 K by thet he rm od yna mic t h e o r y i n t h e d e t o n a t i o n f r o n t .


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C4-236 JOURNALDE PHYSIQUE IV

rea c t io n to l e ad t o a de tona t ion i n t he time obsenred. P re -v io u sl y, Bowden, G urton and J o f f e (Refs. 8 , 9 ) proposed andobserved th a t sma l l c en te r s o f concen t ra ted reac t i on d id occur ,and th ey t hen assumed t h a t a n energ y-conc entrating mechanismproduced "h ot sp ot s" i n th e bulk explosive. Many explana-t i o n s and pro cess es have been proposed f o r t h i s phenomenon:

( a ) Gases i n voids i n t he explos ive were compressed andhea ted ; t h i s hea t was t r an s fe r re d t o t he molecules around th ev o id s ! and t h e r e a c t i o n s t a r t e d on t h e vo id s u r f a ce .( b ) The shock waves co l l i de d o r re in for ced ot he r waveswhen the y moved throug h and around th e exp los ives cr y st al s ,t hus caus ing sp o t s o f h ighe r p re s su re .( c ) The shock caused f r i c t i o n between th e explos ive gra in s ,and t h i s f r i c t i o n p roduced sma l l a re a s o f h igh t empe ra tu re.

Other ex plan atio ns were suggeste d, but none have beenw e l l q u a n t i f i e d .

To check t he concept o f t he gases i n the voids being com-pre sse d and heated, experimenters compacted explo sives i n a t -mosphe re s o f ga se s wi th d i f fe ren t hea t c apac i t i e s . The ideawas t h a t the ga ses th a t were hea ted t o h igh er tempera tures byth e shock compres sion would cause in i t i a t i o n i n sh or t e r t imes .This proposed cor re la t io n w a s not observed.I t has been assumed that there i s compression of gasesi n voids , some f r i c t i o n between gr a in s , and some shock in te r -ac t i on s and re f l ec t i on s , bu t no ver y convinc ing a rgumentshave been made t h a t "proved" any of th es e conc epts as t h e

source s of e f f ec t i ve hot spots . However, th e hypothes i s haspers is ted that some macroscopic process within the shock waveproduces hot spots from which the i n i t i a t i n g r e a c t i o n d ev elo ps.A number o f t e s t s w ere de velo ped i n t h i s e a r l i e r p e r i o dt o measure and compare th e shock s e n s i t i v i t y of explosi vesth en i n use and under s tudy . There were wedge t e s t s , ca rd-gap t e s t s , drop-hammer t e s t s , and gun t e s t s . Analyses o fth e s e t e s t s were g ene ra l ly based on a va lue o f shock p re s su rea t which th e ex plosive would deto nat e , us ua l l y some 50% o fth e t r i a l s . Exper imente rs observed , but d id no t exp la in why,some explos ives were more s en s i t i ve t han o th er s i n one t e s tand l e s s s e n s i t i v e i n a no th er . S ev er al t e s t s , such a s th e

drop-hammer and ski d t e s t s , had components of h ea tin g t h a tr e s u l t e d from f r i c t i o n o r m a t e r i al flow t h a t a l s o l e d t o somec on fu si on i n t h e i n t e r p r e t a t i o n o f t h e r e s u l t s , b ut t h e y d i dp ro v id e u s e f u l i nf or m at io n f o r r a t h e r s p e c i f i c s i t u a t i o n s .A gr ea t s t r en gt h of opin ion had deve loped i n the explo-s i v e s l i t e r a t u r e an d i n t h e community s t ud y in g i n i t i a t i o n andde tona t ion t h a t shock p re s su re (compres sion ) a lone ( o r p re -dominantly) w a s t h e d et er mi na nt i n shock i n i t i a t i o n ( v er yl i k e l y because o f t h e p i s t o n model). A s a r e s u l t of t h i s ,


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when a very pre ci se s e t of some 60 exper iments was l a t e r per-formed on th e i n i t i a t i o n of PBX-9404 (Ref. 10 ) by th e impactof a luminum pl a t es , the experimenter fa i l ed t o ana lyze theda t a p rope r ly.Henry Eyring and co lleag ues (Ref. 11) a t t h e U n iv e rs i t yo f U tah i n t h e 1 94 0s, s t u d i ed r e a c t i o n r a t e s i n d e t o na t in gexp los ives . One s t r i k i n g r e s u l t from t h e i r obse rva t ions anda na ly s es i n t h i s e a r l y p er io d i s t h a t t h e r ea c t i o n r a t e s , asc a l c u l a t e d from t h e d e t o n a ti o n v e l o c i t i e s , a r e q u i t e s i m i l a rf o r a l l o f t he exp los ives they s tud ied , even though the low-temp eratu re decomposition r a t e s and th e thermodynamic energyc o n t en t a r e q u i t e d i f f e r e n t . L a t e r , E y ri ng and o t h e r a s s o c i -a t e s an al yz ed t h i s d i s t u r b i n g o b s e r v a ti o n a g a i n ( Ref. 1 2 ) .They s t u d i e d m a t e r i a l s a s d i f f e r e n t as cyc lopropane , t e t ry l ,and mixed explos ive composit ions. I n a l l cases , the y foundt h a t t h e l o ga r it h ms o f t h e r e a c t i o n r a t e s f o r assumed f i r s t -

order decompositions were about 6.0 + 0.5 (Ref . 13) . Eyr ing ' sa n a l y s i s from r e a t i o n - r a t e t h e o ry l e d t o h i s c on cep t o f" s t a r v a t i o n k i n e t i c s , " i n which h e c a l c u l a te d t h a t o n ly 20degrees o f freedom i n any of the explosi ves molecules he s tud -i e d were c on t r ib ut in g energy to th e bond t h a t was f i r s t t obrea k, no m at te r how la r g e t h e molecule might be. This w a smarkedly d i f f e r en t from Arrhenius k i ne t i cs o r a thermalequ i l ib r ium process .S1GNI ?t CANT EXPERIMENTS AND CALCULATIONS I N SUPPORT

OF THE NEW THEORYSome 25 years ago, Richard Wasley and I began a se r i e sof exper iments on the i n i t i a t i o n and de tona t ion o f exp los iveswi th t h e obj ec t of extending the da ta in to some unexploredar ea s . I n prepara t ion f o r th e ea r l y experiments, we reviewedsome da ta ( ~ e f . 0 ) ob ta ined on th e shock i n i t i a t i o n o f PBX-9404 with impacting aluminum plates. Our i n t e r p r e t a t i o n o fthe da t a was ve ry d i f f e r e n t from t h a t pub l ished , and it l e dt o t h e d e r i v at i o n and p ub l i c a ti o n o f t h e c r i t i c a l e nerg yf luence concep t (Ref . 14) o f shock in i t i a t i o n f o r he te ro -geneous exp los ives . The equ atio n which de sc rib es th e concept,

i s e a s i l y d e r i ve d from t h e k i n e t i c ene rgy and Hugoniot equa-t i o n s . I t s e r v e s w e ll t o d e sc r ib e s hock i n i t i a t i o n i n mosto f t he gene ral ly -used exp losives i n the r ange o f shock anddetona t ion pr ess ures from about 0 .3 t o 40 GPa.I n t h e e qu at io n, t i s t h e t im e w id th o f t h e i n i t i a t i n gshock pu lse , P i s i t s p r e s s u r e , p i s t h e i n i t i a l d e ns it y o fth e explos ive , and Us i s t h e shock v e l o c i t y a t t h e p r e s s u r e P.This concept and th e equa t ion provide t he explan a t ionf o r t h e p r ev i ou s ly o bs erv ed s e n s i t i v i t y an om alies i n t h e i n i -t i a t i o n o f a s p e ci f ic e xp lo si ve i n v ar io u s s e n s i t i v i t y t e s t s .


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C4-238 JOURNALDE PHYSIQUE IV

Addi t iona l ly , it was shown (Ref. 15 ) to prov ide a r a t i o n a lc o r r e l a t i o n f o r d a t a from t e n d i f f e r e n t s o u rc e s and t e s tmethods, over ne ar l y seven ord ers of magnitude i n t ime andth re e i n pr es su re , f o r PBX-9404 and o th e r HMX-basedexp los ives .

The r eason t h i s qu i t e s imple r e l a t ion sh i p was no t d i s -covered f o r so many years appears to be a r e s u l t of t he h is -t o r i c a l development of explos ives th eo r i es based on the p is t onconcept . Thus pr es su re , not energy f lue nce , was consideredt o be the dete rminan t o f i n i t i a t i o n . The p i s ton concep t wasboth the genius and the demon of the C - J and ZND t h e o r i e s .Low-Pressure I n i t i a t i o n o f Nitromethane

The i n i t i a t i o n da t a on ni tromethane were meager i n 1968.I t had been observed th a t about 8 GPa of shock pressure wasr eq ui re d t o i n i t i a t e NM t o de tonat ion . Here aga in , t he o ldconcept was held of pressure being the determinant of i n i t i -a t ion , bu* it was found t h a t th e d eton at io n was observablei n about one microsecond.

