Structural study of supercritical carbon dioxide by neutron diffraction

RBOPII RUILRRIA ELSEVIER

Fluid Phase Equilibria 104 (1995) 291-304

Structural

study

of

supercritical

carbon

dioxide

b~

neutron diffraction

Ryo

I s h i i a, S u s u m u

Masakatsu

O k a z a k i a, O s a m u O d a w a r a a,

M i s a w a b and T o s h i h a r u

aTokyo Institute 227(Japan)

Isao O k a d a a,

Fukunaga c

of Technology,

Nagatsuta,

Midori-ku,

Yokohama

bDepartment of Chemistry, Faculty of Science, Niigata University, Igarashi-Ninomachi, Niigata 950-21(Japan) CDepartment of Crystalline Materials Science, Furo-cho, Chikusa-ku, Nagoya 464(Japan) Keywords:

experiments,

structure,

neutron

data,

supercritical

Nagoya University,

fluid,

carbon

dioxide,

diffraction

R e c e i v e d 2 6 M a y 1 9 9 4 ; a c c e p t e d i n f i n a ] ~ llAugust1994

ABSTRACT

Structure MPa, For

of

9.7 M P a

supercritical

and

comparison,

been

studied.

ent

of

cal

state.

small

the

point present

by

The

that

The

state

is,

(=0.3

by n e u t r o n K and

neutron

diffraction result

is l a r g e

293

shows

This

by

solid

or

a large

at

9.2

diffraction. MPa

has

also

independ-

supercriti-

increase

in t h e

is in c o n t r a s t

to that

state

far from the c r i t i c a l

Bausenwein

substantiates

1.0

K and

is p r a c t i c a l l y

feature

in the r e g i o n

320

at

liquid,

factor

at

studied

structure

gaseous,

A-l).

dioxide

for the s u p e r c r i t i c a l

diffraction

the densities

has b e e n

structure

region found

MPa

gaseous

intramolecular

state,

angle

previously

10.2 the

carbon

et

that

investigated

0378-3812/95/$09.50 © 1995 - Elsevier Science B.V. All rights reserved SSD10378-3812 (94) 02655-6

al.

the .

(1992).

fluctuation

The of

292

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304

INTRODUCTION

Supercritical critical of

liquids

even

fluids

point

with

have

in

that

a small

creasing

density,

prevails

changes

force

is

of t h i s

of t h e

further

Carbon

Large

known

one

one

to the

from

and

those

markedly

region,

with

attractive

where

density

to be

g c m -3.

are,

development

a

in-

force

repulsive

fluctuation

due

to

of t h e c h a r a c t e r i s t i c s

state

can

and

with

condensed

investigations

by means

for

as

be r a t h e r

been

application

readily

the

and

X-ray

MPa

a

as

solvent. the

criti-

and

Pc=0.4661

forms

a simple

how

of

only

the m o l e c u l e s

the

for

Carlo

range

liquid

and

experimental

and n e u t r o n

Monte

well

intermediate

structure

of

as

attained,

to l e a r n

not

Thus,

and d y n a m i c s .

the molecule

a target

these

is u s e f u l

a supercritical

in t h e n e a r

studies

and R I S M

on

microsopic

region

K, P c = 7 . 3 8 2 5

of electron,

simulation

methods

used

Thus,

has

in t h i s

structures

viewpoint,

phase.

fluid

The

far from s u b s t a n t i a l .

Tc=304.21

other

based

years.

fluids

it is i n t e r e s t i n g

each

fluids

recent

industrial

often

being

supercritical

also

the

a structural

structure,

dynamics

in

of l i q u i d

is m o s t

parameters

are correlated

supercritical

however,

of

understanding

From

the

of

popular

of s u p e r c r i t i c a l

supercritical

but

In t h i s an o v e r a l l

liquid-like

predominant. is a l s o

structure

dioxide

cal p o i n t

linear

in w h i c h

the

become

study

for a b e t t e r

in

into

continuously

in p r e s s u r e .

application has

structural

The

vary

densities

close

different

condition.

