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THE STRUCTURE OF DENSE ALKALI HALIDE MELTS
M. Ross, F. Rogers
To cite this version:
M. Ross, F. Rogers. THE STRUCTURE OF DENSE ALKALI HALIDE MELTS. Journal de Physique
Colloques, 1984, 45 (C8), pp.C8-229-C8-233. �10.1051/jphyscol:1984844�. �jpa-00224345�
JOURNAL DE PHYSIQUE
Colloque C8, supplément au n°l 1, Tome H5, novembre 1984 page C8-229
THE S T R U C T U R E OF D E N S E ALKALI H A L I D E M E L T S
M. Ross and F.J. Rogers
University of California, Lawrence Livermore National Laboratory, Livermore, California 94550, U.S.A.
Résumé - On calcule la distribution des paires ion-ion dans les halides alcali qui ont été fondus par un choc. On démontre que le liquide change, progressivement de structure sous l'effet de pression: il évolue à partir d'une structure comparable au NaCl vers un état semblable à celui d'un gaz rare contenant environ douze atomes avoisinants dont certains ont une charge positive et d'autres négative.
Abstract - Calculations of the ion-ion pair distribution functions in shock melted alkali halides show that the melt undergoes a gradual pressure induced structural change from an open NaCl-like structure to one that has a rare gas-like arrangement containing about twelve neighbors of mixed charge.
I. INTRODUCTION
The unique characteristic of Shockwave experiments is that they can be used to explore states of matter at very high pressure and temperature that are inaccessible by other techniques. This property makes it valuable for studying melting at extreme conditions. The usefulness of shock melting data is not that it simply represents more data but that it greatly extends the range of conditions over which to test the applicability of melting laws and concepts. The availability of shock melting data for a number of alkali halides makes it possible to undertake a systematic study.
Figure 1 - Temperature-volume curve for Csl. The sharp break at 3500 K is due to melting. Theoretical Hugoniot of reference 6 is based on a model of the solid which works well below melting.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984844
C8-230 JOURNAL DE PHYSIQUE
When a substance melts a t atmospheric pressure t h e added energy does n o t l e a d t o a r i s e i n temperature u n t i l t h e process has been completed. Under shock compression t h e pressure-temperature p a t h passes through t h e m e l t i n g curve. T h i s f e a t u r e was f i r s t observed by Kormer, e t a1 .l i n shock
temperature measurements on NaCl and KC1. S i m i l a r z s x t s f o r CsI, shown i n F i g . 1, have r e c e n t l y been obtained by Radousky, Ross, M i t c h e l l and N e l l i s2 a t Livermore.
1 1 . CALCULATIONS
X-ray s c a t t e r i n g and neutron d i f f r a c t i o n experiments coupled w i t h Monte C a r l o and hypernetted c h a i n (HNC) equation c a l c u l a t i o n s have e s t a b l i s h e d t h a t a t atmospheric pressure a l k a l i h a l i d e m e l t s a r e c h a r a c t e r i z e d by a r e l a t i v e l y open NaC1-like s t r u c t u r e c o n t a i n i n g about 5 t o 6 atoms i n t h e nearest neighbor s h e l l .3 The a p p l i c a t i o n o f pressure i s be1 ieved t o r e s u l t i n a gradual increase i n t h e c o o r d i n a t i o n number. But v e r y l i t t l e i s known e x p e r i m e n t a l l y .
