DETERMINATION OF THE THIRD ORDER MULTIPLE SCATTERING SIGNAL IN TETRAHEDRAL CLUSTERS IN LIQUID SOLUTIONS

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DETERMINATION OF THE THIRD ORDER MULTIPLE SCATTERING SIGNAL IN TETRAHEDRAL CLUSTERS IN LIQUID

SOLUTIONS

M. Benfatto, C. Natoli, J. Garcia, A. Bianconi

To cite this version:

M. Benfatto, C. Natoli, J. Garcia, A. Bianconi. DETERMINATION OF THE THIRD ORDER MULTIPLE SCATTERING SIGNAL IN TETRAHEDRAL CLUSTERS IN LIQUID SOLUTIONS.

Journal de Physique Colloques, 1986, 47 (C8), pp.C8-25-C8-29. �10.1051/jphyscol:1986803�. �jpa-

00225987�

DETERMINATION OF THE THIRD ORDER MULTIPLE SCATTERING SIGNAL IN TETRAHEDRAL CLUSTERS IN LIQUID SOLUTIONS

M. BENFATTO, C.R. NATOLI, J. GARCIA and A. BIANCONI*

I.N.F.N., Laboratori Nazionali di Frascati, C.P. Box 1 3 , I-00044 Frascati, Italy

'~ipartirnento di Fisica, Universita "La Sapienza", I-00185 Roma, Italy

ABSTRACT

By u s i n g t h e framework o f t h e m u l t i p l e s c a t t e r i n g ( M S ) t h e o r y f o r i n t e r p r e t i n g x - r a y a b s o r p t i o n s p e c t r a we show how t o e x t r a c t t h e t h i r d o r d e r M S s i g n a l i n t h e c a s e of t e t r a h e d r a l t r a n s i t i o n m e t a l c o m p l e x e s i n l i q u i d s o l u t i o n . T h i s s i g n a l i s r e l a t e d t o t h e m e t a l - l i g a n d , - l i g a n d - e t a 1 p a t h l e n g t h a n d c l e a r l y b e a r s i n f o r m a t i o n o n t h e t h r e e p a r t i c l e c o r r e l a t i o n f u n c t i o n .

I n t h e M S f o r m a l i s m t h e p o l a r i z a t i o n a v e r a g e d a b s o r p t i o n c o e f f i c i e n t a ( & ) f r o m a c o r e i n i t i a l s t a t e o f a n g u l a r momentum 1 i s g i v e n by [1,21

where aO1(&) i s t h e smooth a t o m i c a b s o r p t i o n c o e f f i c i e n t o f t h e p h o t o a b s o r b e r a n d X'(&) c o n t a i n s a l l t h e i n t e r e s t i n g s t r u c t u r a l i n f o r m a t i o n on t h e s u r r o u n d i n g . Under c e r t a i n c o n d i t i o n (we r e f e r t o R e f . [ l ] f o r t h e t h e o r e t i c a l b a c k g r o u n d ) i t i s p o s s i b l e t o e x p r e s s t h e " s t r u c t u r e f a c t o r " XI(&) a s a n a b s o l u t e convergent s e r i e s

where e a c h c o n t r i b u t i o n X,!(&) o f o r d e r n h a s a n immediate and d i r e c t p h y s i c a l m e a n i n g . It r e p r e s e n t s a l l p r o c e s s e s w h e r e t h e p h o t o e l e c t r o n e m a n a t i n g from t h e p h o t o a b s o r b e r i s s c a t t e r e d n - l t i m e s by t h e atoms of t h e environment b e f o r e r e t u r n i n g t o i t . The i n t e r f e r e n c e p a t t e r n s i n t h e a b s o r p t i o n c o e f f i c i e n t p r o d u c e d by t h e s e p r o c e s s e s a r e c l e a r l y r e l a t e d t o t h e n - p a r t i c l e c o r r e l a t i o n f u n c t i o n . I t i s t h e r e f o r e o f t h e o u t m o s t i m p o r t a n c e t o d e v i s e

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986803

JOURNAL DE PHYSIQUE

methods for extracting such signals. Up to now only the x~'(E)

( E X A P S ) term, which provides information on the pair correlation

function, has been the monopolising object of extended experimental investigation. We think however the time is now ripe to begin to look beyond this minimal approach and try to exploit all the potentiality of the x-ray absorption spectroscopy ( X A S ) for obtain structural information. In this sense X A S is unparalleled by all other techiniques used for structural investigation.

