cp's OEIS Frontend

A182566 Decimal expansion of Madelung constant (negated) for zinc sulfide ZnS.

%I A182566 #52 Oct 13 2023 10:02:30
%S A182566 1,6,3,8,0,5,5,0,5,3,3,8,8,7,8,9,4,2,3,7,5,0,0,3,4,7,7,6,3,5,8,6,1,9,
%T A182566 4,6,5,3,6,0,1,7,9,6,6,3,1,3,6,6,5,7,8,8,3,9,5,7,6,4,4,6,2,3,9,2,7,7,
%U A182566 0,6,8,1,2,8,3,7,2,2,3,1,3,7,6,9,8,5,4,6,4,2,0,0,4,3,4,9,4,6,6,5,1,6,1
%N A182566 Decimal expansion of Madelung constant (negated) for zinc sulfide ZnS.
%C A182566 This constant is for sphalerite, the more common polymorph of zinc sulfide. - _Jon E. Schoenfield_, Mar 11 2018
%C A182566 The sphalerite (zincblende) structure consists of two interpenetrating face-centered cubic lattices of ions with charges +2 and -2, together occupying all sites of the diamond structure. This constant does not include overall factor 2 from the absolute value of the charges. This constant is normalized to the nearest neighbor distance, not the lattice constant; cf. the values 3.782926104 (or 3.78292610408577750878 from Sarkar & Bhattacharyya) and 7.56584 from pages 41 and 16 of "Lattice Sums Then and Now", which equal 4/sqrt(3) and 8/sqrt(3) times this constant. - _Andrey Zabolotskiy_, Feb 18 2021
%H A182566 J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, and I. J. Zucker, <a href="https://carmamaths.org/resources/jon/LatticeSums/">Lattice Sums Then and Now</a>, Cambridge University Press, 2013.
%H A182566 Leslie Glasser, <a href="https://doi.org/10.1021/ic2023852">Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies</a>, Inorg. Chem., 2012, 51 (4), 2420-2424.
%H A182566 B. Sarkar and K. Bhattacharyya, <a href="https://doi.org/10.1103/PhysRevB.48.6913">Accurate calculation of Coulomb sums: Efficacy of Padé-like methods</a>, Phys. Rev. B 48, 6913 (1993). See Table VI, row ZnS, column Regular.
%H A182566 Sebastian Steiger, Mehdi Salmani-Jelodar, Denis Areshkin, Abhijeet Paul, Tillmann Kubis, Michael Povolotskyi, Hong-Hyun Park and Gerhard Klimeck, <a href="https://doi.org/10.1103/PhysRevB.84.155204">Enhanced valence force field model for the lattice properties of gallium arsenide</a>, Phys. Rev. B 84, 155204 (2011). See Eq. (18).
%H A182566 Nicolas Tavernier, Gian Luigi Bendazzoli, Véronique Brumas, Stefano Evangelisti, and J. A. Berger, <a href="https://arxiv.org/abs/2006.01259">Clifford boundary conditions: a simple direct-sum evaluation of Madelung constants</a>, arXiv:2006.01259 [physics.comp-ph], 2020.
%H A182566 Wikipedia, <a href="https://en.wikipedia.org/wiki/Madelung_constant">Madelung constant</a>.
%H A182566 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zinc_sulfide">Zinc sulfide</a>.
%F A182566 Equals (sqrt(3)/4) * A085469 + (1/2) * A181152. [Glasser] - _Andrey Zabolotskiy_, Oct 12 2023
%e A182566 -1.6380550533887...
%Y A182566 Cf. A085469, A181152, A182565, A182567.
%K A182566 nonn,cons
%O A182566 1,2
%A A182566 _N. J. A. Sloane_, May 05 2012
%E A182566 More terms based on Sarkar & Bhattacharyya and Steiger et al. added by _Andrey Zabolotskiy_, Jul 16 2023
%E A182566 More terms using the formula added by _Andrey Zabolotskiy_, Oct 12 2023