I n t h e p r e s e n t paper we use t h e hypernetted c h a i n equation (HNC) t o o b t a i n t h e p a i r d i s t r i b u t i o n f u n c t i o n s f o r molten CsI. I n a d d i t i o n we have made c a l c u l a t i o n s f o r several o t h e r s a l t s (CsBr, KBr, KC1, NaCL and L i F ) a t t h e pressures and temperatures f o r which shock m e l t i n g has been reported.4
The HNC equation i s now w i d e l y used f o r c a l c u l a t i n g t h e p r o p e r t i e s o f i o n i c f l uids.5 The r e s u l t s demonstrate t h a t f o r r e a l i s t i c p o t e n t i a l s t h e HNC method p r e d i c t s p a i r d i s t r i b u t i o n f u n c t i o n s t h a t are i n good agreement w i t h experiments. HNC c a l c u l a t i o n s were made u s i n g an exponential s i x f u n c t i o n t o r e p r e s e n t t h e p a i r - p o t e n t i a l f o r t h e i n e r t gas xenon and f o r C s I u s i n g an e x p o n e n t i a l - s i x w i t h a coulomb term added. The xenon r e s u l t s p r o v i d e a r e f e r e n c e a g a i n s t which t o judge t h e occurence o f a s t r u c t u r a l change i n C s I t o an i n e r t g a s - l i k e s t r u c t u r e .
The f i r s t p o t e n t i a l ( 1 ) i s t h e simple xenon-1 i k e e x p o n e n t i a l - s i x (X6) used by Radousky,
z.
t o c a l c u l a t e t h e shock Hugoniot and estimate t h e C s I f r e e z i n g curve;where €/k = 235 K, a = 13.0 and r* = 4.408. k i s Boltzmann's constant.
The parameters have been chosen t o f i t t h e t h e o r e t i c a l 0 K CsI i s o t h e r m o f Aidun
&
d . 6 The omission o f t h e coulomb term makes i t d i f f i c u l t t o f i t b o t h t h e l o w and h i g h pressure p a r t o f t h e isotherm. The present f i t i s biased toward f i t t i n g t h e h i g h pressure p a r t .F o r t h e second p o t e n t i a l ( 2 ) we have added a coulomb i n t e r a c t i o n term t o
(7
I
0where 21 and 22 a r e t h e i o n charges.
F i g u r e 2a shows t h e p a r t i a l d i s t r i b u t i o n f u n c t i o n s o f l i q u i d CsI c a l c u l a t e d a t i t s normal m e l t i n g temperature The atomic separations i n t h e f i g u r e a r e p l o t t e d i n u n i t s o f r / a where a i s t h e mean i o n sphere radius, o r a = ( 3 / 4 a ~ / ~ ) 1 / 3 . For these p o t e n t i a l s g++ = g--. The f i g u r e ( 2 a )
e x h i b i t s t h e c h a r a c t e r i s t i c a l k a l i h a l i d e arrangement o f a l t e r n a t i n g s h e l l s of u n l i k e and l i k e charge. F i g u r e 2b compares t h e t o t a l p a i r d i s t r i b u t i o n f u n c t i o n , g ( r ! = (g++(r) + g+-(r))/2, o f CsI w i t h t h a t f o r t h e xenon-like f l u i d ( p o t e n t l a 1 1 ). The f i g u r e shows two v e r y d i f f e r e n t s t r u c t u r e s . The reader may have noted t h a t t h e r e i s a shoulder i n t h e f i r s t g++ peak ( F i g . 2a) near ( r / a ) = 2.3. T h i s has been previous1 observed and i s t h e s t a r t o f a pressure induced s p l i t t i n g i n t o two new peaks.
