REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 69, NUMBER 9 SEPTEMBER 1998 High resolution inelastic x-ray scattering spectrometer at the advanced photon source M. Schwoerer-Bo¨hning,a) A. T. Macrander, and P. M. Abbamonte Argonne National Laboratory, Advanced Photon Source, Experimental Facilities Division, Argonne, Illinois 60439 D. A. Arms Department of Physics and Frederick Seitz Materials Research Laboratory, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801 Received 20 April 1998; accepted for publication 24 June 1998 We have commissioned a new instrument for high resolution inelastic x-ray scattering on the inelastic scattering beamline of the Synchrotron Radiation Instrumentation Collaborative Access Team on sector 3 of the Advanced Photon Source. So far, the instrument is set up at 13.84 keV with a total energy resolution of 7.5 meV and a momentum resolution of 0.1 Ĺ 1. We present technical details of the instrument, which includes an in-line monochromator, a focusing mirror, and a focusing analyzer. The performance of the instrument was demonstrated in studies of phonons in diamond and chromium. © 1998 American Institute of Physics. S0034-6748 98 04109-4 I. INTRODUCTION bandpass.8,9 Changing the energy from an elastic peak to the Inelastic x-ray scattering experiments with a resolution desired phonon peak is no longer time consuming. The high sufficient to study phonons is a new field that has arisen due resolution monochromator follows a mirror, which focuses to the availability of synchrotron radiation.1 The very low the x-ray beam horizontally and vertically onto the sample scattering cross section and the narrow bandpass needed of position of a five-circle diffractometer. A focal size of ca. the order of E/E 10 7 require x-ray sources of high bril- 0.5 0.5 mm2 can be achieved. The horizontal focal length is liance. The pioneering instrument for high resolution inelas- fixed due to a fixed sagittal curvature of the mirror. A verti- tic x-ray scattering HRIXS called INELAX developed by cal bending mechanism can focus the beam at different lo- Burkel, Dorner, and Peisl at the Hamburger Synchrotron- cations downstream. The photon flux at the sample position strahlungs Labor HASYLAB 2,3 is not installed at such a ranges between 3 and 5 109 photons/s in a 5 meV band- high brilliance source. INELAX and the more recent instru- pass. On the five-circle diffractometer, a high resolution ment at the European Synchrotron Radiation Facility backscattering analyzer is mounted at a distance of 2.7 m. A ESRF 4 follow a backscattering geometry for their mono- schematic layout of the beamline is shown in Fig. 1. chromators to achieve the narrow incident bandpass. The ad- vantage of using backscattering geometry in x-ray diffraction II. MONOCHROMATORS an optical arrangement originally used in inelastic neutron The primary high heat load HHL monochromator is a scattering experiments5 was demonstrated by Sykora, Peisl, double-crystal monochromator in configuration. It con- Graeff, and Materlik.6,7 A backscattering monochromator as sists of two diamond crystals employing 111 reflections. used at the ESRF and at HASYLAB limits the space near the The first crystal, which is exposed to the total radiation sample because the premonochromatized beam must pass power emitted by the undulator insertion device, is water- close to the sample. Thus, there is not enough room for large cooled. Details concerning the performance of the water- size sample containments cryostats, high pressure cells . En- cooled diamond crystal are described elsewhere.10,11 A high ergy scanning with a backscattering monochromator is resolution monochromator limits the bandpass of the mono- achieved by tuning the temperature difference between the chromatic photons from the HHL monochromator to 5.2 monochromator and a high resolution analyzer. Such mea- meV at 13.84 keV.12 Its design and performance have al- surements of energy transfers require a continuous scanning ready been detailed by Macrander et al.13 The four-reflection of the crystal temperature. The large energy transfers needed monochromator with one channel-cut crystal nested inside to study optical phonons ( E 100 meV) take long scan another uses asymmetric silicon 422 and 884 reflections times 400 steps with a stepsize of 0.25 meV where diffi- Fig. 2 . Tuning of the incident energy is performed by ro- culties in ascertaining the zero of the energy