Partial structure factors of molten salts

638

Journal of Non-Crystalline Solids 117/118 (1990) 638-641 North-Holland

PARTIAL STRUCTURE FACTORSOF MOLTEN SALTS Yoshiyuki SHIRAKAWA, Shigeru TAMAKI, Masatoshi SAITO,+ ShGzi HARADA++ and S h i n ' i c h i TAKEDA* Department of Physics, Faculty of Science, Niigata University, Niigata 950-21, Japan + Graduate School of Science and Technology, Niigata University, Niigata 950-21, Japan ++ Faculty of Engineering, Niigata University, Niigata 950-21, Japan * College of General Education, Kyushu University, Fukuoka 810, Japan The p a r t i a l structure factors of monovalent molten salts such as NaCI, KCl, RbCl, CsCI and AgCI are estimated by the combination of the X-ray and neutron d i f f r a c t i o n data and of a unified relation between the p a r t i a l structure factors S÷+(q) and S _(q). The obtained results are q u a l i t a t i v e l y and s e m i - q u a n t i t a t i v e l y agreed with those derived by the isotope enrichment method. I.

INTRODUCTION In

recent

mixtures

2. METHODOF DERIVATION OF PARTIAL STRUCTURE

years,

molten

salts

and

their

are l i q u i d of interests from both

FACTORS

the

For

these systems, there are two s i g n i f i c a n t

t h e o r e t i c a l and p r a c ti c a l point of view, because

properties

they

structure factors as follows, i ) the p e a k height

represent

cations

strongly

and

anions,

coupled and

systems

of

of

considerable

can

be

found

importance in technology. In t h i s regard, i t has

structure factors

long and widely been carried out the studies

on

to

the

al

structures of molten salts.

have

established

derive

an

the three p a r t i a l structure

isotope

enrichment

diffraction

but

virtually

technique I,

this

effective

Therefore

in

method f o r

a

deriving

structure factors dominant

KCl,

factors

In

to the to

A beautiful

method is

factors

samples.

but

partial extract

which is,

S__

result

is

obtained.

of the

partial

structure

for molten NaCl obtained by Biggin

and

Enderby3 is very i n s t r u c t i v e to progress a

more

q u a n t i t a t i v e r e l a t i o n between S++(q) and S__(q).

structure

Using t h e i r results, we have found the following relation.

the

partial

S i j ( q ) of molten salts with

ionicity,

and

partial

factors of l i k e ion pairs

and

such as

e.g,,

NaCl,

(S__ - I)

= ( r

S__(q) at the

at least,

relation

p e a k positions

v a l i d fo r the systems of a

small

but f i n i t e amount of penetration

like

species i n t o the f i r s t coordination

by

as discussed by Enderby. 2

the shell

)2(S++

_ I)

(I)

r+

R b C l , and CsCI, using the observed X-ray S++(q)

the

closely related

general

and neutron d i f f r a c t i o n s and a u n i f i e d fo r

S++(q)

neutron

restricted

of

are

partial

the e n t i r e s i m i l a r i t y in the p a r t i a l

structure

by

the

the ionic r a d i i , and

ii)

method to

experimental

complementary

factors, we attempt a

Enderby et

experimental

for

where r+ is the ionic radius of cation and r

is

the

We

ionic radius

assume, for

a

the

salts like

systems of

in

anion,

respectively.

that this r e l a t i o n is v a l i d simple

monovalent molten

which the p o s i t i v e and negative

to

nearest

of

priori,

be next to each other neighbour

distances

and are

ions

hence the located

at

0

about r=3A. 2 On

0022-3093/90/$03.50 (~) Elsevier Science Publishers B.V. (North-Holland)

the

other

hand,

the

observed

total

Y. Shirakawa et al. / Partial structure factors

structure factor of the molten salts by diffraction

is

represented

by

the

neutron following

S~ota I =

are

ascribed

and

scattering

(2) ( c+b+ + c b

)2

In [B(q)] the errors

introduced by the changes of effect,

22 c+b+S++ + c2b2S__ + 2c+c_b+b_S+_

639

in [B(q)] and [ S ( q ) ] . which

form,

ofmolten salts

the

X-ray form

to

the

penetration

uncertainty in

length.

To

the

correct

refer

to

are

factor neutron

these

conditions,

we

the

technique by

McGreevy and M i t c h e l l . 4 The

ill

correction basic

algorithm is as follows.

where

Sij's

b+, b_: scattering length c+, c_: concentration are the Faber-Ziman type partial

structure factors. The total structure factor by X-ray d i f f r a c t i o n is expressed by the following form.

Separation [S(q)] . . . . . . . . . . . . . . .

