Equation of state of detonation products of compact explosives.pdf

7/28/2019 Equation of state of detonation products of compact explosives.pdf

1/6

I 0. M . P . S l a v i n s k i i , P h y s i c o c h e m i c a l P r o p e r t i e s [ i n R u s s i a n ] , N a u k a , M o s c o w ( 19 6 0 ) .ii. R. McQ uee n and S. Ma rsh, J. A ppl. Phys., 31, No. 7, 1253 (1960).12. S. B. Kor mer an d V. D. Urlin, Dokl. Akad. N auk SSSR, 131, No. 3, 542 (1960).1 3. I. I. F r a n t s e v i c h a n d F . F . V o r o n o v , E l a s t i c C o n s t a n t s a n d E l a s t i c M o d u l i o f M e t a l s a n d

N o n m e t a l s [ i n R u s s i a n ] , N a u k a , M o s c o w ( 1 9 8 2 ) .14. V. A. Zhda nov and A. V. Zhukov, Prikl. Mekh. Tekh. Fiz., No. 5, 139 (1978).15. S. N. Ish utk in, G. E. Kuz'm in, and V. V. Pai, Fiz. Go re ni ya Vzryv a, 2__22, o. 5, 96 (1986).16. J. Taylo r, J. Appl. Phys., 34, No. 9, 2727 (1963).17. L. V. Al' tsh ule r, S. B. Korm er, A. A. Bakan ova, et al., Zh. Eksp. Teor. Fiz., 38, No. 3,790 ( 1 9 6 0 ) .1 8 . K . G s c h n e i d e r , S o l i d S t a t e P h y s . , 1 6 , 2 75 ( 1 9 6 4 ) .

E Q U A T I O N O F S T A T E O F D E T O N A T I O N P R O D U C T S O FC O M P A C T E X P L O S I V E S

V . F . K u r o p a t e n k o U D C 6 2 2 : 2 1 5

T h e b e h a v i o r o f d e t o n a t i o n p r o d u c t s ( DP ) o f c o m p a c t e x p l o s i v e s i s d e s c r i b e d s a t i s f a c -t o r i l y i n a n u m b e r o f c a s e s b y t h e e q u a t i o n o f s t a t e [ I- 3]p = / ( p ) T + ~ ( 9 ) , ( 1 )

w h i c h t a k e s a c c o u n t o f t h e m o l e c u l e i n t e r a c t i o n i n a b r o a d r a n g e o f v a r i a t i o n o f t h e t e m p e r -a t u r e T a n d d e n s i t y p . I n a n u m b e r o f c a s e s t h e f u n c t i o n s f ( p ) a n d ~ ( p ) a r e s e l e c t e d i ns i m p l e s t f o r m . T h u s a s i m p l e d e p e n d e n c e o f t h e p r e s s u r e p o n t h e d e n s i t y

p=A 9" ( 2 )i s p r o p o s e d i n [ 2] t o d e s c r i b e t h e D P p r o p e r t i e s i n t h e n e i g h b o r h o o d o f t h e J o u g e t p o i n t .T h e e q u a t i o n o f s t a t e

p=B oT+ Ao ~ ( 3 )w i t h t h r e e c o n s t a n t s i s e x a m i n e d i n [ i ] . T h e e q u a t i o n s o f s t a t e ( 2 ) a n d ( 3 ) h a v e a l i m i t e dr a n g e o f a p p l i c a b i l i t y . I f t h e n u m e r i c a l v a l u e s o f A , n , B a r e c h o s e n s u c h t h a t t h e e r r o rw o u ld be l e a s t i n t h e n e i g h b o r h o o d o f t h e J o u g e t p o i n t , t h e n i t w i l l g ro w n o t i c e a b l y w i t hd i s t a n c e f r o m i t a l o n g t h e i s e n t ro p e . T h e f l i n g i n g p r o p e r t i e s o f e x p l o s i v e s a r e d e s c r i b e db e t t e r a n d t h e p a r a m e t e r s o f t h e no r m a l d e t o n a t i o n w a v e ( DW ) w o r s e f o r a n o t h e r c h o i c e o fc o n s t an t s . I n o r d e r t o i n c r e a s e t h e a c c u r a c y o f d e s c r i b i n g D P b e h a v i o r i n t h e n e i g h b o r h o o do f t h e J o u g e t p o i n t u n d e r i s e n t r o p i c e x p a n s i o n a n d m o d e r a t e c o m p r e s s i o n s , a n u m b e r o f e q u a -t i o n s o f s t a t e [ 4- 6] o f t h e t y p e ( i ) w a s c r e a t e d w i t h d i f f e r e n t f u n c t i o n s f ( p ) a n d ~ ( p ) c o n -t a i n i n g a r o u n d i 0 c on s t a n t s . T h e r i se i n t h e i r a c c u r a c y i s a c h i e v e d b y n o t i c e a b l e c o m p l i c a -t i o n . I t is c h a r a c t e r i s t i c f o r t h e m e n t i o n e d e q u a t i o n s o f s t a t e o f t h e D P t h a t t h e n u m e r i -c a l v a l u e s o f t h e m a j o r p a r t o f t h e p a r a m e t e r s t h e r e i n a r e d e t e r m i n e d i n d i v i d u a l l y f o r e a c he x p l o s i v e .

