The Triple Axis And SPINS Spectrometers

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and Technologygies for which the transmission of the filter isreasonable ( 0.7 for a length of 50 mm) with arejection of 10" for the second order energies. Analternate method of obtaining a "clean" beam is touse a monochromator whose properties are suchthat the second order reflection, for example, isforbidden. Several planes of Si, which has thediamond structure, satisfy this requirement. Thetechnology for treating virgin Si crystals, which areusually too perfect (having very small mosaic 1 min of arc resulting in a very small reflectivity),is only now becoming available. It is always truethat care must be exercised to ensure that ameasured resonance is due to a property of thesample and not some instrumental effect due to acharacteristic of the monochromator or analyzer.Fig. 2. The calculated resolution of a triple axis spectrometer asa function of the monochromator scattering angle 28m. Thecollimation widths are 40, 20, 20, and 20 min of arc for thecoUimators before and after the monochromator and before andafter the analyzer, respectively. The monochromator andanalyzer crystals are both PG (002). The resolution is for elasticscattering (E Eo).2.4 Polarized NeutronsBecause the neutron possess a nuclear magneticmoment, the scattering from a sample whichexhibits magnetism will be sensitive to the properties of the sample. The scattering is, of course, stillalso a function of the nuclear positions andmotions. If the resonance produced by the magnetic properties of the sample is well separatedfrom that produced by the nuclear scattering, nofurther effort is required. If however there isrequired unambiguous identification of the resonances as arising from a magnetic source, one canincrease the sensitivity of the scattering to the magnetic properties, over those which depend only onthe position and motions of the nuclei, by using abeam of space polarized neutrons. The scatteringlaw can then be measured as a function of whetherthe spin of the neutrons is reversed or not in thescattering. Such a spin flip can only be produced bymagnetic interactions. This type of measurement istherefore capable of distinguishing that part of thescattering which is due to the magnetic propertiesof the sample from that which is not. Technologiescapable of producing polarized neutrons andeffecting their spin flip are required for suchmeasurements.The production of polarized neutrons has beeneffected by using magnetic monochromator crystalswhose scattering is strongly dependent on the relative orientation of the neutron magnetic momentand a magnetic field (the guide field) extendingfrom the monochromator to the sample (or thesample to the analyzer). The three most widelyused materials for this purpose are single crystalsof CoFe, Fe", and Heusler alloy. The first two are23 FiltersRecall from Eq. (1) that a crystal with a givenlattice spacing reflects neutrons of several wavelengths, viz. the several orders. The higher orderneutrons being of shorter wavelength, viz. A/2, A/3,etc., are of higher energy, 4 , 9 , etc. It is usual toplace a filter either in the beam incident on thesample or in that scattered from the sample inorder to reduce the "contamination" of these orders so that a clean measurement is possible. Twoof the most widely used filter materials for thisapplication are beryllium (Be) and pyroliticgraphite (PG). The mechanisms by which filteringis produced will not be discussed here but only theresulting properties. Polycrystalline Be is anextremely effective low-pass filter. The cutoffenergy is 5 meV. The rejection ratio for neutronsof energies larger than the cutoff to those smallerthan the cutoff is a function of the length andtemperature of the filter. As an example, for afilter of 100 mm length at a temperature of 78 K(liquid nitrogen), the rejection ratio is 3 x 10' witha transmission of the low energy neutrons of 0.95.More effective rejection can be obtained if required by a particular experiment at a small cost oftransmitted low energy neutrons by using a longercooled filter. There is, unfortunately, no universalfilter for energies larger than 5 meV. The most useful filter in this energy region is PG for energies of13.7, 14.8, 28., 30.5, and 40.3 meV. These are ener62

