Perturbed angular correlation of gamma rays (PAC)

PAC can discriminate among local environments of probe atoms in solids.  Internal fields in solids exert torques on nuclear moments:--  a magnetic field exerts a torque on the magnetic dipole moment and an electric-field gradient (EFG) exerts a torque on the electric quadrupole moment. These nuclear hyperfine interactions lead to frequencies of precession of probe nuclei that are proportional to the internal fields and are characteristic of the probe's lattice location.  . 

Many PAC probes have an excited nuclear state reached through a gamma-gamma cascade.  Start and stop gamma rays signal creation and decay of an intermediate state and (importantly) there is an anisotropic angular correlation between directions of emission of the two gamma rays.  Such is the case, for example, following decay of 60Co, for which the lifetime of the intermediate nuclear state is very short.  A classic experiment in advanced teaching laboratories involves measuring the anisotropy of the angular correlation of radiations from 60Co by measuring the coincidence counting rate of the two gammas as a function of the angle subtended by the two detectors.  For longer-lived states, the nuclear spins can precess through appreciable angles and interaction frequencies can be measured with good precision.  A small number of probes have long lifetimes and other favorable nuclear properties for "table top" PAC experiments, including 111In, decaying into 111Cd, and 181Hf, decaying into 181Ta. 

Internal fields in solids are produced mostly by charges and spins within the first few atomic shells, with more distant charges and spins only contributing to inhomogeneous signal broadening.  As a result, interaction frequencies can be used to characterize the local atomic environments in which probe atoms find themselves. Once a frequency has been identified with an underlying environment, it can be monitored in measurements made following diffferent methods of sample preparation, or for changing conditions and temperature.

PAC  Methodology

In the figure below, a radioactive probe atom in a crystal is shown at top.  Start and stop gamma rays signal formation and decay of the intermediate PAC nuclear state and are detected in scintillation detectors.  A clock and histogramming memory is used to record time intervals between start and stop gamma rays.  In general, this would give the distribution of individual nuclear lifetimes, but here the measured lifetime decay curve is modulated by spin precessions of the nuclei.  The modulating, or perturbation function G2(t) shown at the bottom of the figure contains all information about internal fields in the sample.  It is a kind of "spin rotation" pattern for probe nuclei. 

The perturbation function G2(t) shown in the graphic above comes from measurements on 111In/Cd probe atoms in the ordered intermetallic compound NiAl.  NiAl has the CsCl crystal structure, with interpenetrating simple cubic lattices of Ni and Al atoms.  The sample was almost perfectly stoichiometric, with the In probe sitting on the aluminum sublattice, surrounded in the perfect crystal by eight Ni atoms in the first shell, six Al atoms in the second shell, and so forth.  The spectrum displays a superposition of signals corresponding to two different environments of the probes:

The reasons for the large fraction of probe atoms having a vacancy neighbor is that some Ni-vacancies are quenched into the structure and there is significant binding between oversized, indium impurities and Ni-vacancies. The binding enthalpy has been  determined in other experiments to be about 0.20 eV.
General areas of application of PAC

PAC is widely applied in condensed-matter and materials physics studies.  Applications include the following:
For additional applications, consult PAC worldwide links.  PAC has favorable characteristics as a spectroscopy.  Measurements are unrestricted in temperature, unlike in NMR and Mössbauer effect for which signal amplitudes are reduced at high temperature by Boltzmann factors.   Concentrations of probe atoms are typically as low as ~10 parts-per-billion in 111In/Cd PAC experiments.  On the downside, PAC has a limited number of isotopes with favorable nuclear properties for  "table-top" experiments, the most common ones being 111In/Cd  and 181Hf/Ta, followed by 99Mo/Tc, 99Rh/Ru, and 100Pd/Rh.   Additional probes having parent isotopes with short lives are available at major facilities that produce radioactive ion beams,  such as ISOLDE at CERN, ISAC at TRIUMF. and, perhaps in the future, the rare-ion beam facility at NSCL in Michigan.   We are part of a research group that  was awarded beam time at ISOLDE for  diffusion studies in February 2009;  the spokesperson for the group is Manfred Deicher of the University of the Saarlandes.  Experiments are planned using the isotope 117Cd, which decays into 117In.

