One of the most exciting fields opened by synchrotron radiation is the excitation of nuclei from the ground state into the very sharp nuclear levels. The 14.4 keV excitation in 57Fe is only 5 neV wide, which corresponds to a lifetime of 140 ns of the excited level according to the uncertainty principle. Closely associated with the absorption due to such a nuclear excitation is a strong elastic scattering cross-section equivalent to 500 electrons. If a 100 ps long pulse of synchrotron radiation hits a 57Fe sample, the subsequent fluorescence or the scattering occurs after a mean delay time of the order of 140 ns. This decay in combination with fast detectors (avalanche diodes) is used to separate nuclear resonance processes from instantaneous processes. The high spectral density of undulator radiation provides about 5000 detected photons in the 5 neV bandwidth of the 57Fe nuclear resonance.

  • Compared to radioisotopes used in conventional Mössbauer spectroscopy, synchrotron radiation has the advantage of a higher brilliance and energy tunability making easily accessible a large variety of Mössbauer nuclei.
  • Electric charges, charge gradients and magnetic moments surrounding the nucleus may shift and split the nuclear energy levels (hyperfine interaction). The shifts and splittings of the energy levels can be used to probe the environment in which the nucleus is embedded. In this way the valence state, the local symmetry, the distributions of charges and magnetic moments can be determined locally around the probe nucleus. The dynamics (relaxation, fluctuation) of these properties can also be observed in the corresponding time window. 
  • The main advantage of synchrotron radiation is its time structure. A light pulse from an electron bunch (100 ps length, ~ 1 µs repetition rate) coherently excites the nuclei. In case of hyperfine interaction the de-excitation amplitudes interfere giving rise to oscillations in the scattered intensity with time (quantum beats). The periods and amplitudes of these oscillations contain the magnetic and electronic properties mentioned above. Furthermore, diffusion on a time scale of ns to µs for individual jumps of nuclei from lattice site to lattice site or free diffusion destroys the coherence of the signal and leads to an accelerated decay of the scattered intensity.
  • Nuclear resonance techniques may also be used to investigate quasi-elastic and inelastic scattering from samples. In general, any sample can be investigated with the technique, using a nuclear monochromator and/or analyser. However, in case of 'resonant samples', i.e. samples which contain resonant nuclei, one might omit the nuclear monochromator and/or analyser. They are already a 'built-in' feature in the sample. Then only a high-resolution Bragg monochromator may be used to define the overall energy resolution.
  • Although under ordinary circumstances a set-up where the resolution of monochromator and analyser are not matched at all is considered to be unfavourable, in this case the simplicity of the nuclear analyser and the possibility to collect photons over a large solid angle compensate for this deficiency.
  • The small source size and high collimation of the synchrotron radiation allows, on the one hand, transverse coherence effects to be observed and, on the other, nuclear small-angle scattering. Although still under development, both techniques show promise for investigating spatial variation in the nuclear properties of a sample (e.g. velocity correlations or magnetic field distributions).

On the Nuclear Scattering beamline (ID18)

 

 

 

Nuclear and X-ray inelastic scattering

 

 

These techniques measure the energy distribution of nuclear inelastic absorption (simultaneous X-ray absorption and emission/absorption of a phonon), and (emission or absorption of phonons) integrated over the momentum transfer. In this sense they are complementary to the conventional inelastic X-ray scattering technique with crystal optics analysis and well-defined momentum transfer. The new techniques can be applied to measure Lamb-Mössbauer factors and partial or total densities of phonon states.

The experimental set-up is shown in Figure 47. A compact high resolution monochromator composed of two Si crystals provides an energy resolution of 1.65 meV and a flux of 1.2 108 photons/s at 14.4 keV. Other set-ups using 'nested' channel cut crystals provide 4.4 meV and 6.3 meV resolution.

In case of resonant samples the nuclei in the sample act as energy analyser and the emitted radiation in 4 solid angle is detected by a fast detector system based on avalanche photo diodes. For non-resonant samples the energy of the scattered radiation is analysed by a resonance detector system with a bandpass of 0.5 µeV. The detector system consists of fast avalanche photo diodes covered by 10 µm foils of -57Fe. The resonant performance of the detector system is determined by the process of elastic nuclear scattering in the foil. If the energy of the radiation coincides with the energy of the nuclear levels it excites the nuclei and is re-emitted forward with a time delay determined by the lifetime of the nuclear excited state. X-rays with other energies pass through the foil instantaneously. In both cases the delayed events are separated from the prompt pulse using fast electronics.

First examples of X-ray inelastic scattering were obtained for water, Plexiglas and gaseous Xe (Figure 48).

There are no direct measurements of phonon density of states of iron from neutron scattering due to the very small incoherent cross-section. This is quite different for nuclear inelastic scattering with X-rays. In two days the density of phonon states at different temperatures has been measured with a resolution of 1.65 meV (Figure 49). Furthermore, the temperature dependence of the Lamb-Mössbauer factor and the multi-phonon contribution have been determined and the anharmonicity of lattice vibrations at room temperature has been observed.

