Measurement of polarization anisotropy of the anomalous forward scattering amplitude at the niobium K-edge in LiNbO3

814

MEASUREMENT

Nuclear Instruments and Methods in Physics Research A246 (1986) 814 816 North-Holland, Amsterdam

OF POLARIZATION

ANISOTROPY

OF THE ANOMALOUS

FORWARD

S C A T T E R I N G A M P L I T U D E A T T H E N I O B I U M K - E D G E IN L i N b O 3 Ulrich BONSE

lnstitut fftr Physik, Universitiit Dortmund, Postfach 50 05 00, D-4600 Dortmund 50, FRG Andreas HENNING

lnstitut ff~r Physik, Universitiit Dortmund, Postfach 50 05 00, D-4600 Dortmund 50, FRG

We report polarization effects of the anomalous forward scattering terms at the K-adsorption edge of niobium in a LiNbO 3 single crystal. Nearly linearly polarized synchrotron radiation was used to measure the directional properties of the dispersion corrections f ' and f " by means of X-ray interferometry and adsorption experiments. Anisotropic contributions of the K-shell electrons to the niobium ionic scattering factor are observed in the near edge region for parallel and vertical orientation of the polarization vector c with respect to the hexagonal c-axis of ferroelectric LiNbOa.

The direct measurement of the index of refraction for X-rays with X-ray interferometry offers the possibility to obtain precise data of the real part f ' of the atomic scattering amplitude f = f o + f ' + i f " in the forward direction [1,2]. Since both the X-ray absorption coefficient # ( E ) and the anomalous dispersion correction f ' ( E ) can be measured with the X-ray interferometer under identical experimental conditions we can additionally apply the determination of f ' ( E ) via a K r a m e r s - K r o n i g - T r a n s f o r m a t i o n of f ' ( E ) , where f " ( E ) is proportional to E ~ ( E ) with /L(E) the energy dependent photoelectric absorption coefficient [3]. By measuring f ' ( E ) and /~(E) for the same specimen, errors which might be due to different specimen composition or thickness were minimized. This procedure promises to give more consistent f ' ( E ) values. The knowledge of f ' ( E ) near absorption edges is of particular interest in structure determination. Thus our investigation bears on the so-called "Lambda-Technique" where symmetry constraints on the anomalous scattering terms are to be satisfied [4]. When using synchrotron radiation with that method, it is important to know the dependence of f ' ( E ) on different orientations of the radiation-polarization vector with regard to the crystal axis of the sample under investigation. Referring to this aspect, LiNbO 3 with a well known crystal structure, was selected to provide f ' - d a t a at the niobium K-edge. Below the Curie-temperature (1480 K) LiNbO 3 is ferroelectric. The spontaneous polarization is directed parallel to the c-axis of the hexagonal cell (crystal system: trigonal; space group R3c). The Nb- and Li-cations are positioned alternately along the c-axis where the Nb atom is surrounded by an octahedron of oxygen 0168-9002/86/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

atoms. The system has no center of symmetry. These experiments were performed on the X-ray interferometer at H A S Y L A B (DESY, Hamburg). The experimental arrangement has been described previously in detail [5,6]. Both f ' ( E ) and bt(E) spectra were recorded at the N b K-edge for parallel and perpendicular orientation of the polarization vector respectively to the hexagonal c-axis. The experimental energy resolution in measuring these spectra was about 5 eV at the N b K-edge energy of 18.98 keV. For this energy the polarization at the center of the beam is about P = 0.9 ( D O R I S II, 3.7 GeV, 50 mA). Since the degree of polarization varies with the position along the beam profile and with orbit dynamics which can be unstable, the polarization during our measurements may have been up to 5% lower. In the near future we intend to record the polarization of the beam simultaneously with f ' ( E ) and kt(E) by means of a Compton-polarimeter [71. Figs. 1 and 2 show the measured # ( E ) and f ' ( E ) curves for different polarization directions, f ' ( E ) - d a t a calculated with the K r a m e r s - K r o n i g - t r a n s f o r m a t i o n from ~ ( E ) values of fig. 1 are also plotted in fig. 2. For comparison some numerical data are listed in table 1. Polarization anisotropy is present in the near edge region in both f ' ( E ) and /z(E) spectra. The most distinct differences in the/~(E)-spectra are: (a) there is a peak about 12 eV below the inflection point for the orientation c j , while such a peak is not present for ell, (b) the relative intensities of the first two peaks above the inflection point are different for both directions. Since f ' ( E ) behaves roughly like the derivative of

U. Bonse, A. Henning / Polarizationof the anomalousforward scattering amplitude

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f " ( E ) [8], corresponding anisotropic structures are seen in f ' ( E ) . T h e effects observed here originate from resonance absorption where K-shell electrons exit into unoccupied final states. In the near edge region these states either belong to atomic N b orbitals or to molecular orbitals

due to the N b - O bonds. How far this orientation anisotropy can be explained by an orbital model has to b e found out by subsequent theoretical analysis. We are grateful to Professor K. Fischer, Saarbri~cken, for help with the sample preparation. This

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U. Bonse, A. Henning / Polarization of the anomalous forward scattering amplitude

816

Table 1 Comparison of f ' ( E ) - v a l u e s in electrons at different energies; uncertainties involved in measured f ' ( E ) data are of the order of 0.4 electrons Ek-12eV

Ek

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- 3.2 -3.2

Measurement Parallel Perpendicular

Transformation Parallel Perpendicular

w o r k w a s s u p p o r t e d b y t h e B u n d e s m i n i s t e r ftir F o r s c h u n g u n d T e c h n o l o g i e , B o n n , Az. 05260 B O P.

References [1] U. Bonse and G. Materlik, Z. Phys. 253 (1976) 232. [2] C. Cusatis and M. Hart, Proc. Roy. Soc. Lond. A354 (1977) 291. [3] U. Bonse and I. Hartmann-Lotsch, Nucl. Instr. and Meth. 222 (1984) 185. [4] K. Fischer, Z. Naturf. 36A (198l) 1253. [5] U. Bonse, P. Spieker, J.-T. Hein and G. Materlik, Nucl. Instr. and Meth. 172 (1980) 223. [6] U. Bonse, I. Hartmann-Lotsch and H. Lotsch, Nucl. Instr. and Meth. 208 (1983) 603. [7] F. Smend, D. Schaupp, H. Czerwinsk, A.H. Millhouse and H. Schenk-Strauss, DESY Internal Report, DESY SR-84003 (February 1984) ISSN 0723-7979. [8] T. Kawamura and T. Fukumachi, Jpn. J. Appl. Phys. 17. Suppl. 17-2 (1978) 224.