Quasi-elastic and inelastic scattering using nuclear resonance techniques

PHYSICA ELSEVIER

Physica B 226 (1996) 128 134

Quasi-elastic and inelastic scattering using nuclear resonance techniques Rudolf Riiffer*, Aleksandr Chumakov European Synchrotron Radiation Facility (ESRF), B.P. 220, F-38043 Grenoble Cedex, France

Abstract Third generation synchrotron radiation sources as ESRF offer an X-ray beam of high brilliance, i.e. high intensity, small cross-section, and small divergence, which opens the field of nuclear resonance spectroscopy as a standard technique. Besides this classical field new fields have been and will be opened, namely quasi-elastic and inelastic scattering both with 'resonant' and 'non-resonant' samples. Energy transfers between neV and eV and momentum transfers between l0 4 and 30 A- 1 at energies ranging from 6 to 30 keV are accessible. The general lay-out and the parameters of the nuclear resonance beamline at ESRF are reported. Quasi-elastic and inelastic scattering techniques are discussed and illustrated by first experimental results.

I. Introduction The experiments on the excitation of nuclear levels by synchrotron radiation passed in the last ten years a way from pioneering observations [ l ] to the first applications [2]. The superior spectral density of synchrotron radiation of the third generation sources allows one now to establish these experiments as a standard technique of hyperfine spectroscopy. Moreover, it opens new fields like resonant and non-resonant quasi-elastic and inelastic scattering. The nuclear resonance beamline at ESRF, coming in operation this year, is a first dedicated installation for these purposes. The beamline optics provides a monochromatic X-ray beam which can be tailored from neV to eV energy resolution at the corresponding M6ssbauer transitions. In the following we present the nuclear resonance beamline and the properties of the X-ray * Corresponding author.

beam. Finally the domain of inelastic and quasielastic scattering is discussed and illustrated by first experimental results.

2. General characteristics The beamline lay-out is shown in Fig. 1. A more detailed description of the beamline is given elsewhere [3]. The synchrotron radiation beam is delivered from two standard ESRF undulators [4] of 22.8 and 34 mm period installed in a high-/3 section of the lattice. They are optimized for the nuclear transition energies in 5vFe at 14.4 keV and in 1s 1Eu at 21.5 keV, respectively. However, they cover also the other M6ssbauer transition energies between 6 and 30 keV (Table 1). First measurements showed a flux of 5 x 103 photons/(s. Fo) (Fo = 4.65 x 10 - 9 e g for 57Fe) at 100 mA electron current which was achieved by an 57FeBO3 crystal as a nuclear monochromator. The photon beam size and divergence are given by the design of the insertion device

0921-4526/96/$15.00 ~), 1996Elsevier Science B.V. All rights reserved P I I S092 1 - 4 5 2 6 ( 9 6 ) 0 0 2 5 8 - X

129

R. Ri~ler, A. Chumakov / Physica B 226/1996) 128 134

EH2

EH3

B4

EH1

CR

B3

01t2

DF

OH1

M4

B2

HRM

BI $2

M2

M1 S1 U34 U23

mnm)mmm mmmmmmm A2

60 I

I

I

,

i

,

,

i

,

,

PM

40

50 I

M3 EM

,

i

,

,

i

m

,

I I

A1

30 I

l

l

l

0 l

l

|

m

l

Fig. I. Schematic lay-out of the nuclear resonance beamline. O H I - "white" beam first optics hutch; O H 2 second optics hutch: EH1 EH3 experimental hutches; CC1 CC3 control cabins; U23 and U34 22.8 and 3 4 m m period undulators: S I and $2 slit systems: A1 and A2 attenuators; M I timing/intensity monitor; M2 M4 intensity monitors: PM double crystal water-cooled fixed-exit Si(1 1 1) monochromator; EM energy monitor: BI B4 beam shutters: H R M - high resolution monochromator: DF 6-circle diffractometer; CR cryomagnet system.

