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Physica B 385–386 (2006) 995–999

www.elsevier.com/locate/physb

Multi-wavelength data collection strategies in inelastic neutronscattering

F. Mezei�

Hahn-Meitner-Institut, Glienicker str 100,14109 Berlin, Germany and Los Alamos National Laboratory, Los Alamos, NM 87545, USA

Abstract

The overwhelming tradition in neutron-scattering research was the use of a monochromatic incoming beam with a single wavelength

for essentially all kinds of experiments, with only a very few exceptions in the practice at continuous neutrons sources. The situation

dramatically changed with the spread of pulsed spallation sources, where the wavelength scanning ‘‘energy dispersive’’ time-of-flight

approach is the natural rule in all diffraction type work and in inverted geometry inelastic spectroscopy. In recent years, a number of new

applications of multi-wavelength data collection strategies emerged in inelastic neutron spectroscopy, both at continuous and pulsed

sources. The aim of the present paper is to review these developments. Time-of-flight (TOF) and Neutron Spin Echo (NSE) lend

themselves most easily to such methods, since they allow rather exact comparison of absolute scattering intensities measured at different

instrumental configurations. The use of multiple wavelengths can offer different kinds of advantages in neutron spectroscopy. Since the

resolution of spectrometers rapidly changes with the wavelength, its variation can be effectively used to extend the available dynamic

range. Inelastic multiple scattering effects can be precisely identified and corrected for by their inherently strong wavelength dependence.

At pulsed spallation sources the multi-wavelength approach opens up the way to enhance data collection rates by eliminating at least a

large part of the dead time between too distant source pulses.

r 2006 Elsevier B.V. All rights reserved.

PACS: 61.12.�q

Keywords: Inealstic scattering; Repetition rate multiplication; Multiple scattering; Multiplexing introduction

1. Introduction

Since the early days of diffraction work for studyingcrystal structures by X-rays, both options of practicalexploitation of Bragg’s law have been considered, namelyto perform angular scans at fixed wavelength or to perform‘‘energy dispersive’’ wavelength scans at fixed scatteringangles. In principle the two approaches are equivalent, andin neutron-scattering tradition practicalities lead to adominant role of doing experiments with single wave-length, monochromatic beams both in elastic and inelasticstudies. There are just a few notable exceptions, the mostimportant being energy dispersive diffraction work onpulsed spallation sources, which is the obvious privilegedchoice in view of the pulsed nature of the source and to a

e front matter r 2006 Elsevier B.V. All rights reserved.

ysb.2006.05.319

8062 2031; fax: +49 30 8062 2523.

ss: mezei@lanl.gov.

limited extend backscattering spectroscopy both at con-tinuous and pulsed sources. In the latter case the incomingneutron energy range is limited to a few times 10 meV wideranges at continuous source backscattering instruments, sowe cannot really speak of significant multiple wavelengtheffects. In backscattering spectroscopy the incomingneutron energy scan is quite substantial, however a givenneutron energy change can only occur for a given incomingwavelength. In contrast, the key issue in our presentconsiderations on multiple wavelength data collection is toobserve the same scattering process with different incomingneutron parameters to obtain enhanced information bothin terms of quantity (intensity) and quality. We will findthat multi-wavelength ‘‘energy dispersive’’ techniques arethe data collection strategies of choice significantly moreoften than they are currently effectively used.In general, using several neutron wavelengths in a single

experiment implies taking data at different or very different

ARTICLE IN PRESSF. Mezei / Physica B 385–386 (2006) 995–999996

resolutions, much more so than for X-rays, in particular inview of the de Broglie relation mv ¼ h/l between wave-length and velocity and the E ¼ mv2/2 neutron dispersionrelation. Thus for constant wavelength resolution dl theenergy resolution rapidly varies with wavelength as l�3. Onthe other hand, in the Maxwellian tail of the source spectralintensity drops as l�5. Thus at shorter wavelengths low-intensity broad features can be advantageously observed,while long wavelengths provides for the highest resolutiondata for a particular inelastic-scattering method. Within agiven experiment, one might look for information on bothtype of features, e.g., in view of the extreme variation ofinelastic line width with wave number q in diffusionprocesses.

