Tyler Park’s research while affiliated with Utah Valley University and other places

Inhomogeneous broadening (IHB) of hyperfine interactions in materials arises from a distribution of electric field gradients (EFGs) due to randomly distributed defects contributing non-uniformly to the EFG at probe sites. Hyperfine experiments reflect the inhomogeneous distribution of defects through the joint probability distribution function (PDF) of Vzz and η determined by the defect concentration, crystal structure, and defect sites in the crystal. Czjzek showed how to choose coordinates in the (Vzz, η) plane that are consistent with the physical constraints and ordering convention for these EFG parameters. Here we show how to transform to a new set of coordinates that decreases the distortion inherent in Czjzek’s representation. These new coordinates allow one to express the joint PDF for random distributions of defects in a form reasonably approximated by the product of two independent marginal distributions. This paper focuses on these topologically appropriate coordinates, with simple examples drawn from Czjzek’s work and from our simulations of point defects in cubic lattices as well as random amorphous distributions of defects. Detailed simulations have been carried out for IHB in cubic structures and point charge models relevant to perturbed angular correlation (PAC) experiments.

A perturbed angular correlation (PAC) experiment that measures dynamic damping also needs information about the fundamental quadrupole frequency to relate the damping as a function of temperature to the EFG fluctuation rate. When the experiment is unable to access slow electric field gradient (EFG) fluctuations that show the fundamental quadrupole frequency directly, one needs additional information to determine the hyperfine field parameters and thereby the connection between observed damping and EFG fluctuation rates. One way to solve this problem is to estimate the hyperfine parameters from the fluctuation rate for maximum damping (i.e. at the relaxation peak) or from the rate of maximum damping. This work relates both the maximum damping rate and the fluctuation rate at the relaxation peak to EFG magnitudes (or quadrupole frequencies) for five dynamic N-state symmetric models of fluctuating EFGs.

Our research concerns the effect of a static distribution of defects on the net electric field gradient (EFG) within crystal structures. Defects and vacancies perturb the distribution of gamma rays emitted from radioactive probe nuclei within the crystal. These defects and vacancies produce a net EFG at the site of the probe which causes the magnetic quadrupole moment of the nucleus of the probe to precess about the EFG. The net EFG, which is strongly dependent upon the defect concentration, perturbs the angular correlation (PAC) of the gamma rays, and is seen in the damping of the perturbation function, G2(t), in time and broadening of the spectral peaks in the Fourier transform. We have used computer simulations to study the probability distribution of EFG tensor components in order to uncover the concentration dependence of G2(t). This in turn can be used to analyze experimental PAC data and quantitatively describe properties of the crystal.

Materials contain defects, which affect crystal properties such as damping of the correlation signal,G2(t), in time and broadening of the frequency spectrum in perturbed angular correlation (PAC) experiments. We attribute this inhomogeneous broadening (IHB) to the random static defects that produce a distribution of electric field gradients (EFGs). Our goal is to find a relationship between the amount of broadening and the concentration of defects. After simulating the EFGs from random configurations of defects, we map our results from the Vzz-Vxx plane to a coordinate system optimized for the EFG distribution through a Czjzek transformation, followed by a conformal mapping. From histograms in this space, we can define probability distribution functions with parameters that vary according to defect concentration. This allows us to calculate the broadened G2(t) spectrum for any concentration, and, in reverse, identify concentrations given a broadened G2(t) spectrum.

Defects in crystals affect the electric field gradient (EFG) tensor components at radioactive probe nuclei. We consider the net EFG from a random distribution of vacancies combined with a single trapped vacancy in a near neighbor position. The net EFG perturbs angular correlation (PAC) and provides information about the concentration of vacancies. For various concentrations (.1 to 15 percent) we have simulated PAC spectra in simple cubic, body centered and face centered cubic crystal structures. Using the probability distributions we found for the EFG tensor components we reconstruct G2(t) for various defect concentrations. We take these reconstructions and compare them with the simulated G2(t) functions to check for self-consistency. We can then use the simulated probability distributions to examine the concentration dependence of experimental broadened PAC spectra. This work will be applied initially to broadened PAC data from beta-Mn, Al-doped beta-Mn, and Sr2RuO4.

Independent component analysis (ICA) of electric field gradient (EFG) tensor components has proven useful in analysis of inhomogeneous broadening in perturbed angular correlation (PAC). We have simulated PAC spectra for various concentrations (0.1% to 15%) of randomly distributed defects with a near- neighbor vacancy in simple cubic and face-centered cubic crystal structures. In analyzing this simulation, we used ICA to transform the Vxx and Vzz EFG components to find a joint probability distribution function for the EFGs. ICA allowed us to separate the components and develop the joint probability function as a product of the probability distributions for two independent coordinates. Then we found the broadened G2(t) by integration over the joint probability distribution function. We have compared these results to simulated G2(t) functions, allowing us to analyze the concentration dependence of the broadened PAC spectrum. This work will be applied initially to broadened PAC data from beta-Mn, Al-doped beta-Mn, and Sr2RuO4.

Since real crystals always include defects, the effect of the defects on crystal properties depends on how many defects are present, i.e. on defect concentration. In perturbed angular correlation (PAC), these defects produce damping of the correlation signal in time and broadening of the frequency spectrum. This ``inhomogeneous broadening'' depends quantitatively on defect concentration, so the size of the broadening in a PAC spectrum can be a measure of the concentration of defects. Using simulated PAC spectra and independent component analysis to obtain the probability distribution function for electric field gradient (EFG) components, we have found defect concentration-dependent parameters for the probability functions. This allows us to calculate broadened PAC spectra for any selected defect concentration. It also allows us to fit defect concentration from an experimental PAC spectrum. This work will be applied initially to broadened PAC data from beta-Mn, Al-doped beta-Mn, and Sr2RuO4.

Nuclear relaxation of perturbed angular correlation (PAC) spectra offers insights to diffusion because it arises from motion of defects or of a nuclear probe in a crystal. The N-state symmetric model is a model of fluctuation among N symmetric electric field gradients (EFGs) experienced by a radioactive nuclear probe. By simulating the N-state symmetric model for various rates of hopping among the N EFGs, the resulting spectra can be fitted with a damped perturbation function, G22(t), or an exponential decay function to find the decay constant (lambda). By plotting lambda against the hopping rate, we find the maximum relaxation point. Fitting the raw spectrum, a spectrum weighted by error bars, and a spectrum with simulated errors gives a good indication of the relaxation that would be observed in a PAC experiment. The maximum relaxation point can then be used as an experimental measure of the defect or probe hopping rate, and hence the diffusion rate at that temperature. We report the results of our simulations and their implications, with potential applications to diffusion in intermetallic systems.

All real crystals have defects such as impurities and vacancies which affect their properties. In perturbed angular correlation (PAC), these defects produce damping of the correlation signal in time and broadening of the frequency spectrum. This broadening is termed ``inhomogeneous broadening'' since it is due to the inhomogeneities (i.e. defects) in the crystal. We have simulated PAC spectra for various concentrations (0.1% to 15%) of randomly distributed defects with a near-neighbor vacancy in simple cubic and face-centered cubic crystal structures. For every particular set of defects, the randomly distributed defects and the near-neighbor vacancy together produce a net electric field gradient (EFG), from which we obtain the PAC spectrum. We then average PAC spectra to study the effects of defect concentration and crystal structure on inhomogeneous broadening as an aid to analyzing experimental data. This work will be applied initially to broadened PAC data from beta-Mn, Al-doped beta-Mn, and Sr2RuO4.