Table 1 M6ssbauer transitions in 1he energy range 6 30 keV and lifetimes greater than 1 ns [20]. Displayed are the following quantities: isotope M6ssbauer isotope, energy M6ssbauer transition energy, t~ 2 half-life of the M6ssbauer level, F0 energy width of llSe M6ssbauer level, 7 internal conversion factor, abund, natural abundance of the M6ssbauer isotope Isotope

Energy (keV)

t j : (ns)

Fo (neV)

:~

4"K S'Fe 73Ge S3Kr

29.56 (71 14.4130(11 13.263 (15) 9.405 (1) 23.8"7'1 (7) 27.7"7' 12) 12.29 (5) 22.4c~4 ( I 1) 21.5417 (5) 25.65;5 {3) 8.41031 (2} 0.2155 12j

4.25 (6) 97.81 (14) 2953 (23) 147 (4} 17.75 (12) 16.8 (2) 8.1 (2) 7.12 ( 11 ) 9.7 (3) 28.2 (9} 4.00 (10) 6050 (120)

107.3 4.665 0.154 3.10 25.7 27.15 56.3 64.07 47.03 16.18 114.05 0.075 (1)

6.6 15) 8.21 (12) 1095 (55) 19.6 (71 5.12 (101 5.1 (3) 110 (5) 50 ( I ()) 28.60 i15) 2.9 (3) 268 (5) 70.5 (3)

1 I~!S|]

1>'I 133Ba I"*'~Sm 15~Eu I"~Dy t~'"Tm ls~2ca

and the electron optics of the machine. With a horizontal emittance of ~;H = 4 nm tad and a 1% coupling the electron and photon beam characteristics are the following: (1) electron beam size is 54 }am x 0.8 m m ( F W H M , vertical x horizontal) and electron beam divergence is 4 grad x 28 grad

Abund. {%) 0.012 2.14 7.76 11.55 8.58 0.0 0.0 13.83 47.82 18.88 100.00 99.99

[5]; ( 2 ) p h o t o n beam size is 0.45 mm × 2 . 0 m m @ 30 m downstream of the insertion device and photon beam divergence is 18 grad x 33 grad. Another important feature of synchrotron radiation is their pulsed time structure whieh is essential for time resolved nuclear spectroscopy. Based

130

R. Riiffer, A. Chumakov/Physica B 226 (1996) 128 134

on the circumference of the storage ring of 844 m and the radio frequency of 352 MHz one to 992 buckets may be filled. The corresponding spacing between adjacent buckets ranges from 2.8 ns to 2.8 ~ts [6].

high-order reflections allow best energy resolution as A E / E ~ 3 x 10 -~ with a flux of 3 x 109 photons/s (at 100 mA). The monochromator is tunable over the entire range needed for inelastic scattering applications. A corresponding design is also applicable to the other M6ssbauer transition energies.

3. Monochromatization The monochromatization of the synchrotron radiation down to neV, i.e. A E / E ~ 10 13 can only be achieved with electronic and nuclear monochromators. Three successive steps are necessary: high heat-load monochromator, high resolution monochromator, and nuclear monochromator. The first stage of monochromatization down to about AE/E~ 10 -7 can be achieved by means of 'electronic monochromators'. These monochromators are based on electric charge scattering in a (single) crystal. The obtainable energy bandwidth is related to the width of the rocking curve by the Bragg equation and the divergence of the X-ray beam. A further monochromatization can be obtained only by 'nuclear monochromators'. In this case nuclear levels are involved and the diffraction is a resonant process. Therefore the monochromaticity which can be achieved is related to the nuclear level width F0 (e.g. Fo(57Fe)=4.65x 10 . 9 eV) and is independent of the rocking curve width of the crystal.

3.1. Electronic monochromator The monochromatization by the electronic monochromator is done in two steps. Firstly, there is a conventional Si(1 1 1) monochromator to overcome the heat load. An energy resolution of about 10 4 has been achieved. Secondly, for further monochromatization more sophisticated geometries have to be found. For the 14.4 keV beam the idea of a 'nested monochromator' was conceived some time ago by Ishikawa et al. [7]. Two channelcut crystals, one asymmetric cut Si(42 2) and one symmetric cut Si(1 2 2 2), are nested in a dispersive arrangement [21]. The asymmetric-cut guarantees a perfect matching to the synchrotron radiation beam whereas the dispersive arrangement and the

3.2. Nuclear monochromator In case of the M6ssbauer transition of 57Fe one may achieve an energy bandpass down to 4.65 × 10 - 9 eV with a nuclear monochromator. Depending on the application this nuclear monochromator has to be tailored very carefully. For ultra-high monochromatization and suppression of non-resonant background (10 -~) pure nuclear reflections are used [1, 2]. Best monochromatization has been achieved by 'single line filtering' [8]. Crystals of yttrium iron garnet, FeBO3, and Fe3BO 6 are presently available. For moderate values of energy bandpass and suppression multilayers [9] and GIAR films [10] may be chosen. By default the nuclear monochromators supply a beam at fixed energy. On the other hand for inelastic (quasi-elastic) scattering experiments the energy tunability is a precondition. First approaches of a tunable nuclear monochromator (+2.5 meV) with a ~eV energy bandpass are just reported [11]. As in conventional M6ssbauer spectroscopy the tunability has been achieved by fast Doppler shifting of a resonant medium.