Most significantly, taking data at various neutronwavelengths also offers a powerful tool to check spuriouseffects and correct for them. It is a time honored approachin single crystal diffraction to correct for extinction effectsby extrapolating the results obtained at different neutronwavelengths to l-0, where extinction vanishes. For thisreason, much of single crystal diffraction is being done withhot neutrons, in particular with polarized neutrons whereextinction is a serious worry. Multiple scattering is anotherimportant spurious scattering effect, in particular ininelastic scattering work, and can also display verypronounced wavelength dependence. By fundamentalreasons the inelastic-scattering structure factor contains aq2 kinematic factor, which makes it increase rapidly withthe wave number q. Thus the multiple scattering will ingeneral strongly decrease with increasing wavelength, asthe higher q domain with higher cross sections getsinaccessible. Using this variation has been found to be apowerful approach for precise multiple-scattering correc-tion [1], with a number of advantages in many casescompared to the alternative, more conventional ap-proaches, namely variation of the sample thickness andnumerical simulation based on single wavelength data. Atsmall q values the multiple-scattering contributions caneasily exceed the single scattering signal by an order ofmagnitude for otherwise ideal sample sizes. It is practicallyimpossible to reach the accuracy in numerical simulationcalculations required to correct for the overwhelmingspurious fraction of the signal in such a case. Making thesample sufficiently thin (even for samples divided in smallcells by an absorbing grid in order to laterally limit the pathlength of the neutrons in the sample) can reduce the weaksmall q signal to prohibitively low levels before it wouldreduce the relative weight of the multiple scatteringsufficiently to make it amenable to correction calculations.In contrast, the strong variation of multiple scattering withincoming neutron wavelength can provide a tool forcorrection without reducing the intensity of the singlescattering signal.

Finally, in some significant cases for very specificpractical reasons the multi-wavelength, ‘‘energy dispersive’’approach simply offers better neutron economy byeliminating undue losses, such as the extended dead time

in data collection in TOF inelastic spectroscopy at pulsedspallation sources with source pulse repetition rates farfrom the ones optimal for the conceivable spectrometers.By allowing here several monochromatic neutron burstswith different wavelengths and originating from the samesource pulse to impinge on the sample at regular intervalsone after the other—so-called Repetition Rate Multi-plication—up to an order of magnitude can be gained indata collection efficiency [2].In what follows, the advantages of multi-wavelength

data collection will be illustrated by considering a few keyexamples. Note that the examples are from the field of TOFand NSE spectroscopy. The comparison of spectra taken atdifferent instrumental configurations corresponding todifferent incoming neutron wavelengths is not withoutsystematic errors due to inherent uncertainties in ourknowledge of the instrumental response, in particular interms of data normalization on absolute scale. Concerningabsolute scattering cross sections TOF spectrometers arethe ones which can be calibrated with the highest precision(within of few % with extreme care). In NSE thenormalized intermediate scattering function is measuredwith a comparable level of absolute accuracy. Thesefeatures are important ingredients in a multi-wavelengthstudy.

2. Enhancing the dynamic range

The rapid dEpl�3 variation of the inelastic resolutionwith neutron wavelength in TOF based techniques underconstant instrumental parameters (such as pulse length inTOF spectrometers or the strength of the Larmorprecession field in NSE) offers a powerful handle to extendthe dynamic range of observation in an inelastic scatteringstudy by combining data taken at different wavelengths.The highest resolution is invariably achieved at the longestwavelengths at the price of limiting the accessible range ofmomentum transfer q and working with considerablyreduced incoming beam intensities. The study of manyphenomena requires large dynamic range, for example inpolymer dynamics the characteristic time scale is a veryrapid function of both the length scale (i.e. momentumtransfer q) and temperature. Fig. 1 illustrates an examplefrom NSE spectroscopy, where the variation of relaxationis studied at various wave numbers in a polymer solution(polystyrene d-benzene) [3]. The points with different colorshave been measured by using neutron wavelengths 6, 8 and10 A, and their cover quite different time domains. Thereare two reasons, why it would have been impractical tocomplete the study with the longest wavelength alone,although it offers the best energy resolution, combinedwith—as usual—the lowest beam intensity. On the onehand, the lower limit of the time variable is too high tofollow the full response at the highest momentum transfer(cf. numbers in the table in the figure, A�1 units). On theother hand, the scattering intensity is at 0.183 A�1 nearlytwo orders of magnitude less than at 0.022 A�1, which

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1.0

0.8

0.6

0.4

0.2

0.0

0 10 20 30 40

time [nsec]

Ech

o

Q values0.022 @ 10Å0.0330.0550.069 @ 8Å0.0820.0100.146 @ 6Å0.183

Fig. 1. Neutron Spin echo (NSE) study of the relaxation in the semidilute

polymer solution polystyrene d-benzene accomplished by using three

different neutron wavelengths (colors of points) given in the table in the

figure, together with the momentum transfers in A�1 units [3]. The three

wavelengths together cover a 5 times larger dynamic range than the one

accessible to a single wavelength.

