New opportunities in small-angle X-ray scattering and wide-angle X-ray scattering at a third generation synchrotron radiation source

New opportunities in small-angle X-ray scattering and wide-angle X-ray scattering at a third generation synchrotron radiation source

Journal of MOLECULAR STRUCTURE ELSEVIER Journal of Molecular Structure 383 (1996) 291-302 New opportunities in small-angle X-ray scattering and wid...

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Journal of

MOLECULAR STRUCTURE ELSEVIER

Journal of Molecular Structure 383 (1996) 291-302

New opportunities in small-angle X-ray scattering and wide-angle X-ray scattering at a third generation synchrotron radiation source 1'2 C. Riekel*, P. B6secke, O. Diat, P. E n g s t r 6 m European Synchrotron Radiation Facility, B.P. 220, F-38043 Grenoble Cedex, France Received 27 October 1995; accepted 30 November 1995

Abstract

An overview on developments in small- and wide-angle scattering using undulator sources at the European Synchrotron Radiation Facility (ESRF) is given. The performance of cameras for high momentum-resolution together with small focal spots is demonstrated. Keywords: European synchrotron radiation facility; Small angle X-ray scattering; wide angle X-ray scattering

1. Introduction The introduction o f undulators at third generation synchrotron radiation (SR) sources has increased their brilliance by several orders of magnitude. This increase has a significant influence on small-angle (SAXS) and wide-angle X-ray scattering (WAXS) instrumentation, and therefore also on the science possible with such instruments. In the following we review a number of these developments. 2. Source The ESRF operates a 6 GeV electron storage * Corresponding author. I Paper presented at the conference on 'Horizons in Small Angle Scattering From Mesoscopic Systems', Stromboli, Italy, 27-30 September 1995. 2 Dedicated to the memory of Prof. H.G. Zachmann.

ring which provides high-fl and low-j3 undulators as principal radiation sources [1]. 3-values are properties of the storage ring magnetic lattice which allow the undulator radiation to be optimized either for small source divergence (high/3) or small source size (low/3; Table 1) [2]. A stability of the source parameters of one tenth of the beam size and divergence is achieved in practice over a period of one week [1] which is sufficient for use with the focusing mirror optics [3].

Table 1 Horizontal (x, x' ) and vertical (z, z' ) source sizes and source divergences (FWHM) of two ESRF undulators [i]; the/3 values are related to the magnetic lattice [2]

High/3 Low fl

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1.034 0.13

0.21 0.12

0.042 0.233

0.026 0.042

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

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Fig. 1. Schematic design of pinhole camera with a focusing element. Note the penumbra around the focal spot which limits the lowest 20 value which can be attained.

3. Optics In the following, SAXS cameras operating at fixed wavelength will be discussed. Anomalous dispersion SAXS (ASAXS) will not be mentioned.

Present SAXS optics are mainly based on pinhole collimation systems, usually with one or two focussing elements as shown schematically in Fig. 1 [4-7]. The lowest 20 angle which can be reached is determined by the penumbra around the primary biocrystallography hutch I~. ~ l SAXS hutch

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Fig. 3. Rat-tail collagen pattern measured at A = 0.124 nm at a sample-detector distance of about 10 m (bottom) and about 1 m (top) with a gas-filled detector; pixel size, 0.176 ram. beam. F o r ultrasmall s-values (a high As resolution is required to reach small s-values [4]) up to the light scattering range, B o n s e - H a r t (BH) camera optics with multiple b o u n c e and perfect crystals have been used (Section 4.2) [8-11]. Here the analyzer crystal is scanned and the scattering recorded with a zero-dimensional detector which allows therefore only to study static samples or

