Hyperfine Interactions 90(1994)301-312

301

Developments in time domain M ssbauer spectroscopy E. Gerdau II. lnstitut fiir Experimentalphysik, Universittlt Hamburg, D-22761 Hamburg, Germany

Time differential measurements of nuclear resonance scattering using synchrotron radiation have been performed with the low energy Mrssbauer transitions of 57Fe, l l9Sn, and 169Tm since 1984. Various methods of filtering the nuclear energy band from the incident synchrotron radiation are now available. The possibilities of applying these methods to transition energies above 30 keV are discussed. A new technique is proposed, which is especially effective for the high energy Mrssbauer transitions. It takes advantage of the different dependence of the electronic Debye-Waller factor and the MrssbauerLamb factor on the scattering angle.

The development of time domain MSssbauer spectroscopy has been reviewed recently at the International Conference on Anomalous Scattering in Malente [ 1] and at this conference by the contributions in the main session and by the contributions at this workshop. It is now obvious that time domain MSssbauer spectroscopy with 57Fe has developed from an exotic experiment [2] to a technique which will allow one to perform standard spectroscopic work with 57Fe and, furthermore, with other low energy MSssbauer transitions, as has been shown by the observation of the effect in 169Tm [3] and l l9Sn [4]. Also, results can be expected in fields like inelastic scattering of Mtissbauer quanta and 7-optics which do not belong to standard MSssbauer spectroscopy. In this contribution, possibilities of extending the experimental techniques to transition energies above 30 keV will be discussed and additional techniques especially suitable for the high energy range are proposed. In time domain MSssbauer spectroscopy, an ensemble of nuclei is excited by a wavetrain of ~--10-19 S duration and a corresponding energy width of about 10 keV (At---> 0, AE--> ~ ) if one uses the direct synchrotron light from the storage ring. Then the collective response of the nuclear resonators is recorded as a function of time. The complementary situation to this would be a source of sharp tunable energy, which belongs to an infinitely long wavetrain (At --->~, AE --->0), and the collective response of the nuclear resonators is recorded as a function of energy. Standard MSssbauer spectroscopy lies in-between these two extreme situations. A single-line source is neither sharp in energy nor sharp in time. The fact that energy differential measurements with the standard MSssbauer technique are so successful is due to the fact that the hyperfine splitting of nuclear levels often surpasses the natural linewidth of the transition. 9 J.C. Baltzer AG, Science Publishers

302

E. Gerdau / Time domain Mi~ssbauer spectroscopy

In time domain M 6 s s b a u e r spectroscopy, one has to deal with the e n o r m o u s b a c k g r o u n d that belongs to the broad energetic band of incident radiation. Thus, electronic and also nuclear m o n o c h r o m a t o r s are necessary to reduce the bandwidth. Accordingly, the length of the primary wavetrain is increased by the delayed response o f the m o n o c h r o m a t o r to the incident wave. As long as the energetic width o f the selected band surpasses the natural width of the transition by a factor of 1 0 0 - 1 0 0 0 , the corresponding length of the wavetrain is 1 0 - 2 - 1 0 -3 of the decay time o f the nuclear level and one can still speak of a time differential excitation. The studies on how to reduce the bandwidth of the incident radiation have taken a considerable part o f the efforts o f the work in recent years. M o s t studies dealt with 57Fe radiation. The standard b e a m line starts with pure electronic m o n o c h r o m a t i z a t i o n d o w n nearly to the limit o f dynamic X - r a y diffraction. In the case of 57Fe radiation, this limit is a few meV. The limit can be achieved since Si and Ge single crystals o f sufficient crystalline perfection are available. In the case of STFe, Ge is not recommended because of the high absorption coefficient (EK(Ge) = 11.1 keV), but Ge c o m p e t e s with Si at energies above 30 keV. S o m e properties of Si reflections used for 57Fe spectroscopy are collected in table 1. Table 1 Properties of some Si-Bragg reflections (h k l). Rmax is the maximum reflectivity, 0a the Bragg angle, AE the intrinsic energy width of the reflection, A0 its intrinsic angular width, and AT the temperature step which changes the lattice constant so that at stable angular setting the shift of the energy band equals the intrinsic energy width, b is the asymmetry parameter of the crystal surface. h k l