4. Inelastic scattering 4.1. Nuclear inelastic scattering The new field of nuclear inelastic absorption has been opened in nuclear scattering with synchrotron radiation [12, 13]. Elastic nuclear scattering by definition is not accompanied by lattice excitation. Therefore it may leave the nuclei in the sample untouched (i.e. the quantum state before and after the scattering process is the same). In this case it is delocalized over many nuclei, proceeds coherently and is peaked in forward direction. The intensity of

R. R~ffbr, A. Chumakor/Physica B 226 (1996) 128 134

nuclear forward scattering is determined by the recoilless factor fLM. In contrast nuclear inelastic scattering normally involves the excitation of the lattice. Therefore it is localized on a particular nucleus and proceeds incoherently. This process leads mostly to absorption, not to re-scattering of the ,'-quantum. The products of nuclear inelastic absorption (with dominating X-ray fluorescence resulting from the internal conversion) are emitted into 4rr (incoherent scattering). This channel measures (1 --JLM). The continuous energy distribution of the synchrotron light and the superior spectral density of third-generation sources allow one to excite the nuclei by radiation with an energy several meV apart of the resonance• The difference is transferred to the phonon excitation of the lattice, and an energy dependence of this process gives the probability of nuclear recoil as a function of energy transfer. Thus it is possible, for example, to measure at the same time nuclear forward scattering (the part without recoil,fLM) and the nuclear incoherent scattering (the part with recoil, (1 -ji~M) i.e. to check the balance of the entire nuclear scattering process. As an example, the measurements of nuclear inelastic absorption in a 57Fe foil and [SVFe(bpp)2] [BF,~], were performed in a temperature range between 18 and 300 K. The experimental set-up of a nuclear inelastic absorption experiment is shown in Fig. 2. In case of the 57Fe foil (Fig. 3) the increase of the recoil probability with increasing temperature is nicely seen. The density of phonon stales and the temperature dependence of fkM, the multiphonon contribution, and the anharmonism of the lattice vibrations have been determined [22]. [57Fe(bpp)2] [BF~] z exhibits a temperature driven

APD

RS

APD

PM

Fig. 2. Set-up of resonant nuclear inelastic a b s o r p t i o n experiment. U undulator; PM double crystal water-cooled fixedexit Si(1 1 1) H R M high resolution m o n o c h r o m a t o r : RS resonanl sample; A P D avalanche p h o t o diode detector.

i

131

i

i

i

°.

6000

18K

."

4000

2000

0 6000 t.,9 o u3

I

I

100K

4000

~

li

I

,

"•

2000

c

1

o

i

,

L

,

i

,

i

i

4000 200K

" •

2000•

°

0i

0

i

i

i

i

,

,

.

i

,

i

,

"

296K

800-

,

%

CD q)

400-

g o o

O" •

-80

,

-60

.

,

-40

.

,

-20

.

,

0

.

20

,]

40

6'0

80

relative energy [meV]

Fig. 3. Energy spectra of resonant nuclear inelas]tic absorption in 20 jam 57Fe foil at various temperatures. (from Ref. [311.

low spin ,--, high spin transformation (Fig. 4). The energy width of the central peak shows a considerable broadening at room temperature [13]. At temperatures below the phase transformation, that is in the low spin state, a well localized peak of recoil probability with the characteristic energy transfer of about 50 meV arises whereas at temperatures above the phase transformation, that is in the high spin state, this peak has disappeared and another one at about 25 meV arises• So far these experiments were carried out with an energy resolution of 4.4 and 6.4 meV at 14.4 keV which is determined by the high resolution monochromator. With an improved design the energy resolution may be decreased to I 2meV at 14.4keV. For other MOssbauer transitions this value may vary.

132

R. Ri~ff'er,A. Chumakov/Physica B 226 (1996) 128 134 I

sample and the analyser may be separated and the technique described above may be applied to 'nonresonant' samples. In that case one can use any M6ssbauer transition and may push the energy resolution below the 1 meV level. In general, Qdependence can be tackled, i.e. the measurement of the 'dispersive relation' is accessible. A typical set-up of high resolution X-ray inelastic scattering for 'integrated' (1 15 A - t ) momentum transfer is shown in Fig. 5. As an analyser we used a 'resonance detector' which detects only X-rays capable to excite nuclear levels. By this means the high energy resolution may be reached down to the neV regime. First investigation on solids, liquids, and gases have been carried out [-14] as well as on myoglobin [23].

o o3

200

18K

o LO

"E

i• -

IO0

• ;. : "t~:.gh: 250 0

"

t

~

200-

150K 0 ffl o o

150 100-

~..

