PAC Spectroscopy and Diffusion Effects

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diffusion-fundamentals
The Open-Access Journal for the Basic Principles of Diffusion Theory, Experiment and Application
www.diffusion-fundamentals.org, ISSN 1862-4138; © 2005-2010
Diffusion Fundamentals 12 (2010) 92 © J. Röder
PAC Spectroscopy and Diffusion Effects
Jens Röder,* K.-D. Becker
Technische Universität Braunschweig, Institut für Physikalische und Theoretische Chemie,
Hans-Sommer-Str. 10, 38106 Braunschweig Germany
E-Mail: j.roeder@tu-bs.de
Presented at the Bunsen Colloquium: Spectroscopic Methods in Solid State Diffusion and Reactions
September 24th
−
25th, 2009, Leibniz University Hannover, Germany
Perturbed angular correlation (PAC) spectroscopy is a technique to study the local structure around
probe atoms in materials. It belongs to the nuclear spectroscopy methods such as NMR and Mößbauer
spectroscopy. In PAC spectroscopy the hyperfine interaction between electric and magnetic fields
produced by the sample material and the nuclear moments of the probe atoms results in a perturbation
of the angular correlation of the emitted γ-rays. Fig. 1 illustrates the fundamentals. An appropriate
probe atom decays over an intermediate state, which has a short life time. γ-rays emitted in transitions
to and from that sensitive level are used as start and stop signals to detect the decay curve of the inter-
mediate state. Because of the anisotropy of the two angularly correlated γ-rays and the perturbation by
electric and magnetic fields, the intensity of emitted γ-rays varies slightly over time which can be ob-
Fig. 1 PAC schema.

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served as ripples on the decay curve of the sensitive level. For quadrupole interactions the interesting
parameters which can be obtained by PAC spectroscopy are: fraction of sites (f), quadrupole interac-
tion frequency (νQ) and its damping (δ) and the asymmetry parameter (η). For magnetic dipole interac-
tions: fraction of sites (f), Larmor frequency (ωL) and its damping (δ). Measurements are usually rec-
orded at different temperatures. Changes in the phase or the magnetism can be studied as well as de-
fects or changes of the site’s fraction. Ref. [1] provides an overview.
Atomic dynamics in the material have also an effect on the PAC data. When the first γ-quantum is
emitted and the probe’s neighborhood changes before the second γ-quantum is emitted, the correlated
information gets basically lost. For example, if the change is caused by hopping of atoms close to the
probe atom, the probability that a hop will occur within the time window of this probe atom increases
with time. In the PAC time diagram this results in a decrease of the perturbation’s amplitude with in-
creasing time. From the data, the hopping frequency can be obtained [2,3]. Fig. 2 illustrates such a
PAC spectrum.
Fig. 2 111In/111Cd PAC on Neodymium nickel oxide at 400 °C.
Fig. 3 shows another effect of dynamic processes in a PAC spectrum. With increasing temperature a
sharpening in the spectrum is observed. Such a case has been described and simulated in Ref. [4].
Here, a nucleus is considered which undergoes a transition from a situation at where it “sees” many
different EFGs to a situation which can be characterized by one EFG only. A PAC spectrum with
many different EFGs would correspond to the spectrum at lower temperature in Fig. 3. The spectrum
at the highest temperature in Fig. 3 would correspond to the single EFG case (here in the spectrum
actually two EFGs exist).
For the 111In/111Cd probe the first level has a decay time of 120 ps as seen in Fig. 1. If the dynamic
process is in the time scale of the first decay level, a certain part of the probe’s population is in the
final single EFG when the decay starts from the first level. This population experiences an undisturbed
decay. The other population has a wide distribution due to the many EFGs. In total, this results in a
PAC spectrum with sharp frequencies at lower amplitude but with no damping over time. With in-
creasing temperature the jump rate increases and increasingly populates the group of probe atoms of
the final single EFG, which results in an increase of the amplitude. In Fig. 3 two final EFG are ob-
served.

Röder et al., PAC-Spectroscopy and Diffusion Effects diffusion-fundamentals
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Diffusion Fundamentals 12 (2010) 94 © J. Röder
Fig. 3 111In/111Cd PAC on Lanthanum nickel oxide at different temperatures [5].
PAC spectroscopy is a challenging method to study local structure in materials. It also allows studying
dynamic effects in materials by selecting appropriate probe atoms.
References
[1] G. Schatz, A. Weidinger: Nukleare Festköperpysik, Teubner Studienbücher (1992).
[2] A. Abragam, R. Pound, Phys. Rev. 92 (1953) 943.
[3] U. Bäverstam, R. Othaz, N. de Sousa, B. Ringstöm, Nuc. Phys. A 186 (1972) 500.
[4] D. Lupascu, Dissertation Universität Göttingen (1995).
[5] J. Röder, M. Uhrmacher, K. D. Becker, Hyp. Int. 178 (2007) 31.