slow dynamical processes on the scale o f minutes. As the beam is not focused, small specimens (such as single polymeric fibres) cannot usually be studied. Pinhole collimation S A X S cameras at bending magnet sources are often equipped with a horizontally focusing m o n o c h r o m a t o r in c o m b i n a t i o n with a vertically focusing mirror. In this way up to several m r a d radiation can be horizontally accepted and the flux optimized. This type o f optics does not allow the wavelength to be readily changed. The same optics can be used at undulators [12]. The u n d u l a t o r source parameters provide a flexibility in the position o f the focal spot without degrading too m u c h the As resolution which is o f particular interest for highly demagnifying SAXS cameras. F o r practical reasons the choice o f a double m o n o c h r o m a t o r c o m b i n e d with double focusing mirror optics is, however, preferable [3,13,14]. Thus cooling o f the mirror can be avoided if the m o n o c h r o m a t o r is the first optical element in the beam. While these optics do not provide flexibility in tuning the focal spot size to the sample dimensions, they are easy to align and the wavelength can be changed without varying the angle o f reflection o f the mirror. Thus the possibility o f working at shorter wavelengths is o f interest for special environment experiments such as high pressure S A X S [15,16]. F u r t h e r m o r e these optics can be easily calibrated in order to provide absolute intensies (see Fig. 7 below).

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

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The choice between high-3 and low-3 undulators can also be based on practical considerations. Single stage, highly demagnifying optics require a low-3 undulator in order to produce a rather symmetrical focal spot. In order to obtain the lowest divergence with 1 : 1 demagnifying optics, the beam o f a high-fl undulator is optimal.

4. High As-resolution SAXS 4.1. Mirror/monochromator camera

The High Brilliance Beamline (BL4) [1] combines high As resolution (s = 2sin0/A) with a high flux and a moderate beam size [1,3,13]. A

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302 10 6

schematic design of this beamline is shown in Fig. 2. At the present stage 50% of the beamtime is used for biocrystallography in a separate hutch. The optics consist of a channel-cut Si-lll monochromator and a 1 : 1 demagnifying toroidal mirror. The wavelength range covered is 0.15 nm/> A i> 0.07 nm for a flux of nearly 1013 photons s -1. The overall length of the beamline is about 65 mm. A minimum horizontal and vertical beam size (about 0.4 x 0.7 mm 2) is obtained approximately 55 m from the source and not at the maximum detector position (about 65 m) which is qualitatively explained in Fig. 1. A 10 m vacuum tube equipped with a two-dimensional detector (gas-filled or image intensified chargecoupled device (CCD)) allows the sample-todetector distance to be changed continuously from about 0.7 m to about 10 m. Fig. 3 shows the scattering patterns of rat-tail collagen (first order d ~ 67 nm) measured at the two extreme positions with gas-filled detector. The As resolution is defined as the folding of the beam divergence at the sample position with the angular resolution of the detector

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with ASdetector : - , , ~ - l ~ / ( b / L ) 2 " - ~ - P S F 2, where b is the beam size on t h e d e t e c t o r (FWHM), L is the sample-to-detector distance and PSF is the point spread function of the detector ( F W H M of the detector resolution). Fig. 4 shows the As resolution for A = 0.15 nm as a function of the sample-todetector distance for (i) an ideal detector (PSF = 0), (ii) an image plate (PSF ~ 0.15 mm), and (iii) a two-dimensional gas-filled detector (PSF ~ 0.5 mm). The reduction of the As resolution with increasing PSF is evident. Presently commercially available detectors do not allow the

optimum As resolution to be reached. The resolving power is demonstrated for part of the meridional low angle frog-muscle fibre diffraction pattern recorded with an image plate at a sample-todetector distance of 9.9 m (Fig. 5) [17]. The pattern was recorded in the vertical direction. The As separation of the two peaks at about 11.17 nm and 10.97nm indicated by asterisks is As = 1.6x 10-3 mm -] which is still significantly above the calculated As resolution PSF = 0.15 mm) in Fig. 4. The minimum s value which can be reached is also shown in Fig. 4. Smin ~ 2.2 x 10 - 3 nm -1

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

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(dmax ~ 0.45 #m) has been observed for 300 nm polystyrene spheres with a two-dimensional gasfilled detector at a distance of about 10 m to the sample (Fig. 6). This value might be improved by a reduction of background scattering from windows and slits. 4.2. Bonse-Hart optics B o n s e - H a r t (BH) optics have advantages for experiments at ultralow s values because focal spot size, beam divergence and detector PSF do not influence the resolution. The compact design also has practical advantages. Because the divergence of undulator radiation matches the rocking curve of perfect Si crystals the throughput is optimized. Fig. 7 shows the setup of BH optics tested on BL4 [12]. A diamond crystal is used to premonochromatize the beam and therefore reduce the heatload of the channel-cut crystals. Using Si-220 crystals with a rocking curve width of about 25/zrad ( F W H M ) the observed flux for the full beam (about 1 mm 2) is ~ 101° photons s -1 mm -2 at A = 0.09 nm in air. The theoretical resolution of the BH camera is limited by the width of the rocking curve. For Si-220 this corresponds to Smin ~ 3 × 10 -4 nm -l (dma x ~ 3.6 #m). The experimentally determined rocking curve of a five bounce Si-220 crystal does not follow the