Rmax

0a (deg)

AE (meV)

A0 (Brad)

AT (K)

Remark

111 422 10 6 4 12 2 2 777 840 840

0.98 0.95 0.87 0.87 0.81 0.95 0.88

7.885 22.830 77.538 77.538 73.790 45.104 45.104

2000. 654. 6.6 6.6 5.1 26.6 8.5

19.2 19.1 2.07 2.07 1.13 1.85 0.59

53.3 17.5 0.18 0.18 0.14 0.71 0.23

sym. b = -0.I0 sym. sym. sym. sym. b= -0.11

The intrinsic energy widths are obtained f r o m the d y n a m i c a l theory of X - r a y diffraction. Th~ other data are derived by application of the Bragg equation, where a temperature dependence of the lattice constant is included: n& = 2d0(1 + a ( T -

Troom)) sin 0,

(1)

E. Gerdau / Time domain Mrssbauer spectroscopy

303

or in differential form dE E -ctg0d0+adT"

(2)

The experimental demands which have to be satisfied by an electronic monochromator are easily derived from eq. (2). 1 The band of width dE of the electronic reflection must contain the nuclear transition energy E0. This condition should not be violated by a temperature shift of the reflecting crystal or by an unstable angular setting of the goniometer. The reflection will be lost if dT or dO surpasses the values of AT or A0 given in table 1. A stability of an angular setting of 0.1 grad can be achieved by laser interferometric methods with moderate effort if the system is well protected against external distortions. As far as temperature stability is concerned, one has to keep in mind two facts. Once a reflection is found at a certain temperature, one has to keep this temperature because E0 is fixed. Furthermore, since channel-cut crystals are the standard elements for monochromators, the two reflecting surfaces have to be kept at the same temperature. Therefore, the heat from a stepping motor released within a goniometer may not be acceptable since it creates a temperature gradient which may seriously distort the double reflection of a channel-cut crystal. A stability of 0.01 K is assumed to be possible. Thus, the experimental demands for the premonochromator for 57Fe can be satisfied safely. The situation will be more difficult if one considers transitions of higher energy. Such transitions will become accessible in the near future when wavelength shifters come into operation at electron/positron storage rings like ESRF (6 GeV), APS (7 GeV), or SPring-8 (8 GeV), or when wigglers and undulators are installed at high energy storage rings like PETRA (12.0 GeV). In fig. 1, the predicted brilliance of a PETRA undulator is given as a function of energy. Within the range from 30 to 100 keV, the brilliance varies from 3 x 1017 to 7 x 1016 photons/(s 9mm 2 9mrad 2 90.1% BW). A typical vertical angular divergence of the radiation is 10 grad and thus in almost every case surpasses the angular acceptance of electronic and nuclear reflections. According to dynamical theory, the angular acceptance of a Bragg reflection H = (h, k, l) with Bragg angle 0B is within a good approximation given by

ProX2 AO = ~

7gV sin OB

(3)

cos 0B

P is a polarization factor,2 r0 the classical electron radius, and V the volume of the elementary cell. FH, FH are the atomic structure factors. The asymmetry parameter ~Numerical values for a at room temperature are ace = 5.7 x 2p = 1 corresponds to 0 polarization.

10 -6 K -I

and asi = 2.6 x 10-6 K-~.

