Abstract
The joint probability distribution function (JPDF) of electric field gradient (EFG) tensor components in cubic materials is dominated by coordinated pairings of defects in shells near probe nuclei. The contributions from these inner shell combinations and their surrounding structures contain the essential physics that determine the PAC-relevant quantities derived from them. The JPDF can be used to predict the nature of inhomogeneous broadening (IHB) in perturbed angular correlation (PAC) experiments by modeling the G 2 spectrum and finding expectation values for V zz and η. The ease with which this can be done depends upon the representation of the JPDF. Expanding on an earlier work by Czjzek et al. (Hyperfine Interact. 14, 189–194, 1983), Evenson et al. (Hyperfine Interact. 237, 119, 2016) provide a set of coordinates constructed from the EFG tensor invariants they named W 1 and W 2. Using this parameterization, the JPDF in cubic structures was constructed using a point charge model in which a single trapped defect (TD) is the nearest neighbor to a probe nucleus. Individual defects on nearby lattice sites pair with the TD to provide a locus of points in the W 1−W 2 plane around which an amorphous-like distribution of probability density grows. Interestingly, however, marginal, separable PDFs appear adequate to model IHB relevant cases. We present cases from simulations in cubic materials illustrating the importance of these near-shell coordinations.
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Czjzek, G.: Distribution of nuclear quadrupole splittings in amorphous materials and the topology of the (V zz , η)-parameter Space. Hyperfine Interact. 14, 189–194 (1983)
Evenson, W.E., Adams, M., Bunker, A., Hodges, J.A., Matheson, P.L., Park, T., Stufflebeam, M., Sullivan, F.P., Zacate, M.O.: Topologically Appropriate Coordinates for (V zz , η) Joint Probability Distributions. Hyperfine Interact. 237, 119 (2016)
Czjzek, G., Fink, J., Goetz, F., Schmidt, H., Coey, J.M.D., Rebouillat, J.-P., Lienard, A.: Atomic coordination and the distribution of electric field gradients in amorphous solids. Phys. Rev. B 23, 2513 (1981)
Stöckmann, H.-J.: Electric field gradients resulting from randomly distributed unscreened point charges. J. Mag. Res. 44, 145–158 (1981)
Evenson, W.E., Adams, M., Bunker, A., Hodges, J., Matheson, P., Park, T., Stufflebeam, M., Zacate, M.O.: Inhomogeneous broadening of PAC spectra with V zz and η joint probability distribution functions. Hyperfine Interact. 222, 77–86 (2013)
Nolan, J.P.: Levy Processes, pp. 379–400. Birkhäuser, Boston (2001)
Zacate, M., Jaeger, H.: Perturbed angular correlation spectroscopy—a tool for the study of defects and diffusion at the atomic scale, defect and diffusion forum. ISSN: 1662-9507, 311 3–38 (2011)
Stoneham, A.M.: Shapes of inhomogeneously broadened resonance lines in solids. Rev. Mod. Phys. 41, 82–108 (1969)
Forker, M.: The problematic of the derivation of the electric field gradient asymmetry parameter from TDPAC measurements or Mössbauer spectroscopy in imperfect crystal lattices. Nucl. Instrum. Methods 106, 121–126 (1973)
Collins, G.S, Sinha, P.: Structural, thermal and deformation-induced point defects in PdIn. Hyperfine Interact. 130, 151–179 (2000)
Nieuwenhuis, E.R., Collins, G.S., Favrot, A., Zacate, M.O.: High-temperature polymorph of In 2La. J. Alloys Compd. 387, 20–23 (2005)
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This article is part of the Topical Collection on Proceedings of the International Conference on Hyperfine Interactions and their Applications (HYPERFINE 2016), Leuven, Belgium, 3–8 July 2016
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Matheson, P.L., Sullivan, F.P. & Evenson, W.E. The influence of coordinated defects on inhomogeneous broadening in cubic lattices. Hyperfine Interact 237, 129 (2016). https://doi.org/10.1007/s10751-016-1339-9
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DOI: https://doi.org/10.1007/s10751-016-1339-9