High resolution compton profiles of liquid Li, Na and LiNa alloy

Journal of Non-Crystalline Solids 117/118 (1990) 421-424 North-Holland

421

HIGH RESOLUTION COMPTON PROFILES OF LIQUID Li, Na AND Li-Na ALLOY

Fumitake ITOH, Tomoki SUGAWA*, H i r o s h i SAKURAI, Kenji SUZUKI Nobuhiko SAKAI+, M a s a h i s a ITO+, N o b u h i r o SHIOTANI# H i r o s h i KANATA$ and Masami ANDO$ I n s t i t u t e f o r M a t e r i a l s R e s e a r c h , Tohoku U n i v e r s i t y , Sendai 980, Japan + The I n s t i t u t e of P h y s i c a l and Chemical Research(RIKEN), Wako, S a i t a m a 351-01, Japan # P h y s i c s Lab., Tokyo U n i v e r s i t y of F i s h e r i e s , Konan, Minatoku, Tokyo 108, Japan $ Photon F a c t o r y , N a t i o n a l L a b o r a t o r y f o r High Energy P h y s i c s , Tsukuba, I b a r a k i 305, Japan

High r e s o l u t i o n Compton p r o f i l e s of Li, Na and LisoNaso a l l o y have been measured w i t h a momentum r e s o l u t i o n of 0.085 a . u . in b o t h s o l i d and l i q u i d s t a t e s , u s i n g 29.5 keY X - r a y s of s y n c h r o t r o n r a d i a t i o n . The h i g h momentum c o m p o n e n t s beyond the Fermi momentum and the t h e b l u r r i n g of the Fermi s u r f a c e in the l i q u i d s t a t e were c l e a r l y o b s e r v e d .

1.

Introduction

For i s o t r o p i c

Measurements of e n e r g y s p e c t r a scattered

X - r a y s or

formation about tribution

7-rays

g i v e us d i r e c t

the e l e c t r o n i c

in t h e ground s t a t e

differential

cross section

of Comptonin-

momentum d i s of m a t t e r .

The

s y s t e m s such as l i q u i d s

g a s e s where the r o t a t i o n a l tially

complete,

tained

is a s p h e r i c a l l y

averaging

the q u a n t i t y

or

is e s s e n -

experimentally

averaged J(q),

ob-

where q

i s used i n s t e a d of pz ,

f o r the Compton s c a t co

tering

can be w r i t t e n

profile

J(pz),

integral

down u s i n g t h e Compton

which is d e f i n e d

of the e l e c t r o n

J(q)

=

f

q

2 ~ pn(p)dp.

(3)

as the d o u b l e

momentum d e n s i t y

n(p).

Thus

C o n s e r v a t i o n of m o m e n t u m

and e n e r g y g i v e s us the

expression for q

d2a/dQdwr=F(og~,oJr, k~,kf, O,pz) J(pz),

(1)

q =

m e [ e o l - c o f - c o l c o r ( 1 - c o s 0 )/mc 2]

x (co 12+w,2-Xw lw ~cosO )-1/=.

(4)

with It has been one of i n t e r e s t i n g J(pz)

=

J' f n(p)dpxdpy,

(2)

s o l v e d w h e t h e r the Fermi s u r f a c e a l s and a l l o y s

where t h e e x p l i c i t is given tively tered

e x p r e s s i o n of the f u n c t i o n F

in R i b b e r f o r s ~, w t and w r a r e r e s p e c -

the e n e r g i e s of t h e i n c i d e n t X-rays,

ks and kr t h e i r

and s c a t -

momenta,

p the e l e c t r o n

0

scattering

angle,

the z a x i s

is t a k e n a l o n g the s c a t t e r i n g

the

momentum, and vector

k=kf-kl.

of a l k a l l i n e state

i s well d e f i n e d .

m e t a l s and aluminum in the l i q u i d

have been measured by u s i n g a t r a d i t i o n a l

s e t - u p which c o n s i s t s and a s o l i s rather

in l i q u i d metCompton p r o f i l e s

state

of

d e t e c t o r . 2-3

poor r e s o l u t i o n

s p a c e of t h i s

7-ray

s o u r c e of 24~Am However, due to

of 0.4 a . u .

experimental

set-up,

in momentum only limited

c o n c l u s i o n s have been o b t a i n e d .

* Present hddress:NTT, Japan

0022-3093/90/$03.50 (North-Holland)

p r o b l e m s to be

Ibaraki

Electrical

Communication L a b o r a t o r y ,

@ Elsevier Science Publishers B.V.