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and Technologyused for neutrons of wavelengths 0.05-0.15 nm(0.5-1.5 A) and the last for wavelengths of0.1-0.4 nm (1-4 A). For neutrons of wavelengthslonger than 0.4 nm (4 A), such as those available atthe cold neutron facility, devices constructed ofbilayers, a few nanometers (tens of A) thick, alternately of a magnetic and non-magnetic material,have been constructed with the desired properties(these devices are known as polarizing supermirrors). The efficiency of neutron polarization ofthese devices is on the order of 98 percent orbetter. The additional sensitivity to magneticscattering obtained in this manner is of course notwithout cost in overall sensitivity in that at most 1/2of the neutrons incident on the polarizing deviceswill be scattered by them and available for themeasurement. The trade off in most cases is however well worth the effort. In addition to the abilityto produce and be sensitive to a particular polarization of the neutron, one must be able to effect arotation of the polarization of the neutron beameither before or after scattering from the sample.This can be accomplished by passing the neutronsthrough a magnetic field (the flipping field)directed perpendicular to the plane defined by theneutron wavevector k and the guide field. Themechanism operative in this device is that ofmatching the Larmor frequency of the neutron inthe flipping field to the flight time of the neutronin this field to produce an arbitrary (usually 180 )rotation of the magnetic moment. A second coil isplaced between the guide field and the flippingfield whose function is to cancel the guide fieldfrom the region of space occupied by the flippingfield. These devices are well understood andreadily available.sample is obtained from simple optical considerations [4]. Such a device is capable of producing anincrease in the neutron flux on the sample by afactor of 2.2.6 Spin Polarized Inelastic NeutronScattering (SPINS)In 1962 G. M. Drabkin [5] proposed a scheme bywhich a beam of polarized neutrons could be produced whose energy is determined by the state of amagnetic field through which it passes rather thanby the angle through which it is scattered from acrystal. This method is in principle capable of modifying one of the characteristics of a conventionaltriple-axis spectrometer. In the standard spectrometer, the energy resolution and the momentum(wave vector Q) resolution, both of which aredictated by the characteristics of the crystals andcollimations used, are strongly coupled. In manyapplications, this is not a particular disadvantage inthat a well-defined resolution function is very useful. There would in many instances be an advantage in signal if the momentum resolution could besubstantially relaxed with respect to the energyresolution by decoupling the two. Examples of suchsituations include dispersionless optic modes incrystals and single particle vibrations of hydrogen.The method which Drabkin has proposed producesjust such a decoupling.The device can be understood by consultingFig. 3. An unpolarized beam with a relatively broadenergy bandwidth is first polarized by a supermirror. The beam next traverses a current carryingfoil which is folded in such a manner as to producea small, spatially oscillating magnetic field Hj which is normal to both the propagation directionof the beam and to a larger uniform magnetic fieldHo that is superimposed over the full extent of thefoil. These two fields are related according toH 2HolM where "A/" is the number of spacesbetween adjacent current sheets through which theneutrons pass. The resultant magnetic field actsas a velocity or energy selective resonance flipper.Only those neutrons with velocities near vo ayHol-n'(where y is the gyromagnetic ratio of the neutronand "a " is the spacing between adjacent sheets ofthe foil) will undergo a spin-flip with a high probability. The probability distribution as a function ofvelocity is centered at velocity vo and has a widthproportional to l/M. Those neutrons which are notflipped are subsequently not reflected by a secondsupermirror in which the magnetization directionis opposite to that of the first. Thus, the pair of2.5 FocusingIn the main, the measured quantities of interestare ko and k and these depend on the vertical collimation only in second order. This allows the use ofdevices capable of vertical focusing to increase thesignal without unduly affecting the resolution. Onesuch device is a monochromator which consists ofseveral crystals mounted so that each can berotated about an axis parallel to the scatteringsurface of the crystals. The crystals are arranged soas to approximate a cylindrical scattering surfacewith the normal to the surface along the scatteredneutron direction and with radius of curvature R.The relation between the neutron wavelength, thecurvature radius, and the distance between neutronsource-monochromator and monochromator63