On general physical ground, since we are dealing with an interference process , it is easy to convince oneself that the general functional expression for the quantities X,,'(&) is given by

where C denotes the sum over all paths of order n, R-! the

a ^IJ

corresponding total path length, k = d ~ is the photoelectron wave number, Q,' + ^{2 610} is the phase shift acquired by the electron wave in the path n, including the central atom phase shift SI0 and An is the amplitude of the interference patterns. The theory provides well defined expression for these quantities [l].

ENERGY (ev)

0 80 160 240 320 400 480 560 640

F i q . 1

Comparison between ncrnalized L?

X-edce

a b r o i p z l o n s ? e c t r a o f

[Mn04]- a.?d [ M ~ ( o H ~ ) ~ ] ~ + Ions :rca

s 0 1 u t i o n cf KL?O4 and HnCIZ The r e s p e c t i v e

s c a l e r are Given i n :he Y>per L I C U ~ Z I p a r r of t h e f l g u r a .

p a r t i t : c 3 of :he spectra i n FHS

HSI, 40 120 160 200- 240 280 ^In5 I l ~ i e r m e d l a t e Hsi and S 5 (sir.sle

rca:tcr:ng 1 r e g i c z r

skczched.

ENERGY (ev)

A direct, simple experimental evidence that XAS is actually

capable of "structural selectivity" is provided by Pig.1. Here we

compare the Mn K-edge spectra of [Mn04]- and [ M ~ ( o H ~ ) ~ ~ + complex in

acqueous :ol:tion, after a res.caling ?f the energy scale in the

ratio (R, /R2 )2=~.47, where R, and R 2 are the Mn-0 distances in

the two complexes, corrected for the linear term coefficient of the

phase function@,,(k), in order to eliminate the effect arising in the

dipendence of $,(k) on the energy.

The two spectra, after a further rescaling of the oscillating amplitude to take into account the different number of neighbours in the two complexes (see insert in fig.1) show a superposed behaviour in that energy kegion in which the photoelectron probes only the pair correlatio* function (EXAFS regime). Below the 160 eV (referred to [ ~ n b ~ ] - e n e r g y scale) the two spectra deviate from one other. This fqct is a clear indication that below this energy x-ray can distinguish between the two complexes. A theoretical calculation of the absorption coefficient for the two clusters shows that deviations from the EXAE'S regime first begin to show up in the

[Mn04]- complex. By a fortuitous cancellation of higher .order terms, the EXAFS regime extends down to 40 ev for the [M~(oH~)~]~+

cluster [3,4]. We therefore compare in Fig. 2 calculated and experimental spectra of [Mn04]-.

To evaluate the atomic phase shift we have used the usual Mattheiss prescription for the muffin-tin approximation and the energy dependent Hedin-Lundqvist potential for the exchange-correlation part between the photoelectron and the electrons of the system. In insert (a) the quantity aFC is the calculated absorption coefficient, obtained by exact inversion of the MS matrix, convoluted by an energy dependent Lorentzian broadening function which takes account of the experimental resolution, the core-hole widht and the damping of the electron in the final state. Insert (b) and (c) show the breakdown of aF in term of the partial contribution an= . a X,. The signal ao+ a2 + ^{a3 is}

enough to get good agreement with a ~ i n the range 50+150 eV and in this interval a,, ( n M ) is negligible.

l

This is a fortunate case where the deviation from pure EXAFS behavior is only due to the ag term which therefore can be extracted using the following procedure summarized in the Fig.3.

