ON THE NATURE OF NONSTRUCTURAL LOW-R PEAK IN FOURIER TRANSFORMS OF SOME EXAFS-SPECTRA

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ON THE NATURE OF NONSTRUCTURAL LOW-R PEAK IN FOURIER TRANSFORMS OF SOME

EXAFS-SPECTRA

A. Kochur, A. Nadolinsky, V. Demekhin

To cite this version:

A. Kochur, A. Nadolinsky, V. Demekhin. ON THE NATURE OF NONSTRUCTURAL LOW-R PEAK IN FOURIER TRANSFORMS OF SOME EXAFS-SPECTRA. Journal de Physique Colloques, 1986, 47 (C8), pp.C8-83-C8-87. �10.1051/jphyscol:1986814�. �jpa-00226040�

ON THE NATURE OF NONSTRUCTURAL LOW-R PEAK IN FOURIER TRANSFORMS OF SOME EXAFS-SPECTRA

A.G. KOCHUR, A.M. NADOLINSKY and V.F. DEMEKHIN

Rostov Raifway Ingineers Institute, Chair of Physics, 344017 Rostov-on-Don, U.S.S.R.

ABSTRACT

K-absorption s p e c t r a of k r i p t o n and zirconium a r e c a l c u l a t e d con- s i d e r i n g a d d i t i o n a l monopole e x c i t a t i o n s of 3d-shell. It i s shown t h a t the disturbance of smoothness of t h e atomic photoionization cross s e c t i o n due t o multi-electron e x c i t a t i o n s including 3d-shells lea.' t o t h e appearance 04 low frequency W S - o s c i l l a t i o n s t h a t do not coxespond t o the s t r u c t u r e of atomic encirclement of t h e ab- sorber. Such an e f f e c t can make d a t a analyses d i f f i c u l t f o r t h e s p e c t r a with weak s t r u c t u r a l s i g n a l .

It i s known t h a t magnitudes of t h e f o m e r transforms (FT) of some E m s - s p e c t r a have la;:.-R peaks which cannot be a t t r i b u t e d t o any interatomic d i s t a n c e s C1l. This means t h a t t h e normalised spect-

contain low-frequency o s c i l l a t i o n s . Here

PO

Studying t h e spectrum of gaseous b i p t o n i t was supposedL21 t h a t t h e low frequei~cy o s c i l l a t i o n s of X may be incorporated i a

and be caused by m u l t i e l e c t r o n e x c i t a t i o n s . Peaks i n FT of ZrK-spe- c t r a of amorphous Z r - N i a l l o y s were obtained a t R n 1 %L31. ^{It was}

supposed t h a t each minimum of corresponding low-frequency o s c i l l a - t i o n s of X i s caused by t h e a d d i t i o n a l e x c i t a t i o n of t h e s p e c i f i c nl-level

.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986814

C8-84 JOURNAL DE PHYSIQUE

This paper's aim i s t o study t h e o r e t i c a l l y how t h e e f f e c t s of nu- l t i p l e i o n i z a t i o n influence t h e shape of absorption s p e c t r a far be- yond t h e edge and how t h i s may a f f e c t t h e E W S d a t a analyses v i a FT method.

K-absorption s p e c t r a of I& and Z r were c a l c u l a t e d considering a d d i t i o n a l monopole e x c i t a t i o n s 36 -, j n , E ^d.

Atomic photoionization c r o s s s e c t i o n Day be expressed through a matrix element of d i p o l e t r a n s i t i o n operator :

1 i > and I f > being t h e wavefunctions of i n i t i a l and f i n a l s t a t e s . me-electron wavefunctions of \ i ' > were obtained by solving t h e

2 2 6 Hartree-Fo& (HF) equations f o r t h e configurations KO = I s 2s 2p

-

2 2

3s23g63d1 04s24p6 i n Rr, and KO = [&J ⁴⁶ 5s i n Zr. Calculating

I ^f >, t h e monopole core e l e c t r o n s ' rearrangement was taken i n t o con- s i d e r a t i o n : r a d i a l n l - o r b i t a l s were obtained from HI? equations f o r t h e configuration &1 = IS-' Ep ( t h e populations Nnl w i l l be hereaf- t e r noted r e l a t i v e l y t o X,). S u b s t i t u t i o n of \ ^{i) and} \ ^{f > i n (2)}

by t h e i r one-determinant functuons leadsL41 t o t h e following eapres- s i o n f o r t h e K-ionization matrix element:

where N = 1

n

<ls,lls> n l

of ITo, "+" s i g n denoting t h e nl-functions of ^K,,.

!Be f i n a l s t a t e f o r Dl i o n i z a t i o n i s deccribed by t h e configu-

4,5- f

r a t i o n % ^{= IS" 3d-I}

c~~

.

where k ^{= 0} a t t h e K-ionization threshold.