Tokai,

Naka-gun,

lbaraki

319-ii,

F. Itoh et al. / High resolution Compton profiles of liquid Li, Na and Li-Na alloy

422

Eecently, profiles

it

has been r e p o r t e d

that

Compton

can be m e a s u r e d w i t h a momentum r e s o l u -

t i o n of as h i g h as 0,085

a.u.,

X - r a y s of s y n c h r o t r o n r a d i a t i o n t i o n of a c r y s t a l

analyzer

t i v e d e t e c t o r . *-s D e t a i l e d electronic

structure

tiple

scattering

imaging p l a t e ) .

effeciency

of the

About 4x104 c o u n t s were accumu-

u s i n g 29.5 key

lated

and a c o m b i n a -

measurement took about 8 h o u r s under the o p e r a t -

and a p o s i t i o n

sensi-

i n f o r m a t i o n about t h e

at

and d e t e c t i n g

the compton peak of each sample.

ing c o n d i t i o n

Each

of 300-100 mA r i n g c u r r e n t s

4.5 T of a m a g n e t i c f i e l d

and

of the wiggler.

has been o b t a i n e d . 6-8 3. R e s u l t s and D i s c u s s i o n

In t h i s

p a p e r we r e p o r t

pton profiles alloy.

of l i q u i d

high resolution

Com-

Na m e t a l s and LiNa

Li,

D i s c u s s i o n i s f o c u s e d on the e l e c t r o n

momentum d i s t r i b u t i o n Fermi s u r f a c e

and t h e b l u r r i n g

in the l i q u i d

A Compton p r o f i l e Jr(q)

was e x t r a c t e d

profile

J(q)

from the e x p e r i m e n t a l

by s u b t r a c t i n g

core-electron

of t h e

state.

due to the v a l e n c e e l e c t r o n

profile

the t h e o r e t i c a l

by Biggs et al. 9

1 and 2 show the J r ( q )

Figures

t h u s o b t a i n e d of l i q u i d

Li and Na, r e s p e c t i v e l y . 2. E x p e r i m e n t a l The p r e s e n t

Compton s p e c t r o m e t e r c o n s i s t s

a bent-crystal bent-crystal

monochromator, a n a l y z e r and

position-sensitive descrived

a Cauchoice-type

an imaging p l a t e

detector.

elsewhere4-t

The d e t a i l s

beam l i n e of t h e Photon f a c t o r y

was 0.085

A sample of Li, into a cylindrical ¢

a.u.

steel

x 5 mm) under a p u r i f i e d

Kapton f o i l s

or s t a i n l e s s

at

~. "e.t'

momen-

O

in a vacuum steel

i

during

J(q)

subtracting

corrections

due to t h i n f o i l s

steel,

by

of Kapton or

and making e n e r g y d e p e n d e n t

(absorption

inside

t h e sample,

•

.

•

"-~.%

\, k

from the

i n d e p e n d e n t l y m e a s u r e d background

contributions stainless

were o b t a i n e d

!1

No 150°C

The sample c o n t a i n e r

u s i n g eqs. Q ) - ( 4 ) ,

•

and

the m e a s u r e m e n t s .

Compton p r o f i l e s

•

the

out at

t h a n 1.0 x 10 -6 Torr

observed energy spectra

•

Fig. 1. V a l e n c e - e l e c t r o n Compton p r o f i l e of l i q uid Li at 230 C ° , t o g e t h e r w i t h the P E ( d o t c h a i n ) and the IE ( d o t ) p r o f i l e s ( s e e the t e x t ) . The s t a t i s t i c a l e r r o r s a r e l e s s t h a n the circles.

"-I

better

•

",,¢...

0.5 q (a.u.)

150 °C,80~C and room t e m p e r a t u r e f o r Na, and

was e v a c u a t e d

i

foils

160 °C and room t e m p e r a t u r e f o r Li,

350 °C f o r Li~oNaso a l l o y .

I

put

v e s s e l ( 2 0 mm

sample i n s i d e

I

0

study.

. The m e a s u r e m e n t s were c a r r i e d

230 °C,

"%-~,~,

The

Ar a t m o s p h e r e to

and then p l a c e d

were used to hold the l i q u i d vessel

was used.

in t h i s

¢r

wiggler

Na or LiNa was c a r e f u l l y stainless

avoid o x i d i z a t i o n , chamber.

are

a n g l e was 159.5 ° . The o v e r a l l

tum r e s o l u t o n

Li 230°C

as a

The e n e r g y of the i n c i -

d e n t X - r a y s was 29.5 keV. The v e r t i c a l

scattering

of

mul-

|

0

i

\

i

0.5

q(o.u.)

Fig. 2. V a l e n c e - e l e c t r o n Compton p r o f i l e of l i q uid Na at 150 C ° , t o g e t h e r with the F E ( d o t c h a i n ) and the IE ( d o t ) p r o f i l e s ( s e e the t e x t ) . The s t a t i s t i c a l e r r o r s a r e l e s s than the circles.