CKN

λ=4.0 Å λ=6.3 Å λ=8.5 Å

Sm

(q,

ω=

0.45

meV

) [a

.u]

q [Å-1]

0.16

0.12

0.08

0.04

0.00

0.0 0.5 1.0 1.5 2.0 2.5 3.0

T=410 K

Fig. 2. Apparent dynamic structure factor as directly measured in a

supercooled liquid using standard data reduction methods without

correction for multiple scattering [4]. The difference between data

collected with neutron wavelengths of 4.0, 6.3 and 8.5 A at low momentum

transfers is due to the different amount of multiple-scattering contribu-

tions. The 8.5 A spectrum approaches within 20% the single-scattering

signal.

F. Mezei / Physica B 385–386 (2006) 995–999 997

required working with the about 20 times higher beamintensity at shorter wavelength. Thus multi-wavelengthapproach in this case provided both extended dynamicrange and considerably enhanced effective beam intensityon average over the whole study.

3. Revealing and correcting for multiple scattering

In the second example the observation of the wavelengthdependence of the apparent inelastic signal made possible,for the first time, to precisely observe the wave number q

dependence of the dynamic structure factor below 1 A�1 ina supercooled liquid, delivering critical information on thenature of dynamic processes related to the glass transition[4]. Fig. 2 shows the apparent dynamic structure factor asdetermined using the TOF spectrometer NEAT at HMIwith various incoming neutron wavelengths, by conven-tionally correcting the measured spectra to backgroundand sample absorption. The strong differences at low q’s isa signature of multiple-scattering contributions, which getlower as the wavelength increases. This is quite generallythe case in inelastic scattering, as pointed out above, sincethe higher cross section region at higher q’s are less and lessaccessed as the wavelength increases: at 8.5 A wavelengthwith the indicated energy change the maximum achievablemomentum transfers are 1.47 and 1.61 A�1, in elasticscattering and in inelastic scattering, respectively. In aniterative numerical refinement process [1] the wavelengthdependence of the multiple scattering is the primary inputparameter to allow us to derive the single scatteringstructure factor S(q,o) with high precision, and actually itwas found that about 80% of the signal shown in the figurefor 8.5 A is the true single scattering cross section at smallq’s. Thus at shorter wavelength the overwhelming part ofthe signal in this q range is multiple scattering, which

cannot be calculated with sufficient precision to allowmeaningful correction without the much less affected datataken at longer wavelength. On the other hand, the spectracollected at the shorter wavelengths provide the informa-tion sought for in the range of the higher q’s, as shown, andare also necessary for the precise evaluation of multiplescattering in an refinement process consistently involvingall data.Also notice, that the statistical accuracy of the longer

wavelength data is superior, although all spectra have beentaken for the same time and the Maxwellian cold neutronspectrum of the reactor peaks at about 3 A. The rapid dropof the flux with increasing wavelength is compensated bythe variation of the data collection efficiency of the TOFspectrometer at constant energy resolution scaling with l7

at constant pulse frequency. Namely, l3 for both theprimarily and secondary resolution chopper pulse lengthand approximately l for the increase of the angular domainof detectors covering a given momentum transfer range(q, q+dq). Thus, while selecting the longest feasibleneutron wavelength to achieve the best resolution impliesstrong intensity losses, at equal resolution best intensityconditions are offered by the longest wavelengths, at theexpense of the accessible q range, of course.

4. Enhanced data collection efficiency at pulsed sources:

repetition rate multiplication

Finally we will consider data collection in TOF spectro-scopy at pulsed spallation sources in the ‘‘energy dis-persive’’ Repetition Rate Multiplication (RRM) mode ofoperation [5]. Conventionally at a pulsed spallation sourceTOF spectrometers produce one monochromatic neutron

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5 10 15 20

10

100

1000

10000

Cou

nts/

TO

F c

hann

el [a

.u.]