304

E. Gerdau / Time domain M0ssbauer spectroscopy

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Fig. 1. Brilliance B of an undulator planned for PETRA given as photons/(s - mm2 - mrad2 90.1% BW). The fundamental, the third, and the fifth harmonic are calculated for an electron energy of 12 GeV and a current of 60 mA.

b describes the cut of the crystal surface. 3 The main dependence of A0 on E is given by A0 - A2/sin 0B - 1/E, whereas the energetic width of the transmitted band increases proportionally to E. This is just the contrary to what is desired. For an electronic monochromator, one has to find a compromise between a large angular acceptance and the energetic width of the transmitted band. Highly developed s c h e m e s - the nested monochromator [5] and the bent monochromator [ 6 ] - have been applied in the case of 57Fe radiation. They are described in several contributions to this conference. In the case of a first experiment with ll9Sn radiation [4], it has been shown that the concept of the nested monochromator can be transferred to higher energies. The angular acceptance of a nested monochromator is determined by the asymmetric outer channel-cut crystal, whereas the symmetric inner channelcut crystal defines the transmitted energy band. If for the inner crystal an asymmetric reflection is chosen, one may reduce the bandwidth by a factor o f 2 - 4 but one has to pay for this with a slightly reduced reflectivity and an increased temperature and angular sensitivity, which easily may be above the technically possible limits. In fig. 2, the minimum bandwidth transmitted by a nested monochromator is shown as a function of the nuclear transition energy. Parameters are the angular acceptance of the inner channel-cut crystal and the material. The data for Ge are indicated by solid lines and the data for Si by dotted lines. The widths of the 3b = - 1 corresponds to a symmetric Bragg reflection.

E. Gerdau / Time domain M6ssbauer spectroscopy

305

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Fig. 2. The upper part of the figure shows the minimum bandwidth which can be achieved by pure electronic monochromatization as a function of energy. Solid curves belong to Ge crystals and dotted lines belong to Si crystals. A constant angular acceptance is assumed which is 2.0 ~trad for the upper lines and then changes via 1.0 and 0.6 to 0.3 p.rad. In the lower part, the width of M6ssbauer transitions FMB is given by the empty and full squares at the respective transition energies. The full squares correspond to the high resolution transitions 93.317 keV in 67Zn, 63.917 keV in t57Gd, 67.220 keV in 145Nd, and the broadband transitions 58.00 keV in 159Tb and 94.698 keV in 165Ho. The dashed line at 0.8 I.teV crudely divides the high resolution and the broadband region.

MSssbauer transitions FMB in the region from 3 0 - 1 0 0 keV are also given and indicated by the filled and empty squares. With respect to the determination of hyperfine interactions and with respect to the methods which can be applied for monochromatization of the incident beam, the nuclei are divided into two groups according to the condition if a hyperfine interaction energy EHr can be resolved by FMB or not. How large EHf can be depends on the properties of the special nucleus.

306

E. Gerdau / Time domain MOssbauer spectroscopy

However, for a crude classification a line at 0.8 geV is inserted in fig. 2. The large gap which occurs between electronically achievable bands and the bands which can be obtained by nuclear reflections covers 4 to 10 orders of magnitude. Thus, the availability of narrow bands of y-radiation is not only of interest as a new method for determination of hyperfine interaction parameters, but it is also of interest for the general application of synchrotron radiation. The outstanding energetic width of any beam obtained by nuclear diffraction might be used to learn about submillielectronvolt excitations of matter. Most interesting in this respect are the broad nuclear transitions, since they will yield the most intense beams. Nuclear diffraction is the only means to obtain such beams. However, one has to suppress the strong prompt background. All information on possible means to influence the primary beam can be derived from the scattering amplitude of the target. It is composed of the scattering a m p l i t u d e M (j) for the single atoms ( j ) and the superimposed structure function which originates from the spatial arrangement of resonant and nonresonant atoms in the unit cell and, moreover, in the whole scatterer. The scattering amplitude of a single atom is given by 4 k

(j)

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(j)

(nuclear terms)/~v

+ 2re ,'~(J}ow,'~rl"'_ k)~v~[_roF(eJ)(k" _ k) + i ,k----. 4o'~J} r (co)] t

(4)

The symbols have their usual meaning, k , k ' , ~ u , ~ v are the wave vectors and corresponding unit polarization vectors of the incident and scattered radiation, o"0 is the M6ssbauer cross section. F~L(k) (1) = e-k2{x~}is the M6ssbauer-Lamb factor of the2 atom j. The sum is over all possible nuclear transitions. F(DJ)w(k' - k) = e -~ ( x~) ( 1 - cos0) is the electronic Debye-Waller factor of the atom, Fe(j) (k' - k) the atomic form factor and Crph(CO) the photoelectric cross section. The scattering amplitudes of all scatterers in the sample must be summed so that the phase shifts according to their spatial positions are included:

M(k, ~u ; k', ~v ) = ~ ei(k'-k)R~ M(J)(k, ~lz ; k', ~v ). 1

(5)

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(nuclear terms) uv -

8g p

~-.

