Topologically appropriate coordinates for (Vzz, η) joint probability distributions

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 V_zz and η determined by the defect concentration, crystal structure, and defect sites in the crystal. Czjzek showed how to choose coordinates in the (V_zz, 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.     

Copper-Catalyzed Deaminative Difluoromethylation

The difluoromethyl group (CF₂H) is considered to be a lipophilic and metabolically stable bioisostere of an amino (NH₂) group. Therefore, methods that can rapidly convert an NH₂ group into a CF₂H group would be of great value to medicinal chemistry. We report herein an efficient Cu-catalyzed approach for the conversion of alkyl pyridinium salts, which can be readily synthesized from the corresponding alkyl amines, to their alkyl difluoromethane analogues. This method tolerates a broad range of functional groups and can be applied to the late-stage modification of complex amino-containing pharmaceuticals.     

Inhomogeneous broadening of PAC spectra with V zz and η joint probability distribution functions

The perturbed angular correlation (PAC) spectrum, G ₂(t), is broadened by the presence of randomly distributed defects in crystals due to a distribution of electric field gradients (EFGs) experienced by probe nuclei. Heuristic approaches to fitting spectra that exhibit such inhomogeneous broadening (ihb) consider only the distribution of EFG magnitudes V _zz , but the physical effect actually depends on the joint probability distribution function (pdf) of V _zz and EFG asymmetry parameter η. The difficulty in determining the joint pdf leads us to more appropriate representations of the EFG coordinates, and to express the joint pdf as the product of two approximately independent pdfs describing each coordinate separately. We have pursued this case in detail using as an initial illustration of the method a simple point defect model with nuclear spin I?=?5/2 in several cubic lattices, where G ₂(t) is primarily induced by a defect trapped in the first neighbor shell of a probe and broadening is due to defects distributed at random outside the first neighbor shell. Effects such as lattice relaxation are ignored in this simple test of the method. The simplicity of our model is suitable for gaining insight into ihb with more than V _zz alone. We simulate ihb in this simple case by averaging the net EFGs of 20,000 random defect arrangements, resulting in a broadened average G ₂(t). The 20,000 random cases provide a distribution of EFG components which are first transformed to Czjzek coordinates and then further into the full Czjzek half plane by conformal mapping. The topology of this transformed space yields an approximately separable joint pdf for the EFG components. We then fit the nearly independent pdfs and reconstruct G ₂(t) as a function of defect concentration. We report results for distributions of defects on simple cubic, face-centered cubic, and body-centered cubic lattices. The method explored here for analyzing ihb is applicable to more realistic cases.     

Realistic models of stochastically varying hyperfine interactions caused by vacancy diffusion in L12-structured compounds

Perturbed angular correlation spectroscopy (PAC) is an attractive method for fundamental studies of diffusion because of the possibility to observe directly atomic scale defects involved in a diffusion process. Previous work investigated under what experimental conditions one could observe a contribution to a PAC spectrum that clearly could be attributed to a vacancy in L1₂-structured compounds for the special case of self-diffusion. This has since been extended in the present work to consider the case of impurity diffusion and to explore whether or not distant vacancies or configurations with multiple vacancies affect PAC spectra significantly.     

Dimensionless coordinates for simulations and theory of hyperfine interactions in materials

For problems involving simulations or theory of hyperfine interactions in materials, it is convenient to work in dimensionless coordinates of reasonable magnitude. Such a system is described here that constitutes a consistent and useful “natural” dimensionless unit system that simplifies point-charge approximations, scaling between different crystal structures, scaling charges of various defects in materials, and other computations involving hyperfine interactions. We present the proposed system with examples of its use for data analysis as well as for simulations and theory.     

PAC Probes as Diffusion Tracers in Solids

Perturbed angular correlation (PAC) probe atoms have been used as tracers to study diffusion in solids. The method works for diffusion on a sublattice for which the point symmetry is noncubic and the electric field gradient (EFG) at the probe nucleus reorients in each jump. Such motion leads to relaxation of the nuclear quadrupole interaction. Precise values of the tracer jump frequency have been obtained from fits of measured PAC perturbation functions. Results obtained to date are reviewed for Cd tracer atoms in rare-earth indides such as LaIn3 that have the L1₂ crystal structure, for which each jump on the In-sublattice reorients the EFG by 90°. New results are presented for LaSn3 and prospects for future studies are outlined.     

Stochastic models of hyperfine interactions in nonequilibrium: an examination of the XYZ model with a trapping-detrapping mechanism

Simulations of perturbed angular correlation (PAC) spectra were carried out to investigate the effects of nonequilibrium distributions of PAC probes. The XYZ model with a trapping-detrapping mechanism was chosen to represent a system in which point defects are trapped by, detrap from, and hop around PAC probes. Calculations were based on the method of Winkler and Gerdau.     

Atom movement in In3La studied via nuclear quadrupole relaxation

Jump frequencies of Cd tracer atoms in In3La were measured via nuclear quadrupole relaxation caused by stochastic reorientation of the electric field gradient using the method of perturbed angular correlation of gamma rays. Activation enthalpies of 0.53(1) and 0.81(1) eV were found at the two phase boundaries, which differ in composition by only about 0.1 at. %. The jump frequency was found to be higher at the more In-rich phase boundary, ruling out a simple In-vacancy diffusion mechanism. Possible diffusion mechanisms and general applicability of the method are discussed.     

Charge transfer model for quadrupole interactions and binding energies of point defects with111In/Cd probes in cubic metals

An overview of the experimental approaches to study weak interactions using traps is given. Both charged and neutral weak currents are considered.

     

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.