I n a n e f f o r t (R ef. 1 6 ) t o d et er mi ne i f t h e c r i t i c a lenergy hypothes is might a l so apply i n some degree to i n i t i a -t i o n i n homogeneous systems, we used a n experimental de sig n(shown i n Fig. 2) t o provide ne ar l y rec tan gu la r shock waveso f about 5 .0 t o 6 .5 GPa th a t pe rs i s te d f o r more than 20microseconds. According t o th e thermal-equil ibrium conc ept,t h e t ime t o i n i t i a t i o n of NM a t a press ure o f 6.0 GPa shouldbe near 0 .1 S (R ef. 6 ) , a s s e en i n Fi g. 3 . What we observedmost c le ar ly i n both framing-camera and streak-camera reco rds(s ee f o r example Fig. 3) was t h a t i n i t i a t i o n a t 6.0 , 6 .2 and6.5 GPa occu rred i n approximately 20, 16 and 10 microseconds,r e s p e c t i v e l y . T h i s i s some 4 ord ers of magnitude s h o r t er i nt ime (Fig. 3) th an pre dic ted by the thenna l equi l ibr iumtheory .

T h is ve r y s h o r t t im e t o d e t o n a ti o n w a s n o t t h e o n l y cu r -i o u s r e s u l t . I t was a l so ev iden t t h a t t he de tona t ion had no ts t a r t e d a t t h e n it ro me th an e f a c e f i r s t put under pressure andhea ted , as t h e o l d t h e o r y r e q u i re d , b u t it appeared a t somepo s i t i on ve ry nea r the shock f ro n t . The f i l m records showc l e a r l y t h a t a r e t o n at i o n a l s o p ro ceed s from - t h e i n i t i a lde tona t ion s i t e back toward th e f ace f i r s t impacted. I nf a c t , i f t he de tona t ion had s t a r t ed a t t h i s f ac e f i r s t pu tunder compress ion, th e s t reak-camera f i lm shows t h a t i n i t i a -t i o n a t 6.0 GPa would have occurred i n an even sh o r t e r time--about 8 microsecgnds.

The c ri t i c i s m from t h e e xpl osi ves community was t h a tth e r e must have been some de fec t i n th e f i ve ve ry c ons i s t en texperiments. However, a f t e r more th an 20 ye ar s, no d ef ec thas been found o r repor ted .


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Trigger Quartz pressurepins transducerSlit for streak cmcamera

PlasticPlastic Brasstank

\

PlasticAluminum I

Plane-wave lens

Figure 2. Design of the experiments used to study the lower pressure shock initiationof nitromethane.

Voskoboynlkov et al:--I. Walker & Wasley -

----1r7 104 I@ 104 IO-~ ir2 rl 1

Time (S)Figure 3. The calculated time to initiation as a function ofshock pressure or shock temperature for a thermal equilib-rium process (curve 1) compared with the initiation data fornitromethane?'


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C4-240 JOURNAL DE PHYSIQUE IV

Acce le ra t ion of th e Shock Front i n Ni tromethane wi thNon-Ini t ia t ing ShocksThe re s u l t s from th e NM exper iments jus t desc r ibed

b ro u gh t i n t o d ou bt t h e c l a s s i c a l model o f t h e i n i t i a t i o n ofhomogeneous exp los ive s . Strong evidence ex is te d t h a t somec he mi ca l r e a c t i o n was s t a r t e d a t o r v e r y n e a r t h e shock f r o n tt h a t g rew r a p i d l y c l o s e b eh in d t h e f r o n t i n t o a d e t o n at i o n .Also , s t reak-camera re cords provided evidence th a t be fore t h ede ton a t ion appeared, th e shock f r o n t was being acc e le r a tedsome small amount.To exp lo re t h i s po ss ib i l i t y fu r t he r , we de signed a s e r i e sof exper iments (Ref . 1 6 ) i n which t h e v e l o c i t y o f n o n - i n i ti -a t i n g shock waves developed i n e th ylene g ly co l could be meas-u red as the shocks passed through tanks of NM . Framing cam-e r a s showed t h a t t he shocks were acce ler a t ed above th e ex-

pec ted hydrodynamic va lue s a s th ey passed through t he NM andt h a t t h e i n cr e as e d r a t e o f a c c e le r a t i o n was a d i r e c t f u n c t i onof t h e shock p re s su re p r o f i l e . Add i t i ona l ly , a computer-ca lcu la te d model of th e experiment (F ig . 4) showed that theamount of nitromethane decomposit ion energy (about 1 t o %)requ i red to exp la in t he expe r imen ta l da t a , when inc luded i nt h e c a l c u l a t i o n s , gave a n e x c e l l e n t r e pr o d uc t io n o f t h eexpe r imen ta l r e su l t s .Th i s i s a key obs erv at io n, because it i n d i c a t es a l e v e lo f r e a c t io n i n o r v e r y n e a r t h e shock f r o n t t h a t i s g r e a t e rthan a therm al-equi l i brium proces s would produce. F ' r th er -more, it shows th a t t h e shock- f ron t a cc e l e r a t io n occurs wi th

no subsequen t exp losion o r de tona t ion i n t he NM t o p r o vi d eenergy to the shock frombehind it. More expl ic i t -l y , it says t h e shock f ro n ti s a ve ry narrow, non- I I I 1equi l ib r ium zone. 50-kb sustained pulseentering at 11.0 cm,running 30 ps20 - (spherical configuratioE

84 1 5 -B uwe K reaction

l 0 - C 1D 0

Figure 4. A computer calculation of experi-ments used to study acceleration of a shockfront in shocked nitromethane.


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I n i t i a t i o n Pa t t e rns Produced i n Exp los ives by Low-Pressu reLong-Duration Shock WavesFol lowing the previous experiment , it seemed important

t o i n v e s t i g a t e t h e s hock f r o n t and t h e a r e a n e a r it morec l o s e l y t o s t u dy a ny o b se r va b le p r o ce s se s t h e r e . I n t h r e enew experiments wit h low-pressure shocks (4.0 t o 6.0 GPa),we designed and f i r e d long- durat io n (20 to 40 microseconds)shocks. The reason f o r working i n t h e l ower shock-p ressu reregime i s t h a t t h e i n i t i a t i o n zone a nd t im e a r e le ng th en ed .Th is a l lows more de ta i l e d and e x p l i c i t f raming-camera reco rdst o b e o b t a in e d .I n t h e f i r s t experiment o f t h i s s e t ( s ee Fig. S ) , asp h e r ic a l shock wave produced i n a l a r g e t a n k o f w a t er a s s e sov er two di sk s of LX-l0 ( a plas t ic -bond ed HMX explosiveP.The photo r eco rd ob tai ned by th e fram ing camera shows t h a t

t h e number of i n i t i a t i o n s i t e s i s a d i r e c t f un c ti on o f t h es ho ck p r e s s ur e and t h a t t h e s i t e s a p p e a r q u i t e r andomly i nt ime and space. Th is work w a s c o r ro b o ra t ed i n a s i m i l a rexperiment by L. G. Green a t the Lawrence Llvermore Laboratory.I n a f o l-lowing exper i -ment , i n whichNM w a s shockedjust below ani n i t i a t i o n l e v e l(Ref. l?), ran-dom ce n te rs o f

r e a c t i o n a g a inappeared andcoalesced behindt h e s hock f r o n t ,b u t a h ea d o f t h ef a c e f i r s t pu ti n c ~ mp re ss io n .I n a l l o f t h e s eexperiments , ab-s o l u t e l y no e v i -dence ex i s t edf o r a detona-t i o n d e ve lo pi nga t t h e s u r f a c ef i r s t impacted.

f Explosive light source (argon filled)

at Various positions

1 1 / / "donor 40Pressure tranducer[ L 30cm dlam. x 2.54 cm thkkU-10 sample

--UnconflnedLX-10explosivesample,30cmdfam. X 7.62cm thick- Water-filledtank: plan-2.5 m X 2.5 m-1.2 m deep

Althoughthe photos weres o p l a i n t h a t noa l t e r n a t e e x p l a -n a t i o n s w ere s e r -ious ly p roposed , Figure 5 . Design of experiment to observe effects of low-and a l though an pressure shocks on LX-10.experiment


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C4-242 JOURNALDE PHYSIQUEIV

c on du ct ed i nd ep en d en tl y c o r r o bo r at e d t h e r e s u l t s i n t h e s o l i dexplo s ives , th e d a t a were g ene ra l ly s imply ignored becauset h e y d i d n o t f i t t h e h i s t o r i c m o d e l .Forces and Temperature i n t h e Shock Fro nt

Ana lys i s of our previou s ly desc r ibed experiments ando t h e r a v a i l a b l e d a t a l e d t o t h e c o n s i d er a t i o n o f t h e p o s si -b i l i t y t h a t mechanica l f r a c t u r e o f some o f t he cova len t bondsd id indeed occur i n and nea r t h e shock f ro n t . Experimentshad been (Ref. 1 8) and cont inued t o be (Ref. 19) performed i nwhich mechanical bond s c i s s i o n was proposed and supported bya n a l y s i s . C a l c u l a t i o n ( Re f. 2) o f t h e p r o ba bl e a c c e l e r a t i o nand sh ear fo rc es i n and nea r a shock f r on t showed t h a t mech-an ic a l fo r ce s on a tomic d imensions were l i k e l y t o be s t r on ge rtha n th e cova len t bonds ( i . e . , C-N, N-0, C-C) i n or g an ic ex-p l o s i v e s . I t seemed probab le t h a t a t f r e e s u r f a c es of t h ee x p l o s i v e c r y s t a l s , o r i n vo ids o r a t c r y s t a l and l a t t i c ede fe c t s , mechanica l bond f ra c t ur e could occur th a t wouldproduce f r ee r ad i c a l s and a toms, ve ry e ne rg e t i c i ons , andexc i ted molecules and molecula r fragments t h a t could r e ac tv e r y q u ic kl y ( i n p s t o t e n s o f f s ) , and e s s e n t i a l l y i n p l a ce ,t o produce th e chemica l energy th a t would ac ce le ra te t heshock f ro n t o r de tona t ion f r on t and ma in t ain i t .

