IMPROVED ENERGY RESOLUTION WITH NEUTRON SPIN ECHO TRIPLE-AXIS SPECTROMETERS

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IMPROVED ENERGY RESOLUTION WITH NEUTRON SPIN ECHO TRIPLE-AXIS

SPECTROMETERS

C. Zeyen

To cite this version:

C. Zeyen. IMPROVED ENERGY RESOLUTION WITH NEUTRON SPIN ECHO TRIPLE- AXIS SPECTROMETERS. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-543-C6-546.

�10.1051/jphyscol:19816159�. �jpa-00221236�

JOURNAL DE PHYSIQUE

CoZZoque C6, suppZEment au n012, Tome 42, dSeembre 1981 page C6-543

IMPROVED ENERGY R E S O L U T I O N W I T H NEUTRON S P I N ECHO T R I P L E - A X I S SPECTROMETERS

C.M.E. Zeyen

I n s t i t u t Laue-Langeuin, 1561, 38042 GrenobZe Cedex, Fmnee

Abstract. - A spin echo option added to a classical Triple Axis spectrometer is capable of significantly improving the Energy Resolution. The design and construction of such a machine is described. In particular it is shown that intensity problems can well be overcome by using new focussing polarizerl analyser devices. The method has proven to be very successful for high reso- lution quasielastic scattering. Preliminary phonon experiments yith the aim of lifetime determination have been performed.

Introduction. - Neutron Triple-Axis Spectrometers (TAS) have been a very productive and rather unique tool for the investigation of dispersion surfaces in solids.

Furthermore in certain cases the same technique has been useful to determine the energy linewidth of excitations. In general, however, the latter applications are handicapped by the limited resolution characteristics of TAS.

Their energy resolution is determined by the beam collimations and monochroma- tisations necessary to precisely measure the neutron energies and momenta before and after the scattering process. Hence the practical limits are conditionned by the limited flux of the available contineous neutron sources. In practice relative energy resolutions-of AE about 1 % are typical (Eo is the incident neutron energy).

E0

Thus the very best energy resolutions ('L 50 peV FIJHM) are obtained with very low energy neutrons with the corresponding limited momentum transfer obtainable.

The neutron spin echo (NSE) technique proposed by Mezei 1 , if added to a Triple Axis spectrometer can be used to improve the energy resolution significantly. This is due to the fact that in NSE rather than obtaining the excitation energy as the difference between incoming and outgoing neutron energies it is measured directly.

The principle of the method is analogous to the spin echo method used in NMR 2 with the difference that the time variable is replaced here by a spatial variable : the distance the neutrons travel through magnetic fields with their spins executing Larmor precessions. The total amount of precession angle accunulated by one neutron is proportional to the time spent in the field and the integral of the magnetic field along its trajectory. Thus the well polarized incoming neutron beam will quickly loose its polarization due to its velocity spread but the Lamor lhase angle

02 each neutron spin taken separately will still remain a measure of its own energy.

By arranging two magnetic field areas before and after the scattering sample in such a way as to produce precession in opposite sense and properly tuning the

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816159

C6-544 JOURNAL DE PHYSIQUE

difference in field magnitude to the neutron energy change by the inelastic process under study one can recover the mean beam polarization at the end of the second magnetic field area. This is called obtaining the "Echo". The decay of this final NSE polarization as a function of magnetic field asymmetry around the Echo value can be shown to be related to the energy width of the excitation studied.

The resolution of such a spectrometer is improved by increasing the number of Larmor precessions through stronger magnetic fields. The limit is set by the obtain- able field homogeneities. Indeed field inhomogeneities introduce parasitic Larnor precessions which may destroy the final NSE polarization.

The spectrometer. - The basis of our NSE TAS is the thermal neutron triple-axis spectrometer D103 of the I.L.L.. In its classical mode of operation the spectrome- ter is equipped with sets of both PG and copper vertically focussing monochromator/

analysers. The useful wavelength band is inbetween 1 and 3.5 angstrom and below 1.5 the cut-off of the curved neutron guide is indeed very useful because X / 2 fil- ters are not needed. This is a particularly relevant feature where Heusler crystals are used as the second order reflexion is very strong.

Fig. 1 : Schematic arrangement of the spin-echo TAS M : focussing crystal monochromator/polarizer A : focussing crystal analyser/spin analyser D : detector

S : sample

.rr : spin-turn coils (thetcoils around the sample can be replaced by a single n coil)

H,,H2 : precession fields.