L e t u s c o n s i d e r o n e o f t h e m e t h o d s f o r f i n d i n g t h e f u n c t i o n s y ( p ) a n d ~ ( p ) f o r ( i )p = ( ? ( p ) - - t ) o E + ~ ( p ) . ( 4 )

A p h y s i c a l e x p e r i m e n t p e r m i t s d e t e r m i n a t i o n o f t h e d e p e n d e n c e o f t h e v e l o c i t y D o f t h e n o r m a ld e t o n a t i o n w a v e , t h e m a s s f l o w r a t e u b e h i n d t h e w a v e f r o n t , a n d t h e c a l o r i f i c v a l u e Q o ft h e e x p l o s i v e o n t h e i n i t i a l d e n s i t y P 0 a h e a d o f t h e d e t o n a t i o n w a v e f r o n t. W e w i l l u s et h e s e d e p e n d e n c e s t o s e t u p t h e f o r m o f t h e f u n c t i o n s y ( p ) a n d ~ ( p ) a n d t o d e t e r m i n e t h e n u -m e r i c a l v a l u e s o f t h e p a r a m e t e r s i n t h em .

T h e c o n s e r v a t i o n l a w s on a s t r o n g d i s c o n t i n u i t y w i t h i n s t a n t a n e o u s l i b e r a t i o n o f i n-t e r n a l e n e r g y Q h a v e t h e f o r m

C h e l y a b i n s k . T r a n s l a t e d f r o m F i z i k a G o r e n i y a i V z r y v a , V o l . 2 5, No . 6, p p. 1 1 2 - 1 1 7 ,N o v e m b e r - D e c e m b e r , 1 9 89 . O r i g i n a l a r t i c l e s u b m i t t e d A p r i l 5, 1 98 8 .

7 62 0 0 1 0 - 5 0 8 2 / 8 9 / 2 5 0 6 - 0 7 6 2 5 1 2 . 5 0 9 1 9 9 0 P l e n u m P u b l i s h i n g C o r p o r a t i o n


2/6

p ( D - u ) = p o ( D - - u o ) , p . p o = p o ( D - - u o ) ( u - - u o ) ,E - E o = 0 , 5 ( u - u o ) 2 + Po (u - uo) /,% D uo) + Q,

l o p \D = u + e , & = I - 7 - f j ( 5 )

F o r a g i v e n e q u a t i o n o f s t a t e ( 4) t h e s y s t e m ( 4) a n d ( 5) d e t e r m i n e s t h e l i n e o f t h e J o u g e tp o i n t s o n w h i c h a l l t h e t h e r m o d y n a m i c q u a n t i t i e s a n d v e l o c i t i e s d e p e n d o n 0 0. L e t u s i n t r o -d u c e t h e c o n c e pt o f a c r y s t a l l i n e o r g r e a t e s t p o s s i b l e e x p l o s i v e d e n s i t y P 0 K u n d e r n o r m a lc o n d i t i o n s a n d a n o r m a l d e t o n a t i o n w a v e v e l o c i t y D K i n a n e x p l o s i v e w i t h t h i s d e n s i ty . L e tu s u s e p 0 K a n d D K t o g o o v e r t o d i m e n s i o n l e s s v a r i a b l e s

A = Po/P,~. 6 = P /Po ~ . W = D/D~., o ( 6 )3 I = u,,'D~, Z = c/DK, H = P, po.D~,