theoretical intensity decrease of [0-0Boo s-2n, where 0B is the Bragg angle at the top of the reflection curve and n is the number of reflections, but shows additional scattering at larger angles (Fig. 8) the origin of which is presently under discussion [10,18]. This additional scattering limits the use of the BH optics at small s values for weak scatterers but, for example, in the case of a strong scattering by density fluctuations due to line patterns written by holographic techniques into P M M A substrates [11] very low s values can be attained [18] (Fig. 8).

5. M i c r o b e a m S A X S / W A X S

5.1. Monochromator and Mirror Optics Fig. 9 shows mirror/monochromator optics which have allowed demagnification of the beam to 14/zm in the vertical direction by an elliptically bent mirror while the horizontal compression is restricted to 100-200 /zm by an asymmetrically cut Si-220 crystal [12,19]. For a factor 27 demagnification at A = 0.09 nm the ideal vertical focal size would be about 4/zm F W H M , which suggests the presence of mirror aberrations. For a vertical divergence at the sample position of about 0.4 mrad and a sample-to-detector distance L of

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2.4 m, As ~ 4 × 10 -3 n m -1 with a n image plate detector (Eq. (1)), the first order of collagen (67 n m ) could be resolved. The flux is less t h a n 10 H p h o t o n s s - l due to the limited acceptance of the m i r r o r a n d the b a n d pass r e d u c t i o n o f the Si-220 m o n o c h r o m a t o r [12]. A t this b e a m size s c a n n i n g SAXS-experiments become feasible. Fig. 10 shows schematically the grain b o u n d a r y structure a n d a plasticized zone o f a n a l u m i n u m sample [20,21]. W i t h i n the grain b o u n d a r y structure the SAXS p a t t e r n recorded with a n image plate detector is highly anisotropic

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

299

5.2. Glass capillary optics

Fig. 12. WAXS pattern within a poly-3-hydroxybutyrate spherulite obtained with a 7/zm FWHM beam at A= 0.09 nm [22]; a = 0.576 nm, b = 1.320nm, c = 0.596 nm [23].

due to scattering from two-dimensional grain boundary density fluctuations, while the SAXS pattern becomes diffuse within the plasticized zone. A channel-cut Si-111 monochromator in combination with an ellipsoidal mirror has allowed a focal spot of 20 (h) × 40 (v) #m ~ ( F W H M ) with a flux o f less than 1012 photons s -l to be reached for a 1 : 10 demagnification of the source (Fig. 11) [14]. Mirror aberrations affect in particular the vertical focus size. The beam can be reduced to about 7 # m diameter ( F W H M ) for a flux of about 1011 photons s -1 by a post collimator [14]. Thus a poly-3-hydroxybutyrate spherulite (Biopol ®) could be completely mapped by twodimensional diffraction patterns [22]. An individual WAXS pattern recorded with an image intensified CCD is shown in Fig. 12. The possibility to study local melting/crystallization may provide a more detailed insight into such processes where experiments with larger beams provide averaged information over many spherulites [24]. Pinhole-optics to perform similar SAXS experiments are not yet available but could be easily developed. The use of larger band pass monochromators for microbeam SAXS-applications remains to be explored.

