NEAR EDGE FINE STRUCTURE OF Li, Be AND GRAPHITE BY X-RAY RAMAN SCATTERING

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NEAR EDGE FINE STRUCTURE OF Li, Be AND GRAPHITE BY X-RAY RAMAN SCATTERING

H. Nagasawa

To cite this version:

H. Nagasawa. NEAR EDGE FINE STRUCTURE OF Li, Be AND GRAPHITE BY X-RAY RAMAN SCATTERING. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-863-C9-866.

�10.1051/jphyscol:19879155�. �jpa-00227267�

JOURNAL DE PHYSIQUE

Colloque C9, suppl6ment au n012, Tome 48, d6cembre 1987

NEAR EDGE FINE STRUCTURE OF Li, Be AND GRAPHITE BY X-RAY RAMAN SCATTERING

H. NAGASAWA

Hahn-Meitner-Institut, Glienicker Strasse 100, 0-1000 Berlin 39, F.R.G.

A b s t r a c t

-

The near edge f i n e s t r u c t u r e o f t h e x-ray Raman spectra i n L i , Be and g r a p h i t e was measured i n an x-ray i n e l a s t i c s c a t t e - r i n g experiment w i t h 0.8 eV r e s o l u t i o n . The x-ray Ramandspectrum, which i s i d e n t i c a l t o t h e dynamical s t r u c t u r e f a c t o r S(q, w) o f i n n e r - s h e l l e l e c t r o n s f o r qa

<

1, where hq i s t h e momentum t r a n s f e r and a i s t h e o r b i t a l r a d i u s o f the i n n e r - s h e l l e l e c t r o n s , has been confirmed experimental l y t o be e q u i v a l e n t t o the corresponding s o f t x-ray absorption spectrum. It i s concluded t h a t x-ray Raman s c a t t e - r i n g has several experimental advantages over an a b s o r p t i o n e x p e r i - ment f o r l i g h t elements.

1. I n t r o d u c t i o n

I n t h e 1960's x-ray Raman s c a t t e r i n g , t h e i n e l a s t i c s c a t t e r i n g o f h a r d x- r a y s by t h e i n n e r - s h e l l e l e c t r o n s i n l i g h t elements, was confirmed t o be d i s t i n c t from t h e s o - c a l l e d Compton s c a t t e r i n g and t o y i e l d a s i m i l a r ener- gy spectrum t o t h e s o f t x-ray absorption spectrum as had been expected t h e ~ r e t i c a l l ~ l - 3 . The energy r e s o l u t i o n o f about 20 eV f o r t h e x-ray i n e - l a s t i c s c a t t e r i n g experiments o f those days however was so poor t h a t i t was almost impossible t o compare t h e c h a r a c t e r i s t i c s o f the x-ray Raman spectrum e i t h e r w i t h near edge f i n e s t r u c t u r e measurements o r even w i t h t h e o v e r a l l shape o f t h e h i g h l y accurate absorption experiments o f about 0.1 eV r e s o l u t i o n made u s i n g synchrotron r a d i a t i o n and advanced techniques f o r sample preparations. The e s s e n t i a l f e a t u r e s o f x-ray Raman s c a t t e r i n g r e - main ambiguous w i t h r e s p e c t t o i t s re1 a t i o n t o s o f t x-ray absorption.

The f i r s t synchrotron r a d i a t i o n x-ray Raman measurements f o r L i

,

Be and g r a p h i t e r e p o r t e d here a r e mainly intended t o i n v e s t i g a t e i t s equivalence t o a b s o r p t i o n spectroscopy.

2. T h e o r e t i c a l Background

The double d i f f e r e n t i a l cross s e c t i o n d2cr/dndw f o r i n e l a s t i c x-ray s c a t t e - r i n g i s given i n f i r s t - o r d e r p e r t u r b a t i o n theory by

where r, i s t h e c l a s s i c a l e l e c t r o n radius, fiw, and %w' are t h e energies,

go

and $' are t h e p o l a r i z a t i o ? . v e c t o r s o f t h e i n c i d e n t and the s c a t t e r e d pho- tons, r e s p e c t i v e l y , and S(q, w) i s t h e dynamic s t r u c t u r e f a c t o r which r e - f l e c t s t h e p r o p e r t i e s o f the s c a t t e r i n g system. W i t h i n t h e l i m i t s o f t h e one-electron approximation t h e dynamic s t r u c t u r e f a c t o r s(:, w) due t o t h e e x c i t a t i o n o f an i n n e r - s h e l l one e l e c t r o n s t a t e

10)

w i t h energy

E,

i n t o a one-electron Bloch s t a t e jk> w i t h energy Ek i s given by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879155

JOURNAL DE _PHYSIQUE

s($,

W ) =

~ f < k l e i ? . ? l 0 > / ~

6 ( E k

- ^E, -

^)iw)

k

( 2 )

where i s the transferred momentum and fiw i s the energy t r a n s f e r

T w o

-

3w'.