10 20 30 40 50 60

1

10

100

Cou

nts/

TO

F c

hann

el[a

.u.] 1000

0.01

0.1

Time [ms]

Time [ms](a)

(b)

Fig. 3. Simulated as measured time-of-flight inelastic scattering spectra

for a schematic model scattering function in Repetition Rate Multi-

plication (RRM) mode of operation. The assumed TOF spectrometer has

25m source to sample distance and faces a coupled cold beam moderator.

Top (a): With 2.128ms between the pulses on the sample seven ‘‘RRM

frames’’ show the same incoherent inelastic spectrum measured with

different incoming neutron wavelengths between 1.01 and 3.03 A. For

longer wavelength neutrons the subsequent spectra significantly overlap at

this pulse rate. Bottom (b): With 8.512ms between pulses the six useful

RRM frames span incoming neutron wavelengths from 2.02 to 8.76 A

without overlap or with manageable overlap. The first frame at 0.674 A

carries no useful information.

F. Mezei / Physica B 385–386 (2006) 995–999998

pulse on the sample for each source pulse. Depending onthe incoming neutron wavelength, significant inelasticallyscattered neutron intensity will arrive to the detector forabout 1.5 times the time elastically scattered neutrons coverthe sample to detector distance, from the moment the pulsehits sample. This time interval for the typically few meterdistance between sample and detector varies between 1 and2ms for neutron wavelengths around 1 A and 10–20msaround 10 A. With the time between subsequent sourcepulses for the various pulsed spallation sources and targetstations ranging from about 16.7–100ms, most often usefulscattering data are only collected during a small fraction ofthe time between source pulses. In RRM mode ofoperation the chopper system is tuned to deliver severalpulses with different wavelengths at a regular repetitionrate from each source pulses. Thus RRM makes some useof the potentially as much as some 98% dead time leftunused in a conventional, single wavelength TOF opera-tion. This amounts to performing a number of experimentswith different wavelengths in parallel, within the same datacollection time period. This is illustrated in Fig. 3.

These simulation calculation results represent thedirectly measured TOF detector spectra for a giveninstrument configuration and schematic model scatteringfunction. The detector was assumed to be situated at 901scattering angle in the equatorial scattering plane. The timet is measured from the start of the last source pulse, withthe next occurring at t ¼ 100ms. The schematic incoherentmodel scattering function assumed consists of an elasticline, a pair of sharp excitation peaks at 71.5meV and abroad Debye spectrum with sharp cut-off at730meV. Thedata are assumed to be taken at an elevated temperatureswith kTb30meV. The momentum dependence of theinelastic Debye scattering was assumed to follow the usualq2 law for incoherent scattering. The elastic line wasassumed to have q independent intensity, in order to reflectthe incoming beam intensity, which is a strong function ofwavelength for the coupled cold moderator considered.The assumed TOF spectrometer displayed the parametersof the planned LET instrument at Target Station 2 at theISIS facility, i.e., 25m moderator to sample distance, withthe main energy resolution counter rotating pair discchopper producing triangular pulses with 11 ms FWHM. Itis situated 1.5m upstream from the sample and thedetectors are placed at 3.5m from the sample. In Fig.3(a) the chopper pulses follow each other in 2ms intervals,selecting a series of incoming neutron wavelengths with0.337 A increments. The time coordinate for the elasticscattering lines (highest peaks) show the respective incom-ing neutron wavelengths, given for this geometry by therelation l [A] ¼ 0.1413tel [ms].

For our schematic model scattering function, below30meV incoming neutron energy the scattering withneutron energy loss extends in principle to infinity in time,however due to the kinematic t�4 factor appearing in theTOF spectra it becomes negligible compared to the signalcoming from scattering in the next pulse. Disturbing frame

overlap occurs when the energy gain scattering (the leadingedge of the Debye spectrum) arrives too close to the elasticsignal of the previous pulse, which in the example in Fig.3(a) (2.128ms pulse repetition rate) occurs at times422.5ms. The part of the spectrum shown includes the 7fully useful RRM frames providing perfectly unperturbeddata in this case, in the range between the shortest andlongest incoming wavelengths of 1.01 and 3.03 A, respec-tively. (Theoretically there are two RRM frames at evenshorter wavelengths too, but they do not deliver usefulinformation, both by lacking resolution and suffering fromhigh background due to the diminishing neutron absorp-tion capability of disc choppers as the wavelength gets wellbelow 1 A.) The TOF spectrum clearly shows that all 7frames deliver significant information on the broad Debyespectrum, while the 1.5meV excitation is not well resolvedin the shorter wavelength frames. The substantial gain in

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information collected by RRM is obvious compared withthe traditional single wavelength mode of operation, whichwould mean in this example that one would only collect 1of the 7 groups of data in the figure, with the spectrometerleft idle except for about some 2ms out the 100ms betweensource pulses. In addition the part of the spectrum whichwould be only retained for data collection would have to beselected before starting the measurement, eventually withonly preconceived ideas of what the spectrum will look like.