.7

50-

,,."

200-

0 LO

150.

03

100.

8

50.

250 0 O~ CO 0

:" 1

250 . . . . ~ " ' " " ' ~ 0 d) CI)

~..

"'.6~'

"*" °¢ --~

176K

.'.::"..:.].. 5. Quasi-elastic scattering

,o

-@.

"~""'~*" '

200

293K

150 IO0

C 0 0

502

.." g:¢ . ' , . ~ .

0

-50

6

50

100

relative energy [meV]

Fig. 4. Energy spectra of resonant nuclear inelastic absorption in [57Fe (bpp)2] [BF4]z at various temperatures. (from Ref. [31t.

Spectroscopy with energy transfers below 1-0.1 meV cannot be achieved with standard techniques of crystal optics. However, resonant nuclear techniques are in principle capable to deliver an energy bandpass down to neV or even further down as discussed above. Again the two cases have to be distinguished: 'resonant' and 'non-resonant' samples. Whereas the resonant sample acts as monochromator and analyser as well, there is no such mechanism for a non-resonant sample. In that case an ultra-high monochromatic beam has to be prepared and an analyser is mandatory.

4.2. X-ray inelastic scattering 5.1. Nuclear quasi-elastic scattering So far we have a s s u m e d that the investigated sample contains M 6 s s b a u e r nuclei, i.e. the 'energy analyser' was a built-in feature. H o w e v e r , the

~1

RD2

s ~,

Nuclear quasi-elastic scattering has already been studied in conventional M6ssbauer spectroscopy

HRM ~'~, , ,ii:i~

PM

~-"~"I'l'I'II

I I

RD I

Fig. 5. Set-up of X-ray inelastic scattering experiment. U undulator; PM double crystal water-cooled fixed-exit Si(l 1 I) HRM high resolution monochromator; S 'non-resonant' sample; RD~, RD2 resonance detector.

R. Riffler, A. Chumakov/Physica B 226 t1996) 128 134

with energy transfers ranging from neV to peV and fixed [15] or "variable' momentum transfer exploiting the direction anisotropy of single crystals [16]. In those cases the ultra-high monochromatic beam (neV) from a radioactive source is tunable in energy by means of Doppler shifting up to the geV range. Quasi-elastic contributions show up in a line broadening in the M6ssbauer spectra. This broadening in the energy picture turns to a change in the time spectra of the corresponding channels, nuclear forward scattering and nuclear inelastic scattering as seen by nuclear resonant scattering. In nuclear forward scattering an accelerated decay of the nuclear exciton will be observed whereas the nuclear inelastic scattering channel behaves the other way. Due to the finite width of a synchrotron radiation pulse, 100 ps, and the time resolution of the detector system, 0.1 1 ns, accelerated decays down to 1 ns may be observed. This value corresponds to an energy transfer of about 0.7 peV. In order to go beyond this value other techniques as described above [11] have to be exploited. As an example the "diffusive motion of nuclei' has been treated theoretically by Smirnov and Kohn [17]. First investigations along this line are just under way in case of "diffusional jumps' in F%Si [18].

5.2. X-ray quasi-elastic scattering As in the previous case M6ssbauer investigations in this field known as Rayleigh scattering with M6ssbauer radiation (RSMR) have been carried out. In this case the ultra-high monochromatic beam (neV) from a radioactive source is scattered by a non-resonant sample and analysed in energy and momentum transfer by a M6ssbauer absorber. In spite of low count rates there are quite a lot of investigations as on single crystals, amorphous solids, plastic and liquid crystals and viscous liquids. A review is given by Champeney [19]. Transferring this technique to synchrotron radiation requires either a tunable monochromator or an analyser also. However, due to the exceptional collimation and size of the beam this technique will get new impetus.

133

6. Summary The new third generation synchrotron radiation sources have a new impact on the fields of quasielastic and inelastic scattering. First investigations with an energy transfer in the sub-laeV regime (down to neV) and in the meV regime have demonstrated the strength of the new method. For the first time this technique could bridge the gasp in energy transfer between ~teV and neV.

