Measurements done recently at the NSLS have indicated that the level of intensity found in the wings of diffraction peaks from silicon at higher x-ray energies (>20keV) far exceeds the value which would be predicted based on the dynamical theory. We have measured Si(220) double crystal rocking curves at the 40keV fundamental and harmonics with various crystal scattering geometries: Bragg-Bragg, Laue-Bragg, Laue-Lauel. The comparison of the Bragg and Laue case diffraction geometries was done to determine scattering volume effects. Comparisons with dynamical theory calculations will be discussed. These measurements have been carried out in order to assess the level of harmonic contamination which will be present from a double crystal monochromator being designed for the X17 Superconducting Wiggler Beamline

Chapman, D.

Dilmanian, F. A.

Garrett, R. F.

Hastings, J.

Moulin, H.

Nachaliel, E.

Siddons, D. P.

UNT Digital Library

Submitted to: 7th National Conference onSynchrtron Radiation InstrumentationBaton Rouge, I_ October 28-31, 1991 BNL--47048DE92 007167Measurement of rocking curve wingsat high x.ray energiesD. Chapman, J. Hastings, H. Moulin , D.P. SiddonsNational Synchrotron Light Source,Brookhaven National Laboratory, Upton, New York, USAR, F. Garrett , E. Nachaliel and F.A. Dilmanian , :,, :, ............,,,.,Ub/[Medical Department, FEB 0 [3 Jg_]Brookhaven National Laboratory, Upton, New York, USA I(AbstractMeasurements done recently at the NSLS have indicated that the level of inten-sity found in the wings of diffraction peaks from silicon at higher x-ray energies(>20keV) far exceeds the value which would be predicted based on the dynamicaltheory. We have measured Si(220) double crystal rocking curves at the 40keV funda-mental and harmonics with v,'u'ious crystal scattering geometries: Bragg-Bragg, Laue-Bragg, Laue-Laue. The comparison of the Bragg and Laue case diffraction geometrieswas done to determine scattering volume effects. Comp,'u'isons with dynamical theorycalculations will be discussed.These measurements have been carried out in order to assess the level of har-monic contamination which will ge present from a double crystal monochromator be-ing designed for the X17 Superconducting Wiggler Beamline.DI:,::;;;":IIBUTION OF THIS DOCUM._NT 18 UNLIM.J12- ,1b* Present address:ESRFB.P. 22038043 Grenoble - CEDEXFrance** Present address"Australian Nuclear Science and Techno!ogy OrganisationLucas Heights Laboratories,Private Mail Bag 1,Menai, NSW, 2234, Australia.DISCLAIMERThis report was prepared as an account of work sponsored by an agency of the United StatesGovernment. Neither the United States Government nor any agency thereof, nor any of theiremployees, makes any warranty, express or implied, or _.ssumes any legal liability or responsi-bility for the accuracy, completeness, or usefulness of any information, apparatus, product, orprocess disclosed, or represents that its use would not infringe privately owr.cd rights. Refer-ence herein to any specific commercial product, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom-mendation, or favoring by the United States Government or any agency thereof. The viewsand opinions of authors expressed herein do not necessarily state or reflect those of theUnited States Government or any agency thereof.t,IntroductionRecently we have done measurements to assess the performance of various mono-chromator double crystal geometries at higher x-ray energies (>20keV).Originally measurements were done with a silicon (220) Bragg type double crystalarrangement [1] to determine the level of harmonic contamination which would bepresent as a function of detuning of the second monochromator crystal [2]. In aneffort to model the expected throughput of a double crystal monochromator as a func-tion of crystal detuning we found that the measured intensities in the wings of therocking ( or detuning ) curve far exceeded predictions based on dynamical theory. At40% detuning of the 40keV fundamental from a silicon (220) the measured