Industrial

for

condition

the

a system

forces

properties views

thermodynamic

properties

change

generally

attractive

in the

characteristic

diffractions

and

molecular

(reference-interaction-site-model)

calcu-

lations. The been

structure studied

Their 3;

(2)

cm-3; point.

by

measured 380 (4)

of t h i s

K,

neutron

diffraction

thermodynamic 23.0

380

supercritical

K,

MPa,

range

0.50

75.1MPa,

In t h e i r

study

gcm

angle

has p r e v i o u s l y

by

et

Bausenwein

((i) 330 K,

g cm-3;

0.90

small

carbon dioxide

(3) -3)

380 is

40.2 MPa, K,

far

scattering

ai.(1992).

36.6 from

due

0 . 9 0 g cmMPa,

0.70

g

the

critical

to t h e

fluctua-

t i o n has n o t b e e n o b s e r v e d . The c m -3) liquid

structure

at

relatively state

((2)

the

close 220 K,

gaseous to

the

state

((i)

critical

5.8 MPa,

0.71

303

point

g cm-3;

K, as (3)

6.0

MPa,

well

as

290 K,

1.18 at

g

the

6.0 MPa,

R. lshii et al. / Fluid Phase Equilibria 104 (1995) 291-304

0.49

g cm-3;

(4) 303 K,

ed by n e u t r o n their

diffraction

investigated

supercritical Thus,

in t h r e e

of

320

MPa,

0.396

critical

good

g cm-3;

ones

zero

precise

of

the

high

sample

has

at a c o n s t a n t

-3,

0.396

g c m -3)

most

.

.

.

.

i

.

.

.

.

9.7

relatively

near

the

diffraction. experimental

can be used

scattering

i

of

for

length

In

the

optimally

.

.

.

.

.

this

the

and

designed

i

.

.

study

for

.

E o

1

380

0.4

i~

,~, ....

0.8

.

,.... ,....

j .... ~....

O3

/Y

>., u3 t-

,

i', / 20K/1

Critical

u

o~0.5

Point

~D

C)

0.2

J V//

0

~

,

,

5

t

,

6

,

,

7

n ......

8

9

i.

10 11

,,.~

12

]

Pressure

/

MPa

0 5

15

25

35

Pressure

Fig. on

i. the

The p r e s e n t phase

Bausenwein range Adya

of this

(Vargaftik,

(1992)

phase

and W a r m a l d

the c r i t i c a l

investigated

diagram

et al.

(O)

diagram:

(1991)

point

/

(~).

(C.P.)

(one

45

(0)

1972) point

are c o m p a r e d with

that

is out

of

380 K, 7S.I MPa) A magnified

is g i v e n

55

MPa

range

and that

picture

in the inset.

the

accurate,

32oK

0.6

super-

mechanically

present

.

tool

container,

300K

0.8

carbon

tempera-

measurements. 1

the

(2)

suitable

pressure.

been

of

In

g cm-3;

determination

alloy"

coherent

againt

1992).

of s u p e r c r i t i c a l

by n e u t r o n

structural

"null

nominal

the

be

for

as the

reistivity

container

may

gcm

0.471

studied

and

characteristics

conditions 0.336

(3) 10.2 MPa,

diffraction

fluid,

has

MPa,

has b e e n

available

critical

9.2

the

(1991

investigat-

are not accessed.

the s t r u c t u r e

thermodynamic

((i)

point

Neutron

which

K

however,

study,

has b e e n

and W o r m a l d

above m e n t i o n e d

in t h e p r e s e n t

ture

0.41 g cm -3)

by Adya

region,

fluid

dioxide

among

7.7 MPa,

293

by the by

around

294

R. lshii et al. / Fluid Phase Equilibria 104 (1995) 291-304

The m e a s u r e d

range in the present study is compared on the phase

d i a g r a m in Fig. et al.