(2ji + 1) M.LSo .

C2 (jo L Jl ; m o M ) [x
M)

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E. Gerdau

/ Time

domain M6ssbauer spectroscopy

307

Three different attempts to solve the problem of suppression of the prompt background have been applied so far: 9

polarization dependence of electronic diffraction,

9

structure factors of the unit cell of a crystalline material, artificial macroscopic structure of the scatterer.

9

The use of purely electronic suppression has been very successfully demonstrated for the 57Fe resonance and will be one of the main components in future work with the low energy nuclear transitions in ISlTa, 169Tm, 73Ge and 57Fe [7]. It uses the term ev 9 e# of the electronic scattering amplitude, which is zero for crossed polarizer and analyzer. A nuclear signal is obtained under these conditions if the n u c l e a r t e r m is polarization mixing. This inevitably occurs if the nuclear transition is split by a hyperfine interaction which can be obtained at least by an external magnetic field. The application of this method for nuclear transitions is restricted to the nuclei below the dashed line in fig. 2. A stringent condition is the need to produce a beam of nearly 100% polarization. This is achieved by an electronic reflection with a Bragg angle of nearly 45 ~ Irrespective of the fact of whether there exists a suitable reflection in a special case, fig. 3 shows the approximate angular acceptance for 45~ in Ge. The

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[keV]

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values lie at and below the technical limit. Furthermore, the temperature stability of the monochromator crystal has to be better than 0.01 K and the reflectivity drops from 0.50 at ~ 30 keV to 0.20 at ~--50 keV.

308

E. Gerdau / Time domain Mi~ssbauer spectroscopy

The two other approaches are based on the vanishing of the structure factor at energies outside the nuclear resonance. Pure nuclear reflections use the structure factor of the unit cell. If it vanishes for the electronic part, it may not vanish for the nuclear part if subgroups of nuclei within the unit cell are distinguishable by different hyperfine interactions. Since pure nuclear reflections are a common property of crystalline material [8], the observation of the delayed signal in Debye-Scherrer rings [1] may become the standard method to perform time domain Mtissbauer spectroscopy with transition energies above 30 keV. Artificial structures were proposed in [9, 10] and are successfully realized in the form of GIAR-films [11] and multilayers [12]. They are not dependent on a resolved hyperfine splitting and thus can be applied for all available resonant transitions. GIAR-films and multilayers possess a transversal structure. The scattering strength of the layer system varies as a function of depth. An alternative method is the diffraction occurring at a longitudinal structure (diffraction grating) within the surface of a flat mirror. The phase shifts which occur at different places of such a mirror add up in diffraction maxima of all orders. Strong suppression of the 0 th order can be achieved by a proper design of the mirror. This was proved with 57Fe radiation [13]. The mirror consisted of a 100/k Pd layer on a superpolished ZERODUR backing. The longitudinal structure was achieved by deposition of an additional Pd grating with a period of 200 ~tm consisting of rectangular bars of 66/~ height and 100 ktm width perpendicular to the incoming beam. The angular intensity distribution of the radiation diffracted at this grating is measured at different angles of incidence. Figure 4 shows the 0 th and + 1 st orders of diffraction. Clearly, at about 3.3 mrad the intensity of the 0 th order is strongly suppressed. Figure 5 shows the intensity of the 0 th order reflection as a function of the angle of incidence of the synchrotron radiation. A suppression by a factor of 100-1000 of the electronic band can be achieved. Reflectivity within the nuclear band is obtained by the same principle as in a GIAR-film. If the structure contains resonant nuclei, which supply additional scattering strength at a certain energy, the condition for suppression is no longer fulfilled. This method can also be applied to high energy transitions and combines high reflectivity with relatively low demands for the production of the mirror. Finally, an inspection of eq. (4) shows that there is still another source of different behaviour of electronic and nuclear scattering amplitude which can be used to reduce the electronic background. This is the dependence of both the electronic D e b y e - W a l l e r factor FDC~ and the atomic form factor F~j) on the Bragg angle in contrast to the independence of the Mtissbauer-Lamb factor FC~j). The electronic D e b y e - W a l l e r factor, which is unity for forward scattering, takes its lowest value for backscattering. For deflection angles 20B = 180 ~ its value is -- ( F ~ ) 2. Thus, the strongest reduction of FDC~ is achieved for backreflection of the radiation and low values of Fr~. Similarly, the atomic form factor, which is equal to Z (the charge number of the nucleus j) for forward scattering, is strongly reduced for