first har-monic at 80keV from the Si(440) was a factor of 10 higher than the predicted valueand the second harmonic at 120keV was a factor of 100 higher than the prediction.In an effort to better understand the origin of the excess scattering in the rockingcurve wings at higher x-ray energies, we undertook a study of various crystal scatter-ing types• The crystal arrangements investigated were Laue-Laue (LL), Laue-Bragg(LB) and Bragg-Bragg (BB). The first crystal type was the fixed monochromator cry-stal and the second crystal type was the analyzer crystal which was scanned to give therocking curves.The intent was to show that the excess scattering was due to thermal diffusescattering (TDS) of the x-rays. At high x-ray energies the absorption length, Ia, of theincident x-ray beam ( 6mm at 40keV ) allows the off-Bragg peak beam to penetratedeep into the crystal and enhance the probability of TDS scattering to occur for aBragg type crystal. However for a Laue type c_Tstal the scattering volume is lirr,itedby the crystal thickness• If the crystal is thin compared to the absorption length butthick compared to the extinction length then good intensity can be obtained whileminimizing the total scattering volume.,I® 4 -iFor the Bragg case the scattering volume is proportional to Ala/2, where A is thecross-sectional area of the beam and Ia is the absorption length [3]. For the thin crystalLaue case the scattering volume is At; proportional to the crystal thickness, t, andbeam area, A.For the cases reported here at 40keV, the ratio of scattering volume for the Braggcase crystals compared to the Laue case is about 10. Therefore, one might expect theintensity of the wings for the BB, LB and LL at a given rocking angle away from thecentral pe',tk to follow the approximate relation' BB = 10xLB = 100xLL.In ali cases the TDS should fall off with rocking angle. The TDS has a 1/q2dependence on relative scattering vector, q, away from the Bragg reciprocal lattice vec-tor. For small angle deviations away from the Bragg peak, then we expect that therocking angle will be proportional to q.-5-ExperimentalThe measurements were done at the NSLS Superconducting Wiggler beamline inthe materials science hutch, X17B1. The angular resolution required to obtain thesub-arc-second rocking curves was achieved by using a high-energy spectrometer [4].The axes of this spectrometer were driven by long tangent arms pushed by stepper mo-tor controlled micrometers giving a minimum step size of 0.02 arc-second. The cry-stals were float zone silicon which were strain relief mounted to the axes.Long steel collimators on the incident beam path, between crystals and after thesecond crystal helped reduce the background level reaching the detector after thesecond crystal. The detector was an intrinsic germanium detector 17mm thick whichgave good stopping power and energy resolution at 40keV and the harmonics. The40keV fundamental from the Si(220) and the 80keV first harmonic were simultaneous-ly recorded as a function of rocking angle of the second ( analyzer ) crystal. The useof a solid state detector also helped control the background in the measurement to afew counts per minute. Single channel analyzers were used to energy analyze theamplified detector pulses.The count rates were limited by filtering the incident beam on the first crystal suchthat the count rate at the fundamental very nearly equaled the count rate at the firstharmonic. Any further filtering would only enhance the intensity of the first harmonicrelative to the fundamental. If only filtering is used to control the total count rate to apileup free value ( approx, 10kcps ) then there is very little intensity left at the funda-mental wavelength. This makes the measurement very difficult to perform since thestatistics are poor for the fundamental and the spectrum is altered if filters are removedto increase the intensity for the far wings of the rocking curves.The total count rate in this measurement was limited by a variable horizontal widthtungsten slit upstream of the first crystal. Using a horizontal slit will not alter thel0t- 6 "spectral content of the filtered synchrotron beam striking the first crystal nor will thehorizontal divergence of the beam affect the diffraction properties of the double crystalsystem since the scattering occurs in the,,vertical plane. The V-wedge shaped slit wasmounted such that moving the wedge vertically would prepare a variable horizontalwidth beam. The rocking curve of the Bragg peak was taken at near minimum hor-izontal beam width ( approx. 