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and TER IFIRST MULTILAYER1AFTER FLIPPERAFTER2N0 MULTILAYERIVELOCITY-DEPENDENT RESONANCE SPIN AYERPOLARIZINGMULTILAYERFig. 3. A schematic diagram of the Drablcin neutron spin-flipper device.supermirrors and the flipper act as an energydependent filter whose characteristics are controlled electrically. Table 1 compares the relativeintensity to be expected for a given energy resolution obtained with a spin flip analyzer compared tothe conventional triple axis configuration. Notethat as the energy resolution is increased, the advantage of the spin flip method is substantial evenif the polarized nature of the neutrons is not used.A spectrometer can be constructed such that onehas the option of using the spin flipper asmonochromator or analyzer or both in place of theconventional crystal monochromator. In any case, avertically bent PG crystal will be used to pre-monochromate the beam. Either a Be or PG filter isused to remove order contamination. The spectrometer will be capable of incident energies from15 to 2 meV with resolutions from 1 meV to almost10 (leV with adjustable resolution parameters. Itshould be noted that although the energy-dependent analyzer makes use of the neutron spin, thesample scattering need not be spin dependent.Table 1. Relative intensity / and energy resolution A obtainedwith a single spin flipper and 80 min collimation compared withthat obtained with a conventional triple-axis spectrometer usingPG(002) crystals and various collimationsSpin 20'3. Applications10'3.1 PhononsA Rel A RelA RelAERel AE(meV) / (meV) /(meV) /(meV) / (meV)0.320 1 OJ080.1601/10 0.1540.0801/33 0.0770.0401/2000 0.039The triple-axis spectrometer was originallydesigned specifically for the purpose of measuringthe phonons which a crystalline substance cansustain. A phonon is characterized by a quantizedenergy A(o,{q), momentum q and eigenvector64

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and Technologyffj {q). Here s numbers the various normal modes.This quasi-particle is used as a description of vibrations of the atoms and molecules which constitutethe crystal. The energy fius is easily understood asthe vibrational energy of the "normal mode," themomentum q, relates the phase of the motions ofthe atoms whose vibrations constitute the phonon.Two atoms whose spatial position is determinedonly by the distance R(h,k,l) between thecrystalline unit cell in which they exist vibratetemporally with a phase difference of g, * /? (ft ,k,l),(h,k,l) being the cell indices of one cell withrespect to the other. The eigenvector e,, ofdimension 3N, N being the number of atoms in theunit cell of the crystal, describes in detail thespatial character of the vibrational mode. One consequence of such a description of the mechanicalvibrations of the atoms and molecules is that to,and c, are functions ofq. The detailed dependenceis governed by the interactions between the atomsand molecules of the crystal. An important reasonfor the experimental determination of the values ofoil (9) as functions of q (termed the dispersioncurves) is the investigation of these interactions. Aneutron when scattered by a substance can interactwith these phonons if the requirements of energyAntisymSycnSymand momentum are satisfied. That is, the neutronenergy and momentum change must equal thephonon energy and momentum if a scattering resonance is to occur. This requires thatE -Eo o)si{q)(8)and/iQ fi{q T),(9) T being a reciprocal lattice vector of the crystal[2]. The fact that these two quantities can be readily controlled by the triple axis spectrometer makesit the obvious choice as the instrument for theirdetermination. Many substances have yielded tosuch measurements. The more complicated theunit cell (in number of atoms or molecules), themore complicated is the pattern of dispersioncurves. An example of a rather complete measurement of the dispersion curves of a moderatelycomplex crystal is presented in Fig. 4. The crystal isof deuterated anthracene [6] (CuDio). There aretwo molecules in the primitive cell giving rise to 12external modes, 3 translational and 3 rotational foreach molecule. There are symmetry-imposedrequirements on the properties of the phonons.AntisymAntisymSymPhonon wavevectorFig. 4. Measured dispersion curves for the 12 external and the 4 lowest internal modes in anthracne at 12K for the [{00], [0 0] and [00?] directions. The presentation is given in the extended zone scheme such thatbranches must not cross. Some dispersion curves in the [0.5, 5, 0] direction are also shown [6].65