1 with the p r e v i o u s l y m e a s u r e d ones by B a u s e n w e i n

(1992) and by Adya and Wormald

For comparison,

(1991).

gaseous carbon dioxide has also been measured

at

293 K, 1.0 MPa and 0.0557 g cm -3. As for the structure of the liquid, ((i) 222 K, cm -3)

0.65 MPa,

close

1.15 g cm-3;

to the triple point (1984).

239 K, 1.45 MPa,

(216.6 K, 0.52 MPa,

have also p r e v i o u s l y been studied Tricht et al.

two thermodynamic conditions (2)

1.18

by n e u t r o n d i f f r a c t i o n

1.09 g g cm -3) by

van

Our results are compared also with theirs.

EXPERIMENTAL I11111

The High Intensity Total scattering intensity

~--i

(HIT2) time-of-flight

dif fractometer

at

Physics Institute

High

~ x ~ [ ~ ~ !~--

Energy

(KEK),

in Japan, was used. Pulsed neutron beam generated by a spallation reaction

was

used.

Samplefluid

at Tsukuba Neutronfltl

The container

~

) tl l

was made of alloy of titanium (68.5 mol%)

and

zirconium

which is

shown

in

coherent

scattering

(31.5 mol%), Fig. 2.

The

lengths

titanium and zirconium

are

and 7.16 fm, respectively, 1984).

70mm

of

-3.30 fm (Sears,

The overall nominal coherent

scattering length of therefore

zero,

this alloy is

which

is

called

Fig.

2.

Container

for neutron diffraction.

"null alloy". Since the tribute

container did not con-

to the coherent

neutron scattering,

structural

information

which was representative of only the carbon dioxide in the container c o u l d

be o b t a i n e d .

The wall

thickness

of

the

container

taken to be 0.8 mm by taking account of two contradictory

was

require-

ments of mechanical resistivity against the pressure and of minimal scattering The

from the container itself.

container

was

connected

schematically shown in Fig. 3.

with

the

supplying

cylinder,

as

295

R. lshii et al. /Fluid Phase Equilibria 104 (1995) 291-304

Vacuum system Valve.-, Chamber Container

12

3

Tee ]

Sample gas cylinder N2 gas cylinder for compressioi: I I I I

Pressure Safetyvalve transducer

Fig. the

The

A diagram

temperature

1K.

were

9.2

measurements parison, also

measured duration

For

which MPa,

were

carbon

urements

9.7

31

with

by

and

MPa.

24

hr,

a container gaseous

of

the

the

10.2

and

20

sample

from

whose

obtained the

a

hr,

The

K within

±

strain

duration

respecively.

of For

(293 K,

1.0 M P a )

wall

thickness

was

the com-

was

0.3

mm.

87 hr.

intensity, samples

container,

at 3 2 0

semiconductor

state

sample was

(i)

empty

the

was maintained

at the g a s e o u s

performed:

(2)

filling

measured

MPa

hr,

for this

were

for

the container.

were

dioxide

normalization

mentioned,

into

of t h e c o n t a i n e r

Pressures,

gauge,

The

3.

cylinder

in

(3)

the the

following container

a vanadium

rod

measabove

and

(4)

background. As

the

detector,

3He counters

10°-15 ° and

40°-50 ° were

RESULTS

DISCUSSION

AND

After the

correction

structure

vector. available

With at

and

factor the

a small

at t h e

scattering

angles

of

used.

normalization

has

HIT2

located

been

of

derived

spectrometer Q region,

say,

the

as

scattering

a function

reliable below

data 0.3

of

A -I.

intensity,

of

scattering

S(Q) a r e n o t The

obtained

296

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304

S(Q)'s

are

shown

in Fig.