Combining these two techniques allows one to determine the total density of phonon states and also the partial density of phonon states (e.g. at an iron site).

 

 

Publications

[1] A.I. Chumakov (a), A.Q.R. Baron (a), R. Rüffer (a), H. Grünsteudel (a,b), H.F. Grünsteudel (a), A. Meyer (a,c), Physical Review Letters 76, 4258 (1996).

[2] A.I. Chumakov (a), R. Rüffer (a), A.Q.R. Baron (a), H. Grünsteudel (a,b), H.F. Grünsteudel (a), Physical Review B Rapid Comm. 54, 9596 (1996)

(a) ESRF

(b) MU zu Lübeck, Lübeck (Germany)

(c) TU München, Munich (Germany)

 

 

 

Quasi-elastic scattering: diffusion in Fe3Si

 

 

Nuclear resonance scattering opens a window in the ns- to µs-regime for diffusion studies directly in the time domain.

The synchrotron pulse hits the sample and creates a coherent collective nuclear excited state which subsequently decays in the forward direction. For the static case this decay obeys an exponential behaviour in a very first approximation. Diffusing atoms/nuclei, however, lead to a loss of the coherence of the radiation and therefore to an accelerated decay. From this acceleration the diffusivity is determined. Furthermore, the diffusion mechanism can be derived from the direction dependence in a single crystal.

A single crystal of the intermetallic alloy Fe3Si (cubic, D03) has been used in order to investigate the diffusivity and the diffusion mechanism. Figure 50 shows the time spectra taken in the [113] direction and at various temperatures. From the initial slope the diffusivity is determined whereas the two-step exponential decay is in accordance with the model of jump diffusion between the three lattice sites of Fe in Fe3Si.

 

 

Publication

B. Sepiol (a), A. Meyer (b,c), G. Vogl (a), R. Rüffer (b), A.I. Chumakov (b), A.Q.R. Baron (b), Physical Review Letters 76, 3220 (1996)

(a) Univ. of Vienna (Austria)

(b) ESRF

(c) TU München, Munich (Germany)

 

 

 

Transverse coherence in the time-domain

 

 

Nuclear scattering experiments at synchrotrons typically emphasise the pulsed excitation of the very narrow nuclear resonance and the corresponding extremely large longitudinal coherence length of the scattered radiation. This has allowed the performance of spectroscopy experiments in the time domain: shifts in resonance frequencies appear as corresponding quantum beats in the time response. However, the effects of transverse coherence have not been investigated. Consider a sample with two domains transverse to the X-ray beam, each having a single line response, but with different absolute resonance frequencies. The frequency difference leads to a time-dependent phase factor that will be different for the two domains. If the responses of the two domains add incoherently, this phase is of no importance, and one observes only the single line response. However, coherent combination of the responses will show this phase, leading to a temporal modulation (quantum beat) in the scattered intensity.

This behaviour was demonstrated for the first time. Instead of a sample with two domains, a continuous spatial variation in the nuclear resonance energy was introduced by spinning a stainless steel foil. With a horizontal rotation axis, oblique to the beam, one introduces a uniform vertical gradient in the Doppler shift of the nuclear resonance. The coherent addition of the scattering form transversely separated portions of the sample leads to the faster decay seen in Figure 51. Aside from the intrinsic physical interest, these effects have important implications for spectroscopy on samples with finite domain sizes.

 

 

Publication

A.Q.R. Baron (a), A.I. Chumakov (a), H.F. Grünsteudel (a), H. Grünsteudel (a,b), L. Niesen (a,c) and R. Rüffer (a), Phys. Rev. Lett., accepted for publication (1996)

(a) ESRF

(b) MU zu Lübeck, Lübeck (Germany)

(c) Univ. of Groningen (Netherlands)

 

 

 

Nuclear small-angle scattering

 

 

Nuclear resonance scattering is sensitive to magnetic hyperfine fields, electric field gradients and charge densities at the nucleus. Therefore nuclear small-angle scattering is a new tool to probe spatial variation of magnetisation, electric field gradients and chemical bonding in solids.

In small-angle scattering the forward scattering geometry is used (Figure 47) with an additional crystal analyser (Si(111)) between the sample and the detector (FWD). The analyser profile of the forward scattered nuclear and electronic signal from magnetised and unmagnetised a-Fe has been measured. They reveal in case of unmagnetised a-Fe a pronounced contribution from small-angle scattering as shown in Figure 52.

The analysis of the data shows a Lorentzian dependence of the small-angle scattered signal and a correlation length of 0.3 µm. This is in good agreement with the domain wall width in iron. Furthermore, the comparison of the angular integrated nuclear small-angle scattering and the nuclear forward scattering intensities may serve as a measure of the long-range spatial dispersion of magnetisation in a given substance.

 

 

Publication

Y.V. Shvyd'ko (a), A.I. Chumakov (b), A.Q.R. Baron (a), E. Gerdau (a), R. Rüffer (b), A. Bernhard (b), J. Metge (b), Physical Review B (1996), in press

(a) Univ. of Hamburg (Germany)

(b) ESRF