Applications of perfect crystal X-ray optics

356

Nuclear Instruments and Methods in Physics Research A308 (1991) 356-362 North-Holland

Applications of perfect crystal X-ray optics Tetsuya Ishikawa, Keiichi Hirano and Seishi Kikuta

Department of Applied Physics, Faculty of Engineering, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113, Japan Recent progress in perfect crystal X-ray optics at the Photon Factory is described. As an application of the ultra-plane-wave X-ray optics, experimental observations of nearly intrinsic rocking curves for a parallel-sided perfect crystal in Lane geometry and their thickness dependence are shown. Applications to X-ray polarization optics are also described. 1. Introduction Perfect crystal X-ray optics plays an important role to incident beam preprocessing for synchrotron radiation (SR) experiments [1]. For current SR sources, it is widely used for monochromatization, focusing and/or collimation, because it works most effectively for sharply directed SR . In the next generation of SR facilities in the hard X-ray region such as ESRF [2], APS [3] and SPRING8 [4], it will gain further importance because much better optical matching will be achieved between the small emittance of the undulator X-radiation and the narrow acceptance of the perfect crystal devices. For this reason, development of new types of perfect crystal X-ray optics are proceeded at the Photon Factory . In order to make experiments for the perfect crystal X-ray optics and many other dynamical diffraction studies, we have constructed two experimental stations at the Photon Factory. One is a vertical axis precision diffractometer [5] for the use of the vertical wiggler radiation [6] at beamline 14B [7]. The other is a horizontal axis precision diffractometer [8,9] for the use of bending magnet radiation at beamline 15C. Both diffractometers are designed to have a 0.01 arc sec finest step when driven by stepping motors . The mechanical stability of these diffractometers is so high that they can keep 0.1 arc sec stability more than three days without any feedback system . Several new types of X-ray optics have been proposed and tested by using these diffractometers for both X-ray goniometry and topography. The former includes the application of the X-ray standing waves to interface structure analysis [10-12] and to layered synthetic microstructures (LSM) [13], angle-resolved X-ray scattering measurements of X-ray mirrors and LSM [14] and triple-crystal diffractometry for diffraction of the thermal diffuse scattered X-rays [15] . As for X-ray topography, SR plane-wave X-ray topography with (+,+)

separated collimator crystals [16,17], equi-lattice-spacing mapping X-ray topography [18], SR angle-resolved plane-wave X-ray topography [19] and ultra-plane-wave X-ray topography [20-22] were developed by using these diffractometers . Most of these investigations stated above make use of the high momentum and energy resolution of the perfect crystal X-ray optics . In addition to these properties, phase and polarization control capability of the perfect crystal optics will be envisaged in the future SR utilization. In this context, we will show some recent results with ultra-plane-wave optics as well as X-ray polarization optics . 2. Applications of ultra-plane-wave X-ray optics Ultra-plane-wave X-ray optics was first constructed for the direct measurement of the X-ray coherence length from the visibility of the equal-thickness fringes [20] in 1987 . Since then, this optics has been applied to X-ray topographic investigations of microdefects in asgrown silicon crystals [21,22] and unintegrated planewave images of dislocations in silicon crystals [1]. Fig. 1 shows the crystal arrangement for ultraplane-wave X-ray optics [20] . Beam collimation is made by using two successive asymmetric diffractions [23-25] of silicon 220 reflection, where asymmetric factors are adjusted between 1/30 and 1/40 by changing the X-ray energy selected by a Si(111) premonochromator . Extremely collimated X-rays with an angular divergence of less than 0.01 arc sec are delivered by this crystal arrangement . The measurement of the coherence length of X-rays produced by these optics gave the maximum lowest limit of longitudinal (temporal) and transverse (spatial) coherence length as 41 Win and 220 ltm, respectively . These values are obtained in a coupled manner, so that one of these can be underestimated . The value for

0168-9002/91/$03 .50 © 1991 - Elsevier Science Publishers B.V. All rights reserved