A no th er f a c e t o f t h i s s t u d y o f t h e shock f o r c e s i n andn e a r t h e f r o n t i s t h a t t h e m ic ro sc op ic l a t t i c e c an be d i s t o r -t e d , and t h e atom s r i g h t i n t h e f r o n t must be a c c e l e r a t e d f o ra t l e a s t some s m al l d i s t a n c e (about 1 t o 4 angstroms) up tot h e v el oc i t y o f th e shock o r de ton at io n wave by t he momentumfrom the atoms immediately behind them. A s t h e shock f r on ti s , i n r e a l i t y , t h e motion o f t h es e atoms i n t h e f r o n t , t h eya r e acc el er at ed from some random thermal motion t o t h e velo-c i t y and wi th t he more nea r ly un i ax i a l motion o f t he shock .The magni tude o f t he average a cc el er a t io n can be c a l c u l a t e de a s i l y fromva = % . ( 2 )The force , f = ma, p rov id ing t h i s a cce l e r a t io n can exceed t hecova le nt bond s t r en gt h (Ref . 2 ) , so th a t t he explos ive mate r -i a l ( o r o t h e r o r g a n i cs ) would b e f rag men ted a t open f a c e s ,vo id s , and some de fe ct s . Thi s has been corrob orated i n manymol ecul ar dynamics (MD) c a l c u l a t i o n s , w i t h i n d i c a t i o n s t h a ta t v e r y hi gh sh ock p r e s s u r e s , s c i s s i o n c an o c c u r w i t h i n t h el a t t i c e and wi th in enclosed molecu le s.One o t h e r s i g n i f i c a n t f a c t t h a t must be c o ns i de r ed i n f h i scon tex t i s t h a t a t t h e f r o n t , t h e m ajo r m otio n o f t h e a tomsi s d i r ec t ed i n one d imension, a long the a x i s o f t he shock ,so t h a t t empera ture , normally cons idered a s random gauss ianmotion of the a toms, i s n o t a viable concept wi th in the shockf r o n t ( Re f. 2 0 ) . A t some di s t an ce behind th e f ro n t wherethermal equi l ibr ium i s aga in approached ( t en s o f ps t o ns )a temperature may be measured. Gr eat ef f o r t s t o measuret empe ra tu re i n t h e f r on t have been d i sappo in t ing . Es t imate s


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o f th e "one-dimensiona l" tempera tures i n var i ous de ton a t ingexplo s ives , based on th e one-dimensional v e l o c i t i es a long th eshock a x i s , have ranged from 10,000 t o 30,000 K (Ref. 20).F r ee R a di ca l I n i t i a t i o n o f G ases

P. Urtiew, E. Lee and I conducted some experim ents t os t u d y t h e h y p o th e si s t h a t c o n c e n tr a t io n s of f r e e r a d i c a l scould l ead to de tona t ion . I n a system of s i l a ne and t e t r a -f luorohydraz ine , i n which ra d ic al s formed r ap id ly upon mixingo f th e two gases , we mixed a scavenger, c is-2-butene, i n th es i l a n e i n s u f f i c i e n t c o nc en tr at io n t o k eep t h e r e a c t io n u nd erco nt ro l u n t i l th e two gas es were wel l mixed. Otherwise, re -ac t i o n would have occur red immedia te ly on cont ac t a t th e gas-gas in te r f ac e . We thu s demonst ra ted (Ref . 21) t h a t t h e w el l-mixed gase s would det ona te once t h e f re e-r ad ica l scavengerhad been consumed.Thi s demons tr at ion o f th e p roduc t ion o f a de tona t ionf rom a h igh concen t r a t ion o f f r ee r ad ic a l s w ithou t an impac t-i n shock was suppor ted i n exper iments by J . Lee e t a l . (Ref.227 on xenon -ir radiated mixtures o f hydrogen and ch lo r in e,hydrogen and oxygen, and ace ty len e and oxygen. The c l a s s i c a lthe ory pro vides no exp lana t ion f o r th es e phenomena.I n ano the r se r i e s o f exper iments (Ref. 4), several chem-i c a l s known t o be a b l e t o s u p pl y o r c ap t u r e f r e e r a d i c a l s wereadded t o TNT a t t h e 5 weight perc ent le v el . The impact se ns i-t i v i t y o f t h e TNT i n a dr op hammer Etudy was changed drama t-i c a l l y by the se ad di t iv es . This work was cont inued by i m -

pac t in g samples o f TNT and th e add i t iv es w i th f ly in g p l a t e si n a n a i r gun. The re s u l t s were co ns is te nt wi th the drop-hammer results.I n e r t s o l i d s and l i q u i d s , v e r y ha rd and g r a i n y m a t e r i a l s ,and some ve ry s e n s it i v e e xpl osiv es were added t o t he TNT i nsepa ra t e con t ro l s tu d ie s . However, t h e changes i n s e n s i t iv i t ymade by th e f r ee -r ad ic al donors and g e t t e r s were much gr e a t e rt h a n w i t h an y o f t h e c o n t r o l a d d i t i v e s .

I n i t i a t i o n and Detona t ion of Ni tromethane wi t h DiethyleneTriamine (DETA) AddedAlthough amines were known t o s e n s i t i z e NM t o shock in i -t i a t i o n , n o t much q u a n t i t a t i v e d a t a r e l a t i n g t o t h i s ob se rv a-t i o n exis ted . Therefore , Wasley and I conducted a s e r i e s o fexperimen ts (Ref. 23) us in g t h e same geometry shown i n Fig.2,but now s m a l l amounts (0 .0 1 t o 5.0 W%) of DETA were added t ot h e n i t romethane ju s t b efore the exper iments were f i r ed . Thed ecre as e i n time t o i n i t i a t i o n a s a fun c t io n of DETA concen-t r a t i o n i s shown i n Table 2. and Fig. 6a.Table 2 and Fig. 6b a l s o show t h a t t h e de to na t ion ve lo-c i t y o f th e n i trome thane changed as a f u n c t i o n o f DETA concen-


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Table 2 . Results of initiation experi-ments in which DETA is addedto nitromethme.DETA Time to DetonationCone. Y) dtt. @S) velocity (mmlps)

0.0 (control) 182 2 6.40'0.0 ((rontrol) sb 6.34'0.01 0.4~ 6.45'0.02 7.ab 6.4V0005 73b 6.76'0.05 6.ab 6.W095 6.F &45'0.10 5.1b 6.Sf1.0 2.0 20.5 6.41.5.0 0.52 0.3 6 2 1' 10.07.' l .

t r a t io n . Th i s was ano the rs p e c i f ic v i o l a t i o n o f t h eC - J , ZND, and o t h e r c l a s s i -

6.2c a l concepts . Changes i nr e a c t i o n k i n e t i c s w ere n o tsupposed to a f f ec t de tona - L,t i o n v e l o c i t i e s . F ur th er , 6.10 0.01 0.10 1D 10.0w i t h t h e u s e o f a n eq u a t i onderived by Skidmore and DETA (%)Har t (Ref . 24) t h a t r e - Figure 6 . (a) Time to initiation of nitrel a t e s changes i n d eto na- methane at 6.0 GPa a function of DETA con-t i o n v e l o c i t i e s t o o ver- centration; (b) Detonation velocity of nitro-d r i v i n g d e t o n at i o n p r e s s- methane as a function of DETA concentration.u r e s , t h e " C - J pressure"o f th e new ni t romethaner e a c t i o n w i th 0.05% o f DETA added would a ppear t o be n ea r 1 9GPa. This would requ i re a dramatic change i n rea c t io n ra t e .A t a l e v e l o f 0.05% DETA, t h e measured de to na ti on v e l o c i t yi n t h r e e s ep ar at e exper iments was about 6.72 km/s, comparedt o t h e normal valu e o f 6.32. Thi s would seem t o req ui ret h a t f r e e -r a d i c a l mechanisms enhanced by th e DETA be inv olv edt o g i v e t h e r e s u l t s shown i n Ta bl e 2 and Fig . 6b. The dashedl i n e i n F ig . 6b shows t h e d e t o n at i o n v e l o c i t y t h a t was c a l cu -l a t e d wi th t h e TIGER code (Ref. 25 ). us in g a s el ec te d EOS andt h e thermodynamic p r i n ci p le s from th e o ld model .

S e v er al o t h e r i n t e r e s t i n g r e s u l t s were observed i n t h i ss e r i e s o f t e n h i g h l y t e c h n i c a l a nd c o s t l y e xp erim en ts. A s i nt h e e a r l i e r work w i t h n e a t NM, t h e o r i g i n o f t h e d e to n a ti o ni s a t o r v er y n ea r t he shock f r on t i n th e exper iments w i th0.1% o r l e s s of added DETA. The re to n at io n from t h e zonewhere the de tona t ion o r i g in a te d i s c l ea r l y evident . The red-brown c ol or (probably from ni t rog en dio xid e) , a l so see n byCook (Ref. 25) i n h i s NM i n i t i a t i o n s t ud ie s , i s shown i n th e


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framing-camera re co rd s t o sweep Sackwards toward t h e f ac ef i r s t impac ted, i n consanance wi th t h e re ton a t ion . I n t he seexperim ents wi th t h e lower c on ce ntr ati on s of DETA, some i n i -t i a t i o n s i t e s a pp eared a t s e p a r a t e d p o i n t s a t t he shock f ron ta nd c o al es ce d i n t o t h e d e to n a ti o n f r o n t , a s s e en i n o u r e a r -l i e r expe r imen ts wi th l ow p re s su re shocks.