Applications at WSU

1.  Point Defects in Solids

Point defects nearby probe nuclei modify internal fields.  All of the following types of defects have been detected in this laboratory over the past two decades:
To illustrate a study of point defects, consider the study of vacancy-probe complexes in FeAl. in which bound states of indium impurities with from one to four near-neighbor vacancies were observed to form and dissolve reversibly by "condensation" and "evaporation" as the temperature was lowered and increased.  The very first PAC study of lattice defects was made in the early 1960's by George Hinman, who, by coincidence, is currently Emeritus Professor of Environmental Science at WSU.  Click on the following link for a  well-written brief history of PAC by Frits Pleiter of the Groningen hyperfine group.

2.  Site Preferences of Impurities in Compounds

When a compound contains sites havingl different symmetries, one can identify the site occupied by an impurity PAC probe atom by measuring the quadrupole interaction.  A particularly simple and common structure having this feature is the Cu3Au, or L12, crystal structure.   Atoms at corners of the unit cell have cubic point symmetry, which makes the quadrupole interaction frequency zero.  Atoms at face-centers of the cubic unit cell have tetragonal symmetry, leading to a non-zero quadrupole interaction.  Therefore, simple observation of a zero or non-zero quadrupole interaction serves to identify the site occupied by the impurity.  We did a large study of site preferences of indium solutes in GdAl2, which has the Cu2Mg , or C15 structure and was studied in exactly the same way.  Green atoms in the pictured structure are at cubic sites while brown atoms are not.   We found that indium solutes can appreciably occupy both sites in thermal equilibrium and that they move from Gd sites (green) to Al sites (brown) as temperature increases.  The enthalpy to transfer an indium solute from the Gd-site to Al-site was measured to be 0.347 eV.

3.  Jump Frequencies of PAC Tracer Atoms in Solids

If tracer atoms jump on a sublattice whose sites have non-cubic symmetry and if the axis of symmetry reorients in each jump, then the quadrupole interaction will lose coherence over time.  Roughly speaking, quadrupole moments precess around the principal axis of the local EFG tensor., so that reorientation of the EFG leads to signal decoherence.  In a slow fluctuation regime, in which the jump frequency is less than the quadrupole interaction frequency, the decoherence is exhibited in good approximation as exponential damping  of the quadrupole perturbation pattern.   In many situations, the damping time is equal to the mean residence time of the probe on a site, and can be fitted very accurately to obtain the jump frequency.   Amazingly, this simple approach to the study of diffusion in solids went unnoticed in the PAC community for fifty years before we happened upon it.  Our first paper, in Physical Review Letters, involved PAC probe atoms jumping on the In-sublattice in the compound In3La, which has the Cu3Au, or L12, crystal structure.   A great deal of additional research has been carried out and is in progress. 

Recently, we showed, also in Physical Review Letters, that  one can gain insight into diffusion mechanisms in highly ordered binary compounds by comparing jump frequencies measured at opposing boundary compositions.   In most solids, atom movement is made possible by the presence of vacancies into which neighboring atoms can jump.   Consider for simplicity two samples of a compound A3B, one prepared to be A-rich and the other B-rich.   It turns out that the concentration of A-vacancies must increase as the composition becomes more B-rich and, similarly, the B-vacancy concentration  increases as the composition becomes more A-rich.   Since jump frequencies are proportional to the number of vacancies available, it is a simple matter to determine which type of vacancy is involved in the predominant difffusion mechanism.  For example, if the principal diffusion mechanism involves B-vacancies, then a greater jump frequency will be observed in the A-rich sample.    As a case in point, we presented measurements on an entire series of In3R phases having the L12 structure, in which R is a rare-earth element, that show that diffusion on the A-sublattice is dominated by A-vacancies in the "heavy" lanthanide indides (e.g., Lu, Tm, Er,...) but by B-vacancies in the "light" lanthanide indides (e.g., La, Ce, Pr).   This change in the dominant mechanism along the series is very surprising given the great chemical similarity of rare-earch elements.  

(See publication pages for more examples.)

References for PAC spectroscopy        

Other web descriptions and graphics picturing PAC spectroscopy
PAC theses and monographs on the web (please notify me of others)
PACMAN in the universe

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