In order to transform the spectrometer into a polarization analysis spectrome- ter vertically focussing composite Heusler systems were especially developed for this purpose. These systems give a focussed beam of 30 X 30 mm cross section start- ing from a white beam of 120 X 30 mm. The polarization efficiency obtained is 96 %.

The final polarization of the spectrometer including the flipper efficiency reaches 92 % provided the sample presents no spin incoherent scattering. In order to keep the spectrometer rather compact an Iron core precession magnet-type with the field transverse to the neutron trajectories was chosen. The magnets have a wide window frame iron core dimensioned so that the iron does not saturate anywhere at maximum field. The windings were chosen of the racetrack type because they give a maximum of homogeneity. The maximum field in the magnet gap is 1.5 k Oersted. For particular

small sample geometries extra pole pieces may be added to give a maximum field of 3 k Oersted. For NSE the relevant property of the precession magnets is the line inte- gral of the magnetic field H along neutron path and over the distance R where the neutron spins are allowed to precess around the field direction. This integral was calculated to be about$HdR 'L 5.10 Oe.cm the value depending of course on the 4 precise integration length R. In practice and at maximum field the value of 5.63.10 Oe.cm was found. This corresponds to 4 1000 Larmor precessions for 2 . 4 A (N = 7.37. I O - ~ g~dll). This number of precessions N has to be as homogeneous as pos- sible for all neutrons of identical wavelength. For our magnets experiments have shown that practical beam sizes lead to a loss of NSE signal of about 30 X at maxi- mum field mainly due to field inh~mo~eneities. Further experimental details can be found in

.

Performance and results. - From the point of view of polarized neutron flux the pre- sent solutions are very satisfactorily. The flux loss with respect to the standard graphite crystal monochromator/analyser is of a factor 5 only.

The quantity measured in an NSE experiment is the beam average of the final NSE polarisation. As extensively discussed in this quantity is related to the scattering function S(Q,o) of the sample by

PNsE = P ~ P ( Q , ~ ) cos ot do

where t is a Fourier time variable depending on the machine constants and the inci- dent wavelength. P is a normalising polarization which contains eventual changes of polarisation by the sample. This relation can be specialised to particular scatter- ing examples. For quasi-elastic Lorentzian scattering the polarisation is just giv- en by

PNSE = Poexp (-l't)

where r is the linewidth parameter of the Lorentzian.

For phonon linewidth studies the measured polarisation is given by PNSE = PO COS 2Tl (N -N 1 2)

where NI and N stand for the mean numbers of spin recessions in the initial and 2

final beams. The quantity P describes the decay of the echo signal as a function of N and contains both the energy width of the classical resolution function of the

1

spectrometer as the standard deviation of the phonon lineshape.

The resolution function of an NSE spectrometer is given hy the decay of the NSE polarisation with increasing precession field strength. Fig. 2 shows a typical reso- lution curve of DlO-NSE for an incident wavelength of 2 . 4 1. One sometimes defines the spectral resolution which gives rise to a 5 % change in PNSE at the maximum Fourier time t obtainable. In our case this quantity amounts to 0.3 UeV. He have

max

verified that for quasi-elastic scattering this is indeed measurable.

Concerning the measurement of phonon lifetimes only very preliminary measure- ments have been made. It can be stated that there is no experimental problem for non dispersive branches although the data treatment and corrections are not yet complete- ly under control. More experimentation is needed to determine the resolution

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improvements o b t a i n a b l e f o r s t r o n g l y d i s p e r s i v e phonon b r a n c h e s .

F i g . 2 : Example of DIO-NSE R e s o l u t i o n a s a func- t i o n of t h e P o u r i e r time (Xo = 2.4 11).

References

I . FEZEI F., 2 . P h y s i k ,

255,

2 . HAHPJ, E.L. (1950) SPIN ECHOES, Phys. Rev.

80,

3 . I . L . L . YELLOF BOOK, Neutron Beam F a c i l i t i e s a t t h e HPR, B. H a i e r ( J 2 8 0 ) . 4. ZEYEN, C.M.E., Proceedings of t h e Sjrmposium on Neutron S c a t t e r i n g , Argonne,

August 1981, t o b e p u b l i s h e d by AI?.