* = ~ / v o , D ~ , J = E / D ~ , K = Q / D ~ .F o r s i m p l i c i t y w e s h a l l c o n s i d e r u 0 = 0, P 0 = 0 , E 0 = 0 i n ( 5 ) . A f t e r h a v i n g g o n e o v e r t ot h e d i m e n s i o n l e s s v a r i a b l e s ( 6) , t h e e q u a t i o n s ( 5) b e c o m e

6 = W A / ( W - - M ) , I I = W J [ A , ~r~ (7)] = o . 5 ~ ] z ~ + ~ , w = ~ , + z , z = ( ~ - ) s .L e t u s w r i t e ( 4) i n d i m e n s i o n l e s s v a r i a b l e s

I I = (~ t - - l ) S ] + O . ( 8 )The syst em of six equ ati ons (7) and (8) contai ns n ine fun ctio ns of A: E, 5, J, W, M, K, Z,y , 0. T h e s y s t e m b e c o m e s d e f i n i t e i f a n y t h r e e o f t h e n i n e m e n t i o n e d f u n c t i o n s o f A a r eg i v e n , i . e . , a r e d e f i n e d w i t h o u t u t i l i z a t i o n o f ( 7 ) a n d ( 8 ).

L e t u s i n t r o d u c e t h e i n d e x o f a d i a b a t i c i t y N( 0 1 n P / ( 9 )N = ~a -i~ /s"

G o i n g o v e r t o d i m e n s i o n l e s s q u a n t i t i e s a n d u s i n g ( 5 ) a n d ( 7) , w e o b t a i nN = Z 2 6 / I I . ( i 0 )

L e t u s e l i m i n a t e Z a n d M i n (7 ) a n d ( i 0 )6 = A ( N + l ) / N .

w 2J = + K ,2 (N + t) 21-I = W 2A ,'(N + 1),

s = \:Y+ I/L e t u s f i n d a n e x p r s s i o n f o r t h e d e r i v a t i v e ( 8 E / 3 6 ) S .e q u a t i o n

(ii)

T o do t hi s , w e u s e t h e t h e r m o d y n a m i c

I t f o l l o w s f r o m t h e m a i n t h e r m o d y n a m i c s e q u a t i o n s t h a t al o n g t h e i s e n t r o p eb . I \ = N-d ~ s 6--T._

L e t u s s u b s t i t u t e e x p r e s s i o n s f o r t he d e r i v a t i v e s

(12)

( 1 3 )

Or[) d(D d ?~ - = - ~ - 6 ,,' 7 E'(an)~ = ( y _ ~ )6

i n t o ( 1 2 ) a n d l e t u s e l i m i n a t e ( 8 J / 8 6 ) S b y u s i n g ( 1 3 )d ~ d y { y - - t ) r i ( W A " /~d -T + ( Y - - t ) J + 6 J ~ + 6 \ , v - 7 1 7

U s i n g ( 8 ) w e e l i m i n a t e J i n ( 1 6 ). W e c o n s e q u e n t l y o b t a i n= 0 .

( 14 )( t 5 )

( 1 6 )

7 6 3


3/6

d~ (I3 , ( ] ) - - N ) I 1 ( I I - - (D) d? = 0 .d6 b (5 + 'Z--"""""'Td 6 ( t 7 )A l l t h e q u a n t i t i e s o n t h e l i n e o f J o u g e t p o i n t s d e p e n d o n A.w i t h r e s p e c t t o 6 b y d i f f e r e n t i a t i o n w i t h r e s p e c t t o 5 i n (1 7 ).f e r e n t i a t e 6 w i t h r e s p e c t t o A :

d8 N ~ t h d NdA N N 2 dA "M u l t i p l y i n g ( 1 7) b y d S / d S , w e o b t a i n

L e t u s r e p l a c e d i f f e r e n t i a t i o nT o d o t h i s , w e f i r s t d i f -

( 1 8 )

dA 7 6 A, .,V z dA ~ ? - - t dAU s i n g ( 8 ) a n d ( 1 1 ) w e e x p r e s s r i n t e r m s o f E , 6 , N a n d K :

q ) = H - - ( ? - - t) A ( W2 = 2 K ( : V + l ) "~) ( 2 0 )2N ( :u + l )U s i n g ( 1 8 ) w e e l i m i n a t e r i n ( 1 7 ) . T o e l i m i n a t e d e / d 5 a l s o , w e p r o c e e d a s f o l l o w s . W e s u b -s t i t u t e t h e e x p r e s s i o n f o r 1I f r o m ( 1 1 ) i n t o ( 2 0 ) a n d d i f f e r e n t i a t e t h e e x p r e s s i o n o b t a i n e d

