FINE STRUCTURE OF RESONANT RAMAN SCATTERING

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FINE STRUCTURE OF RESONANT RAMAN SCATTERING

P. Suortti, V. Eteläniemi, K. Hämäläinen, S. Manninen

To cite this version:

P. Suortti, V. Eteläniemi, K. Hämäläinen, S. Manninen. FINE STRUCTURE OF RESO- NANT RAMAN SCATTERING. Journal de Physique Colloques, 1987, 48 (C9), pp.C9-831-C9-834.

�10.1051/jphyscol:19879147�. �jpa-00227258�

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FINE STRUCTURE OF RESONANT RAMAN SCATTERING

P. SUORTTI, V. ETELANIEMI, K.

HMLAINEN

and S. MANNINEN

Department of Physics, University of Helsinki, Siltavuorenpenger 20 D. SF-00170 Helsinki 17, Finland

La diffusion Raman rksonnante par nickel a Btk mesurke avec rayonnement CuK,, et une spec- troinktre B cristal courb6

.

Pour la premiire fois de modulations pareilles B EXAFS ont 6t6 observCes dans le spectre diffusk. Les differences fonda~l~entales entre ces deux types de st,ructures de la modulation sont discutkes.

Abstract

Resonant Raman scattering from nickel sample has been measured using Cuh',, radiation and a focusing crystal spectrometer. For the first time EXAFS-like modulations has been observed in the scattered spectrum. The basic differences between these two type of modulation stxuctures is discussed.

1 Introduction

In the resonant Raman scattering process (RRS) the energy of the incident x-ray photon is just.

below the K-absorption threshold of the target. There is a virtual K-shell hole in the intermediate

state, and the final state is that of an L-shell (or higher shell) hole, an electron in the c o ~ ~ t i ~ ~ u ~ u i ~ i and an emitted photon. As the photon energy, tLwl

,

approaches the threshold K-shell binding

energy hR1,

,

the scattered intensity increases approximately as (R1, - wl)-l

.

The spectrunl is continuous, because the photon and the electron share the available energy, tLwl - tiwnpl

,

where n p j denotes the final hole state, e.g. 2 p l l z or 2p3jz for KL-RRS.

The theory of inelastic x-ray scattering, including the resonance phenomena, has been reviewed recently by Aberg and Tulkki [I]. The differential cross sect,ion per unit. frequency for the K- resonance scattering by np, electrons is

where b2 is the energy of scattered photon, FIuthe kinet.ic energy of the ejected elec.tron,

rl,

the width of the 1s level, gnpj,l, the oscillator strength and (dgl,/dw) the oscillator density which is proportional to the density of states.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19879147

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C9-832 JOURNAL DE PHYSIQUE

The above expression can be written in a slightly different form, where the structure of the spectrum ^ISmore transparent. The average differelitial cross section per unit frequency and solid angle for the scattering by 2p3 electrons (1 =

f

,;) is

where the condition w2

+

w = wl - R2pI is used [2].

The aim of the present work is t o study the fine structure of the emission spectrum and conipare the results with those from the absorption spectroscopy. Particularly, EXAFS-like modulations of tlie spectrum are searched for. When the energy of tlie incident is larger then the K-absorption tliresliold energy, K-shell fluorescence results. The energy of tlie Km photon is hw2 = hOl, - finzp, and the rest of the energy, hwl ^-hw2 ^-hfhp, is carried by the ejected electron.

The electron is scattered from the n e i g l ~ b o u r i n ~ atoms, and the transition probability, or the oscillator density dgl,/dw, is modulated. This is seen as the EXAFS of the absorption cross section, when the energy of the incident photon is varied. In the RRS spectroscopy, the incident energy is kept constant, and the scattered radiation is analyzed. It is seen from equation (2) that a t a given energy hw2 = hwl - hwz, ^-hw the cross section is proportional t o ( d g l , / d ~ ) n l s + w , and the RRS spectrum resembles the mirror image of the absorption spectrum as a function of FLU.

Particularly t h e RRS spectrum is expected to exhibit tlie lliodulations seen in the EXAFS.

2

Experimental

The measurements where made on a Ni powder sample using CuK,, ~ a d i a t i o n from a conventional fine focus x-ray tube. The energy of the irlciderlt photons is 284 eV below the threshold energy, 8333 eV. T h e cross section of the RRS a t this energy is about 7~: [3], which is only about 0.3 % of the total scattering cross section. On the other hand closer t o the threshold the intensity of the R R S spectrum increases, but the shape approaches the narrow fluorescence line, where the modulations due t o the oscillator density could be observed only with a high resolution spectrometer. Is was concluded t h a t the low intensity of the RRS at C u h h , could be coltlpensated by the use of a n efficient spectrometer which has moderate resolut,ion.

Figure 1. Design of the spectrometer.

X-rays from the Cu fine focus tube (F1) are monochromatized (M) arid focussed ( F z ) onto the sample (S). Scattered radiation is analyzed using a curved crystal analyzer (A) and focussed onto the receiving slit (RS). Detector (D) is a scin- tillatio~l counter. There is a beam tunnel i n front of the receiving slit and two lead _"

plat,es (shadowed areas) t,o minimize air and slit scattering.

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narrow line at the sample. This serves as the source of radiation for the focusing analyzer, where the sample, cylindrically bent perfect crystal and the detector are on the Rowland circle, as shown in Fig. 1 . The scattering angle is constant, and the crystal and the detector move at a constant linear velocity. The coupling of the sample, crystal and detector to the center of the Rowland circle ensures the correct angle of the crystal location of the receiving slit. The scan is linear in t.he wavelength X z of the scattered radiation. The efficiency of the ~pectromet~er is good as the solid angle subtended by the analyzer crystal can be made large. At the same time, the background is essentially that of the detector noise, because beam tunnels and a very narrow receiving slit can be used.