For the case in which

q

i s small such t h a t

On

the other hand, the to- t a l cross section f o r the s o f t x-ray absorption due t o the inner-shell elec- trons of l i g h t elements i s given in the dipole appro- ximation by

where a i s the o r b i t a l radius of inner-shell electrons, Mizuno and Ohmura have applied the dipole approximation by retaining only the f i r s t two terms in the pow r,series expan-

sion of el*.' in eq. (21

where

n u

i s the absorbed s o f t x-ray photon energy, which i s identical t o the energy t r a n s f e r i n the x- ray Raman s c a t t e r i n g pro- cess, '6 i s i t s polarization vector, and

T ( w )

has the same functional form a s de- fined in eq.

(511.

As has been pointed out by Mizuno and Ohmura, the x-ray Raman spectrum should have esse- n t i a l l y the same shape a s the corresponding s o f t x- ray absrption spectrum1. I t i s a l s o found t h a t the mo- mentum t r a n s f e r 6 plays the same role a s the polariza- t i o n vector 8 in absroption spectroscopy in defining the c r y s t a l l i n e direction i n which information about the density of unoccupied s t a t e s may be obtained.

and derived the following

expression f o r the dynamic

^{4 -}

s t r u c t u r e f a c t o r s($,

w )

of

the x-ray Raman scattering1

7 3 -

4

2

s(?,

W ) =

b

^{T ( w )}

-

^{q, ( 4 )} _{0 2 -}

wehre

^T?

-

ffl 1 -

T ( w ) ^E

cl<k/?l0>12

6 ( E k

-

^EO

- n u ) .

⁽⁵⁾

Beryllium qo = 0.34 q = 1.25 O.U.

Lithium qo = 0.35 q = 0.93 a,".

o o o o 3 // n j o l o n o m 3 // [I001

A "'Ad 3 N 11111

0 0

. ~ ~ b * g ~ ~ 8 ,

8

2 Gmphits qa = 0.29 q = 1.67 0.u.

2

Y

"sl

- '

*

;

Q

0

0 - 4 5 $0 $5 Yo 7'5

Fig. 1 X-ray Raman spectra f o r single crys-

t a l lithium ( a ) , single crystal beryl1 ium

( b ) and pyrolytic graphite ( c ) .

3. Experiments

The double d i f f e r e n t i a l c r o s s s e c t i o n f o r t h e x-ray Raman s c a t t e r i n g by L i , Be and g r a p h i t e was measured by means of a s p h e r i c a l l y bent Si-crystal-ana- l y z e r i n connection with a double-crystal monochromator mounted on t h e two- axi s-di f f r a c t o m e t e r a t HASYLAB using synchrotron x-rays from DORIS 114. The experimental setup and t h e data processing were t h e same a s f o r t h e mea- surement of t h e dynamic s t r u c t u r e f a c t o r of t h e valence e l e c t r o n s i n L i me- t a l reported i n Ref. 5. Some of t h e measurements were performed by means of a Si (333) s p h e r i c a l l y bent c r y s t a l analyzer combined with a Ge(220) double- crystal-monochromator f o r t h e photon energy of 5.95 KeV with an o v e r a l l energy r e s o l u t i o n of t h e s p e c t r a l a n a l y s i s of 1.0 eV measured f o r t h e FWHM o f t h e Rayleigh l i n e s . For t h e o t h e r measurements t h e Si(444) r e f l e c t i o n of t h e s p h e r i c a l l y bent c r y s t a l analyzer was used i n connection with a Ge(311) asymmetric-cut double-crystal monochromator f o r t h e photon energy of 7.93 KeV with an energy r e s o l u t i o n of 0.8 eV. Each of t h e followin experimental r e s u l t s a r e c h a r a c t e r i z e d by the dimensionless parameter qa.

4. Eperimental R e s u l t s

A f t e r normalization using t h e f sum r u l e f o r t h e s(:, w ) p r o f i l e from t h e valence e l e c t r o n s , an almost f l a t background due t o t h e t a i l of t h e valence e l e c t r o n p r o f i l e was subtracted. The f i n a l experimental values of t h e

x-

ray Raman spectrum were reduced t o an a b s o l u t e s c a l e per K-electron hy mul- t i p l i c a t i o n with a f a c t o r a = V / K , where V and K a r e t h e numbers of va- lence- and K-electrons i n t h e sample, r e s p e c t i v e l y : a = 0.5 f o r L i

,

a = 1 f o r Be and a = 2 f o r g r a p h i t e .

The Li-Raman s p e c t r a a r e shown i n Fig. l ( a ) . Within t h e s t a t i s t i c a l accura- c y , t h e s p e c t r a a r e independent of q - d i r e c t i o n . In c o n t r a s t , t h e Be-Raman s p e c t r a e x h i b i t an anisotropy a s shown i n Fig. l ( b ) . A remarkable a n i s o t r o - py e x i s t s f o r t h e highly o r i e n t e d p y r o l y t i c g r a p h i t e data a s seen i n Fig.

l ( c ) .