y
5 I I I
P
4 - CSI -
g+- V = 40.89 cm3/mol-atom T = 9 0 0 K
3 - -
-
m2
-
m2 - -
1 - I
0 1 1 1 I I
1 2 3 4 5
F i g u r e 2
-
( a ) P a r t i a l d i s t r i b u t i o n f u n c t i o n s f o r CsI; ( b ) Comparison o f t o t a l d i s t r i b u t i o n f u n c t i o n s f o r CsI and Xe.As t h e pressure along t h e f r e e z i n g l i n e increases t h e s p l i t t i n g o f t h e g++ peak becomes more pronounced. I n c r e a s i n g t h e pressure t o about 300 kbar (3650 K) t o near t h e observed shock f r e e z i n g p o i n t s h i f t s t h e f i r s t g++ peak t o i n s i d e t h e g+- f i r s t peak envelope (Fig. 3a). As a r e s u l t t h e t o t a l d i s t r i b u t i o n f u n c t i o n s o f Xe and CsI ( F i g . 3b) a r e now v i r t u a l l y i d e n t i c a l . Each i o n has about 12 nearest neighbors, as i n a close-packed system, of which seven are o p p o s i t e l y charged and f i v e have t h e same charge. F i g u r e 3a
demonstrates t h a t t h e o p p o s i t e l y charged neighbors on t h e average approach each o t h e r more c l o s e l y than do i o n s w i t h t h e same charge. But a considerable degree o f i n t e r p e n e t r a t i o n e x i s t s . A t pressures up t o 700 kbar no i m p o r t a n t changes were observed.
C a l c u l a t i o n s o f t h e p a i r - d i s t r i b u t i o n f u n c t i o n made f o r shock me1 t e d CsBr (540 kbar and 4650 K), KBr (400 kbar and 4000 K) and KC1 (480 kbar and 4100 K) a t t h e pressures and temperatures r e p o r t e d by Kormer show r e s u l t s t h a t a r e s i m i l a r t o those f o r CsI. These c a l c u l a t i o n s were made using Tosi-Fumi p o t e n t i a l s . 8 I n t h e case o f NaCl (700 kbar and 3700 K) t h e conversion t o a dense s t a t e i s o n l y p a r t i a l l y complete. I n t h e case o f L i F (2.8 Mbar and 6000 K) o n l y a small change i n t h e s t r u c t u r e has occurred.
JOURNAL DE PHYSIQUE
\
CSI V = 18.0 cm3/mol-atomk 1
g+- T = 3650 Krla rla
F i g u r e 3
-
( a ) P a r t i a l d i s t r i b u t i o n f u n c t i o n s f o r CsI; ( b ) Comparison o f t o t a l d i s t r i b u t i o n f u n c t i o n s f o r CsI and Xe.These r e s u l t s demonstrate t h a t a t s u f f i c i e n t l y h i g h d e n s i t y t h e s h o r t range r e p u l s i v e f o r c e s w i l l be dominant over t h e l o n g range a t t r a c t i o n . Fig.
4 compares t h e r a t i o o f t h e exp-6 c o n t r i b u t i o n t o t h e pressure t o t h a t o f t h e Coulomb c o n t r i b u t i o n i s p l o t t e d versus volume. Near t h e pressure of 300 kbar, where t h e Hugoniot e n t e r s t h e f l u i d , t h e c o n t r i b u t i o n o f t h e exp-6 i s an order o f magnitude l a r g e r than t h a t o f t h e Coulomb term. Thus t h e p r o p e r t i e s are dominated by t h e s t r o n g r e p u l s i v e f o r c e s and t h e l i q u i d adopts a xenon o r hard s p h e r e - l i k e s t r u c t u r e . The a p p l i c a t i o n o f pressure has t h e e f f e c t of " d i a l i n g down," o r decoupling t h e i n f l u e n c e o f t h e coulomb forces.
F i g u r e 4
-
The r a t i o o f t h e i n e r t gas c o n t r i b u t i o n o f t h e t o t a l pressure t o t h e coulomb c o n t r i b u t i o n as a f u n c t i o n o f t o t a l pressure along t h e estimated f r e e z i n g 1 ine.111. DISCUSSION
The p r e s e n t r e s u l t s demonstrate t h e e x i s t e n c e o f a g r a d u a l
p r e s s u r e - i n d u c e d s h i f t i n t h e s t r u c t u r e of an a l k a l i h a l i d e m e l t f r o m an open NaC1-like arrangement t o one c h a r a c t e r i s t i c o f a s i m p l e n o n - i o n i c f l u i d . T h i s e f f e c t i s caused b y t h e growing dominance o f t h e r e p u l s i v e f o r c e s and i s g r e a t e s t i n t h e l a r g e r i o n s where t h e Coulomb f o r c e s a r e r e l a t i v e l y weaker compared t o t h e r e p u l s i v e f o r c e s . Thus, C s I i s a f a v o r a b l e case f o r f u r t h e r s t u d y . The r e s u l t s have i m p o r t a n t consequences f o r t h e t h e o r y o f m e l t i n g .