0.1mm ). In the far wings where the count rate was lowthe horizontal beam width was increased ( approx. 1.0mm ) as well as the countingtime per point and the step size per point. This allowed us to obtain better statistics ina shorter data acquisition time. At no time was the total count rate allowed to exceed10kcps.With this system the total +/- 100 arc-second scan range was made up of sevenoverlapping scans; one centr'd peak scan with three symmetric scans on the high andlow angle sides of the central peak.This procedure allowed us to measure in a nearly pileup free way the wings andBragg peak over a wide dynamic range without a significant background contribution.Once the basic setup and scan ranges were established, then ali three crystalgeomeu_.es reported here were measured in a similar fashion. It should be noted thatthe factors which scaled the wing scans to each other are the same for ali threegeometries ( LL, LB and BB ).ResultsData were taken at the 40keV Si(220) fundamental and also at the 80keV Si(440)harmonic, Figure 1 shows the data as taken for the LL ( f,gure la ), LB ( fig. l b )and BB ( fig. lc ). The solid lines are the data for the fundamental and the dotted lineare for the first harmonic. A logarithmic vertical axis was chosed to emphasize thewings of each. However, the logarithmic axis does not show the structure of the rock--7-ing curve near the peak region. Table 1 shows the measured and calculated rockingcurve widths for the three crystal geometries for the 40keV fundamental. It is interest-ing to note that the measured BB width is somewhat narrower than the calculation.Three measurements of the BB rocking curve at later times gave similar widths to themeasured 0.88 arc-second value quoted. However, for the LL and LB cases the meas-ured and calculated values give good agreement.Figure 2 shows a comparison of the LL, LB and BB cases for the 40keV funda-mental alone. "['his figure shows the surprising result that the BB case has the lowestintensity wings in conflict with the hypothesis that the excess scattering in the wingswas related to scattering volume effects. In the far wings the order of intensity is: LB> LL > BB. In the wing region below 20 arc-seconds the intensity order is: LL > LB> BB. In either case the BB case has the lowest wing contribution.Figure 3 shows the calculation for the same scattering cases for comparison withfigure 2. The convoluted throughput [5] shown here has wings which drop much morerapidly than any of the measured throughputs as expected based on the previous results[2].The next figure ( fig. 4 ) shows excess scattering which is the difference of the cal-culated intensities from the measured values. Here the plotted data is the average ofthe wings on the high and low angle side of the central peak. The LL case has thelowest excess scattering which indicates that part of the measured wing contribution isa result of the thin crystal Laue case diffr,'_ction properties. However, the LB case hasthe highest excess scattering and the BB case has an intermediate value in conflict withthe TDS ,,;cattering hypothesis.Finally, the last figure ( fig. 5 ) shows the reciprocal of the square root of the ex-cess scattering shown in figure 4. The purpose of this plot is to graphically indicate ifthe excess scattering has a 1/q2 dependence indicative of TDS which would _ppear asa straight line on this plot. None of the cases display a true 1/q2 behavior, though atrelatively small rocking angle ( <20 arc-seconds ) the dependence is nearly so.