Fitting PAC spectra with stochastic models: PolyPacFit

PolyPacFit is an advanced fitting program for time-differential perturbed angular correlation (PAC) spectroscopy. It incorporates stochastic models and provides robust options for customization of fits. Notable features of the program include platform independence and support for (1) fits to stochastic models of hyperfine interactions, (2) user-defined constraints among model parameters, (3) fits to multiple spectra simultaneously, and (4) any spin nuclear probe.     

Vacancy encounter model for stochastically fluctuating electric field gradients in the Cu3Au crystal structure

A class of experimental techniques known as hyperfine methods can be used to measure electric field gradients (EFGs) through the hyperfine interaction experienced by tracer nuclei. When EFGs fluctuate at rates comparable to the inverse characteristic timescale of the hyperfine method, there is a loss of signal coherence that can be used to determine EFG fluctuation rates. This has been used to measure, for example, EFG fluctuations accompanying atomic jumps of radiotracers using perturbed angular correlation spectroscopy (PAC). Nominally, there is a one-to-one correspondence between EFG fluctuation and tracer jump, but when tracer jumps are mediated by a vacancy diffusion mechanism, a subset of multiple tracer-vacancy exchanges will not affect spectra when they occur much faster than the hyperfine timescale, leading to an underestimate of underlying tracer jump rate if this correlated random-walk effect is not taken into consideration. The present work calculates the factor by which EFG fluctuation rate differs from tracer jump rate based on a time-dependent, random-walk analysis of tracer displacement probabilities in a vacancy encounter model for the special case of self-diffusion in the L1₂ crystal structure.     

Relating PAC damping to EFG fluctuation rates through the PAC relaxation peak

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.     

Simulation of Al/Fe disorder in Ca2FexAl2−xO5

A method is described which is capable of simulating disorder across a range of composition. It is used to study the disorder of iron and aluminium on the octahedral and tetrahedral cation sites in the Brownmillerite phase Ca₂Fe_xAl_2−xO₅. The arrangements with the lowest lattice energies are those that maximize the number of Fe³⁺ on octahedral sites throughout the composition range. An exchange of one Fe³⁺ with one Al³⁺, which results in a decrease in the number of iron ions on octahedral sites, increases the lattice energy by an amount that is dependent on x but is independent of the number of exchanges. The exchange of trivalent cations also results in an expansion in the b lattice direction, accompanied by a decrease in the a and c directions across the full range of composition.