The Lindemann approach t o m e l t i n g t a k e s t h e v i e w t h a t i f we were a b l e t o see t h e m e l t i n g t r a n s i t i o n on a m i c r o s c o p i c l e v e l , we would always see t h e same s c a l e d p i c t u r e i n t h e s o l i d . A t d i f f e r e n t temperatures, because of t h e i r a b i l i t y t o i n t e r p e n e t r a t e each o t h e r ' s e l e c t r o n i c cores, t h e atoms w i l l have d i f f e r e n t e f f e c t i v e s i z e s . However, f o r a g i v e n c r y s t a l s t r u c t u r e , t h e r a t i o s o f t h e i r e f f e c t i v e volumes t o t h e t o t a l volume o f t h e system w i l l always r e m a i n c o n s t a n t a t a l l p o i n t s a l o n g t h e m e l t i n g curve, and t h e i r r e l a t i v e arrangements i n space w i l l always remain t h e same. Consequently, t h e p i c t u r e s a l o n g t h e m e l t i n g c u r v e w i l l always be i d e n t i c a l i f p r o p e r l y scaled. T h i s v i e w o f m e l t i n g does n o t c o r r e s p o n d t o t h e s i t u a t i o n i n t h e a l k a l i h a l i d e s and we c o n c l u d e t h a t t h e s e s i m p l e m e l t i n g l a w s w i l l n o t b e a p p l i c a b l e t o t h e s e m a t e r i a l s .
A second i m p o r t a n t f e a t u r e concerns t h e shapes o f m e l t i n g curves.
~ a l l o n g has c o n s i d e r e d t h e p o s s i b i l i t y t h a t t h e shapes o f m e l t i n g c u r v e s c o u l d be u n d e r s t o o d b y a c o n t i n u o u s p r e s s u r e induced change i n t h e m e l t t o a more c l o s e l y packed s t a t e . T a l l o n e x p l a i n s t h e c u r v a t u r e and p r o j e c t e d occurence of t h e maxima i n terms of a c o n t i n u o u s t r a n s i t i o n i n t h e m e l t f r o m t h e l o w e r d e n s i t y s i x - c o o r d i n a t e d s t a t e t o a h i g h e r d e n s i t y e i g h t - c o o r d i n a t e d s t a t e a t h i g h e r p r e s s u r e . H i s c o n c l u s i o n s a r e q e n e r a l l y c o n f i r m e d by t h e p r e s e n t r e s u l t s i n t h e sense t h a t we a l s o b e l i e v e t h a t t h e f l u i d becomes more d e n s e l y packed. However, i t i s n o t p o s s i b l e t o c o n c l u d e on t h e b a s i s o f HNC c a l c u l a t i o n s as t o what t h e f l u i d s t r u c t u r e s are. T h i s w i l l r e q u i r e d e t a i l e d computer s i m u l a t i o n s b y Monte C a r l o o r mol e c u l a r dynamics.
R e c e n t l y s e v e r a l a u t h o r s have suggested t h a t l i q u i d s i l i c a t e s and magmas undergo an i n c r e a s e i n c o o r d i n a t i o n number w i t h i n c r e a s i n g p r e s s u r e . l 0 , l l ,I2 Thus, i t appears t h a t t h e phenomena observed i n a l k a l i h a l i d e s i s n o t i s o l a t e d b u t i s a more g e n e r a l f e a t u r e of i o n i c m a t e r i a l s t h a t has i m p o r t a n t consequences f o r geophysics.
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