arise. The in- tating the inner crystal. A scan range of a few electron volt is elastic scattering beamline in the Synchronotron Radiation achievable. Instrumentation Collaborative Access Team SRI-CAT of the Advanced Photon Source APS has instead employed angle-tuned in-line monochromators to set a narrow III. HIGH RESOLUTION FOCUSING ANALYZER Perfect crystals are required to achieve an energy reso- a Electronic mail address: schwoere@aps.anl.gov lution approaching the intrinsic Darwin width. The current 0034-6748/98/69(9)/3109/4/$15.00 3109 © 1998 American Institute of Physics 3110 Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 Schwoerer-Bo¨hning et al. FIG. 1. Instrument layout at the APS HRM high resolution monochro- mator . setup uses silicon wafers obtained from Virgina Semicon- ductors. Strain due to bending broadens the width of their reflections. Various methods have been developed to solve this problem.1,14 The contributions to the energy resolution of an analyzer separate into two major terms, the intrinsic and the geomet- ric: dE 2 2 2 E dE E dEg E . 1 The intrinsic term dE denotes a particular x-ray reflec- tion of the energy resolution is mainly given by the Darwin FIG. 3. Backscattering setup for HRIXS: L analyzer-to-sample distance L Rowland circle , D analyzer diameter, and d image-to-scattering- width of the reflection used. In the case of propagating strain source distance. in the crystal, the intrinsic width is strain broadened. The geometric term dEg considers the divergence of the scat- tered beam at nonzero deviation from backscattering ( tion of fabricating such a ``sandwich'' analyzer is given ) Fig. 3 . Usually the detector sits very close to the elsewhere.16 So far, analyzers have been made for bending sample to keep small. Thus, there are always contributions radii of 2.6 and 1 m, with the latter one intended for medium due to the geometric term. The contributions to the total energy resolution a few 100 meV . The propagating strain energy resolution do not necessarily add as do Gaussian dis- from the backwall is reduced because glass is softer than tributions, but for our purpose it is a good approximation.15 silicon. Furthermore, the strained glass backwall does not To avoid strain broadening in the bent crystal, Dorner contribute to the scattering. et al.2 had the silicon wafers diced into a pattern of 0.8 We note that the magnitude of the intrinsic term depends 0.8 mm2 blocks. The blocks were kept oriented by leaving on the material and on the order of the back reflection used. a 200 m-thick backwall. Nevertheless, this kind of prepared High energy resolution ( 1 meV) requires high order re- wafer still shows significant strain propagating from the bent flections, i.e., high energy x-rays ( 20 keV). At these high backwall into the remaining blocks. Furthermore, the re- energies, the penetration of the x-rays can exceed a few mil- flected x-rays also probe the severely strained backwall ex- limeters, in which case the x-rays become even more sensi- posed by the grooves. The current work was motivated by tive to strain. the need to relieve the residual strain and avoid scattering The geometric term to second order is given by from within the grooves. dE The new approach is a silicon wafer bonded to a glass g 2 . 2 wafer using epoxy. After dicing through the silicon into the E tan 2 cos2 glass, a backwall is left in the glass only. A detailed descrip- One can see that the magnitude of the geometric contri- bution mainly scales with . The divergence is given by a convolution of contributions due to the source size scatter- ing volume and the block sizes of the analyzer Fig. 3 b and is affected by the demagnification the Johann error , i.e., because the detector and the sample do not sit exactly on the Rowland circle of the analyzer Fig. 3 a . The size of the detector aperture influences the degree to which these terms contribute as does the perfection of the analyzer.15 The con- tribution due to demagnification can be kept small by em- ploying analyzers of large bending radius large focal dis- FIG. 2. The high resolution monochromator. tance . Focusing the incoming beam onto the sample Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 Schwoerer-Bo¨hning et al. 3111 FIG. 4. Total energy resolution function of the monochromator and the analyzer measured using a a flat crystal, and b a focusing analyzer. The elastic scattering is from a Plexiglas, and the employed reflection was the Si 777 . minimizes the source size. Besides the detector pixel size, FIG. 5. Spectra at different momentum transfers representing longitudinal the block size preferably matches the acceptance angle of the modes in diamond a and chromium b . reflection used at the specified angle away from back- scattering. Choosing a large bending radius is a convenient presence of a slope error of about 150 rad Ref. 15 i.e., method to reduce the geometrical contributions dominated the mismatch of focus and detector aperture explains the by the first order term in Eq. 2 Ref. 17 . 