In t h e e x p e r i m e n t tainer

was

times,

their

and 21.5 shows

even

whose

inner

and o u t e r

a Bragg

Fig.

presumably

E

probably

I

S(Q)

due

viz.,

the

than

of the

their

elements,

et al.

thicker

diameters

Therefore,

better

was

Thus,

pattern

material

i).

by Bausenwein

wall

respectively.

the c o n t a i n e r their

performed

employed

mm,

4. (1992),

ours

by

container

a con-

about

being

i0

5 mm

of the e m p t y c o n t a i n e r

to i n h o m o g e n e o u s

titanium

accuracy

mixing

and z i r c o n i u m

itself

of

our

of

(c.f.

data

is

t h a n theirs.

i

i

I

2 1 20

02 1 0

I

!- ¢ . . . . . . . . . .

|I

,

0

Figure

with

have

,

Q/~-I15

that

been 1972)

L

Fig.

,

20

the

radial

form based

(Vargaftik,

In

I

transformation

interpolation

S(0):

,

increasing

weighted

Lorentzian

values

I

10

4 reveals

Neutron

for

,

5

pronounced

Fourier

I'

92MPa

25

first

Structure

peak

pressure,

around

viz.,

distribution of

Q{S(Q)-I}.

evaluated using

between from

1.5 A -I b e c o m e s

more

density. has b e e n d e r i v e d

In

transformation

Q=0.3

the

factors.

function

on the O r n s t e i n - Z e r n i k e

for S ( Q ) ' s

4+

the

relation

A -I and

isothemal

was

0 A -I.

a

assumed The

S(0)

compressibilities

the r e l a t i o n

pkTK T the

Gaussian

[i]

transformation, window

by

S(Q) v a l u e s

function M(Q)=

were

cut

at

25

e x p ( - 0 . 0 0 7 Q 2) was used.

A -I,

and

a

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304

297

Qmax

GN(r)=l+(i/2a2pr) I Q{S(Q)-I}

M(Q)

sin

(Qr)dQ

[2]

0 The GN(r)'s

thus

obtained

are s h o w n

in Fig.

5.

t" :.

•

:-. • "

0

•

] 0.2MPa

°

Z

ol 1 0

Fig.

5.

Neutron

0

2

weighted

4

6

,-/~ radial

8

distribution

functions.

Intramolecular correlation It are

is

conjectured

assignable

to

from the

Fig.

5 that

intramolecular

the C-O

first

and

and

0-0

correlations,

second

peaks

the

intramolecular

respecively. For detailed correlations squares

fit b y Eq.

contribution bly

small.

pressed

analysis

of t h e p e a k

have been calculated

from The

positions,

from the

[2]

in the r a n g e

the

intermolecular

intramolecular

part

S(Q)

curves

with

i0 A -i~ Q ~ 20 A -1, part

of the

is r e g a r d e d structure

a least

where

as

the

negligi-

factor

is ex-

by

Sintra(Q)={I/(bc+2bo)2}x{4bcbo(sin(Qrco)/Qrco)exp(-ico2Q2/2) + 2bo2(sin(Qroo)/QroO)exp(-loo2Q2/2)} The

bC

(Sears,

and

b 0 values

1984).

are

6.6484

fm

and

5.805

fm,

[3]

respectively

298

R. lshii et a l . / Fluid Phase Equilibria 104 (1995) 291-304

The obtained Table

rco values

1 in c o m p a r i s o n

with

together with those

so

far

the 1 values found

are given

in o t h e r

The C - O a n d O - O d i s t a n c e s h a v e b e e n m e a s u r e d to be 1.17 A a n d A,

respectively.

distances

are

2.33

T a b l e 1 shows that the i n t r a m o l e c u l a r C - O and O-O

independent

dioxide molecule

TABLE

in

conditions.

of

the

conditions

and

that

the

carbon

is l i n e a r - s h a p e d .

1

Intramolecular

a t o m - a t o m d i s t a n c e s of CO 2 in the s e v e r a l

conditions

77K

P/MPa

IEo/~

1/2 / / ~

Zbo/Z~ 1 / 2 / . \

10.2_

1.17

0.08

2.33

0.11

9.7

1.17

0.08

2.32

0.10

9.2

1.17

0.07

2.32

0.10

Method a

Ref.

