Nuclear resonant inelastic x-ray scattering (NRIXS) experiments are possible at third-generation synchrotrons, where beam flux optics and high-resolution monochromators can tune the incident x-ray beam to a few meV. Beamlines are most commonly configured for the 57Fe isotope, but monochromators are available for some other M¨ossbauer isotopes [5]. The incident beam is focused using Kirkpatrick-Baez mirrors to a spot size of 30 x 50µm, which makes it possible to measure very small samples. The work described in this thesis was performed at beamlines 3-ID-B and 16-ID-D at the Advanced Photon Source of the Argonne National Laboratory [21,18,19].
When the sample is irradiated withγ-rays matching the nuclear transition energy, both nuclear and electronic excitations occur. Scattering of x-rays by electronic processes is very fast, less than 1 ps. However, the natural lifetime of the57Fe nucleus isτ=¯h/Γ=141 ns. This creates a scattering intensity profile shown schematically in Fig.3.1. A pulse of radiation arrives at time=0, and intense electronic scattering occurs almost immediately, while the decay of resonant nuclei from the excited
1While limiting, this was what was done prior to M¨ossbauer’s discovery of recoil-free absorption and emission in a solid. The first experiment measuring the phonon spectrum of TbOxwas performed in 1979 by rotating a radioactive source at high speeds to produce Doppler shifts up to 30 meV for the 58 keV radiation of the159Tb isotope [17].
Figure 3.1: Scattered intensity versus time demonstrates the convenient discrimination possible between electronic scattering, which occurs immediately after arrival of the synchrotron pulse at time=0, and nuclear scattering, which has a longer lifetime. The detector is programmed with ’dead time’ between time =0 and the dashed line to ignore electronic scattering. Figure adapted from [5].
state is delayed. Thus, the nuclear and electronic scattering can be separated using time discrim- ination. Avalanche photodiode detectors with a time resolution on the order of 1 ns are used to measure decay products, and are gated for 20 ns of ’dead time’ to ignore electronic scattering [5].
Effective time discrimination also requires that the pulses of incident radiation be spaced far enough apart to allow de-excitation from the excited state and measurement of decay products before the next pulse re-excites the nuclei. The standard time structure at the Advanced Photon Source is 150 ns between bunches (groups of electrons) and a 70 ps duration for each pulse, making it well-suited for these measurements.
As with traditional M¨ossbauer spectroscopy, resonance excitation occurs if the energy of the incident photon exactly matches the resonance energy of the nucleus. When the incident energy is is greater or less than the resonant energy, an additional amount of energy must be absorbed or emitted to achieve the exact resonance energy for nuclear excitation. This compensating energy can come from the creation or annihilation of phonons. As shown schematically in Fig. 3.2, if the incident γ-ray is lower than the resonance energy, a phonon must be annihilated for the nucleus to absorb the photon, and if the incidentγ-ray has an energy higher than the resonance energy, a phonon is created to reduce the energy of the incident photon and permit absorption.
In= 1/2
!E 57 Fe
14.41 keV
In = 3/2
In= 1/2
!E 57 Fe
14.41 keV
In = 3/2 In = 3/2
In= 1/2
!E 57 Fe
14.41 keV
Phonon
Annihilation Resonance Phonon Creation
Figure 3.2: Incident photons may not always have the exact energy necessary for nuclear excitation (middle), in which case the creation or annihilation of a phonon can compensate for incident photons with too much or not enough energy for resonance excitation. Diagram courtesy of Lisa Mauger.
Thus, by sweeping the incident x-ray energy with steps of 0.5 meV and ranges of typically±120 meV, the phonon density of states is built as a histogram of phonons created or annihilated at each energy. The strength of the vibrational transition is determined by the number of phonon states at a given energy and their thermal occupation number.
The observed phonon spectra have three main features. An elastic peak for resonance excitation occurs at E=0 (this is the M¨ossbauer effect). The excitation probability of an Einstein solid predicts that the elastic line will dominate, followed by one phonon processes, two phonon processes, etc.
Inelastic side bands result from the creation or annihilation of one phonon or multiple phonons. The positive energy side features phonons created by photons incident with too much energy to excite the nuclear resonance. The negative energy side features the phonons annihilated by incident photons with not enough to excite the nuclear resonance. A phonon spectrum demonstrating these features is shown in Fig.3.3for a bcc Fe foil measured at room temperature.
An additional intrinsic feature of the phonon spectrum is the imbalance between excitation probability densities for phonon creation, S(E), and phonon annihilation S(-E). This imbalance is known as ‘detailed balance.’ Relating these excitation probability densities using the Botlzmann factor,S(-E)=S(E)exp(-E/kBT) allows determination of the temperatureT at which the spectrum was recorded [22].
Counts
-60 -40 -20 0 20 40 60
Energy (meV) Phonon Creation Phonon
Annihilation
0
Figure 3.3: A phonon spectrum for bcc Fe at room temperature, measured with NRIXS. Typical features are the elastic scattering at E=0, and inelastic sidebands resulting from photon creation and annihilation from incident photon energies detuned from the nuclear resonance energy.