( ? - - t ) (W " ~ 2 K ( N z _ t ! 2 ) __ W A ( 2 N - - ? - - I ) dW__2 N ( N - - 1) ~ N ( N t t ) d A( W 2 A ( ? - - I - - . V ~ ~ I 7 - - ( ? - - t ) K A ' 2 " V N N dA

d(I) W 2d h N = - I( ? - - ~ ) ( N ') h v - dK

5 ( W 2 - - 2 K t N : I f ' ) __dr (21)2N ( N - : - t ~ dA"

w i t h r e s p e c t t o 5

N dA

S u b s t i t u t i n g ( 2 0) a n d ( 2 1 ) i n t o ( 19 ) , we o b t a i n t h e e q u a t i o n o f t h e J o u g e t l i n edW . , dKW A ( 2 N - - ? + 1 ) 7 - - ( ~ - - t ) ( N + I ) ~- A~ -~ + N W 2 ( ? - - N ) = 0 . ( 2 2 )

t h a t c o n t a i n s t h r e e f ~ n c t i o n s o f 5 ( W ( 5) , K ( A ) , N ( & ) ) t h a t c a n b e m e a s u r e d e x p e r i m e n t a l l y .A f t e r h a v i n g d e t e r m i n e d t h e f u n c t i o n s m e n t i o n e d , t h e e x p r e s s i o n ( 2 2) p e r m i t s f i n d i n g t h ed e p e n d e n c e

d W2 A NW ~ - - - N W z ( N - - 1 )?----- i - - d W d K ( 2 3 )

Wa -~f + (N . I) " -s -- NW ~

I t f o l l o w s f r o m ( 2 3 ) t h a t t h e r e a r e c e r t a i n c o n n e c t i o n s b e t w e e n W , N a n d K . S i n c e 7 -> 1 t h e nt h e n u m e r a t o r a n d d e n o m i n a t o r i n ( 2 3) s h o u l d v a n i s h s i m u l t a n e o u s l y . F o r m a n y e x p l o s i v e st h e s e W ( 5 ) a r e d e s c r i b e d w i t h s a t i s f a c t o r y a c c u r a c y b y t h e d e p e n d en c e

W = A ~ , ( 2 4 )w h e r e a = 0 . 7 . S u b s t i t u t i n g ( 2 4 ) i n t o ( 2 3 ) a n d i n t r o d u c i n g t h e n o t a t i o n m = 4 I- 2 a d K / d S , w e o b -t a i n

N ( N -- i -- 20 0 ( 5 )? = i + N _ a _ ( o ( N + t)2 9L e t u s i n t r o d u c e a n o t h e r s e t o f a d d i t i o n a l c o n s t r a i n t s o n t h e n a t u r e o f t he f u n c t i o n s

N ( 5 ) a n d m ( 5 ) . L e t u s d e m a n d t h a t N + ~ + 7 0 = c o n s t a s 5 + O. F o r s m a l l p w e c o n s i d e r t h ee q u a t i o n o f s t a t e ( 4 ) f o r 7 = ~ 0 - W e r e p r e s e n t p a n d E i n t h e f o r m o f t h e h o t a n d c o l d c o m -p o n e n t s

p = p T ( p , T ) + p . ~ ( p ) , E = E ~ ( o , T ) + E ~ ( p ) . ( 2 6 )L e t u s c o n s i d e r t h a t

U s i n g ( 2 6 ) a n d ( 2 7 ) t h e n ( 4 )

w h e r e

p ~ - - - - ( 7 0 - t ) p E ~ , E ~ = c r T , c v = c o n s t . ( 2 7 )is

p V = ( ~ , o l ) c , , r + / ( V ) , ( 2 8 )

/ ( V ) = V q o ( V ) + ( ? o - - i ) E ~ ( V ) ; V - - - - ' l _ / p .7 6 4


4/6

Let us consider the DP to be a mixt ure of gases under condit ions of mech anic al and thermalequi libri um and subject to the equations of state

PY~ = ( ] o ~ - t ) c y s t + / ~ ( ~ ) . ( 2 9 )Using the a dditivit y of V and E in the mixture

I " = ~ z J - i . E = ~ ( 3 0 )( ~ i i s t h e m a s s c o n c e n t r a t i o n o f t h e i - t h c o m p o n e n t ) , w e w r i t e ( 2 7 ) - ( 2 9 ) i n t h e fo r m