Beam sizes down to 2 #m (full width) have been reached by tapered glass capillary optics in combination with a Si- 111 monochromator while increasing the flux density by factor of four as compared to the 7 # m collimator discussed above [14,25,26]. Capillaries used are rather short (less than 150 mm) and act principally as post-collimators. For borosilicate glass the angle of exit is defined by the angle of total reflection which is about 2.3 mrad at 0.09 nm. In order to avoid too large a spreading of the beam it is therefore necessary to bring the sample to within a few hundred micrometers of the exit tip. A WAXS pattern of a 10 #m cellulose-II fibre obtained with a 2 #m beam is shown in Fig. 13 [29]. The pattern was recorded within 24 s at room temperature by an image intensified CCD. The diffraction pattern is lost within less than a minute. Cryocooling techniques allow to extend the lifetime of the sample for several minutes. SAXS experiments are possible after carefully reducing the background by an aperture at the exit of the capillary [29]. For a 10 #m aperture Smin was found to be limited to about 10 -I nm -l but could theoretically not become smaller than about 2.5"10 -2 nm -l due to the beam divergence at the exit of the borosilicate capillary [26]. Fig. 14 shows a SAXS pattern obtained with an image intensified CCD from a poly(tetramethyl-psilphenyle-siloxane) spherulite with a 5 #m capillary beam [30,31]. The pattern shows a peak corresponding to a long period of 7.1 nm and with an azimuthal width of ~ 10 degrees (fwhm) due to density fluctuations in the fibrils. The orientation of the 2-spot diagram changes with the orientation o f fibrils as also observed for Biopol ® [22]. This suggests that it will be possible to develop instrumentation for combined SAXS/WAXS experiments at the level of a few #m beam size. 5.3. Monochromator and Bragg-Fresnel optics

Phase contrast Bragg-Fresnel (BF) optics [32] are based on one- or two-dimensional Fresnel patterns etched into a perfect (Si or Ge) crystal. In addition to the scattering from the substrate, the Fresnel pattern will produce a focus (line or

300

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

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Fig. 13. WAXS pattern of 10/zm diameter cellulose-II fibre obtained with a 2 #m beam [27]. A = 0.09 nm. P21, a = 0.801 nm, b = 0.904 nm, c = 1.036 nm, "7 = 117.10 [28].

Fig. 14. SAXS pattern recorded within a poly(tetramethyl-psilphenylesiloxane) spherulite with about 5 #m beam from a glass capillary [3].

spot) which is l o c a t e d in an area o f p r a c t i c a l l y zero scattering. T h e focal s p o t can therefore be easily s e p a r a t e d f r o m the rest o f the scattering p a t t e r n by a simple aperture. In c o n t r a s t to glass c a p i l l a r y optics the larger distance optics to focal s p o t facilitates special e n v i r o n m e n t experiments. T h e theoretical m i n i m u m in focal s p o t size c o r r e s p o n d s to the size o f the last fringe ( A m ) which is in Si t e c h n o l o g y a b o u t O. 1 #m. The optical a p e r t u r e A o f a B F lens is defined by A = ( F A ) / A r n where F is the focal length. A l i m i t a t i o n o f present single crystal B F optics is the r e d u c t i o n o f the b a n d pass A A / A in b a c k reflection g e o m e t r y to a b o u t 10 - 6 which limits the intensity b y a factor o f a b o u t 100 as c o m p a r e d to f o r w a r d reflection g e o m e t r y [33]. Fig. 15 shows the schematic setup

C. Riekel et al./Journal of Molecular Structure 383 (1996) 291-302

301

BF-lens

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::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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of a back reflection BF camera which has reached a focal spot of about 3 /zm2 and a flux of about 108 photons s -1 at A = 0.124 nm [33]. For an optical aperture of 200 #m the angular acceptance of the BF lens is 0.3 mrad which corresponds to As = 3 × 10 -3 nm -l for an image plate detector (Eq. (1)) and Smin ~> 3 x 10 -3 nm -l (dmax ~< 300 nm). This has allowed the first order peak of native rat-tail collagen to be resolved (67 nm) [34].

6. Conclusions Undulators at third generation SR sources allow new approaches to be developed in SAXS/WAXS instrumentation reaching into the light scattering range and to beam sizes in the micrometer. Due to the high stability of the source, double focusing mirrors are easy to align and preserve the brilliance of the source. SAXS/WAXS cameras routinely available to users are based on these optics. Research and development on complimentary optics for ultra-low s values (Bonse-Hart) and small focal spots (glass capillary, Bragg-Fresnel) are in progress.