When t h e DETA concent ra t ions were 1% and 546, t he de to -na t ion developed i n abou t 2 and 0 .5 microseconds , respec t ive ly .Th i s i s s i m i l a r t o t h e t im e t o d et on a ti on i n NM with no addi-t i v e s with shock p re s s u re s o f abou t 7 .5 t o 9.0 GPa, comparedt o t he 6.0 GPa i n th es e experiments . An in t e r e s t i n g phenom-enon seen i n th e f raming-camera photos of th es e two f i r i n g swas t h a t t h e i n i t i a t i o n o cc ur re d i n hundreds o f small c e n t e r so f r e a c t i o n , w hich q u i c k l y c oa l es c ed i n t o t h e d e t o n a t io nf r on t . The sma l l c en te r s appea red f i r s t t o be d i s t r i b u t e dq u i t e randomly i n t ime and space . The pa t t e rn was f i n e r a tt h e h i g h e r c o n c e n tr a t i on . T h i s i s r em is ce nt o f t h e r e s u l t ss e e n p r ev i o us l y i n t h e i n i t i a t i o n s t u d i e s o f h ete ro gen eo use x pl os iv e s ( ~ e f . ? ) , e xc ep t t h a t h e r e t h e number o f r e a c t i o ns i t e s i s a f un ct io n of i nc re as ed DETA con cen tra t ion r a t h e rth an incr eas ed pre ssu re . However, both inc reas ed DETA con-c e n t r a t i o n and i n c r e as e d p r e s s u re l o w er t h e t im e t o d e t o n a t io n .

Here i s a n o t h e r o bs e rv a ti o n o f c o ns i de r ab l e i n t e r e s t .Now t h a t t h e de tona t ion occ urs i n about 1 microsecond, a s i nt h e e a r l i e r work ( Re f. 6 ) a t 8 .0 GPa, t he de tona t ion appea rsi n t h e s tr ea k- ca me ra p ho to s t o o r i g i n a t e a t t h e n it ro me th an ef a c e f i r s t impacted. However, it c an b e s e en e a s i l y i n t h eframinp-camera photos t h a t th e de ton a t ion i s a c t u a l l y f o rm in gi n t h e narrow band where t h e r e a c t i o n s i t e s a r e c o a l e s c in g .Thus, i n t h e o l d s t r e a k r e c o r d s ( Re f. 6 ) , the de tona t ion wouldhave appeared t o come from t h e container-NM i n t e r f a c e . I nf a c t , i n some o f t h o se e a r l y r e co r ds , t h e r e a c t i o n l i g h tseems t o r each ra th e r tenuous ly toward the i n t e r f ac e . Th i ssame phenomenon would have made it d i f f i c u l t f o r H ardesty(Ref. 26 ) t o o b se rv e t h e e x a c t p o s i t i o n o f t h e d e t o n at i onf r o n t i n h i s i n i t i a t i o n s t ud y . Recent ex per im en ts ( Re f. 2 5 )o n t h e i n i t i a t i o n o f l i q u i d n i t r i c o xid e s up po rt t h e con-t e n t i o n t h a t t h e d e to n at io n i s formed i n a narrow zone wheret h e r e a c t io n s i t e s a r e c o a le sc in g and n o t a t t h e c o n t a i n e r -e x p lo s iv e i n t e r f a c e .The BTNEA Experiment

A homo eneous id e a l explos ive , b i s - t r in i t ro e t hy l ad i -p a t e (BTNEAY w a s s y n th e s iz e d w i t h t h e i s o t o p i c l a b e l s ( ca rb o nt h i r t e e n a n d oxygen e i g h t ee n ) i n tr o d uc e d i n t o t h e p o s i t i o n si n d i c a te d i n Fig . 7 . This explos ive w a s chosen f o r t h i s ex-perinient, because it a p p e a r e d t h a t t h e CO and carbon dioxidemolecules expec ted a s de ton a t ion produc ts were a l r ea dy formed,a nd t h e i s o t o p i c l a b e l s would be fo un d i n t h e CO and carbondioxide produc ts .


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JOURNAL DE PHYSIQUE IV

Figure 7 . The s t r u c t u r e o f b i s - t r i n i c , i r o e t h y l a d i p a t e . Thea s t e r i s k s i n d i c a t e c a r b o n a t o m s o f i s o t o p e 13 andoxygen atoms of isotope 18.The explosive was detonated i n a bomb ca lor ime ter i nwhich the prod ucts were c o l l ec ted and then analyzed f o r thei s o t op ic r a t i o s - ~ e f . 7). The experimental r e s u l t s show

t h a t t h e r a t i o s o f c12/c13 and 0 6)018 a r e es se n t i a l l y t hesame f o r a l l o f t h e p r od u c ts c o n t ai n in g C and/or 0 , and theya r e n e a rl y e qua l t o t h e i s o to p i c r a t i o s i n t h e o r i g i n a lBTNEA sample. The a n a ly ti c a l va lu es of th e ra t i o s were s a i dt o be we l l w i th i n t he exper imen tal p rec i s ion o f t he de te rmin -a t io n . The conclusion t h a t i s obvious i s t h a t a lmost everyco va le nt bond was broken, t h e atoms were scrambled, and the ywere randomly combined i n t o th e detona tion produ cts. Qu otin gfrom th e paper , "We must conclude t h a t , i n th e case o f t hehomogeneous i d e a l explos ive , a l l o f the bonds of th e or ig in alexp los ive molecu les a r e , i n e f fe c t , broken du r ing the detona-t i o n p r o c es s. These molec ular fragments th en must recombinei n a s t a t i s t i c a l l y random f a sh io n p r i o r t o t h e k i n e t i c " f re e z eou t " o f p roduc ts du r ing th e ad i ab a t i c expansion. Cer t a in ly ,d i f fus ion on a molecu la r l e ve l canno t be a n import ant r a t e -c o n t r o l l i n g p r o c e s s . "I s Detonation Velocity Determined by Thermodynamics o rAtomic Vibra t ional Veloci t ies?

From the ea r l y days of t he s tudy of explos ives , de to-na t io n ve lo c i t i e s have been known t o be r e l a t i ve ly cons t an tf o r a g i ve n e x p lo s iv e . I n t h e ZND and other hydrodynamicmodels, the major ve lo ci ty determinant i s cons idered to bethe thermodynamic content of the explosive, which provides ade f i n i t i v e p res su re du r ing the de tona tion . Reac tion k ine t -i c s a r e c on si de re d t o be i r r e l e v a n t t o t h e p r oc e ss .The NM-DETA ex perim en ts pr evi ous ly di sc us se d in d i c a t et h a t k i ne t i c s may a f fe c t de tona t ion ve lo c i t i e s . However, a sseen i n the DETA work ( ~ e f . 3 ) , even wi th a n a lmos t 50%i n c r e a s e i n d e to n a ti o n p re s su r e , t h e d e to n a ti o n v e l o c i t y o f

NM incre ased only about 6%. I t appears obv ious t ha t t he re i ssome la rg e energy lo s s o r some re s t ra in in g f ac to r . I s t h e r esome p r o ce s s t h a t c o n t r o l s t h e d e t o n a ti o n ' s r e a c t i o n r a t e i na chemical o r phys i ca l s ense t h a t w a s not previously con-s i d e r e d ?Many re ce nt quantum-mechanical and oth er ( ~ e f . 5 )k i n e t i c s s t u d i e s have s u pp or te d t h e c o n t e n t i o n t h a t t h eshocked system i s no t i n t hermal ewuil ib rium, p r i nc ipa l ly


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because th e ca lc ula t io ns show th a t th e a cou s t ic energy fromshock waves i s t r a n s f e r r e d t o o s lo w ly t o a t h e r m a l l y e q u i l i -b r a t ed s t a t e o f th e in t ra rno lecu lar v ib rons . These r e su l t ssuppor t t h e concept of t he nonequi libr ium na t ure o f t he shock-f r o n t pro cesses ( ~ e f . ) , but they do no t he lp much to ex pl ainwhat i s o c cu r ri n g a t o r v e ry n e a r t h e s hock f r o n t t o c au se itt o a c c e l e r a t e , what c a u s es t h e r e a c t i o n p a t t e r n s s e en , andwhat causes the appea rance o f the de tona t ion a t o r ve ry nea rt h e f r o n t ; n o r does it t e l l u s why d e t o na t io n v e l o c i t i e sshould have the va lu es the y do o r why they should be re la t i v -e l y cons tan t . These ques t ions w i l l be addressed below.