Supercritical fluid 320

330 380

39.7

N

1.147

this work

N I3ausenwein ct al. b

22.7

1.154

36.1

1.152

74.1

1.154

0.65

1.1569

0.0683

2.3406

239

1.45

1.1569

0.0719

2.3401

0.1027

220

0.85

1.1663

0.0692

2.3159

0.0747

1.1657

0.0693

2.3314

0.0735

Liquid 222

0.0988

N

wm Tricht et al. b

N Adya & Worlnald b

Gas 293

1.0

1.16

2.33

1.162

0.034

2.31(1

this work

N

0.040

E

Katie & Katie

X

Simon &Pelers

SoLid

1.155

aN:

Neutron

diffraction,

E: E l e c t r o n

diffraction,

X: X - r a y

diffrac-

tion bThe

precisions

of

these experiments.

the

values

are

presumably

within

3 digits

in

299

R. Ishii et al. /Fluid Phase Equilibria 104 (1995) 291-304 The cal

root

fluid

liquid

in t h e

states,

gaseous ry

mean-square

at

of

the

not

the by

their 1 values gaseous

Karle,

1949)

large

conditions

present

data. et

i.

state

than

As al.

measured

As for the i v a l u e s

at the

because

of u n s a t i s f a c t o -

is p o i n t e d may

state

by be

themselves, unreasonable

is s m a l l e r

diffraction

2.5 times.

that the i v a l u e

at t h e

supercritiat the

electron

of at least

either,

ours

by

the

to t h o s e

(1992)

at the s u p e r c r i t i c a l

by a f a c t o r

for

are c o m p a r a b l e

from T a b l e

Bausenwein

to be r e a s o n a b l e ,

is s m a l l e r

of v i b r a t i o n

t h e s e c o u l d not be o b t a i n e d

observation

that

present

as is seen

state,

statistics

the

amplitudes

supercritical

than (Karle

Further,

and

it seems

at the g a s e o u s

state

that

by a f a c t o r

state of

as

as 2~

In v i e w between

of

the

liquid

intramolecular pendent

fact

that

the

force

and s u p e r c r i t i c a l distance

and

states

seems

of t h e s e

fields

fluid,

root

mean

are

not

the p r e s e n t square

so

different

result

amplitude

that are

the

inde-

to be r e a s o n a b l e .

Intermolecular correlation The

intermolecular

part

of

the

structure

factor

is

expressed

by

Sinter(Q)={i/(bc+2bo)2}X{bc2Scc 4bcboSco

inter(Q) +

inter(Q)

+ 4b02S00

[4]

inter(Q)}

where

Sij

inter(Q)

=4~P

[5]

r(gij(r)-l)[sin(Qr)/Q}dr 0

As s e e n clearly

from

separated

of G N i n t e r ( r ) , from insight

the

al.

tally

5,

the

intermolecular

from the i n t r a m o l e c u l a r

however,

three

into

simulation et

Fig.

pairs

(1981), obtained.

been which The

for

one.

Only

it is h a r d to d i s e n t a n g l e viz.,

the 3 - d i m e n s i o n a l

has

part

performed has

well

C-C,

0-O

and

structure. using

Thus,

the m o d e l

reproduced

GNinter(r)

C-O

curve

the can

the

is

from the d a t a

the c o n t r i b u t i o n s pairs

and

molecular presented

GNinter(r) be

GN(r)

obtained

to

gain

dynamics by Murthy

experimenfrom

the

3~

R.~hiietal./FluidPhaseEquilibria104(1995)291-304

calculated

g(r)

by

GNinter(r)={(bc2gcc(r) + 4bo2goo(r)+4bcbogco(r)}/(bc+2bo )2 =O.133gcc(r)+O.404goo(r)+O.463gco(r) The

Ginter(r)'s

to the M D

contributions. measured

at

difference

a shorter

(1992). the

densities

hand,

in the

1984,

and A d y a

distance

also

attributed

between

et

According C-C

and

to t h o s e al.