-9-ConclusionsIn conclusion, we have measured the rocking curves of various case double crystalscattering geometries ( Laue-Laue, Laue-Bragg and Bragg-Bragg ) in an effort tounderstand the origin of excess scattering in the wings of the profiles. We believe thatthe excess scattering is due to a sample volume effect which is more important athigher x-ray energies due to beam penetration. When the excess scattering is plottedthe order of intensities does not completely follow the order expected for a sam?levolume effect alone ( measured order of intensities: LB > BB > LL as compared to theexpected result of BB > LB > LL ).We are planning future measurements to confirm the results reported here and hopeto understand better the origin of the excess scattering in the rocking curve wings.AcknowledgmentsThis work was performed under US Department of Energy contract number DE-AC02-76CH 00016 to the National Synchrotron Light Source, Brookhaven NationalLaboratory.r-10-REFERENCES1 R.F. Garrett, F.A. Dilmaniaa, T. Oversluizen, L.D. Chapman, L,E. Berman, A.Lenhard, W. Stoeber, Proceedings of the 4th International Conference on Syn-chrotron Radiation Instrumentation, Chester, UK, July, 1991, to be published inRev. Sci. Instr.2 D. Chapman, H. Moulin and R.F. G,'u'rett, Proceedings of the 4th InternationalConference on Synchrotron Radiation Instrumentation, Chester, UK, July, 1991, /to be published in Rev. Sci. Instr.3 B.E. Warren, "X-Ray Diffraction", Addison-Wesley Publishing Co., pp. 151-203(1969).4 J.B. Hastings, D.P. Siddons, L.E. Berman and J.R. Schneider, Proceedings of the3rd International Conference on Synchrotron Radiation Instrumentation, Rev. Sci.Instrum., 60 (7), pp. 2398-2401, (1989).5 D. Chapman, NIM, A291, Nos. 1,2, pp. 205-208 (1989).tl, -11-,FIGURESFigure 1Rocking cu:rves for Si(220) at 40keV (solid lines) and Si(440) at 80keV (dottedlines) for the Laue - Laue ( figure a ), Laue - Bragg ( figure b ) and Bragg -Bragg (figure c ) cases.Figure 2Comparison of the measured Si(220) rocking curves at 40keV for the Laue-Laue (solid line ), Laue-Bragg ( dotted line ) and Bragg-Bragg ( dashed line )cases.iFigure 3Comparison of the calculated Si(220) rocking curves at 40keV for the Laue-Laue( solid line ), Laue-Bragg ( dotted line ) and Bragg-Bragg ( dashed line ) cases.Figure 4' Excess scattering ( difference of the measured and calculated intensities ) for theSi(220) at 40kev as a function of rocking angle away from the central peak forthe Laue-Laue ( solid line ), Laue-Bragg ( dotted line ) and Bragg-Bragg ( dashedline ) cases.Figure 5Plot of the reciprocal of the square root of the excess scattering from figure 4 forthe Laue-Laue ( solid line ), Laue-Bragg ( dotted line ) and Bragg-Bragg ( dashedline ) cases.-12-TABLESFWHM Widths (are.seconds)Crystal Arrangement Measured CalculatedLaue- Laue (LL) 2.40 2.10Laue - Bragg (LB) 2.10 1.87Bragg- Bragg (BB) 0.88 1.33Table 1Comparison of measured rocking curve widths with calculated widths for the LL,LB and BB cases for the Si(220) at 40keV.0_n _ _-) e_ .- 0 _ I0 0 0 C) 0 C) I,- 0,{),!sue),uIeA!_Dle&lv0m m0_ _ c'q _ 0 _ I0 0 0 0 0 0 I"- "-- "-- "-- '-- "- 0 .__!sua_ui aAlIDla_ _j•'1 °_"0_>°° l i0 0- _ CO !" 0 0 _,i "C_ _"_ _ _ /,. _ o- _ m -' i c-O?,:- - (DI_ L_'''''''"°''''''''''''°" " " " " " " -- 0__,,:: ...._ - (=.._ -.c_- - 0on,"0-- L_,. J-- 0°00i I oi I I IaO ,_ _ _ ,- 0 "- I0 0 0 0 0 0 I_ _ _ _ _ 00ill, , i i i,,,,, , , , liIWWi , , , iii, , , , .........o- C_- 0 _- m 03J 03II Io o _- , 03_j _j m i -o- : - (-: 0, (j: 00) ©i- i : (/)I : i - 0I ' I 0I -' _: I CY_- CP.- ,. _ <," ,_ _ 0-- \ _- c"L__ 0! o,7' I_ rv_' _,_ (_o- C,4.o. _,m-- .o''''''' _w, .mij'_ , rI i .liill i i I I.i,,,, i I I liilii I i i 00 0 0 0 _-0 0 0 ",-0 00 _-- _('SID:::)--'SDSm) 6U!Je_]DO s SS83X 3 _

Measurement of rocking curve wings at high x-ray energies

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Measurement of rocking curve wings at high x-ray energies

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