The 'scale of km/s i n which shock o r deto na tio n ve lo ci - -13t i e s a r e u s u a ll y gi ve n i s th e same s ca le a s angstroms pe r s .The s ign i f i can ce o f t h i s obse rvat ion i s tha t dur ing shocki n i t i a t i o n o r d et on at io n, t h e f r o n t i s moving across a cova-l e n t bond o f an e x pl o si v e i n a p e r i od o n t h e o r d e r o f t h evi br a t io na l f requency. When one ca lc ul a t es th e re la t i v ev e l o c i t y o f t h e v i b r a t i n g atoms i n a C , H , O , N system by threed i f f e r e n t methods (Re f. 25) , t he se ve l oc i t i e s a r e found t of a l l i n the same magnitude a s the shock and de tona t io n ve lo-c i t i e s . Could t h i s be t h e k ey t o t h e v e l o c i t y r e s t r a i n t andt h e s t a b i l i z a t i o n o f d et on a ti on v e l o c i t i e s ?

I n MD ca l cul a t io ns o f cova lent sys tems ( se e Ref. 25 f o rt h e r e fe re n ce s t o s t u d i e s r e p o rt e d i n t h i s pa ra gr ap h) r e l a t e dt o org anic ex pl os iv es , John Hardy, Arnold Karo and I founda shock f ro nt t o be q ui te nar row (about 10 t o 100 angstroms) .This same r e s u l t was obta ined i n MD calculat ions by Dremin(Ref. 20) and Holian; i n MD ca l cu l a t i ons o f de tona t ing sys -tems by Peyrard e t a l . , Lambrakos e t a l . , and E l e r t e t a l . ;i n quantum mechanical ( W ) calculat ions by Coffey and Toton,Dancz and Rice, Z e r i l l i and o the r s ; i n l i g h t - r e f l ec t i on ex-p e ri m en t s i n NM and water by Harris and Presles, and Kormer,Campillo e t a l . , and o the r s . I f t h i s i s so , the n the shockf ron t ene rgy i s h e ld i n a v er y narrow band, and th e energy-o r momentum-transfer r a t e i s enormous, as was calculated byu s p rev ious ly (Re f. 5 ) . T h i s s u g g e s t s t h a t t h e a c c e l e r a t i o nand sh ea r fo r ces i n the shock f ro n t a r e o f the magnitudeprev ious ly ca lcu la t ed (Re f. 2 ) , which a r e o f t he o rde r tom ec ha ni ca ll y s c i s s i o n c o v a l e n t bonds, p a r t i c u l a r l y a t v o id s ,s u r f ac e s , c r y s t a l d e f e ct s , e t c .

If th e Hugoniot curves o f a number of org anic mat er ia ls a r ecompared f o r th e pressu re range of 0 .2 t o 30 GPa, the shockv e l oc i t i e s a l l f a l l q u i t e c lo se , running from about 3 t o 9km/s. The unreactive Hugoniots (no chemical energy released)o f t h e o r g a n i c explos ives a re very n ea r ly th e same. Now, i ft h e de tona t ion p re ssure s and ve l oc i t i e s o f most o f th e com-mon explos ives a r e p l o t te d on th e same graph wi th t hes e o t he rv a l u e s , t h e y f a l l v e r y n e a r t h i s shock v e l o c i t y c ur ve o f t h ei n e r t o r unreac ted ma te ri al s ( ~ e f . and Fig. 8 ) .


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I f a small al lowance (about 10%) i s made f o r th e addi-t i o n to th e shock v e lo c i t i e s due to the much h igher t empera-t u r e s i n t h e d e to n at in g ex pl os iv es , a l l o f t h e D values o ft h e s e 15 commonly-used and stu di ed exp losi ves a r e enc losedi n t h i s sm a ll space between t he Hugoniot shown fo r t h e i n e r tm a t e r i a l s , o r t h e un r e ac t ed c u rv e f o r t r i a m i no t r i n it r o b a n z e n e(TATB), and th e 10% in cr ea se l i n e . This means th a t t h e ex-t re m el y r a p id r e l e a s e o f t h e g r e a t q u a n t i t i e s of chemica le ne rg y i n t h e d e t o n a t in g e xp l os i ve s h as o n l y a r e l a t i v e l ys m a ll e f f e c t o n t h e shock o r d e to n a ti o n v e l o c i t y ( D ) . Thepi s t on formalism denies t h e importance of and excludesk in e t i c s from cons idera t ion . However, s i nce th e D s a r e i n -deed r e l a t i v e l y c o n s t an t f o r a s p e c i f i c m a t e ri a l , a p h y si c alo r chem ical exp l ana ti on i s requ i red .

Remembering t h a tsh oc k f r o n t s c r o s s t h e i n -te ra t omic bonds o f o rgan icm a t e r i a l s i n ti me s o f t h esame o rd e r a s t h e v ib ra -t i o n per iods ( ~ e f . 8 ) , Ia tt em p te d t o c a l c u l a t e t h er e l a t i v e v i b r a t i o n a l v e lo -c i t i e s o f t h e atoms o fthese bonds us ing th reed i s t i nc t m e thods : (1)i n f r a r e d and x -r ay c r y s t a l -10 r aph i c da t a (Ref . e 8 ) ,( 2 7 MD ca l cu l a t i ons (Ref .25) , and ( 3 ) the Hulburt -H i r sch fe lde r equa t i ons( ~ e f . 5 ) . I t was seent h a t t h e d e t on a t io n v e lo -c i t i e s f o r a l l o f t h e o r -g an ic e xp lo si ve s l i e i nth e band o f v ib ra t i onv e l o c i t i e s c h a r a c t e r i s t ico f t h e C ,H ,O ,N a tom pai rs(Ref. 28 ) . Add i t i ona l l y ,we found t h a t th e re la -t i v e v i b r a ti o n a l v e l o c i-t i e s r i s e s lo w ly t o mod-e r a t e maxima e ven a t ex-t remely h igh tempera tures .

30 TATB

- 201u(loniOtA, ;rdriven 1Baratoip TNM10 ' 10% increase inTATB vibrational velocity(unreacted-b tor increased T5 ugoniot) Averaged Hugonlot

C. H, 0 ,and N (inert)

Figure 8. Comparison of Hugoniot curves fororganic materials with the detonation velocitiesof common explosives.

A r a t h e r s im pl e p h y s i c a l e x pl a na t io n e x i s t s , t h e n , f o r an e a r c on st an cy o f d e t o n a t io n v e l o c i t i e s . The v ibra t ionalm otio n t h a t c a r r i e s t h e p r i n c i p a l ba n d- sc is si on a c t i v a t i n genergy can proceed th rough t he de ton at ing explos ive , even a tv e r y h ig h t em p er at ur e s, o n ly a t o r ne a r t h e r e l a t i v e v i b r a -t i 0 rBl v e l o c i t i e s . T h a t i s why g re a t l y i nc reased l ev e l s ofshock p res su re and h igh t em pera tures add l i t t l e t o de tona t i onv e l o c i t i e s .


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Thus, a s shown i n Ref. 23, k in e t i c s i s impor tan t andc a n change d e to n a t i o n v e l o c i t i e s , b u t a l a r g e i n c r e a s e i nr e a c t i o n r a t e ( o r e ne rg y r e l e a s e r a t e ) and hi gh a d d i t i o n a lpres sure (Ref . 24) make on ly a smal l incre ase i n th e D. Thi sdoes no t mean th a t thermodynamic energ y con ten t does n ot i n -f l ue nce de tona t i on ve lo c i t i e s o r explos ive power ou tpu t . I tdoe s mean, however, t h a t it i s not the thermodynamic energyc o nt en t t h a t r e s t r a i n s t h e v e l o c i t i e s t o a r ange o f a b ou t5 t o 9 km/s.

Another obser va t io n (Ref . 29) on de ton at ion th a t addsconcern about a purely thermodynamic const raint i s t h a t D smeasured a lo n g d i f f e r e n t c r y s t a l a xe s i n s i n g l e c r y s t a l s o fRDX and FETN have di f fe r e n t va lu es . Thi s can be explainedi n t h e new t h e or y a s a . r e s u l t of d i f f e r e n t k i n e t i c s due t od i f f e ren t f r ee r ad i ca l s and m o lecu l a r f r agm en t s and i onspec i es formed by t h e m echanica l fo rc es on t h e d i f f e re n tm ole cu la r or i e nt a t io n s i n t h e c r y s t a l l a t t i c e s .

SIGN1FI CANT MOLECULAR DYNAMICS CALCULATIONSTwo-Dimensional Calc u la t io ns o f t he E ff ec t s o f L at t i ce Defec t s

The macroscopic e f f e c t s o f t h e i n c r e a s e i n s e n s i t i v i t yt o shock i n i t i a t i o n ca use d by c r y s t a l d e f e c t s s uch a s v o i dso r c r ac ks o r v e ry i r r e g u l a r c r y s t a l s t r u c t u r e o r t h e i nc lu -s i on o f heavy pa r t i c l e s i n an exp los ive had been exper im ent -a l l y observed . However, no ca l cu la t io ns on th e a tomic sc a lehad been found t h a t s imula ted the se condi t ions . Therefore ,we completed a s e r i e s of two-dimensional (2D) MD c a l c u l a t i o n st o s t u d y t h e s e c o n d it i o n s . I n e ve r y c a s e , t h e d e f e c t s t u d i e dshowed a s u b s t a n t i a l i n c r e a s e i n t h e number o f bond s c i s s i o n sand Energy c o n c e n tr a t i o ns a t t h e s i t e s o f t h e d e f e c t s (R ef.25)