F. Itoh et al. / High resolution Compton profiles of liquid Li, Na and Li-Na alloy Two t h e o r e t i c a l figures

profiles

for comparison.

free electron(F£) valence electron

a r e shown in t h e s e

One i s b a s e d on t h e

model where t h e n ( p )

f o r the

LiNG 350°C

i s g i v e n by a s t e p f u n c t i o n

n(p) = 1

423

for

0

(5)

p g

pv

p ~

pv,

•:Experiment ,:Li÷NG

G1

v "-I

"I, where pF i s t h e Fermi momentum. The o t h e r interacting Daniel

(lg)

electron

gas model b a s e d upon

and Vosko 1°. The Two p r o f i l e s

v o l u t e d w i t h the e x p e r i m e n t a l tion.

Thus t h e s t e p - w i s e

resolution

function

I t can be seen from F i g s . t h e FE nor the

q(a.u.)

funcFig. 3. V a l e n c e - e l e c t r o n Compton p r o f i l e of l i q uid L i s ~ a s o metal at 350 C ° , t o g e t h e r w i t h the F E ( d o t - c h a i n ) and t h e IE ( d o t ) p r o f i l e s ( s e e the t e x t ) . The s t a t i s t i c a l uncertaintities are less than the c i r c l e s .

i s smeared

perimental

profiles,

Fermi momentum. momentum t a i l s 'melting'

electrons states

particularly

that

is,

in t h e s t a t e s

below t h e

disordered

electron-electron count

in the

interaction

IE p r o f i l e .

represents

electron-ion

causes further

due to

of the

In o r d e r

to see t h i s

the momentum d e n s i t y

the d i f -

-(2~p)-1

F i g u r e 4 shows the n ( p ) ' s

difference

the i n t e r a c t i o n in Li

°C,

liquid

at 350°C.

I t can be seen t h a t alloy

+J~,(q)

),

is a l s o

not s i m p l y the w e i g h t e d sum of t h e p r o f i l e s constituent

liquids.

The h i g h momentum t a i l

disorder.

the Fermi s u r f a c e

shown f o r comof the a l l o y

that

is

Li at 230

the o b t a i n e d n(p)

i s much more smeared out The c h e m i c a l d i s o r d e r

in the a l l o y has s t r o n g e r

on the momentum d i s t r i b u t i o n

topological

i.e.,

of l i q u i d

Na at 160°C and l i q u i d LisoNaso a l l o y

of the l i q u i d

effects

h w e i g h t e d sum of

of the p u r e e l e m e n t s ,

(6)

dJv(p)/dp.

than t h o s e of Li and Na.

The Compton p r o f i l e

more c l e a r l y ,

and the

of the

The l a r g e r that

n(p):

F i g u r e 3 shows the Jv(q) of LisoNaso l i q u i d

0.5*(JLt(q)

situation

n(p) was deduced from Jv(q)

in the ion p o t e n t i a l s

parison.

severe smearing

by the f o l l o w i n g e q u a t i o n ,

and i o n s i s s t r o n g e r

a l l o y m e a s u r e d at 350 °C.

the

intro-

of the momentum d i s t r i b u t i o n .

and (2) the

than in Na.

Compton p r o f i l e s

that

is taken into ac-

the e f f e c t

in Li t h a n in Na i n d i c a t e s between t h e e l e c t r o n s

indicates

duced by a l l o y i n g

Therefore,

interaction.

observed fact

pr to t h e

and t o p o l o g i -

The e f f e c t

this

in t h e ion p o t e n t i a l s

interaction

ions.

alloying,

on the

does not change much upon

chemical d i s o r d e r

f e r e n c e between t h e e x p e r i m e n t a l p r o f i l e Ig p r o f i l e

momentum d i s t r i b u t i o n

Since the e f -

interaction

of the

pv t h r o u g h s c a t t e r i n g

between t h e e l e c t r o n s

i s much i n t e n s e .

f e c t of the e l e c t r o n - e l e c t r o n

Fermi momentum

the e x c i t a t i o n

(1)the electron-electron

cally

the a l l o y p r o f i l e

beyond t h e

beyond t h e p~ comes from

above t h e

interaction

the ex-

The a p p e a r e n c e of the h i g h

of the s t e p - w i s e

distribution;

i and 2 t h a t

IE e x p l a i n s

0.5

are con-

accordingly.

neither

", 8

i s the

than the

The l a r g e b l u r r i n g

in l i q u i d

of

a l l o y compared to

in p u r e m e t a l s has been a l r e a d y

predicted

by Itami and S h i m o j i 11 u s i n g t h e Green f u n c t i o n

of of

method. culation.

The p r e s e n t

results

support this

cal-

F. Itoh et al./ High resolution Compton profiles of liquid Li, Na and Li-Na alloy

424

0.1-(a) Li

Li 230°C

• .'"t"". . .,.~::'., .