(?o - ! ) cv r + / ( Y ) = x~ [(yo~ ~)cv ~ + ( vo] ~ ( ~ i )c v T + E ~ ( V ) = ~ [ - - (V i ) ] . ( 3 2 )i

For T = 0 a relation follows from (31) and (32) between the cold c omponen ts of the mixtu reequatio n of state and the compone nts

/ r = ~ . ( Y + Ex( v )= ~ ( 3 3 ){ {It follows from (30)-(33) that for any value of T there should be

( % - - ] ) c v = ~ ( % i - - ! ) ( 3 4 )iCV = ~ (3 5 )

Therefore, to determine the X0 of the mixtur e it is neces sary to know the ~i, 7i and cvi ofeach component. Such data are presen ted in [i, 7, 8] for a number of explosives. Accordi ngto differ ent theories, the mass concen tratio ns of the DP componen ts are distinct. Conse-quently, we limit ourselve s to consid eratio n of the average concent rations. In such an ap-p r o a c h

" o = t + ( ~ . ~ ( ( Y ' i - - l ) X ~ C v ~ ' ~-a)/(~ 0 . (36)

w /~ a

j

0 ,2 iE I Ir 64 ~ s ~ e 4

N ~ . b

t a o ~ 1 7 6

o 7 A 2 . x0 0,25 0~50 0,75 A

o, o9

o , 0 7

o, 05 o ,25

Cc 0 0

o o o A ~o +

o

/ ~ A A o A ~0 00 0 0

0,'50 0/75 AFig. I

7 6 5


5/6

T A B L E ih00~, g/cm D g , k m / s e ~ Explosive Pom g/cm Dg, km/secxplosive

Trot yl i,663 7,15 TEN i,770 8,35Tet ryl i,730 7, 74 Hexogen i,820 8,80

For t ro tyl 70 = 1 .373 , which is c lo se to the value 7o = 1 .3"78 for hexogene. Sinc e this d i f -f e r e n c e l i e s w i t h i n t h e l i m i t s o f e r r o r s a l l o w e d f o r a v e r a g i n g o f ~ i , t h e n we t a k e t h e s i n g l eval ue 7o = 1 .375 for t ro tyl and hexogene that i s c lo se to 70 = 1 .33 taken in [4] for a num-b e r o f m i s c i b l e e x p l o s i v e s .

L i t t l e d a t a o n t h e c a l o r i f i c v a l u e s o f e x p l o s i v e s a r e c o n t a i n e d in t h e l i t e r a t u r e . E x-ac t ly as r esu l t s on N(A) , t hey have a no t i c eab le sp rea d . Le t us use da ta f rom [1 , 3 -9 ] byrepres en t ing them in d imens ion les s fo rm and approx imat in g them by s ing l e d imens ion les s de -pendences on A fo r d i f f e r e n t exp los ives . I t f o l low s f rom (22) and (24) tha t a s p + 0 , A0 and N + 7 ~ ~0 th er e sh ou ld be

(37)F u r t h e r m o r e , f r o m t h e c o n d i t i o n o f f i n i t e n e s s o f y , i .e . , f r o m t h e c o n d i t i o n o f s i m u l t a n e o u sd i s a p p e a r a n c e o f t h e n u m e r a t o r a n d d e n o m i n a t o r i n ( 2 5 ), t h e r e f o l l o w s t h a t t h e r e s h o u l d b e

i for Iu = i + 2~. (38)= O , = 4 ( i + a )M o r e o v e r , w e d e m a n d t h a t w s t i l l s a t i s f y t w o c o n d i t i o n s f o r 5 = i:

1~ 52~-IodA = o = 0,~ ~ ( 390

w h e r e K K i s t h e v a l u e o f th e d i m e n s i o n l e s s c a l o r i c v a l u e of t h e e x p l o s i v e f o r 5 = i. T h ec o n d i t i o n s ( 3 9) a r e s u g g e s t e d a f t e r a n a n a l ys i s o f t h e e x p e r i m e n t a l d a t a o n c a l o r i c v a l u e so f e x p l o s i v e s . C o n d i t i o n s ( 3 7 ) - (3 9 ) a nd e q u a Z i o n ( 22 ) s u b s t a n t i a l l y c o n s t r a i n t h e c l a s s off u n c t i o n s t h a t c a n b e u s e d t o a p p r o x i m a t e e x p e r i m e n t a l d a t a o n K ( 5 ) a n d N ( 5 ) .

