Modified EFG Components and Their Joint pdf for Use in Modeling ihb in PAC

ORAL

Abstract

Spectra of hyperfine interactions involving the electric field gradient tensor (EFG) are subject to broadening by statistical variations of EFG components. In perturbed angular correlation (PAC) experiments, the inhomogeneous broadening (ihb) of the $G_{2}$(c,$t)$ spectrum is produced by randomly distributed lattice defects of concentration, $c$. The EFG tensor has two independent components. The concentration dependence of ihb is determined by the joint probability distribution function (pdf) of these components. In typical PAC analyses, the independent coordinates are assumed to be$ V_{zz}$ and the asymmetry parameter $\eta =$ $(2V_{xx}+V_{zz})/V_{zz}$. However, the pdf $P(c,V_{zz}$,$\eta )$ is not known, and in any case it is easy to show that $V_{zz}$ and $\eta $ are highly correlated, and not independent. We have found that the application of the Czjzek transformation [1], followed by a simple conformal mapping produces two, nearly independent EFG coordinates $W_{1}(c,V_{zz},\eta )$ and $W_{2}(c,V_{zz},\eta )$. The pdfs of each coordinate are readily characterized, and their product $P(c,W_{1},W_{2})=P_{1}(c,W_{1})P_{2}(c,W_{2})$ forms an appropriate joint pdf that can be used to model ihb in a variety of situations. We show the application of this method by reporting results modeling the concentration dependence of ihb in various PAC models, for simple cubic (sc), face-centered cubic (fcc) and body-centered cubic (bcc) lattices. \\[4pt] [1] Czjzek, G. Hyperfine Interactions 14(1983) 189-194.

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Authors

  • M. Adams

    Utah Valley University

  • P. Matheson

    Utah Valley University

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines

  • Norm Buchanan

    Brigham Young University, Stanford University, University of Central Florida, NCAR/High Altitude Observatory, Arizona Vitro-retinal consultants, University of Michigan, Arizona State University, University of Denver, Arizona State University Dept of Physics, Arizona State University Dept of Chemistry and Biochemistry, LASP, University of Colorado Boulder, Center for Atmospheric and Space Science, Utah State University, Dixie State College, Utah, USU Materials Physics Group, UVU Physics Department, Box Elder Innovations, Space Telescope Science Institute, Northern Kentucky University, Retired, Utah Valley University, Univ. of California, Los Angelos, Colorado State University, St. Petersburg Electro-technical University, Universidad Nacional Aut\'onoma de M\'exico, New Mexico State University, University of New Mexico, University of Wurtzberg, Theoretical Division, Los Alamos National Laboratory, National High Magnetic Field Laboratory, LANL, UCLA, Max-planck-Institut f\"{u}r Astronomie, W. M. Keck Observatory, University of Arizona, Nuclear Physics Group, Brigham Young University, GLOBALFOUNDRIES, IBM Systems and Technology Group, IBM Research Division, T.J. Watson Research Center, Sandia National Laboratory, NMSU, Military University of Technology, Warsaw, Poland, James Franck Institute and Department of Physics, University of Chicago, Department of Atmospheric Sciences, University of Washington, JISAO, University of Washington, New Mexico Institute of Mining and Technology, NorthWest Research Associates, University of Alaska, Fairbanks, Utah State University, New Mexico Tech, University of Cambridge, Los Alamos National Laboratory, RAPTOR Science, Institute of Space and Astronomical Science, Japanese Aerospace Exploration Agency, Weber State University, Department of Physics, New Mexico State University, BYU Physics, Physics Department, University of Arizona, ABQMR, University of Colorado at Boulder, SNL and CINT, Los Alamos National Lab, Center for Quantum Information and Control, University of Arizona, Center for Quantum Information and Control, University of New Mexico, University of Calgary, Colorado School of Mines