230°C - R'T"

O ~'-":-':::::~'I"•~ ":!:~: ----~....... ~:"'~:::....-'.' ................ . . . . . .,-..

-0.I 2

-'1

o'

0.15

•

i

T-. ,b No "1"" "'-

• " - ..-T. " 0 - - : : ' : : ~ - . . . . . . . . . '-~v 7 " . . . . . .

.~

i.

..

I

-°15-7

'

-1

I

160°C - R.T.

/

. .. -..-.I -k-),,:".-.---.----'" ~:-"1 "

".."

.

•

/ ,

L

|

o

1

2

cl(a.u.)

LiNct 350°C

Fig. 5. D i f f e r e n c e of Compton p r o f i l e A J ( q ) f o r ( a ) L i and (b)Na. The v e r t i c a l b a r s d e n o t e statistical errors.

i I

I<..~ ....

of the e l e c t r o n - i o n

I

be e s t i m a t e d

0.5

O

p(a.u.)

difference

interaction.

The f o r m e r can

from t h e IE model.

T h e r e f o r e , the

between the e x p e r i m e n t a l

the IE c u r v e is a s c r i b e d Fig. 4. Momentum d e n s i t y n(p) f o r l i q u i d Li, Na and Li5ONa50 a l l o y , t o g e t h e r w i t h t h e p r e d i c t e d c u r v e by t h e FE and the I E ( s e e the t e x t ) . The vertical bars denote statistical e r r o r s . The e f f e c t of t h e e x p e r i m e n t a l r e s o l u t i o n can be seen in the ' m e l t i n g ' of the s t e p - w i s e f u n c t i o n of the FE p r o f i l e . In o r d e r electron

to see the change of c o n d u c t i o n -

b e h a v i o r upon s o l i d - l i q u i d

sition,

the d i f f e r e n c e

of A J ( q )

phase tran-

d e f i n e d by,

(7)

A J(q)= J,,q(q)-J,ot(q),

was examined.

F i g u r e 5 shows the d i f f e r e n c e

c u r v e s of Li and Na, which i s drawn in both positive

and n e g a t i v e momentum s p a c e s to show

symmetrical features. A J(q)

is c o n s i s t e n t

The p r e s e n t

experimental

w i t h the p r e v i o u s

7-ray

e x p e r i m e n t s . 8-t The A J ( q ) difference

contains

in the e f f e c t

electron

interaction

electron

density

i n f o r m a t i o n about

the

of the e l e c t r o n -

due to the change in the

c a u s e d by the volume change

upon m e l t i n g , and the d i f f e r n c e

in the e f f e c t

teraction

titative

elaboration

and

to t h e e l e c t r o n - i o n

acompanied by the m e l t i n g .

theoretical

A J(q)

is r e q u i r e d

in-

Further to get qan-

agreement.

1. R. R i b b e r f o r s , Phys. Rev. B 12(1975)3136. 2. F. I t o h , T. Honda and K. Suzuki, J. Phys. Soc. Jpn. 47(1979)122. 3. T. Honda, F. I t o h and g. Suzuki, J. Phys. Soe. Jpn. 47(1979)133. 4. N. S h i o t a n i , N. Sakai, F. I t o h , M. S a k u r a i , H. Kawata, V. Amemiya and M. Ando, Nucl. l n s t r u m . Methods A275(1989)447. 5. F. I t o h , M. S a k u r a i , T. Sugawa, K. Suzuki, N. Sakai, M. I t o , O. Mao, N. S h i o t a n i , Y. Tanaka, Y. S a k u r a i , S. Nanao, H. Kawata, Y. Amemiya and M. Ando, Rev. Sci. l n s t r u m . 60(1989)2402. 6. N. S h i o t a n i , N. S a k a i , M. l t o , O. Mao, F. I t o h , H. Kawata, Y. Amemiya and M. Ando, J . P h y s . : C o n d e n s . M a t t e r I(1989)SA27. 7. F. I t o h , M. S a k u r a i , T. Sugawa, K. Suzuki, N. Sakai, N. S h i o t a n i , O. Mao, M. l t o , H. Kawata, Y. Amemiya and M. Ando, P o r t u g a l P h y s i c a in press 8. N. Sakai, N. S h i o t a n i . F. I t o h , O. Mao, M. I t o , H. Kawata, Y. Amemiya and M. Ando, J . P h y s . Soc. Jpn. in p r e s s 9. F. Biggs, L.B. Mendelsohn and J.B. Mann, At. Data Nucl. Data T a b l e s 16(1975)201. 10. E. Daniel and S. Yosko, Phys. Rev. 120(1960) 2041. I i . T. ltami and M. S h i m o j i , P h i l . Mag. 25(1972)229.