The monochromator is of Johansson type. The radius of the Rowland circle is 250 mm, and the 10.1 reflection of quartz is used. The optical width of the source is 30 ~ i m , and the monochoromator rejects completely the K,, component of the characteristic radiation. The width of the focal line at the sample is about 50 pm, and the flux about 5

.

^10' photons. The analyzer uses the 220 reflection from a Johann type silicon crystal, which is bent to a radius of 500 mm. The surface of the crystal is lapped, so that the reflecting power is several times larger than that of a polished crystal. The resolution, AX/& is about 2.10-3 at CuK,. The detector is a low noise scintillation counter, which has a thin B e window.

The over-all spectrum was scanned with a collst,ant Sa step starting below the (almost) elastic line that arises from the thermal diffuse scattering. This scan provided the energy calibration and a extrapolation of the resolution function to the wavelengths of the RRS spectrum. The scans of the RRS were started just below the edge at X=1.72345

A,

which corresponds to the energy of fiwl - fiRp,l,

,

and typically the length of the scan was AX=70 mA or il\E=300 eV. The scans were repeated several times in order to eliminate the possible effects of the drifts of the measuring system. A typical step size Sa was 0.2 mm which corresponds to 6X=1.535 mA or about 6.5 eV, measuring time t=5000 sec and total of 20000 counts were collected at the peak of the RRS spectrum.

The experimental data were not corrected for the effects of the wavelength-depended response function of the analyzer, nor for the effects of absorption, although these are included in t,he generalized deconvolution process developed in our laboratory. In the present case the deter- mination of the response function of the lapped analyzer crystal would have required extensive subsidiary measurements, and those were deemed not worthwhile, as the resulting corrections vary monotonically with the wavelength.

3 Discussion

It is seen from Eq. ( 2 ) that the RRS intensity has t,he Lorenzian tail of the corresponding fluorescent line centered at wz = R1, - Rz,. When wl

<

R1,

,

the RRS spectrum begins at wl - RzP3

,

and the intensity falls of with increasing w (decreasing ^{w z )}Actually, there are two overlapping spectra corresponding to j = i and j=:. Each one is expected to be modulated by the fluctuations of the oscillator density (dgl,/d~)n,,+,.

For the comparison with the experiment the theoretical RRS cross section was modulated by the experimental oscillator density as taken from EXAFS measurements, and the two colliponents

( j = f and j = ! ) were suninled and cotivoluted with resolutio11 function. Unfortunately the energy difference fiRzp,l, ^-fiRz,,l, is about a half of the most prolninent EXAFS period. The IIC-t effect is reduced even further, when the theoretical result is convoluted by the resolution function of the spectrometer.

The calculation does not reproduce all the features of the experimental RRS spectrum, alt.hough t,he general features are similar. Perhaps the most renmrkable difference is that the modulations of t,he measured spectrum are more prominent t,has t.hose deduced from the EXAFS spectrum.

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C9-834 JOURNAL DE PHYSIQUE

This may point t o a fundamental difference between t.he absorption and RRS spect,ra : all t.he features of the first one are convoluted by t,he final width of the Is-level, while t,liis does not ta.ke place i n the RRS spectrum. The corresponding narrowing of the leading edge of RRS spect,rum was observed by Eisenberger, Platzman and Winick [5]

The present work demonstrates the existence of the EXAFS-like nlodulations of the RRS spectrum, but also highlights the difficulties and deficiencies of spectroscopy with a conventional source.

Presumably more favorable cases in regarcl to hf12,,,, - hC22,,,, vs. the EXAFS period can be formed, but the accessible cases are limited by the available characteristic x-ray wavele~~gths. For example if Z r target and MoK,, radiation is used the partial cancellation of the niodulation periods and two overlapping RRS lines can be avoided and the details in the RRS spectrum can be studied much more effectively. Also the intensity is a problem, although it could be increased by a factor of 5 to 10 by a larger detector and evacuated beam paths. All of these problems are removed by the use of a high-resolution (order of 1 eV) spectrometer operation at a synchrotron source. Preparations for such a measurement are in progress.

resonant Rarnan scattering

. ( . - ( ' l . - . l . l . c . . = q .

-38. 8. sa. 88. 0s. 126. 158. 18s. 21s. 24s. 278.

d w t d w frantke ab. edge (oV)

Figure 2. Experimental resonant Raman spect,rum (dashed line) of Ni and the t,heoretical model (solid line) which is based on the calculated cross section (Eq. 2) modulat,ed with experiinent,al Ni-EXAFS oscillator density. Both j =

$

and j = contributions t o KL-RRS are taken into account and t h e model spectrum is finally convolut,ed with the experimental resolution fundion.

The error bars include the statistical error only.

Acknowledgements

The work reported here has been supported by the Academy of Finland (grant 01/54.5).

References

[I] ABERG T., T U L K K I J . in Afomic Inner-Shell Physlcs, edited by Crasemann B. (Plenum, New York, 1985) Chap. 10.

[2] MANNINEN S., SUORTTI P., COOPER M. J., C'HOMILIER J., LOUPIAS G., Phys. Rct,., B34, 353 (1986).

[3] SUORTTI P., Phys. Stat. Sol. ( b ) 91, 657 (1979).

[4] SUORTTI P., PATTISON P., WEYRICH W., J. Appl. Cryst., 19, 336, 343 and 3.53 (1986).

[5] EISENBERGER P . , PLATZMAN P . M., WINICI< H., Phys. Rev. Lett., 36, 623 (1976).