T lshikawa et al. / Applications of perfect crystal X-ray optics

35 7

Fig 1 . Crystal arrangement for ultra-plane-wave X-ray optics A: beamlme double-crystal monochromator, 111 symmetric reflection of Si . The first crystal is water-cooled ; B: ionization chamber for Io monitoring ; C and D: 220 asymmetric reflection of Si with asymmetric factor 1/40 at X = 0.70 .4 ; E: sample crystal, 220 reflection in the Laue geometry ; F: nuclear emulsion plate position ; G : Nal detector for reflected beam, H : Nal detector for transmitted beam .

longitudinal coherence length agrees well with that from X2 geometrical consideration, /0X. The transverse coherence length d, is expressed as : di

=

ríX h2Aa

.

where r is the distance between the radiation source and observation point, X is the X-ray wavelength, b is

the asymmetric factor of both crystals and Da is the vertical size of the radiation source . We use r = 30 m,

Jt = 0.70 Á, b = 1/40 and Da = 0.3 mm for the evaluation of dt. Then the calculated transverse coherence length is 11 .2 mm .

tions is good except for the absolute value of reflectivity and transmissivity .

3. X-ray polarization optics Control and analysis of the polarization states of X-rays are important especially when we deal with spin-dependent

scattering and/or diffraction. Perfect crystal X-ray optics is effectively utilized for polarization control and analysis . This includes a phase plate

An interesting application of this extremely collimated X-ray beam is an observation of nearly intrinsic profiles of rocking curves in Lane geometry for a paral-

lel-sided perfect crystal. From the dynamical theory of

X-ray diffraction, it is well known that these rocking curves have oscillatory profiles and are quite sensitive to

crystal thickness. We use a parallel-sided floating zone silicon wafer of approximately 290 lum thick as a sample. X-ray wavelength was adjusted at A = 0.7310 .4 for

this experiment . Fig. 2 shows the diffraction geometry of the sample crystal. The effective thickness of the sample crystal was changed by rotating along rl-axis . Both reflected (h-beam) and transmitted (o-beam) were

measured simultaneously. Figs . 3a-h show observed profiles for q=0.0 ° , 10 .6 ° , 18 .0 °, 20 .7 ° , 23 .0 ° , 25 .0 ° and 26 .8 °, respectively . The corresponding calculated

profiles are shown in fig. 4a-h. In each figure, solid and dotted lines correspond to reflectivity and transmissivity, respectively . For the calculation, angular divergence of the incident beam is not taken into account . Nevertheless, agreement between observations and calcula-

Fig. 2. Diffraction geometry of the sample crystal for profile measurements . The parallelism of netplanes between the collimator crystal and the sample was adjusted by rotating along 4p-axis. Effective thickness of the sample crystal was changed by rotating along ii-axis, which is parallel to the diffracting vector, h. Diffraction profiles were measured by rocking the sample crystal along 0-axis . VII INSTRUMENTATION

T Ishikawa et al / Applications of perfect crystal X-ray optics

358

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Fig. 3 Measured diffraction profiles of a parallel-sided sample crystal m Laue geometry at X = 0.7310 P.. Original thickness of the win . The 71-angles and corresponding effective thicknesses are (a) 0 °, 293 win, (b) 10 .6 ° , 298 gym, (c) 14.8 ° , 303 gym, sample was 293 (d) 18 .0 ° , 308 Wm, (e) 20 .7 ° , 313 Wm, (f) 23 .0 ° , 318 Wm, (g) 25 .0 °, 323 ~tm and (h) 26 .8 ° , 328 gym, respectively