References [I] E. Gerdau, R. Rfiffer, H. Winkler, W. TolksdorL C.P. Klages and J.P. Hannon, Plays. Re',. Lett. 54 (1985) 835. [2] Sec e.g., E. Gerdau and U. van Bi.irck, in: Resonant Anomalous X-Ray Scattering. Theory and Applications, eds. G. Materlik and K. Fischer (Elsevier, Am*tcrdam, 19941 p. 589; R. Riiffer, E. Gerdau, M. Grote, R. Hollatz, R. R6hlsberger, H.D. Riiter and W. Sturhahn, Nucl. |nstr. and Meth. Phys. Res. A 303 (1991p 495. [3] R. Riiffer and A.I. Chumakov. Hyperfine hateractions 9 7 98 (1996) 589. [4] P. Elleaume, Nucl. Instr. Meth. Phys. Res: A 266 (1988) 125. [5] L. Farvaeque, J.L. Laclare, C. Limborg and A. Ropert. ESRF Newsletter 24 (1995) 12. [6] J.-L. Revoh E. Plouviez and R. R/ifli~r, Synchrotron Radiation News 7 (1994) 23. [7] T. lshikawa, Y. Yoda, K. Izumi. C.K. Suzuki. X.W. Zhang, M. Ando and S. Kikuta, Rcv. Sci. |nslr. 63 (1992) 1015. [8] A.1. C h u m a k o v , M.V. Zelepukhin, G.V. Smirnov. U. van Biirck, R. Rfiffer, R. Hollatz, H.D. Ri.iter and E. Gerdau, Plays. Rev. B 41 (1990) 9545. [9] A.I. Chumakov. G.V. Smirno,,, A.Q.R. Baron, J. Arthur, D.E. Brown, S.L. Ruby, G.S. Brown and; N.N. Salashchenko, Phys. Rev. Lett. 71 (19931 2489. [10] R. Rghlsberger. E. Gerdau, M. Harsdoff, O. Let@old, E. Liiken, J. Metge, R. R/_ifl'er, H.D. Riiteli, W. Sturhahn and E. Witthoff, Europhys. Len. 18 (1992) 561. [ l l ] R. R6hlsberger, E. Gerdau. W. Slurhahn, E.E. Alp and R. Rtiffer, in: Proc. hat. Conf. on the Appiications of the M6ssbauer Effect, Rimini, Italy (1995). [12] M. Seto, Y. Yoda, S. Kikuta. X.W. Z h a n g a n d M. Ando. Plays. Rev. Lett. 74 (19951 3828: W. Slurhahn, T.S. Toelher, E.E. Alp. X.W. Zhang, M. Ando, Y. Yoda. S. Kikuta, m. Seto, C.W. Kimball and B. Dabrowski, Plays. Rex'. Lctt. 74 (19951 3832. [13] A.I. Chumakov, R. Rtiffer, H. Griinsteudel, H.F. Grfinstcudel, G. Grfibel, J. Merge, O. Leupold and H.A. Goodwin, Europhys. Lett. 30 (1995) 427.

134

R. Riiffer, A. Chumakov / Physica B 226 (1996) 128-134

[14] A.I. Chumakov et al., Phys. Rev. Lett. 76 (1996) 4257. [15] See e.g.A.N. Artem'ev, G.V. Smirnov and E.P. Stepanov, Zh. Eksp. Teor. Fiz. 54 1968) 1028 (Sov. Phys. JETP 27 (1968) 547); B. Balko, G.R. Hoy, Phys. Lett. 47 A (1974) 171. [16] B. Sepiol and G. Vogl, Phys. Rev. Lett. 71 (1993) 731. [17] G.V. Smirnov and V.G. Kohn, Phys. Rev. B, B 52 (1995) 3356. [18] B. Sepiol et aL Phys. Rev. Lett. 76 (1996) 3220. [19] D.C. Champeney, Rep. Prog. Phys. 42 (1979) 1017.

[20] M6ssbauer Effect Data Center, Asheville, NC 28804-3299, USA. Nuclear Data Sheets 62 (1991) 101. [21] T.S. Toellner, T. Mooney, S. Shastry, E.E. Alp. Proc. SPIE 1740 (1992) 218. [22] A.I. Chumakov, R. Riiffer, A.Q.R. Baron, H. Grfinsteudek H.F. Grfinsteudel, to be published. [23] K. Achterhold, C. Keppler, U. van Biirck, W. Potzel, P. Schindelmann, E.-W. Knapp, B. Melchers, A.I. Chumakov, A.Q.R. Baron, R. Riiffer, Eur. Biophys. J. 1(1996).