-+[a~j]

I Smoothing

Comparison Recombination

[S(q)]'÷ ............... c2#2~ +-+~++ + c2f2S . . . + .2c+c . f+f . . S+ S~otal =

+ [Aij]'

Transformation 1 +

(3)

[gij]

( c+f+ + c_f_ )2 where f+ and f_ are the form factors of ions and both depend on wave vector q. Using those equation ( I ) , (2) and (3), and the experimental data observed by the neutron and X-ray d i f f r a c t i o n s , the Faber-Ziman type partial structure factors can be obtained as follows. The set of equations to be solved is

klm] s+,1 S"otal1 -r2+ 0

k' r2 _

I'

m'

S__

S+_

SXtotal r2-r 2

+

I

"""

3 t

o -I

(4) 0 + u~-1

where

k = c~b~/( c+b+ + c b 1 = c2b2/( c+b+ + c b

)2 )2

-2 -3

I

0

m = 2c+c+b+b_/( c+b+ + c_b_ )2

4

6

8

10

q (IlA)

k' : c~f~l( c+f+ + c_f_ )2 I' = c 2 f 2 / (

c+f+ + c_f_ )2

m' = 2c+c_f+f_/( c+f+ + c_f_ )2 which may be rewritten as [B(q)][S(q)] = [ S t o t a l ( q ) ] (5) In practice, the separation of partial structure factors from the observed total structure factors is extremely sensitive to the errors

FIGURE l Partial structure factors f o r molten NaCl.2 Full curve, derived from isotope enrichment; broken curve, calculated from present method The

procedure was repeated u n t i l the

converges. molten NaCl

The by

p a r t i a l structure this

algorithm

factors

for

method are shown in F i g . l

Y. Shirakawa et al. / Partial structure factors of molten salts

640

and

their

transformations

distribution Comparing

functions

to

are

our p a r t i a l

the

radial

straightforward.

structure

those of

Enderby e t a l ,

justified

as to be good enough.

factors with

the present method is

"t" 03

i

3. EXTENSION TO OTHER SYSTEMS Using neutron

diffraction

partial KCl,

2

the data measured by the X-ray and the structure

RbCl,

studies 2'5'6'7'8, factors

CsCl

are

Sij(q)

the

for

molten

c a l c u l a t e d and they

shown in F i g s . 2 ,

3, and 4, r e s p e c t i v e l y .

transformations

to

functions

for

the

radial

derived

-2

o-

2

4 q (I/A)

Their

distribution

molten KCl are shown

factors

0

are

in

Fig.5,

These r e s u l t s are almost agreed w i t h the p a r t i a l structure

1 i

+ u3 - 1

by

the

isotope

FIGURE 3 P a r t i a l s t r u c t u r e f a c t o r s f o r molten RbCI. 7 Full curve, d e r i v e d from i s o t o p e enrichment; broken curve, c a l c u l a t e d from present method

enrichment method. 2 ' 7 ' 8 ' 9

2 3

+

1

2 0 ÷

I

o -I

2

4 3 2~t l

I

I 4-

o

0

2

6

4, qCl/A)

-I

8

2 I

,+

FIGURE 4 P a r t i a l s t r u c t u r e f a c t o r s f o r molten CsCI. 8 Full curve, d e r i v e d from i s o t o p e enrichment; broken curve, c a l c u l a t e d from present method

0

-2 i 0

i

2

J

J

i

i

~ 6 q(I/A)

i

i

8

, 10

The a t t e n t i o n is ,however, necessary f o r the molten ionic

FIGURE 2 P a r t i a l s t r u c t u r e f a c t o r s f o r molten KCI. 9 Full curve, d e r i v e d from i s o t o p e enrichment; broken curve, c a l c u l a t e d from present method

AgCl p a r t i a l radius

r+

of

structure factors. silver

ion

s m a l l e r than 0,98~ as an i n i t i a l the p a r t i a l This

the

taken

condition,

the as then

s t r u c t u r e f a c t o r s are not converged.

r e s u l t may suggest t h a t the

of Ag+ i s l a r g e r The

is

If

ionic

radius

than 0.98~ in the molten AgCI.

present method might be

applicable

for

monovalent molten s a l t s in which the u n l i k e

Y. Shirakawa et al. / Partial structure factors of molten salts

ions l i k e to be next to each other and the

like

charges

pair

repel

distribution quite

each other and the p a r t i a l function

similar.

enrich

In

g~_~(r) and

particular if

g__(r) the

are

isotope

factors

of molten

salts,

then

the

present method is useful. In

order

structure however,

to obtain the factors

by

plausible

the

partial

present

method,

the s u f f i c i e n t accuracies are required

for the X-ray and the neutron d i f f r a c t i o n the

data.

the present stage is somewhat d i f f i c u l t equation

monovalent

(I)

molten

is a good r e l a t i o n

for

salts.

will

This point

why the be

solved in future.

0

6. H.A. Levy, P.A. Agron, M.A. Bredig and M.D.Danford, Ann. New York Acad. Sci. Art I I , 79 (1969) 762 7. E.W.J.Mitchell, P.F.J.Poncet and R.J.Stewart, Phil.Mag., 34 (1976) 721

method were unable to derive the p a r t i a l

structure

At

641

o

i

I

2

I 3

I ~

I 5

k 6

I 7

I 8

L __ 9 10

r(~,)

FIGURE 5 Pair d i s t r i b u t i o n functions derived from present method for molten KCI. Full curve, g+_; broken curve, g++ ; dotted curve, g__

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P.A. Egelstaff,

2. J.EoEnderby, Contemp. Phys., 24 (1983) 561 3. S.Biggin.

J.E.Enderby,

J.Phys. C, 15 (1982)

L305 4. R.L.McGreevy, (1982) 5537

E.W.J.Mitchell,

J.Phys. C, 15

5. H.Ohno, K.Furukawa, J.Chem. Soc., Trans. I, 77 (1981) 1981

Faraday

8. J.Locke, S.Messoloras, R.a. Stewart, RoL.McGreevy and E.W.J.Mitchell, Phil.Mag., 51 (1985) 301 9. J.Y.Derrien, (1975) 191

J.Duppy,

J.de

Physique,

36