We ne xt i n t rodu ced a mathematical concept by which anamount of energy equa l t o approximately the h ea t of detona-t i o n pe r bond was added t o t h e ca l cu l a t i on a long a r e ac t i o ncoo rdi nat e where bond sc is s io n had occurred. The id ea con-s i de re d was t h a t t h e r a d ic a ls formed from th e endothermic bondf r a c t u r e would r e a c t i n a bo ut 10-13s, the reb y adding exoth er-m ic r ea c t i on energy t o t he sys tem no t f a r from where t h e s c i s -s io n occu rred, when th e ra d ic a ls rea ct ed . We made a numbero f c a l c u l a t i o n s i n d i f f e r e n t g eo me tr ie s and a t d i f f e r e n t i n i t -i a l t e m pe r a tu r e s u s i n g t h i s " r e a c t i v e " p o t e n t i a l . The e f f e c twas dram at i c (Ref . 3 ) . Th i s s t udy i l l um ina t e d ano the r f ac to r - -t h e t im e s c a l e s i nv olv ed i n t h e d i f f e r e n t i n i t i a t i o n modelst h a t had been proposed. The mechanical bond s c is s i o n couldl e ad t o exothe rm ic r ea c t i on a t t im e s o n t h e o r d e r of10-I3s , and t h i s could , t he re fo r e , i n f l u ence t he shock ve lo -c i t y by p ro vi di ng s i g n i f i c a n t r e a c t i o n energy a t o r ve r y n e a rt h e shock f r on t . On the o t he r hand , t he equ i l ib r i um the rm alp roces ses proposed (gas com press ion , f r i c t i o n hea t i ng , e t c . )a l l re qu i r e much lon ge r t imes (on th e ,o rder o f nanoseconds


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t o microseconds) t o provide s ig ni f i ca nt exothermic response .The shock f r o n t i n the se ca se s would be f a r downstream bysuch t imes.The shock energy i n both t h e l - D and 2-D ca lc u la ti o n sd i d n o t c ou pl e w e l l w i t h t h e t he rm al o r v i b r a t i o n a l e ne rg yi n t h e l a t t i c e s . T h is su pp or te d t h e c on cl us io n s t a t e d e ar -l i e r t h a t " t h e energy i n t h e shock f r o n t i s hig hly nonergodicand th a t t he rma l equ il ib rium, pa r t i c u la r l y between the t r ans -l a t i o n a l a nd v i b r a t i o n a l e ne rg y modes, does n o t e x i s t i n t h ef r o n t ."We completed seve ra l s e r i e s o f 2-D and some 3-D MD c a l -c u l a t i o n s t o e xp lo re t h e f a c t o r s i n vo lv ed i n shock r i s e t i m esand th e ass oc i a ted shockfront widths , I n both th e 2-D and3-D st ud ie s, th e shock energy stayed lo ca l i ze d i n some smallnumber o f l a ye r s (4 t o 15) o f atoms. I n ca l cu l a t io ns wi th

t h e i n i t i a l v i b r a t i o n a l motion of t h e l a t t i c e atoms s im ula -t i n g c o n d i t io n s n e a r t h e m el ti n g p o i n t o r c o ld ( w i t h noi n i t i a l th er ma l m o ti on ), t h e n e t r e s u l t s a s t o t h e shock-f r on t w idths and thus th e r i s e t imes were s im i l a r (Re f. 25) .I f one cons id ers the case i n which th e shock f ro nt s t ay sc o he re n t i n 1 2 l a y e r s o f atoms (about 24 angstroms) and ani n i t i a t i n g shock was p ro ce ed in g i n t o t h e m a t e r i a l a t 4 a ng s-

t roms i n 10-13s (4 km/s) t h e microscopic r i s e t ime would be6 X 10-13s. I n th e ca se o f a deton a t ion f r o n t moving a t 8angst roms i n 10-I3s, t h e mic roscop ic r i s e t ime i s 3 X 10-13s.Allow ing f o r some l a t t i c e i r r e g u l a r i t i e s and s l i g h t l y i n -c r e a se d i n te r m o le c u l ar d i s t a n c e s i n r e a l s ys te ms , r i s e t i me scou ld be ne ac pico seco nds , and th e shock width would bec l o s e t o t h e s pa n o f 15 wat er molecules, a s proposed byHarris and Pre s l e s (Ref . 30) .Ca lc ul at io ns of Shock-Induced Chemistry

A new f i e l d t h a t combines physic s and chemi stry has comein to prominence i n th e pas t decade. This research and de-velopment invo lve s th e sy nt he si s and fa b r i ca t i o n o f new com-pounds, a l lo ys , and ot he r ma ter ia l s through shock-inducedchemica l and phys ica l r eac* ion ( ~ e f . 5 ) . The chemis t ry andp h y si c s i n th e s e p r oc es se s a r e d i r e c t l y r e l a t e d t o t h e shock-induced re ac t io n proposed i n th e new theory .To add more re al is m t o t h e MD c a l c u l a t io n s , we made twod ia to m ic s t u d i e s i n which n i t r i c o xi de and s u l f u r n i t r i d el a t t i c e s were s im ul at ed : i n t h e f i r s t case we cal cu lat ed th ee f f e c t o f th e impact of a n aluminum p la te on a model face-c en te re d- cu bi c n i t r i c o xi de l a t t i c e c o nt a in i ng a void ; and i nthe second case , a s i m i l a r geometry was used i n which t h ealuminum p l a t e impacted a model face-centered-cub ic s u l f u rn i t r i d e l a t t i c e . The c a l c u l a t i o n s were made i n each c a s e w i t hth e i n i t i a l random mot ion o f the atoms r epre s en ta t iv e o f room


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t empera ture and aga in when t h e sys tems were "co ld ," wi th noi n i t i a l t he rm al m otio n.These fou r s e t s o f c a l c u l a t i o ns w ere compared w i t h t ho s e

o f an e a r l i e r , more gen e ra l , cova l en t s yst em. The same qua l -i t a t i v e r e s u l t s were o b t a in e d o f bond s c i s s i o n , w i th a tom sa nd m o l ec u l a r f r ag m en t s f l y i n g a cC oss t h e v o i d t o i m pa c t t h eo p p o s i t e w a l l s an d c a us e f u r t h e r s c i s s i o n . When t h e r e a c t i v ep o t e n t i a l was u se d i n a s i m i l a r ge om et ry i n a more g e n e r a ll a t t i c e , t h e i n i t i a l " s p a l l " f rom t h e i n n e r s ur fa ce of t h ev o i d a nd t h e i mp ac t on t h e o p p o s it e v o id f a c e l e d t o a c t i v -i t y o f t h e a to ms t h a t was v e r y s u g g e s t i v e o f h o t s p o t form a-t i o n t h rough f r ee - r ad i ca l chem i s t ry . These moti ons and s i m -u l a t e d r e a c t i o n s a r e a l l n on er go di c, n on eq ui li br iu m p r o c e ss e s .SUMMARY OF MORE RECENT SUPPORTIVE EVIDENCE

Sharma e t a l . r ep or te d ( ~ e f . 1) s t u d i es o f i n i t i a t i o ns i t e s f ou nd i n TATB s ho ck ed t o n e a r - i n i t i a t i o n l e v e l s . T heyf ou nd t h e s i t e s , by s c a n n in g e l e c t r o n m ic ro sc op y (SHVI) ,o bet i n y h o l e s o n t h e s u r f a c e s an d ed ges o f t h e e x p l o s iv e g r a i n s .They showed, by x-ray ph ot oe lec t ro n spec t ros cop y (XPS), t h a td e p o s i t s o f a c et o ne - so l ub l e r e a c t i o n p r od u ct s i n t h e h o l e swere furoxan and fur aza n de r i va t i ve s of TATB. Th e i r an a l y s i ss u g g es t e d t h a t t h e f u r o x a n p r od u ct c o u l d r e a c t w i t h a d j a c e n tTATB mol ecu l e s i n a n exo the rmi c cha i n r e ac t i o n t o g i v e a w a t e rmolecule and a new furo xan. Thus t h e shock=formed fu ro xa nc o u l d i mm ed ia te ly ( i . e . , i n 10 - l~o 1 0 -I 2 s ) p r o vi d e r e a c t i o ne n e r g y v e r y n e a r t h e sh oc k f r o n t . Sharma su g ge st e d t h a t t h i sr e a c t i o n c o u ld be i n v ol v ed i n t h e i n i t i a t i o n o f TNT a s w e l l .

Tanaka e t a l . p rov i de a s t ro ng de fens e o f t h e new t heo ry .They r e p o r t ( R ef . 3 2 ) t h a t a n e x p lo s i v e d e s ig n a t ed a s E25(75% P E T N / ~ ~ $a r a f f i n ) a t a d e n s i t y o f 1 .2 65 &cc h a s a meas-u r e d D o f 7.230 km/s, whereas pur e PETN (p e n ta e r y th r i t o l t e t r a -n i t r a t e ) a t t h e same den s i t y ha s a measured D o f 6.60 km/s.However, t h e ca l c u l a t i o n us i n g shock ve l o c i t i e s and t h e empir -i c a l f or mu la g a ve a v a l u e o f 7.267 km/s, w i t h i n o. 51% o f t h emeasured va l ue . Thi s i s w e l l w i t h i n t h e p r e c i s i o n o f D meas-u r em e nt s. The c l a s s i c a l t h e o r y c a l c u l a t i o n m is se d t h e meas-ured value by 14.24%. The au t h o r o f t h e pape r who r ep or t edt h e E25 d a t a s t a t e d t h a t , " A l l e q u a t i o n s - o f - s t a t e a v a i l a b l et o u s c an no t re pr od uc e t h e s e r e s u l t s . "I n 1 9 9 2 , B re nn er , R ob er ts on e t a l . p u b li sh e d r e s u l t s o ft h e i r MD s t ud i e s i n wh ich t h ey us e many-body i n t e r a t o mi cp o t e n t i a l s t o p r ov i de more r e a l i sm t o t h e i r c a l c u l a t i o n s .T h e i r e x c e l l e n t g r a p h i c s show i n un m is ta ka bl e d e t a i l ( F i g . 9 )t h e nar row s hock and de t ona t i on zones , t h e mass ive mechan ica lf r a c t u r e o f t h e c o v a l en t b on ds, t h e f r e e atom s a nd m o l e c u la rf r ag m e nt s, and t h e f r e e - r a d i c a l c h em i st r y i n a nd v e r y n e a r t h ef r o n t . T hese p r o c e s s e s a r e n o n e q u il i b ri u m a nd n o n t h e m a l .