If E, i s t h e K-ionization threshold energy and

q,,,,

E = A E ~ , + ti' + E'

where AE& = - ^{EK; AEK* = EKM} - ^Er,

Let GI ( ) * NIsMl 2 ( E ) be t h e $-ionization c r o s s s e c t i o n a t t h e energy 6 beyond t h e edge. Then using (4,5) and omitting a weak de- pendance of cross s e c t i o n on photon energy one has t h e following expression f o r t h e multiple e x c i t a t i o n c r o s s s e c t i o n :

0

Here ~ f $ i s t h e number of vacancies i n nd-shell. A%.,, and A E m were c a l c u l a t e d a s d i f f e r e n c i e s 09 f u l l energies of corresponding atomic h o l e s t a t e s , they axe A E K N = 4 117.4 eU, oEKh;: 126.1 eV f o r and

4 5

AEKM ⁼ 207.6 eV, AEic,,= 225.9 eV, A E k M = 231.3 eV f o r Z r . Gnly two terms i n t h e sum of (6) were considered because t h e overlap integ- r a l s ( n d \ 3d> decrease sharply while i n c r e a s i n g n (see t a b l e I),

Calculated s p e c t r a are shown i n f i g . 1. Bor t h e comparison with t h e experiment t h e s p e c t r a were convoluted with a gaussian curve. A t t h e KM4,5 threshold t h e r e i s a s l i g h t r i s e of spect- rum due t o t h e opening of chann- Table 1. e l s f o r t h e a d d i t i o n a l d i s c r e t e Gverlap i n t e g r a l s < nd 1 3d). 3d --, nd e x c i t a t i o n s . A t t h e re-

gion beyond t h e KM4,g threshold t h e descent of spectrum becomes noticeably l e s s s t e e p which is cau- sed by t h e donation of double t r a n s i t i o n s l s 3 d * E ~ E ' & , 3d-elect- rons going i n t o t h e s t a t e s of continuous spectrum.

Calculated s p e c t r a were t r e a t e d v i a t h e standard FT method using a polynomial approximation f o r ,Ma

.

C8-86 JOURNAL DE PHYSIQUE

spectra.

-

UU14

-

(1.013-

1

-

-..I_

.

^{. . .} -

L .

I

7 . l .

-

EK M:E Exn

2 - c a l c u l a t e d consi-

0 '80 '160 '240 Figure I.

I ^{13'0 320ev} Atomic H-absorption

d e r i n g Dl4 5-ioniza- t i o n ; ⁹

PI

3 - experiment

.

Zr

1

-

-

\ ctmun of gaseous fi

C21

(102- /

\ I \

\ 3

-

\ ctrum of amorphous alOy N i ~ . 24+r0.75B1

' I '2 '3

@,A

may appear i n FT1s of another atoms' absorption spectra. m e lead- i n g r o l e must be played by the a d d i t i o n a l monopole e x c i t a t i o n s nl-

{ n , E?j1 having the thresholds 100 + 300 eV beyond the edge of s i n g l e ionization. I n t h i s case t h e smoothness of atomic cross s e c t i o n i s a f f e c t e d i n t h e r e e o n c r u c i a l f o r M A P S d a t a analyses. IChe main donation w i l l be from t h e a d d i t i o n a l i o n i z a t i o n s of nl-shells with the highest 1 f o r they have maximnm p r ~ b a b i l i t y ~ ~ ~ . m e r e f o r t h e e f f e c t discussed w i l l be most noticeable i n s p e c t r a of heavy atoms where 100 -t 300 eV deep a r e the l e v e l s of d- and 9-symmetry, though t h e influenoe of 2p-additional i o n i z a t i o n s must be investigated f o r l i g h t e r elements.

'Phe amplitude of s t r u c t u r a l o s c i l l a t i o n s of X/ due t o t h e influ- ence of atomic encirclement nay be s e v e r a l times g r e a t e r than t h a t caused by double i o n i z a t i o n s , thus low-R nonstructural PT peak be- i n g n e g l i g i b l e compared t o t h e s t r u c t u r a l ones. Elevertheless those amplitudes may become of t h e same order of magnitude i n s p e c t r a with weak EXAPS-signal, t h e meddling F'P peak being q u i t e high compared t o s t r u c t u r a l ones. Such a s i t u a t i o n may take plase i n s p e c t r a of amor- phous c ~ m ~ o u n d s ~ ~ ~ . &e e f f e c t s discussed may be noticeable a l s o i n s p e c t r a of t h e compounds where a heavy absorber i s surrounded by l i g h t ligands having weak backscattering amplitudes. F i n a l l y , struc- t u r a l o s c i l l a t i o n s may be small a t high tempera-t;ures of substance under study. In t h i s case, a s it i s known, the s t r u c t u r a l FT peaks become s h o r t e r and widen while multiple i o n i z a t i o n peaks must remain unchanged.

1, COOK J.W., SAPERS D.E., 9. Appl. &rs. 52 (1981) 5024.

2. MALDEI;I)T W., NIEMAN W., HAENSEL R., RABE P., I n t . Cog. X-Ray and Inner S h e l l Proc. i n Atoms, Molecules and Solids. (Leipzig)

-

1984, p. 291.

3. FRAHM R., RAEmSEL R., RAEE P., J. Phys. F. Metal Phys. 11 (1984) 1029.

4. SlJKHORUROV V.L., DEKEXHIN V.F., T I M w S f l A Y A V.V,, LAVKEXTT'EV S.V.

Opt. Spectrosc. (USSR) 47 ^{(1979) 407.}

5. BIRUgCm A,P. , TIMCGHEVS~YA V,V., SUP;3IORUKOV V.L., VIETITI (1982) No 5515-82 Dep.