The experimental modulated part of the absorption coefficient is obtained as

Xtot = (a - ao)/ao that it is.

equal toX2+X3in the energy

F:9.2 a ) Ccr;.pariton between e x p e r i n e n t a l a and c a l c u l a t e aFC f o r -

[Mn04r c c ~ p l ~ x .

b) >:*akdcvn o r t h e d

c a l c u l a t e d bare spectrcm a? i n t o p a r t i a l c o n t r i 5 u t i o n r

c )

HS contributions of

n-th crder t o the absorption c o e f f i c i e n t

..- _{, v , , , , , , , ]}

0 20 CO 60 80 100 120 140

ENERGY I eV)

JOURNAL DE PHYSIQUE

range 50j150 ev. To extract X3 we have subtracted from Xtot the X2 term obtained by the theory [3,5] suitably convoluted. The difference is re- ported in insert (b) of Fig.3. Comparison with the calculated X3(€) si- gnal shows that one oscillation is missing. We have assigned the extra ob- served intensity to a double electron transition involving simultaneously the Mn ls(A1) - 3d(T2) and 3p(T2) - 3d(T2) excitations. A deeper discus- sion and a full self-consistent calculation of the two electron excitation will be presented in a forthcoming paper 161.

The "one-electron" spectrum is obtained by subtracting from the measured absorption coefficient the contribution of the multielectron excitation assumed to have a Lorentzian shape. The result is shown in insert (c) of Fig. 3 while the comparison between the theoretical X3 (E) and the "one-electron" experimental X3 (E) is reported in insert (d) .

9 1 5 . 4 -1Cppei p a a e l l - P h a s e f u n c t i o n f o r f o r t h l r d o r d e r s c a t t e r l n q p a t h i n [Mn04j' c1us:er ( f u l l curve). The s t r a i g h t l i n e ( d a s > e d curve). o b t a i n e d by

l e a s t S q u a r e f i t t i n g p r o c e d u r e , g i v e r a n i n d i c a t i o n o f t h e s l o p e o f $31.

- ( l o v e r p a n e l l - C o n p a r i r o n between t h e o r e t i c a l a n d e x p e r i m e n t a l F o u r i e r t r a r f o r m e d s i g n a l s .

L.00

2.00

- -c

7

e 3 1 ( k ) - ^{-alk + c}

al - ^{0 . 8 5 A}

, -

m

S

"ern

-2.00 -

- ^{c.00 I I I I}

L 9 0 2 3 0 3 1 0 a.70 a 0 6 5 0

k(A')

e x t r a e t X, c c n t r i b u r i o n . Go:ng from t o ? t o b o t t ~ m

have:

( a ) 1) E x p e r i r e t t a l X t O t 2 ) i h c 0 r e t : c a l X2

( b ) 1 ) E x p e r i r e a t a l X3

2 ) T E e o r o r i c a l X 3 a

( c )

11 E x p e r i s e n t a l X t c t

2 )

e l e c t r o n " ex?. X t o r \ / - \ -

I I b ,

-

(c) 1 ) 'one e l e c t r o n . ^{e x p . X 3 0.0 2 L L8 7.2 9 6 12}

1 )

Tbeciet:cal X j R I ~ I

position of the central metal ion with respect to any two oxigen ligands .

Its period is obviously related to the perimeter of the 12 equivalent triangular paths (see Eq. 3) Mn-0-0-Mn as shown in Fig.

4, where the Fourier trasform of the signal and the total phase (upper panel) of the third order scattering process is reported.a By adding the observed maximum in the Fourier trasform at about 5 A to the abgolute value of the slope of the total phase function of the X3 (E) signal ( = 0.85 A ^{) ,} as done in EXAFS analysis, we obtain 5.85 A, ^{face to} a real value of 5.87 A .

This preliminary analysis can and must be improved. The aim however was to show, convincingly we hope, that XAS has the potentiality to go beyond the pair distribution function and can provided useful structural information.

[l] C.R.Natoli and M.Benfatto, these proceeding (21 W.L. Schaich, Phys Rev. , 6513 (1984)

l 3 1 M.Benfatto, C.R.Natoli, A.Bianconi, J.Garcia, A.Marcelli, M.Fanfoni and I.Davoli, Phys Rev B in press

[41 J.Garcia, A.Bianconi, M.Benfatto and C.R.Natoli, these proceedings

[5] J.Garcia, M.~enfatto, C.R.Natoli, ~.Bianconi, I .Davoli, A.Marcelli, Solid State Comm. 58 , 595 (1986)

(61 A.Bianconi, J.Garcia, M.Ruiz, C.R.Natoli and M.Benfatto ,

submitted to Phys. Rev A and references therein.