C-O

(3.8 A)

(1992).

there

the

are

The

1991,

two m a x i m a

1992);

The

O-0 c o r r e l a t i o n ,

(1991)

that

is m o r e

state

to the

difference

molecules

are c o m p a r a b l e Bausenwein

and Wormald,

Wormald

suggests

4 A.

to the

in the d e n s i t i e s .

and

state

neighbouring

by

liquid

is a s s i g n e d

by Adya

This

liquid

at a p p r o x i m a t e l y

is m a i n l y

m a y be d u e to that

et al.,

cussed

a maximum this

These peak positions

higher

On the o t h e r Tricht

have

simulation,

[6]

and

by

supercritical

the

mutual

flexible

as

fluid

former

at

diset

al.

state

and

orientation

in the

one

is

Bausenwein

(van

between

than

in the

appear

in

latter. The

detailed

forthcoming

analysis

using

the

MD

simulation

will

paper.

1

20

....

1

.... . ........... ....

0 2

%..

...... ) ~ "'---,

" eeluoeeeee°

.............. ,9 7M Pa.3201" °OOOe

u~

2 0F "... ....................... ...~,2M Pa,3201~ 1 P - - ' - . ~ . t i e. '.l e. e. ,. . . i. . . . "-"-''-----.~.~.

k

0 2~ 1~

....... . ......... ,1,nMp~,293~ .~.,~ ~ . . . . . "'""""'-~--

/ 0 /

0

,

I

,

1

I

,

2

3

Q/At Fig.

6. C o m p a r i s o n

0.3 A -I

< Q < 3 A -I

(i.0 MPa, liquid

of the s t r u c t u r e with

those

293 K in the p r e s e n t

state

(0.85 MPa,

at

factors the

experiment)

in t h e r e g i o n gaseous and

220 K; A d y a and Wormald,

state at

the

1992).

a

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304 For

further

insight

experimental

The peak gaseous

in Fig.

curves

around

is a s s i g n a b l e

positions

and

for

MPa,

These

will

although

clear.

Thus,

the

other

molar

G(r)

the

range

is

of t h e

liquid,

as

existence

of

the

while S(Q) the

6

shows

Fig.

that

of

in t h e

the

small

angle

of a n o t h e r The

S(Q)

point

show

and

A,

: 1.03

small

so

: i.

On

of

the

that

the

root

reveal

fact

respenot

as

the

molar

that

the

short

is r u l e d

by attractive

ones,

the

latter

markedly not

so

on the h i g h Q

observed

associated

between

for

the

with

the

neighbouring

in the p r e s e n t

much.

mole-

measurements

as Q r e a c h e s

As

the

are u n d e r

at the same

increase

of

structure,

progress

by means

facility.

fluid

far

at a small

substantiate

for c a r b o n

+ 0 A -1,

behaviour

for a s t u d y of long r a n g e

supercritical

These

been

increase

data

also

is

1992).

experiments

no a p p r e c i a b l e

to t h e c r i t i c a l

1.50 A -I

5 are

the s h o u l d e r

has

(WINK)

1992).

so

which

correlations

Q is c r u c i a l

is l a r g e

facts

fluid

found,

6,

does

the

4.05

cube

by r e p u l s i v e

spectrometer

et al.,

densities

state

scatteing

of

the

the

A -1,

Fig.

is 1.07

become

reflect

conditions

1991,

gas

for the

respectively.

A and in

of

These

the S(Q) v a l u e s

that

found

1.45

MPa,

4.19

ratio

than

not

orientational

supercritical

small

wein

is

(Adya a n d Wormald,

Figure of

in Fig.

in liquids.

peak

from

A,

not

rather

at

10.2

distances

may

experimental

seen

on the

Q region

is not

of G(r)

supercritical

the c a s e

first

and

: i.

does This

molecules

the

4.33

: 1.06

between

of

cules

1.12

distance

In t h e p r e s e n t side

at

located

positions

of these

compressed.

generally

MPa

corresponding

structure

forces being

ratio the

intermolecular is

peak

are

9.7

peaks

the

hand,

volumes

volume

9.2

yield

cively,

smaller

based

to the one b a s e d on the i n t e r m o l e c u l a r

The p e a k

A -I

at the

1.5 A -1, w h i c h

correlation. 1.55

correlation

6.

of t h e S ( Q ) ' s

state,

intermolecular

the S(Q)

data,

4 are magnified

into

301

that the

dioxide

from

angle

the

critical

region

(Bausen-

fluctuation

in the c o n d i t i o n s

of the close

point.