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10a

/ Time

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[mrad] Fig. 4, Diffraction of a planar mirror with longitudinal structure (see text). The diffraction maxima of 0 th and +_1st order are shown. The angle of incidence of the synchrotron radiation is given on top.

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310

E. Gerdau / Time domain MOssbauer spectroscopy

backscattering and large values of E as F~J)(sin 0B/2) ~ 1/sin20a 9 E 2 for arguments sin 0a/~,[/~] > 1. High energy M6ssbauer transitions observed in a backscattering geometry are the candidates for applications of this different behaviour of electronic and nuclear scattering amplitudes. There are attractive candidates in the broadband region for non-M6ssbauer applications (159Tb, 165Ho), as well as in the high resolution region (67Zn, 61Ni, 145Nd, 157Gd). In some of these cases, a radioactive source is difficult to obtain. Whereas in the high resolution region the use of pure nuclear reflections will be a reliable method for monochromatization, there is no experimental evidence whether a sufficient monochromatization can be achieved in the broadband region. To study this question, theoretical calculations were performed for 58.00 keV radiation of 159Tb. Tb has the attractive isotopic abundance of 100%. Therefore, the standard methods for the production of single crystals can be applied. The calculations were performed for terbium aluminum garnet (TAG) using the program package CoNuss [15]. Single crystals of TAG are available by the Czochralski method. The Debye temperature is 640 K and the lattice constant is 12.075/~ [14]. The intrinsic width of the 58 keV transition is 8 lxeV. Inspection of fig. 2 shows that electronically a band of 100 meV can be supplied. Thus, a suppression factor of ~ 104 is needed. The easy direction of growth for garnets is the [111] direction. Backscattering is achieved with the (64, 64, 64) reflection, which belongs to a Bragg angle of 78.88 ~ Since then sin 0a = 1 and E are fixed, only the temperature and accordingly the ratio o f l~'(J)ll;'(J) remain to be varied. The result is shown in fig. 6. At room temperature, " ML "" DM the maximum of the nuclear rocking curve (dashed line) lies at about 40% reflectivity with a width of 1.05 ktrad. The reflectivity decreases only slowly and is still 26%

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E. Gerdau / Time domain M6ssbauer spectroscopy

311

at 800 K. In parallel, the electronic reflectivity drops dramatically and the ratio o f integrated nuclear reflectivity to integrated electronic reflectivity approaches 2 x 104 (solid line). Even without devices which use artificial nuclear structures, a beam of almost pure nuclear radiation can be extracted from the primary radiation. The intensity of the beam can only crudely be estimated. It depends on the unknown broadening of the nuclear rocking curve by a slight mosaicity of the crystal. But again, this point is in favour of the nuclear reflection. Whereas the primary extinction is much larger than the absorption length of the radiation (300 ~tm), the nuclear extinction length is 5 - 2 0 times less than the absorption length. Therefore, a slight mosaicity would increase the nuclear reflectivity. For a conservative estimation of the expected counting rate, the following data were taken: brilliance: 2 x 1017 photons/(s 9 mm 2 9 mrad 2. 0.1% BW); transmission o f the first crystal, which bears the heat load: 0.3; transmission of the nested monochromator: 0.5; solid angle: 4 x 10 -6 mrad 2 (no mosaicity allowed); mean nuclear reflectivity: 0.1. This yields an expected counting rate of ~ 2 • 106 s -1. For every nuclear transition, the appropriate concept of the beam line has to be worked out. However, the prediction that the methods developed in recent years and that the full use of the dependencies of the scattering amplitude on various parameters will allow us to extract beams for all transitions below 100 keV is justified.