5. Comparison with absorption s p e c t r a

Since t h e L i Raman s p e c t r a a r e independent of q - d i r e c t i o n , t h e x-ray Raman

B~rylllum X-ray Roman o e s o qa = 0.28

I

-

2

2

C

t.

Fig. 2 Comparison of x-ray Raman s p e c t r a and s o f t x-ray absorption s p e c t r a f o r L i ( a ) and Be ( b )

-

^Lithium X-ray Raman

0 . 0 0 q 0 = 0 . 2 2 o 0 0 qa

-

^0.38

Absorption

---- e

-.

V 1 -

d

C9-866 JOURNAL DE PHYSIQUE

spectrum on t h e L i s i n g l e c r y s t a l w i t h

6

// [ I 1 0 1 may be compared w i t h t h e s o f t x-ray absorption spectrum on p o l y c r i s t a l l i n e L i f o i l . Two L i Raman spectra f o r d i f f e r e n t values o f qa a r e shown i n Fig. 2(a) i n comparison w i t h t h e a b s o r p t i o n spectrum measured by R. Haensel e t a l . a t D E S Y ~ . The a b s o r p t i o n curve Sa was d e r i v e d from t h e p u b l i s h e d data u by t h e r e l a t i o n

u

-

Uv S a = c -

W

'

^{( 7 )}

where I.IV i s t h e c o n t r i b u t i o n o f t h e valence e l e c t r o n s t o t h e absorption c o e f f i c i e n t (here we assume uv ^a w-31, w i s t h e absorbed phonen energy, and c i s t h e n o r m a l i z a t i o n c o n s t a n t g i v i n g the same area as t h e Raman spectra over t h e energy range up t o 57.5 eV. I n Fig. 2 ( b ) t h e p o l y c r y s t a l l i n e Be Raman s ectrum i s compared w i t h t h e a b s o r p t i o n curve measured by t h e same authorsp. The a b s o r p t i o n data was d e r i v e d i n t h e same way as f o r L i w i t h t h e n o r m a l i z a t i o n range up t o 116 eV. The agreement between t h e two types of measurement i s good b o t h over t h e i r f i n e s t r u c t u r e and over t h e i r over- a l l shape. It can be concluded t h a t t h e x-ray Raman spectrum i s e s s e n t i a l l y e q u i v a l e n t t o the corresponding s o f t x-ray a b s o r p t i o n spectrum. I n t h e case o f Be, however, a discrepancy can be seen a t about 14 eV from t h e edge.

T h i s may be due t o t h e samples used. Sample p r e p a r a t i o n f o r s o f t x-ray ab- s o r p t i o n spectroscopy i s a r e a l problem when r e l i a b l e b u l k i n f o r m a t i o n i s t o be obtained. X-ray Raman s c a t t e r i n g w i l l , t h e r e f o r e , p r o v i d e a powerful a l t e r n a t i v e experimental t o o l t o EXAFS f o r s t r u c t u r e i n v e s t i g a t i o n s i n 1 ig h t elements.

The x-ray Raman s c a t t e r i n g experiment has t h e f o l l o w i n g advantages over t h e s o f t x-ray a b s o r p t i o n experiment f o r l i g h t elements:

1. One can e a s i l y b u l k s i n g l e c r y s t a l s , t h e s i z e o f which i s o f the o r d e r of a few

mm.

The c o n t r i b u t i o n from t h e sample surface i s o f much l e s s importance.

2. One can simply make an a n i s o t r o p y measurement. The s c a t t e r i n g v e c t o r

$,

which p l a y s t h e same r o l e as the p o l a r i z a t i o n v e c t o r $ i n a b s o r p t i o n spectroscopy, can be a1 i gned w i t h any c r y s t a l o r i e n t a t i o n near1 y i nde- pendently o f t h e sample geometry.

3. One can o b t a i n a d d i t i o n a l i n f o r m a t i o n t o t h e s o f t x-ray absorption expe- r i m e n t through t h e q-dependent measurement o f the x-ray Raman spectrum.

4. The experimental values o f t h e x-ray Raman spectrum can be brought on t o an a b s o l u t e scale by means o f t h e f-sum r u l e . This i s o f g r e a t advantage f o r comparison w i t h t h e o r e t i c a l c a l c u l a t i o n s .

References

1 Y. Mizuno and Y. Ohmura, J. Phys. Soc. Japan

22,

⁴⁴⁵ (1967) 2 T. Suzuki, J. Phys. Soc. Japan

22,

1139 (1967)

3 T. Suzuki e t al., J. Phys. Soc. Japan

2,

730 (1970)

4 W. Schulke and H. Nagasawa, Nucl. I n s t r . and Meth. 222, 203 (1984)

-

5 W. Schulke, H. Nagasawa, S. M o u r i k i s and

P.

Lanzki, Phys. Rev. B 33,

6744 (1986)

-

6 R. Haensel e t a1

. ^,

Phys. S t a t . Sol

;

( a ) - 2, 85 (1970)