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Summation of lattice contributions

  • Electric Field Gradients
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Abstract

A new method is discussed to improve the convergence of the lattice sums encountered in the theory of electric field gradients (EFG). It used Euler-Maclaurin (EM) summation formula to evaluate the sum in the direct crystal space without any special regrouping of charges. Working with reference to a tetragonal crystal, it is pointed out that the poor convergence properties in a direct sum are due to overweighting of positive contributions to EFG. If contribution from an entire plane is obtained before moving on to the next plane, the convergence in thec direction presents no problem. The EM formula may be used for this purpose and the EFG may be summed in direct crystal space with much less numerical computation. Results are presented for a simple tetragonal crystal withc/a=1.5, where the values are known from the conventional Fourier transform technique.

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Authors and Affiliations

  1. Department of Physics, Patna Science College, Patna University, 800005, Patna, India

    H. C. Verma

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  1. H. C. Verma
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Verma, H.C. Summation of lattice contributions. Hyperfine Interact 25, 539–545 (1985). https://doi.org/10.1007/BF02354665

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  • DOI: https://doi.org/10.1007/BF02354665

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