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and Technologyof localized diffusional motion. As the temperatureincreases, the energy width of the quasielasticincreases reflecting a shortening of the rotationaldiffusion time of the molecule. At 5 K, this time isso long that the quasielastic peak is too narrow tobe resolved, and at 120 K the time is so short, leading to such a broad quasielastic peak as to bealmost unobservable. The temperature and Qdependence of the spectrum yields quantitativeresults for the structural model, residence timesand thermal activation energy of this motion.For those values of q for which these restrictionsare greatest, a consequence is that substantialdegeneracy occurs in the values of the eigenfrequencies of several normal modes thus restrictingthe number of independent oscillators to be measured. This is reflected in the data presented inFig. 4. Even with these restrictions, there stillremain a substantial number of energy levelsfi( s{q) for each q. In practice an approximateknowledge of the eigenvector e,{q) is extremelyuseful in planning a strategy for the measurementand increasing confidence in the correct identification of the observed resonances. Equation (51) ofBerk's [2] article gives the cross-section dependence on these quantities. These eigenvectors areusually obtained from a first approximation of amodel describing the crystalline interaction. Thereare also model independent group theoretical sumrules [7] for the structure factor which have provedvery useful in the past [8].S «X)0-I30003.2 Rotational DifTusionDiffusional motion of atoms whether they belocal, such as rotational, or non-local, translational,are detectable in neutron scattering through thequasielastic spectrum which they produce. Theenergy width of the broadened line centered atfibi 0, and the Q dependence of its intensity withrespect to the unbroadened elastic line containinformation of both the structural and dynamicalcharacter of the motion [2]. The time scale of themotion available in neutron spectroscopy isinversely proportional to the energy resolution ofthe instrument, hence the motivation for CNRFtriple axis spectrometer. The most extensively studied motions are those involving the hydrogen atomsboth because it has the largest incoherent scattering cross section for neutrons and because its lightmass produces motions of the appropriate timescale. Motions of other light atoms are notexcluded and have indeed been investigated. Theexample used here is that of the rotational dynamics of the ammonia molecule in Ni(NH3)6l2 [8]. Inthe fee phase of this material, the ammoniamolecules are coordinated with the Ni such thatthe threefold axis of the molecule is directedtoward it. This allows for rotation of the moleculeabout this threefold axis. In Fig. 6 is presented thetemperature dependence of the quasielastic scattering spectrum from this substance. Severalfeatures are to be noted. The existence of both anelastic and quasielastic component is characteristic 2A0tio) (meV)-1*1.10-1tiwImeVIFig. 5. Temperature dependence of the quasielastic scatteringspectrum from NI(NH})6l2 (after Ref. [9]).3.3 Incoherent Inelastic ScatteringThese are studies of motions of hydrogen atomsin materials for reasons of cross section givenabove. Because of its light mass, hydrogen oftenflnds itself in environments in which measurablequantum mechanical tunneling occurs. Many suchsituations occur for systems in which hydrogenousmolecular groups (CH3, NH3, CH4,.) producequantum tunneling in the presence of a reorientational potential [10]. We use here an example of Htrapped at an interstitial oxygen impurity site inNb(OH)y [11]. The tunneling spectrum of H ispresented in Fig. 6 as a function of concentration.At very low concentrations there is only onenarrow peak suggesting a small number of equivalent sites between which the H tunnels. As theconcentration increases, the tunneling peak broadens substantially. This has been interpreted asreflecting interaction between defects, even forthese low concentrations, producing a distributionof local potentials. The properties of tunnelingmodes are extremely sensitive to the environmentmaking their measurement a very useful probe.66

Volume 98, Number 1, January-February 1993Journal of Research of the National Institute of Standards and Technologysented by its use in detecting spin wave excitationsof

The Triple Axis and SPINS Spectrometers Volume 98 Number 1 January-February 1993 S. F. Trevino ARDEC Picatinny Arsenal, NJ 07806 and National Institute of Standards and Technology, Gaithersburg, MD 20899 In this paper are described the triple axis and spin polarized inelastic neutron scattering (SPINS) spectrometers which