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JOURNALDE PHYSIQUEIV

B . O 4 4 4 4 4 4 4 4P P P P P P P PP P P P P P p P4 4 4 4 4 4 4 4

P P P P P P P P

Snapshot from r simulaliun d dc(onating film. The bg t b d bc -&ernxlwmn r 60h.

Figure 9 . Molecu lar dynamics ca lc u l a t io n o f a model detonat ings o l i d wi th two typ es o f a toms and wi th exothermicr e a c t i v i t y i n co r p or a te d i n t o t h e dynamics.Simpson, Helm and Kury (Ref. 34) st ud ie d th e no nr ea ct iv eHugoniot f o r water m ix tu res , and t hey r epo r t ed t h a t w i thshocks of 5 .17 t o 5 .99 GPa th er e w a s no ev idence of HMX r e -a c t i o n . However, th ey showed by comparison wi th the se r e s u l t st h a t i n s ol ve nt -p re ss ed HMX i n wedge t e s t s a bo ut 3 t o 7% oft h e HMX had r e a c t e d i n l e s s t h a n a b o ut 100 n s . They r e p o r t ,"The observed h ighe r shock ve lo c i t i e s i n t he so lven t-p res sedda t a we a t t r i b u t e t o a r eac ti on - suppor t ed shock f ro n t . "Othe r pe r t i nen t comments from t h i s pape r a re : " Im p l i c i t i nt h e u se o f a deton at ion product EOS i s t he assumption t h a tchemica l re ac t i on s oc curr ing under the shock load in g condi -t i o n s o f t he wedge t e s t s go t o comple ti on . There fo re, s i n cee a r l y t im e r e a c t i o n s may o n l y p ro ce ed t o i n t e r m e d i a t e s t a t e s ,t h e e x t e n t o f r e a c t i o n i n f e r r e d t hr ou gh r e a c t i v e m od elin g w i l lbe c o n s e r va t i v e ." "The g r e a t e s t u n c e r t a i n t y i n d e t e r m i n a ti o no f s t a t e b eh av io r o f HMX from measurements on a mixture i st h e assumption of a one-dimensional shock wave pas sing througha homogeneous medium. "The i n fo r ma ti on i n t h e s e f o u r r e f er e n ce s e x p l i c i t l y ad dss t ro n g suppo rt f o r th e new Walker , Wasley, Karo (WWK) t h e o r y .

NEM EQUATIONS USED TO CALCULATE DETONATION VELOCITIESI n 1968, Kamlet and Jacob s (Ref . 35) r epo r t ed t he deve l -opment o f two em p i r i ca l equa t i ons f o r ca l cu l a t i ng d e ton a t i onp r e s s u r e s and v e l o c i t i e s . W ith some s i m p l i f i c a t i o n o f t h e i rc o nc e pt and a n a l g e b r a i c d e r i v a t i o n , a s im p le e q u a t i o n f o rc a l c u l a t i n g D = f (P ) was ob ta ined :

When t h e d e t o n a t i o n d a t a f o r 1 4 v e r y d i f f e r e n t e x p l o s iv e s a r ecompared by means of t h i s re la t io ns h i p , two in te r e s t i n gr e s u l t s a pp ea r:


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( 1 ) T he a l i p h a t i c compounds a r e a l l o n o ne s i d e o f a na v er a ge d c ur v e, a nd t h e a r o m a ti c s ( p l u s s t e r i c a l l y - h i n d e r e dPETN) a r e a l l on t h e o t h e r s i d e .( 2 ) W ith a s m a l l p o s i t i v e c o r r e c t i o n f o r h yd ro ge n a n d n i -

t r o g e n c o n te n t ( t o com pensate f o r t h e i r r e l a t i v e l y h i g he rshock v e l o c i t i e s a t a g i ve n p r e s s u r e ) and a s m al l o f f s e t f o ra r o m a t i c i t y , a n e q u a t i o n was f o rm u la te d t h a t r e pr o du c es t h ed a t a f o r t h e 14 e x p l o si v e s w i t h i n +l .57 and -1 -03%. Tha te q u a t i o n f o l l o w s :

where a = 0 i f t h e compound i s a r o m a t i c and a = 1 i f i t i sa l i p h a t i c , and H and N a r e t h e w e ig ht p e r c e n t s o f h yd ro ge nP Pa nd n i t r o g e n , r e s p e c t i v e l y .The c o n ce p t u n d e r l y i n g t h e e q u a t i o n i s t h a t d e to n a ti o nv e l o c i t y i s p r i n c i p a l l y a r a t h e r si mp le H ug onio t r e l a t i o n s h i p ,D = f ( P ) . More e x p l i c i t l y , th erm od yn am ic f a c t o r s , t h e EOSs,a nd e ve n r e a c t i o n r a t e s have l i m i t e d i n f l u e n c e on t h e a c t u a lv a l u e s o f D .K a m le t 's e m p i r ic a l e q u a t i o n f o r c a l c u l a t i n g d e t o n a t i o np r e s s u r e s i s pro bab ly a s us e f u l a s t h e TIGER thermodynamiccode w i t h t h e complex EOSs t h a t a r e used , and we have shownt h a t t h e D s f o r 48 v e r y d i f f e r e n t e x p l o si v e s c a n be c a l c u -l a t e d a c c u r a t e l y ( w e l l w i t h i n t h e e xp er im e nt al e r r o r o f t h eb e t t e r me as ur ed v a l u e s ) from t h e H ug on io t v a l u e s o f t h e e l e -m e nt s t h a t make u p t h e e x p l o s i v e s . The e q u a t i o n u s e d i s a s

f o l l o w s :

where USi i s t h e s ho ck v e l o c i t y o f t h e e l em e nt s a t PC-,J,f i i s t h e a to m ic w e ig h t f r a c t i o n o f t h e e l e m en t , a nd Tc i s as m a l l c o r r e c t i o n ( a b o ut 3 t o 8%) ~ e f . 5 ) r eq u ir e d becauset h e d e t o n a t i o n t e m p e r a t u r e s a r e c o n s i d e r e d t o b e a b o u t 2500t o 5000 K , w h e r e as t h e Hu go ni ot v a l u e s o f t h e e l e m en t s a r eu s u a l l y m e as u re d be twee n a bou t 70 a nd 950 K . The DS f o r 21o f t h e b e s t - c h a r a c t e r i z e d e x p l o s i v e s w ere c a l c u l a t e d w i t hEq. 5, and t h e c o r r e l a t i o n c o e f f i c i e n t o b ta in e d f o r th e s ev a l u e s i s 0 .976 . D v a l u e s were c a l c u l a t e d f o r 25 o t h e re x p l o s i v e s f o r wh ic h l e s s d a t a were a v a i l a b l e , a nd t h ec o r r e l a t i o n c o e f f i c i e n t f o r t h i s s e t i s 0 . 932 , ( R e f . 3 6 ) .

CONCLUSIONSI t i s conc luded : ( 1 ) T h a t t h e new c o n c e pt o f p h y s i c a lk i n e t i c s i s a v a l i d c on ce pt f o r d et er mi ni ng r e a c t i o n r a t e s i nd e t o n a t i o n s a nd i n h i g h l y s ho ck ed s y st em s . Shock and detona-t i o n v e l o c i t i e s a r e r e l a t e d d i r e c t l y t o t h e a ve ra ge r e l a t i v ev i b r a t i o n a l v e l o c i t i e s o f t h e atom p a i r s i n C , H , 0 , N m a t e r i a l s .