34% loss in the efficiency . Besides the high efficiency, the The latest innovation in fabrication has yielded an ana- analyzer also performs with the same total energy resolution lyzer with very good energy resolution and high reflectivity. of 7.6 meV FWHM as was achieved with the flat crystal To quantify the reflectivity we have done measurements us- Fig. 4 . The profile of the energy resolution function is not ing the Si 777 reflection. The elastic scattering from Plexi- purely Lorentzian. The line is the energy resolution calcu- glas at 8.5° scattering angle maximum of S(Q) was mea- lated via ray tracing considering the intrinsic resolution of sured using a strain-free flat crystal at a distance of 3 m. The the Si 777 reflection, a block size of 0.9 mm2, and a source detector was positioned 0.6 mrad away from backscattering, size of 0.5 mm2. During the reflectivity measurements, the which implies an acceptance angle of 0.6 mrad for the flux of the monochromatized incident beam was 3 Si 777 reflection. The detector aperture was 2 2 mm2. 109 photons/s. Finally, the use of a well-designed detector This setup yielded a count rate of 6 counts/s for a flat 111 is essential to the efficiency and reliability of the instrument. crystal positioned at 3 m distance Fig. 4 a . The acceptance The detector that we used is a CdZnTe detector specially angle of 0.6 mrad implies a reflecting area of 1.8 adapted by Amptek Inc. The measured background was 0.03 1.8 mm2. But, the source size and the small aperture of the counts/s at 14 keV. detector only permit the detection of x-rays from a reduced To demonstrate the feasibility of our new instrument to area of 1.4 1.4 mm2. Instead, with a focusing analyzer study high frequency phonons, we measured longitudinal placed at a distance of 2.7 m, this area reduces further to acoustical and optical phonons in diamond Fig. 5 a .18 Our 1.1 1.1 mm2. The block sizes of current analyzers sitting at work on phonon scattering by a high Z element chromium a distance of 2.7 m cover an area of ca. 0.9 0.9 mm2, i.e., yields intensities of 15 counts/s comparable with the intensi- the whole area of each block contributes to the reflectivity. ties in diamond, i.e., the higher electron density compensates However, one loses 20% reflectivity in the 0.1 mm wide the loss due to absorption Fig. 5 b . grooves. The exposed area of our analyzer is 83 mm in di- ameter, which encompasses 5411 blocks. Assuming all blocks are well aligned, we calculate an expected count rate ACKNOWLEDGMENTS with the focusing analyzer of 21.7 103 counts/s 0.9/1.1 2 6 counts/s 5411 . In fact, we measure a count The authors are indebted to V. I. Kushnir for assistance rate of 14.3 103 counts/s Fig. 4 b , which represents an and to SRI-CAT staff of sector 3 at the APS for the perfor- analyzer efficiency of 66%. We note that this is a net gain mance of the beamline. We are also indebted to the manage- provided by the analyzer of about 2400. The measured full ment of the APS, the Experimental Facilities Division, and width at half maximum FWHM of the analyzer focus of 2.6 the SRI-CAT for their support. Use of the APS was sup- mm was larger than the detector aperture and indicates the ported by the U.S. Department of Energy, Basic Energy Sci- 3112 Rev. Sci. Instrum., Vol. 69, No. 9, September 1998 Schwoerer-Bo¨hning et al. ences, Office of Energy Research, under Contract No. W-31- 10 L. Assoufid, K. W. Quast, and H. T. L. Nain, SPIE Proceedings Series 109-ENG-38, and the Division of Materials Sciences, under Society of Photo-Optical Instrumentation Engineers, Bellingham, Wash- Contract No. DEFG02-96ER45439. ington, 1996 , Vol. 2855, p. 250. 11 P. Fernandez, T. Graber, W.-K. Lee, D. M. Mills, C. S. Rogers, and L. 1 Assoufid, Nucl. Instrum. Methods Phys. Res. A 400, 476 1997 . E. 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