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

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, 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, 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

Offset

1,2

Comments

This constant is for sphalerite, the more common polymorph of zinc sulfide. - Jon E. Schoenfield, Mar 11 2018

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

Links

Table of n, a(n) for n=1..103.

J. M. Borwein, M. L. Glasser, R. C. McPhedran, J. G. Wan, and I. J. Zucker, Lattice Sums Then and Now, Cambridge University Press, 2013.

Leslie Glasser, Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies, Inorg. Chem., 2012, 51 (4), 2420-2424.

B. Sarkar and K. Bhattacharyya, Accurate calculation of Coulomb sums: Efficacy of Padé-like methods, Phys. Rev. B 48, 6913 (1993). See Table VI, row ZnS, column Regular.

Sebastian Steiger, Mehdi Salmani-Jelodar, Denis Areshkin, Abhijeet Paul, Tillmann Kubis, Michael Povolotskyi, Hong-Hyun Park and Gerhard Klimeck, Enhanced valence force field model for the lattice properties of gallium arsenide, Phys. Rev. B 84, 155204 (2011). See Eq. (18).

Nicolas Tavernier, Gian Luigi Bendazzoli, Véronique Brumas, Stefano Evangelisti, and J. A. Berger, Clifford boundary conditions: a simple direct-sum evaluation of Madelung constants, arXiv:2006.01259 [physics.comp-ph], 2020.

Wikipedia, Madelung constant.

Wikipedia, Zinc sulfide.

Formula

Equals (sqrt(3)/4) * A085469 + (1/2) * A181152. [Glasser] - Andrey Zabolotskiy, Oct 12 2023

Example

-1.6380550533887...

Crossrefs

Cf. A085469, A181152, A182565, A182567.

Sequence in context: A115371 A371376 A096253 * A115287 A061533 A317969

Adjacent sequences: A182563 A182564 A182565 * A182567 A182568 A182569

Keyword

nonn,cons

Author

N. J. A. Sloane, May 05 2012

Extensions

More terms based on Sarkar & Bhattacharyya and Steiger et al. added by Andrey Zabolotskiy, Jul 16 2023

More terms using the formula added by Andrey Zabolotskiy, Oct 12 2023

Status

approved