CONCLUSION

Neutron mination namic

diffraction

is p r o v e d

of s u p e r c r i t i c a l

conditions,

that

is,

to be u s e f u l

c a r b o n dioxide. close

for

structural

At the p r e s e n t

to the c r i t i c a l

pressure,

deter-

thermodythe wall

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304

302

of t h e c o n t a i n e r mm)

and c o n s e q u e n t l y

collected.

The

structure becomes

is

critical

between

in

linear-shaped

the

neighbouring

+0

A,

is large

measured

to the l i q u i d

be m a d e

by

of

which near

for the

and

the

the

state.

molecules

critical

et

is m o r e

c o u l d be

The

al.

two maxima.

flexible

This

than

far

scattering

c(r)

radial

g(r)

intermolecular

k

Boltzmann

constant

1

root

square

M(Q)

window

P

pressure

Q

scattering

s(e)

structure

distribution

mean

in

the

function

for F o u r i e r

of e q u i l i b r i u m

transformation

vector factor

T

temperature

r

atomic

distance

x

atomic

fraction

Greek

function

displacement

letters compressibility number

density

Superscripts N

neutron-weighted

max

upper

limit

for F o u r i e r

transformation

is

difference

length

p a r t of the p a i r c o r r e l a t i o n

The

orientation

LIST OF S Y M B O L S

coherent

from

which

state°

b

the This

(1992). 4 A,

the

S(Q)

that

point.

state

at a b o u t

conditions

(0°8

intramolecular

supercritical

Bausenwein

state having

thin

substantiates the

has one maximum

supercritical

rather

d a t a of the s a m p l e

independent

feature

correlation

that

is

could

intensity

reaches

the

point

intermolecular

suggests

Q

the d e n s i t y to

alloy

accurate

molecule

as

of

is in c o n t r a s t

in c o n t r a s t

null

practically

large,

fluctuation

the

of t h e

function

distance

liquid

R. Ishii et al. / Fluid Phase Equilibria 104 (1995) 291-304

303

Subscripts c

critical

C

carbon

point

CC

carbon-carbon

CO

carbon-oxygen

i

atom

i

ij

atom

i-atom

inter

intermolecular

intra

intramolecular

j

0

oxygen

OO

oxygen-oxygen

T

isothermal

ACKNOWLEDGEMENT

The for

expenses

of

Scientific

Ministry One

this

Research

of E d u c a t i o n ,

of

Society

work

were

on

Priority

Science

us

(R.

I.)

has

for

the

Promotion

partly

defrayed

Areas

and Culture,

been

granted

of

the

Science

by

Grant-in-Aid

(05222207)

from

the

Japan. fellowship

for

of

Japanese

the

Junior

Japan Scien-

tists. The at

HITAC

M-660

Okazaki

Tsukuba

and

were

computers

National

at the

Institute

Laboratory

for

for M o l e c u l a r

High

Energy

Science

Physics

at

used.

REFERENCES

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A.K.

a n d Wormald,

orientationally fraction. Adya,

A.

Mol.

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Chieux,

1992.

tron diffraction Phys.,

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structure

First d i r e c t

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C. J.,

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T. B e r t a g n o l l i , P.,

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Bausenwein,

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K.

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A.

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J.B.,

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H.,

1981.

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B36:

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2750-2751.

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Mol.

B.,

K.,

Fredrikze,

tron diffraction namic

K.,

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structure van

Singer,

J.,

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on T h e r m o p h y s i c a l Nauka publisher,

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