The choice of 2.128ms RRM pulse repetition time(�470Hz repetition rate!) in Fig. 3(a) allows us in thisexample to fully explore the information what can beobtained with wavelengths up to about 3 A, beforedisturbing RRM frame overlap sets in with increasingtime (i.e. l). Fig. 3(b) shows another choice for the sameconfiguration and scattering model function, where theRRM repetition time is chosen to be 8.512ms (i.e., 3chopper pulses out of 4 are suppressed by an additionalchopper). Here disturbing RRM frame overlap only occursfor the Debye like spectrum after about 65ms, i.e., therange of incoming wavelengths delivering unperturbedspectra is extended up to 8.7 A. This choice of datacollection mode might be privileged if one is (also)interested in high resolution information, e.g., to reveal aslight broadening of the elastic line with a resolution of lessthan 10 meV FWHM. Note that the signal intensitydecreases with increasing wavelength, while the resolutionimproves. The RRM disc chopper systems built or beingconsidered by now will operate with constant chopperpulse length for all wavelengths; hence the quasielasticenergy resolution rapidly improves with increasing wave-length, proportionally to l3. Maintaining constant energyresolution (as in the example considered in connection withFig. 2) would be of considerably interest, but no ideasurfaced by now how to practically achieve it in RRM.

These examples show that RRM mode of operationessentially means performing in parallel 6 or 7 TOFexperiments on the same sample with different instru-mental resolution characteristics, in q domains of differentextension and with different beam intensities due to thedifferent incoming neutron wavelengths. Combining theinformation obtained by these 6 or 7 independentexperiments is certainly a computational challenge, but isbasically straightforward. A simplest approach can be

deducing the model parameters of interest for the inter-pretation of the results (together with their properlyevaluated errors!) independently for each sub-experimentwith a given incoming neutron wavelength. The combinedresult of the full RRM experiment is than the weightedaverage of the results obtained at each wavelength. In arepresentative experimental emulation study of RRM itwas found, that the uncertainty of this weighted average—compared to the conventional single wavelength ap-proach—roughly corresponds to a data collection ratemultiplied by the number of usable incoming wavelengths[6]. Of course, this is just a first approximation, the exactgain in data rates will vary somewhat from one experimentto the other.

5. Conclusions

The presented arguments and examples clearly show thatmulti-wavelength data collection offers valuable, novel, bynow mostly unexploited potentials in inelastic neutronscattering research both at continuous and pulsed neutronsources. These new opportunities include the extension ofthe dynamic range, the most precise identification andcorrection for the characteristically wavelength-dependentmultiple-scattering effects and the enhanced data collectionefficiency both in terms of intensity and sensitivity to bothsmall signals and fine resolution details offered by RRM inTOF spectroscopy at pulsed spallation sources. Theserecent approaches are expected to prominently figure in theforthcoming evolution of neutron research.

References

[1] M. Russina, F. Mezei, AIP Proc. 479 (1998) 47.

[2] F. Mezei, Acta Phys Hungar, Heavy Ion Phys. 1 (1995) 209.

[3] B. Farago, private communication.

[4] M. Russina, F. Mezei, R. Lechner, S. Longeville, B. Urban, Phys. Rev.

Lett. 84 (16) (2000) 3630.

[5] F. Mezei, M. Russina, In: I.S. Anderson, B. Guerard (Eds.), Advances

in Neutron Scattering Instrumentation, 2002, SPIE, Seattle, Washing-

ton, USA. Bellingham, Wash, 2002, SPIE proceedings series, 4785), p.

24.

[6] O. Russina, F. Mezei, M. Russina, R. Lechner, J. Ollivier, in: G.

Mank, H. Conrad (Eds.), Proc. ICANS XVI, FZ Julich, Germany,

2003, p. 315.