Acknowledgement This work has been funded by the Bundesministerium fiir Forschung und Technologie under Contract No. 05 5GUAA6.

References [1] E. Gerdau and U. van B0rck, Proc. Int. Conf. on Anomalous Scattering, ICAS-92, Malente, to be published. [2] E. Gerdau, R. RiJffer, H. Winkler, W. Tolksdorf, C.P. Klages and J.P. Hannon, Phys. Rev. Lett. 54(1985)835. [3] W. Sturhahn, E. Gerdau, R. Hollatz, R. Rtiffer, H.D. Rtiter and W. Tolksdorf, Europhys. Lett. 14(1991)821. [4] E.E. Alp, T.M. Mooney, T. Toellner, W. Sturhahn, E. Witthoff, R. R6hlsberger, E. Gerdau, H. Homma and M. Kentjana, Phys. Rev. Lett. 70(1993)3351. [5] T. Ishikawa, Y. Yoda, K. Izumi, C.K. Suzuki, X.W. Zhang, M. Ando and S. Kikuta, Rev. Sci. Instr. 63(1992) 1015. [6] D.P. Siddons, J.B. Hastings and G. Faigel, Nucl. Instr. Meth. A266(1988)329. [7] D.P. Siddons, U. Bergmann and J.B. Hastings, Phys. Rev. Lett. 70(1993)359. [8] R. Rilffer, E. Gerdau, H.D. Rtiter, W. Sturhahn, R. Hollatz and A. Schneider, Phys. Rev. Lett. 63(1989)2677. [9] J.P. Hannon, G.T. Trammell, M. Mueller, E. Gerdau, H. Winkler and R. Ri~ffer, Phys. Rev. Lett. 43(1979)636. [10l T.M. Mooney, E.E. Alp and W.B. Yun, J. Appl. Phys. 71(1992)5709.

312

E. Gerdau / Time domain MOssbauer spectroscopy

[11] M. Grote, R. R6hlsberger, M. Dimer, E. Gerdau, R. Hellmich, R. Hollatz, J. Jiischke, E. Liiken, J. Metge, R. Rtiffer, H.D. Rtiter, W. Sturhahn, E. Witthoff, M. Harsdorff, W. Pftitzner, M. Chambers and J.P. Hannon, Europhys. Lett. 17(1991)707; R. R6hlsberger, E. Gerdau, M. Harsdorff, O. Leupold, E. Ltiken, J. Metge, R. Rtiffer, H.D. Rtiter, W. Sturhahn and E. Witthoff, Europhys. Lett. 18(1992)561; R. R6hlsberger, E. Gerdau, E. Ltiken, H.D. Rtiter, J. Metge and O. Leupold, Z. Phys. B92(1993)489. [12] A.I. Chumakov, G.V. Smirnov, S.S. Andreev, N.N. Salashchenko and S.I. Shinkarev, Pis'ma ZhETF 55(1992)495; JETP Lett. 55(1992)509; R. R6hlsberger, E. Witthoff, E. Ltiken and E. Gerdau, in: Physics of X-ray Multilayer Structures Technical Digest, Vol. 7 (Optical Society of America, 1992) p. 178. [13] R. R6hlsberger, Thesis, University of Hamburg (1994). [14] G. Winkler, Magnetic Garnets (Vieweg, Braunschweig/Wiesbaden, 1981), Vieweg Tracts in Pure and Applied Physics, Vol. 5. [15] W. Sturhahn and E. Gerdau, Evaluation of time differential measurements of nuclear resonance scattering of X-rays, Phys. Rev. B49 (1994), to be published.