Mössbauer spectroscopy

Chapter II: Experimental methods

2.3 Mössbauer spectroscopy

45 ever accounting for the background of neutrons scattering at the cell remains a challenge. We opt for well-established nuclear resonant x-ray scattering tech- niques described below.

Figure 2.5: Mössbauer spectrum of Fe-Ni Invar. (a)Shifts of the nuclear energy levels of

57Fe (with principal quantum numberI) by an isomer shift and by the presence of a mag- netic hyperfine field. States with different spinsmIwith respect to the magnetic field shift by different amounts, resulting in a splitting of the energy levels.(b)Mössbauer spectrum of ferromagnetic⁵⁷Fe65Ni35at ambient conditions measured with a conventional Doppler drive (velocity of the drive is the lower axis). It has the six absorption lines corresponding to the different nuclear transitions of panel a. The isomer shift is seen as a shift of the entire spectrum from zero energy shift (only a very weak effect for Fe65Ni35)

with respect to the magnetic field. Analogously to the Zeeman splitting of electrons, a magnetic field raises the spin degeneracy, and the nuclear states with different spins are split. For ⁵⁷Fe, there are six possible transition be- tween the ground and the first excited states, as shown in Fig.2.5. Since the splitting of the spectral lines is directly proportional to the magnetic field expe- rienced by the nucleus, called the hyperfine magnetic field (HMF), Mössbauer spectroscopy is an effective method to measure this field [22].

Figure 2.6a shows the effect of ferromagnetism on the Mössbauer spectrum of Fe-Ni Invar in different conditions. As the magnetization of the material decreases from a fully ferromagnetic state at 20 K, to ambient conditions, the

47 strength of the HMF decreases and the absorption lines are closer together. At 21 GPa, with the magnetism squeezed out by the high pressures, the material is paramagnetic and there is only a single absorption line.

In⁵⁷Fe, the magnetic field experienced at the nucleus originates from unpaired d-electrons. The spin density of these outer unpaired electrons, polarize the core electrons, resulting in a net magnetic field at the nucleus [23–25]. The effective field at the nucleus is negative, or opposite to the direction of mag- netization. Its intensity, however, is proportional to the bulk magnetization [26], so measurements of the hyperfine field can be used to determine the net magnetization of a material.

Mössbauer spectra can be fit to models of the hyperfine interactions, to extract hyperfine parameters such as isomer shifts, and strength of the HMF. We fitted our measurements using the CONUSS software package [27, 28]. The distri- bution of the HMF, P(B_hf), was approximated by two assymmetric Gaussian distributions, giving the field distributions of Fig.2.6b. At 20 K, the mean of the distribution is 33.7 Tesla (26.2 T at ambient conditions). This is a remark- ably strong field; much stronger the field produced by an MRI magnet of about 1.5-3 T, and comparable to the 45 T field of the strongest (superconducting) magnet ever build.

In this thesis we use Mössbauer experiments to determine the magnetic state and the strength of the magnetic field of our materials. It can, however, be used to extract other parameters such as recoil-free fractions, isomer shifts and quadrupole splitting (which occurs in the presence of an electric field gradient) [21, 22]. These are sensitive to the chemical environments and can be used for quantitative phase analyses and determinations of the concentrations of resonant element in different phases, even for amorphous or nanostructured materials [20].

Experimental observation of nuclear resonance

In a conventional Mössbauer experiment, the resonant nuclei in the sample are excited by γ-radiation emitted from a source. For exciting ⁵⁷Fe nuclei, a ⁵⁷Co radioisotope embedded in a Rh matrix is typically used as a radiation source.

The unstable ⁵⁷Co nucleus absorbs an inner-shell electron, and decays into a ⁵⁷Fe nucleus while emitting a 122 keV γ-ray [20]. The new ⁵⁷Fe nucleus is formed in the excited state (I = 3/2), and decays to the ground state emitting

10 5 0 5 10

velocity (mm/s)

75 50 25 0 25 50 75 100 125

intensity (a.u.)

^{20 K}

ambient 21 GPa

(a)

^{0 10}

B

hf

(T)

^{20 30 40}

0.00 0.05 0.10 0.15 0.20 0.25

P( B

hf

)

20 K

ambient 21 GPa

(b)

Figure 2.6:Dependence of Mössbauer spectra and hyperfine magnetic field of⁵⁷Fe65Ni35

on temperature and pressure. (a)Energy spectra at different conditions. At 20 K the ma- terial is strongly ferromagnetic, with well defined nuclear absorption lines. The magne- tization is reduced at ambient conditions, so the nuclear energies are less split. At high pressures (21 GPa) well above the Curie transition, the material is paramagnetic with a sin- gle nuclear transition energy.(b)Distribution of the hyperfine magnetic field, showing the strength of the field experienced by the⁵⁷Fe nuclei. They were computed from the spectra of panel a using CONUSS [27,28].

anotherγ-ray of 14.41 keV. This is the useful emission which can be resonantly absorbed by the ⁵⁷Fe in the sample.