Acknowledgments We wish to acknowledge the support and helpful discussions with C. Ferrero, S. Fiedler, J. Gorini,

M. Lorenzen, A. Snigirev, I. Snigireva and P. Wattecamps.

References and notes [1] ESRF Beamline Handbook (copies may be obtained from the ESRF Users Office, ESRF, B.P.220, F-38043, Grenoble Cedex, France). [2] C. Riekel, Top. Curr. Chem. 151 (1989). [3] C. Riekel, P. B6secke, M. Sanchez del Rio, Rev. Sci. Instrum., 63(1) (1992) 974. [4] G. Rosenbaum and K.C. Holmes, in H. Winick and S. Doniach (Eds.), Synchrotron Radiation Research, Plenum, New York, 1980. [5] G. Elsner, C. Riekel and H.G. Zachmann, in H. Kausch (Ed.), Advances in Polymer Science, Springer Verlag, Heidelberg, 1985. [6] M.H.J. Koch and J. Bordas, Nuch Instrum. Methods, 208 (1983) 461. [7] M.H.J. Koch, Makromol. Chem., Macromol. Symp., 15 (1988) 79. [8] D.P. Siddons, C. Riekel and J.B. Hastings, J. Appl. Crystallogr., 23 (1990) 401. [9] B. Chu, Y. Li, J. Harney and F. Yeh, Rev. Sci. Instrum., 64(6) (1993) 1510. [10] R. Pahl and U. Bonse, J. X-Ray Sci. Techn., in press. [11] O. Diat, P. B6secke, C. Ferrero, A. Freund, R. Heintzmann and J. Lambard, Nucl. Instrum. Methods Phys. Res. A, 356 (1995) 566. [12] C. Riekel, P. Bfsecke, O. Diat, M. Lorenzen, M. Sanchez del Rio and I. Snigireva, Rev. Sci. Instrum., 66(2) (1995) 987. [13] P. B6secke, O. Diat and B. Rasmussen, Rev. Sci. Instrum., 66(2) (1995) 1636. [14] P. Engstr6m, S. Fiedler and C. Riekel, Rev. Sci. Instrum., 66(2) (1995) 1348.

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[15] M. Lorenzen, PhD Thesis, University of Braunschweig, 1995. [16] M. Lorenzen, P. B6secke, C. Riekel, K. Reynders, H. Reynaers and N. Overbergh, Macrom. Rapid Comm., 17 (1996) 189. [17] We thank J. Bordas for providing this image prior to publication. [18] O. Diat et al., unpublished results. [19] C. Riekel and P. Engstr6m, Nucl. Instrum. Methods Phys. Res. B, 97 (1995) 224. [20] We thank M. Grosse for providing this image prior to publication. [21] M. Grosse, A. Hempel, J. Boehmert, F. Eichhorn, C. Riekel and P. Engstr6m, J. Mol. Struct., [22] A. Mahendrasingam, C. Martin, W. Fuller, D.J. Blundell, D. MacKerron, R.J. Rule, R.J. Oldman, J. Liggat, C. Riekel and P. Engstr6m, J. Synchr. Radiat., 2 (1995) 308. [23] P.J. Barham, A. Keller, E.L. Otun, P.A. Holmes, J. Mater. Sci., 14 (1984) 2781.

[24] P.J. Barham, in E.L. Thomas (Ed.), Materials Science and Technology, Vol. 12, VCH, Weinheim, 1993. [25] C. Riekel and P. Engstr6m, Nucl. Instrum. Methods, B97 (1995) 224. [26] P. Engstr6m and C. Riekel, J. Synchr. Rad., 3 (1996) 97. [27] H. Chanzy and C. Riekel, unpublished image. [28] F.J. Kolpak and J. Blackwell, Macromolecules, 9(2) (1976) 273. [29] P. Engstr6m and C. Riekel, Rev. Sci. Instrum., in press. [30] M.J. Shanker et al., J. Polym. Sci., Polym. Phys. Ed., 22 0984) 223. [31] J. Magill and C. Riekel, unpublished image. [32] V. Aristov. Y.A. Basov, S.N. Kulipanov, V.F. Pindyurin, A. Snigirev and A.S. Sokolov, Nucl. Instrum. Methods A, 274 (1983) 390. [33] Y.A. Basov, T.L. Pravdivtseva, A. Snigirev, M. Belakhovsky, P. Dhez and A. Freund, Nucl. Instrum. Methods A, 308 (1991) 363. [34] A. Snigirev, I. Snigireva, C. Riekel, A. Miller, L. Wess and T. Wess, J. Phys. (Paris) 3, C8 (1993) 443.