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C4-254 JOURNAL DE PHYSIQUEIV( 2 ) T h a t t h e e x ce e di n gl y h ig h k i n e t i c e n er g y i n t h e d e to -n a t i o n f r o n t i s s u f f i c i e n t t o c a us e m ass iv e f r a c t u r e o f t h ec o v a l e n t b on ds o f t h e m o le c ul e s o f e x p l o s i v e s ( a nd o t h e ro r g a n i c s ) a t and n e a r t h e f r o n t , s o t h a t t h e l a r g e m a j o r i t y

o f t h e m ol ec ul es a r e b r ok en t o i n d i v i d u a l a tom s o r r a d i c a l sa nd a r e r e a r ra n g e d e x t e n s i v e l y , a nd t h a t t h e r a t e s of t h es u b s eq u e n t v e r y r a p i d c he mi ca l r e a c t i o n s c a n be i n f l u e n c e dby t h e a d d i t i o n i n t h e e x p l os i v e s o f c he mi ca ls p r o v i d in ge nh an cin g o r i n h i b i t i n g r e a c t i o n s .( 3 ) T h a t t h e s i m pl e Eq. 5 i s a r a t i o n a l e q u a t i o n , b a se do n a p p r o p r i a t e H u go ni ot p r i n c i p l e s , w hich p r o v i d e s f o r v e r ya c c u r a t e c a l c u l a t i o n o f d e t o n a t i o n v e l o c i t i e s from t h e shockv e l o c i t i e s o f t h e e l em e nt s i n t h e e m p i r i c a l fo rm ul ae o ft h e e x p l o s i ve s .( 4 ) T h at t h e c o nc e pt s o f p h y s i c a l k i n e t i c s a nd t h e s m a l li n c r e a s e i n v i b r a t i o n a l v e l o c i t i e s w i t h i n c r e a s i n g tempera-t u r e p r o vi d e t h e e a r l i e r m i s s in g p i e c e s t h a t now e x p l a i nt h e r e l a t i v e c o ns ta nc y o f d e t o n a t i o n v e l o c i t i e s .( 5 ) T ha t t h e c o mp ar is on p r e se n t e d h e r e i n s hows t h a t t h i snew modern t heo ry ( t he WWK t h eo r y ) o f t h e i n i t i a t i o n an dd e t o n a t i o n o f e x p l os i v e s pr o v i de s a r e a l i s t i c m ic r os c op i cd e s c r i p t i o n o f and s i g n i f i c a n t u t i l i t y i n u nd er st an di ng andc a l c u l a t i n g e x p l o s i v e s phenomena.

REFERENCESW.C. D a v i s , S c i . Am. 2 5 6 ( 5 ) , 1 0 6 ( 1 9 8 7 ) .F.E. Walker and R.J. W as le y, P r o p e l l a n t s a n d E x p l o s i v e s1 , 7 3 ( 1 9 7 6) .F .E . W al ke r, P r o c e e d i n g s o f t h e 1 9 t h I n t e r n a t i o n a l Py ro -t e c hn i c s Semina r , 20 -25 Feb rua ry 1994 , pp . 297-318 , Sou thP a c i f i c In f or m . S e r v i c e s L t d , C h r i s t c h u r c h , N . Z . ( 1 9 9 4 ) .F.E. W a lk e r, P r o p e l l a n t s , E x p l o s i v e s , P y r o t e c h n i c s 7 ,2 ( 1 9 8 2 ) .F.E. Walker , J. Appl . Phys. 63 (1 1) , 5548-5554 (1 988 ) .A . W . Campbel l , W.C. D a v i s, a n d J . R . T r a v i s , P hy s. F l u i d s4 , 4 9 8 ( 1 9 6 1 ).A.W. Campbel l , W.C. D a v i s , J . B . Ramsay, and J . R . T r a v i s ,P h y s i c s F l u i d s 4, 511 ( 1 9 6 1 ) .F.P . Bowden an d 0 A Gur ton , Na tu re 16 1 , 348 (194 8) .A . J o f f e , N a t u r e 1 6 1 , 3 49 ( 1 9 4 8 ) .E. F. G i t t i n g s , F o u r t h Symposium o n D e t o n a t i o n ( P r e p r i n t s )V o l . 1 1 , C - 1 5 ( U . S . GPO, Wash ingto n, D.C., 19 65 ).H . E y r i n g , R .E . Pow el l , G.E. Duf fey , and R .B . P a r l i n ,Chem. Rev. 45 , 69 ( 1 9 4 9 ).H . E yr in g and An-Lu Leu , Proc . Nat . Acad. S c i . USA 7 2 ( 5 ) ,1717 (1975) .H . E y r i n g , S c i e n c e 1 9 9 , 7 40 ( 1 9 7 8 ) .F.E. Walker an d R . J . W as le y, E x p l o s i v s t o f f e 1 7 , 9 ( 1 9 6 9 ) .


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H. Cheung, A . Weston, L. Green, and E. James, Ex plo siv eI n i t i a t i o n , L awrence L iv er mo re Na t i o n a l L a b o r a t o r y ,Livermore, CA, UCRL-76578 (1975).F.E. Walker and R . J . Wasley, Combust. Flame 15, 233(1970)F.E. Walker and R . J . Wasley, Combust. Flame 22, 53( 1 9 7 4 ) .W. T a y l o r a n d A . Weale, Tra ns . Faraday Soc. 34, 995( 1 9 3 8 ) .M . Held , Ex p l os iv s t o f fe 11/12 , 241 (1969) .A.N. Dremin and V . Yu. Klimenko, Progress i n Astronau-t i c s and A e r on a ut ic s 7 5 , J . Ray Bowen, N . Manson, A.K .Oppenheim, and R . I . So lo ukh in , Eds. (AIAA, New York ,NY, 1 9 81 ). pp.1 53-1 68.P.A. U rt ie w, E.L. Le e, a nd F.E. Wal ker, Arch. Thermodyn.Combust. 9 , 259 (1978).J . H . Lee, R . Knystautos , and N . Yoshikawa, ActaAs t r o n a u t . 5, 971 (1978) .F.E. Walker , Acta As t ron aut . 6 , 807 (1979) .I . C . Skidmore and S. Ha r t , P r o c . 4 t h Symp. ( I n t e r n a t . )De tona t ion , U .S . Naval Ordnance Laboratory, White Oak,MD, 12-15 Oc to be r 19 65 (U.S . GPO, Washington , D.C.) p. 47 .F.E. Wa lk er , I n i t i a t i o n a nd Det o n at i o n o f E xp l o s iv e s - -a n A l t e r n a t iv e Concept , Lawrence Livermore Nat iona l Lab-o r a t o r y , L i v e r m o r e , CA , UCRL-53860, 11 January 1988.D.R. Hardesty, Combust. Flame 27, 229 (1976).R . R . McGuire and D.L. O rn el la s , Pr op el la nt s and Explo-s i v e s 4 , 23 ( 1 97 9 ).F .E. Walke r, Pr op e l l an t s and Exp los ives 6 , 15 ( 1 9 8 1 ) .H.W. Koch and Ch. B aras , I n s t i t u t Franco-Allemand deRecherches de Sa i nt -L oui s , France , Rappor t 28/71 (19 71) .P. H ar r i s and H.-N. P r e s l e s , J . Chem. Phys. 8 0 ( 1 ) , 524(1984)J . Sharma, J . W . Forbes , C .S . Coffey , and T . P . L i d d i a r d ,J . Phys. Chem. 91, 5139 ( 1 9 8 7 ).K . Tanaka, S. Oinuma, e t a l . , Shock Compression o f Con-densed M at te r 1989, S.C. Schmidt , J . N . Johnson, L.W.D a vi so n, ( e d i t o r s ) , E l s e v i e r S ci e n c e P u b l i s h e r s B.V.,( 1 9 9 0 ) .D.W. Brenner , D .H . R o b e r tso n , e t a l . , Mi cr o sc o pi c S imu-l a t i o n ~ f Complex Hydrodynamic Phenomena, Ed i te d byM . Ma res cha l and B.L. H ol ia n, Plenum P r e s s , New York,NY, pp. 111-123 (1 99 2) .R . L . Simpson, F .H . Helm, and J . W . Ku r y , P r o p e l l a n t s ,Exp los ives , Pyro tec hn ics 18 , 150-154 (1993) .M . J . Kamlet and S. Jacobs, S . Chem. Phys. 4 8 ( 1 ) , 23( 1 9 6 8 ) .F .E . Wa lk er , P r o p e l l a n t s , E x p l o s i v e s , Py r o t e c h n i c s 1 5 ,157-160 (1990).


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C4-256 JOURNALDE PHYSIQUE IVT a b l e 3. Corre la t ions Between React ion Dynamics Exper iments and

Detona t ion Energy and Time Ch ar ac te r i s t i c s .P r o p e r t y Re act ion Dynamics De ton atio nV e l oc i t i e s o f a toms a nd m o l e c u l e sCe n t e r o f m a ss ( I . * * C N ) * 2 km/sT r a n s l a t i o n o f H atoms 20 km/sV e l oc i t i e s o f a toms and m o l e c u l e s

i n d e to n at io n f r o n t"C" and "H" atoms from MD c a l c s .V i b r a t i o n a l v e l o c i t i e s o f a tom

p a i r s a s f ( T ) a t second v i b .l e ve l - - f rom QM c a l c u l a t i o n s * *

H a toms f rom de to na t in g chargeEnergy of a toms and moleculesF o r t h e r e a c t i o n :( I - CN ) - I . " ~ ~ ) * + CN(E nerg y a v a i l a b l e f o r r e a c t i o n )H + OCO - H " ' O CO ) * - H + C O

( H k i n e t i c e n e r g y )Energy of PES bar r i e r to TSK i n e t i c e n er gy o f a to ms a t 8 km/s

Bond ene rg ie s i n RDX

Tim es t o r e a c t i o nL ife t im e of TS(I. c N ) *( H . ..OCO)*


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T a b l e 3 . ( c o n t . )From MD c a l c u l a t i o n s"Time t o r e a c t i o n"C-H i n "CH2"C-H i n "PETN" i n t e r i o rN-0 i n "PETN" i n t e r i o rC -C i n " C " m a t r i xE s ti m at e o f t im e t o r e a c t i o n

i n d e to n a ti o n a t 8 km/sI n 20 angstrom zoneI n 40 angstrom zone

** From H u l be r t -H i r sc h fe l de r c a l c u l a t i o ns

Documents

F.E. Walker- A Comparison of the Classical and a Modern Theory of Detonation