Experiments are usually performed in a transmission geometry, as depicted in Fig.2.7, with the radiation from the source going through thin samples and into detectors. When the sample resonantly absorbs theγ-ray from the source, it re-emits radiation in all directions, removing intensity from the forward direction and lowering the count rate. We can correlate the measured count rate with the velocity of the Doppler drive to get the Mössbauer spectrum of Fig.2.5.

As mentioned previously, these nuclear energies are extremely narrow with

∆E ∼5neV. Any disturbance in the nuclear environments of either the source of the sample would cause a mismatch and hinder the resonant absorption of the γ-rays, even the recoil of a nucleus when emitting or absorbing the radiation. Therefore recoilless emission by the source and absorption by the sample are necessary. An isolated nucleus cannot be in resonance because it recoils. If embedded in a solid, the recoil energy can be transferred to the entire lattice and resonance becomes possible.

49

Figure 2.7:Schematic of Mössbauer experiment. (a)Conventional experimental setup in transmission geometry.γ-radiation is produced by a⁵⁷Co source, placed on a Doppler drive to provide an energy scan. The radiation is partially absorbed by the sample, whenever the energy matches precisely an absorption line of the⁵⁷Fe nuclei. The absorbed radiation is re-emitted in all directions through different channels (see panel b for details). This reduces the intensity of the radiation reaching the detectors, causing a dip in the count rate and resulting in the spectrum of Fig.2.5.(b)Resonant absorption at the⁵⁷Fe nuclei and re-emission through different channels. Only part of the radiation is emitted as 14.4 keV γ-rays. Most of it decays through the internal conversion channels interacting with the inner electronic shells (see text). Adapted with permission from [29].

Such a recoil-free resonance of γ-radiation was first observed in 1957 at the Max Planck Institute in Heidelberg, Germany. Its discoverer, a 29 year old PhD student named Rudolf Mössbauer, was quickly awarded the 1961 Nobel Prize in physics. Shortly after hearing the news about the resonant γ-ray absorption in ¹91Ir, Richard Feynman invited Mössbauer to come work in California. Mössbauer was a researcher at Caltech when the Nobel Prize was announced, and after an emergency faculty meeting, he was promoted to full professor in early 1962, the fastest promotion case in Caltech history.

In order to see such a recoil-free absorption we need to scan the incident energy around 14.413 keV. An energy scan in the subµeV range is achieved by placing the⁵⁷Co source on a electromagnetic Doppler drive. It shifts the energy of the emitted radiation depending on the relative speed of the source to the sample by ∆E = (v/c)·14.41keV. The velocity of the oscillating drive is typically plotted as the horizontal axis in a Mössbauer spectrum.

After resonantly absorbing γ-rays, only 10.9% of the energy is re-emitted by the ⁵⁷Fe nuclei as γ-rays [20, 29]. Most of it is transferred to the electrons through internal conversion processes, where an electron is ejected from the atom and a lower energy x-ray is emitted. Figure 2.7b shows more details of these different decay channels. Gas-filled proportional counters or solid-state detectors are used for detecting such electrons and x-rays. A backstatter (re- flection) geometry is also possible, where electrons emitted from the sample surface are counted by detectors. This is especially useful when thin samples are difficult to prepare. Backscatter geometry was also used for the minia- ture Mössbauer spectrometers that are on board the Mars Exploration Rovers (Spirit and Opportunity), to probe the landscape of and provide evidence of water on the surface of Mars [30, 31].

Mössbauer experiments are solely sensitive to the resonant isotopes. There is no background from other materials placed in the experimental setup, although an uniform and constant background occurs from other x-ray processes and detector noise. The samples, however, have to be prepared with such isotopes.

The natural abundance of⁵⁷Fe is 2.2%, so samples are often made with 95-99%

enriched ⁵⁷Fe to shorten the collection time.

With due care and the use of point-sources, it is possible to perform Mössbauer spectroscopy at high pressures, with samples in diamond-anvil cells. Due to the small sample sizes, however, long acquisition times are necessary resulting

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Figure 2.8:Advanced Photon Source (APS) at the Argonne National Laboratory. (a)Aerial view of the APS. (b)Electromagnets used to keep the electrons in a narrow beam while traveling around the storage ring. (c)Cross-sectional view of a sextupole electromagnet, showing the vacuum tubes in which the electrons travel close to the speed of light.(d)Un- dulator insertion device. The series of magnets with alternating polarity make the electrons wiggle along their path, creating a coherent beam of x-rays in the propagation direction.

in lower signal-to-noise ratios. The strong and narrow x-ray beam produced at synchrotron provides a better alternative.