T Ishikawa et al. / Applications of perfect crystal X-ray optics w F

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utilizing dynamical diffraction in Bragg geometry [26], an X-ray monochromator for transferring circular polarizations [27] and a tunable-wavelength X-ray linear polarizer [28] . So far, Laue case phase plates are widely used, but Hirano et al . [26] have shown the possibility of the Bragg case phase plate. If we use the transmitted wave through a thin perfect crystal wafer on the tail of the Bragg case rocking curve, this crystal works as a phase plate. The advantage of this method is that the phase shift is a function of the deviation angle from the exact Bragg position, so that we can easily make a tunablewavelength phase plate. We can change the sign of the phase shift by adjusting the crystal on lower or higher angle tail of the rocking curve. Accordingly, we can get circularly polarized X-ray both right- and left-handed by changing the crystal angle by only several tens of arcseconds . This fact opens up a new possibility of constructing an experimental scheme of alternating circular polarization with quite high frequency . It is well known that the phase of the Bragg reflected beam changes by iT inside the width of the rocking curve. Since the diffraction widths for both polarization components, say ~7 and a, differs by the polarization factor, cos 26 8, the phase shifts suffered in the diffraction process are not equal for 7T and a polarizations. Accordingly, when the incident beam is the achromatic circularly polarized X-ray, the monochromatized X-rays are not necessarily in the same polarization state. The question is how we can keep the polarization states after monochromatization by a crystal monochromator . When we use a single flat crystal, the phase difference between 7T and a polarization changes in the diffraction width. So, the monochromatized X-rays are made of the super-

A 0 (arcsec)

position of the elliptically polarized X-rays, when the incident beam is an achromatic circularly polarized beam . In the widely used double-crystal monochromator of parallel setting, the phase differences are made two times bigger than the single flat crystal, so that the smearing of the polarization state after monochromatization becomes bigger . One of the promising solutions is to use a (+, -, -, +) four-crystal monochromator [27] . In this case, there are no phase differences between 7 and a inside the diffraction width. One of the most important devices for X-ray polarization optics is an X-ray linear polarizer/analyzer. Usually, the Bragg angle of 45 ° is used for the perfect linear polarizer in the X-ray region . However, this scheme can be used only for discrete values of wavelength according to the Bragg condition. A tunablewavelength X-ray polarizer was realized by Hart [28] taking advantage of the difference in angular widths between 7 and a polarized X-rays . He realized this polarizer by using a monolithic double-crystal . However, when we deal with higher-energy X-rays, a separated double-crystal scheme is preferable, because we cannot obtain good quality crystals for monolithic polarizers for high Z materials . So, we designed a small double-crystal aligner with an elastic torsion mechanism for a separated double-crystal tunable-wavelength polarizer as shown in fig. 5. The offset angle from the parallel position is adjusted by a stepping motor. The performance test of this polarizer was made on a laboratory X-ray source . Experimental setup is schematically shown in fig. 6. We used Si 440 reflection for polarizer at Ji = 1 .54 A, where 68 is 53 .32° . Ge 333 reflection was used for the polarization analyzer. Fig. 7 shows the calculated and measured ratio of the inVII . INSTRUMENTATION

360 w

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T Ishikawa et al. / Apphcattons of perfect crystal X-ray optics w F

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3 4 z 2 3 4 2 -4 -3 -2 -1 0 1 t10 (aresec) 40 (aresec) Fig . 4 Calculated diffraction profiles at X = 0 .7310 A without considering the angular divergence of the incident beam. Crystal thicknesses are (a) 293 win, (b) 298 Win, (c) 303 j-tm, (d) 308 win, (e) 313 win, (f) 318 win, (g) 323 win and (h) 328 win, respectively z

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T lshikawa et al / Apphcations ofperfect crystal X-ray optics

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1 0

2.0

A8 (arcsec) Fig. 7. Ratio of integrated diffraction intensities of the polarization analyzer between vertical and honzontal positions as a function of the offset angle, AB, from the parallel position . The calculated value is shown as a dotted line . Open circles with error bar indicate the measured values .

Fig 6. Experimental setup for testing the tunable-wavelength X-ray polanzer Cu Ka radiation (N=1 .54 ,\) was used . A. double-crystal tunable-wavelength X-ray polanzer, Si 440 reflection, B : polarization analyzer, Ge 333 reflection VII INSTRUMENTATION

362

T Ishikaxa et al / Applications of perfect crystal X-ray optics

tegrated diffraction intensities between 7r and a polarizations, respectively, as a function of the offset angle, AO, from the parallel position . The experimentally attained degree of linear polarization is close to that from theoretical calculation, being more than 97 .0%.