B e c a u s e o f i t s a w k w a r d n e s s w e o m i t t h e p r o c e d u r e f o r t he n u m e r i c a l s o l u t i o n o f ( 2 2) w i t hc o n s e r v a t i o n o f t h e c o n s t r a i n t s o n w (A ) a n d 7 ( 5 ) l i s t e d a b o v e a n d w i t h s i m u l t a n e o u s o p t i m i -z a t i o n o f t h e a p p r o x i m a t i o n s o f t h e e x p e r i m e n t a l d a t a on t he b e h a v i o r of N ( 5 ) a n d K( A ). W ea p p r o x i m a t e t h e t a b u l a t e d d e p e n d e n c e s o b t a i n e d , i n t u rn , b y t h e f u n c t i o n s

{ ~ f o r X > ~ ( 4 0 )? = ?o + (? -- - ?o) x( 3- -3 x+ x 2) for xi , ( 41)

t o for x ~ t ,whe re x = 6/6,; A = 0.0139; 70 = 1.375; y~ = 1.667; 6, = 0.35; m = 2.284.

F o r a f i n a l c o n s t r u c t i o n o f t h e D P e q u a t i o n o f s t a t e f o r a s p e c i f i c c o m p a c t e x p l o s i v et h e p a r a m e t e r s P 0 K a n d D K m u s t b e d e t e r m i n e d ( t h e y a r e p r e s e n t e d i n t h e t a b l e f o r c e r t a i ne x p l o s i v e s ) . F o r m i s c i b l e e x p l o s i v e s t h e v a l u e s o f P a K a n d D K a r e e x p r e s s e d b y us i n g t h es i m p l e e q u a t i o n s

A c o m p a r i s o n o f t h e f u n c t i o n s W ( A ) ( a ) , N (A ) ( b) a n d K ( A ) ( c ) ( l i n e s ) w i t h e x p e r i m e n t a ldata from [i, 3-9] is pre sen ted in the figure: i) trotyl; 2) hexoge n; 3) TEN; 4) tetryl.

i .

2.

L I T E R A T U R E C I T E DF . A . B a u m , K . P. S t a n y u k o v i c h , a n d B. I . S h e k h t e r , P h y s i c s o f E x p l o s i o n [ i n R u s s i a n ]F i z m a t g i z , M o s c o w ( 1 95 9 ) .L . D. L a n d a u a n d K . P . S t a n y u k o v i c h ~ D o k l . A k a d . N a u k S S S R , 4 6 , 3 9 9 ( 1 9 4 5 ) .

766


6/6

3 . K . J o h a n n s o n a n d P . P e r s o n , E x p l o s i v e D e t O n a t i o n s [ R u s s i a n t r a n s l a t i o n ] , M i r , M o s c o w( 1 9 7 3 ) .

4 . M . V . Z h e r n o k l e t o v , V o N . Z u b a r e v , a n d G . S . T e l e g i n , P r i k l . M e k h . T e kh o F i z ., N o. 4( 1969 ) .5 o V . N . Z u b a r e v , P r i k l . M e k h . T e k h . F i z . , N o. 2 ( 1 9 6 5 ).6. N . M . K u z n e t s o v a n d K. K. S h v e d o v , F i z . G o r e n i y a V z r y v a , ~ , N o . 4 , 8 5 ( 19 6 5 ) .7 . A . N . D r e m i n , S . D . S a v r o v , V . S . T r o f i m o v , e t a l o , D e t o n a t i o n W a v e s a n d C o n d e n s e d

M e d i a [ i n R u s s i a n ] , N a u k a , M o s c o w ( 1 9 7 0 ) .8 . B . Y a . S v e t l o v a n d N . B . Y a r e m e n k o , T h e o r y a n d P r o p e r t i e s o f I n d u s t r i a l E x p l o s i v e s [ i n

R u s s i a n ] , N e d r a , M o s c o w ( 1 9 7 3 ) .9. R . M i l l e r , " A p p r o x i m a t e e q u a t i o n s o f s t a t e o f d e t o n a t i o n p r o d u c t s , " i n: D e t o n a t i o n a ndT w o - P h a s e F l o w [ R u s s i a n t r a n s l a t i o n ] , M i r , M o s c o w ( 1 9 6 6 ).

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