Acknowledgements We appreciate Messrs . K. Mabuchi and M. Miura for their help in experiments on the tunable-wavelength X-ray polarizer . Thanks are also due to Profs. K. Kohra,

T. Matsushita and M. Ando of the Photon Factory for fruitful discussions.

References [1] T Ishikawa and K Kohra, Synchrotron Radiation Handbook, vol. 3, eds GS . Brown and D.E . Moncton (North-Holland, Amsterdam, 1990). [2] J-L Laclare, Rev. Sci. Instr. 60 (1989) 1399 [3] D.E. Moncton, E. Crosbie and G.K. Shenoy, Rev. Set. Instr. 60 (1989) 1403 . [4] H. Kamitsubo, S.H . Be, M. Hara, R. Nagaoka, S. Sasaki and T. Wada, Rev. Set. Instr. 60 (1989) 1719. [5] K. Nakayama, M. Tanaka, S. Annaka, K Sugu, T. Takahashi, S Kikuta, T Ishikawa, M. Ando and K. Kohra, in : X-Ray Instrumentation for the Photon Factory: Dynamic Analysis of Micro Structures in Matter, eds. S Hosoya, Y. litaka and H Hashizume (KTK Scientific Publishers, Tokyo, 1986) pp 269-274. [6] T Yamakawa, S. Sato, H Kitamura, E. Terasaki, T. Shioya, T Mitsuhashi, M. Khara and C Lesmond, Nucl . Instr. and Meth A246 (1986) 32 [71 M Ando, Y Satow, H. Kawata, T. Ishikawa, P Spieker and S Suzuki, Nucl Instr. Meth. A246 (1986) 144.

[81 T Ishikawa, J Matsui and T Krtano, Nucl . Instr and Meth A246 (1986) 613. [9] T Islukawa, Rev Sci Instr. 60 (1989) 1493 . [10] K. Akimoto, T Ishikawa, T Takahashi and S. Kikuta, Jpn. J. Appl . Phys . 22 (1983) L798 . [111 K. Akimoto, T Ishikawa, T Takahashi and S. Kikuta, Jpn. J. Appl . Phys . 24 (1985) 1425 . [12] T. Nakagin, K. Sakai, A lida, T. Ishikawa and T Matsushita, Thin Solid Films 133 (1985) 219 [131 T Matsushita, A. lida, T. Ishikawa, T Nakagin and K Sakai, Nucl Instr. and Meth . A246 (1986) 751 . [14] T Ishikawa, T. Matsushita and A. Iida, Nucl . Instr and Meth A246 (1986) 348. [15] K. Kashiwase, M Mori, M Kogiso, K. Usliida, M. Mmoura, T Ishikawa and S. Sasaki, Phys Rev Lett 62 (1989) 925 [16] T Ishikawa, T Krtano and J Matsui, Jpn. J. Appl Phys. 24 (1985) L968 . [17] T Krtano, T Ishikawa and J Matsw, Jpn. J. Appl . Phys. 25 (1986) L282 . [18] T Ishikawa, T. Krtano and J. Matsm, J. Appl . Crystallogr. 20 (1987) 344. [19] T. Kitano, T. Ishikawa and J. Matsui, Philos . Mag A 63

(1991) 95 [201 T Ishikawa, Acta Crystallogr. A44 (1988) 496. [21] T Islukawa, in : Semiconductor Silicon/1990, eds. H .R. Huff. K G Barraclough and J-1 Clukawa (The Electrochemical Society Inc., Pennington, 1990) pp . 951-963 [22] T Islukawa, J Cryst. Growth 103 (1990) 131 . [23] M. Renmnger, Z Naturforsch A16 (1961) 1110 . [24] K. Kohra, J. Phys . Soc. Jpn. 1 7 (1962) 589. [251 K. Kohra and S. Kikuta, Acta Crystallogr. A24 (1968) 200. (26] K. Hirano, K . Izumi, T. Ishikawa, S. Annaka and S. Kkuta, Jpn. J. Appl . Phys . 30 (1990) L407 [27] T Ishikawa, Rev Set Instr. 60 (1989) 2058 . [28] M Hart and A.R .D . Rodngues, Philos . Mag. 43 (1981) 321 .