Solid-State Energetics and Electrostatics: Madelung Constants and Madelung Energies

Abstract

The Madelung constants of ionic solids relate to their geometry and electrostatic interactions. Furthermore, because of issues in their evaluation, they are also of considerable mathematical interest. The corresponding Madelung (electrostatic, coulomb) energy is the principal contributor to the lattice energies of ionic systems, and these energies largely influence many of their physical properties. The Madelung constants are here defined and their properties considered. A difficulty with their application is that they may be defined relative to various lattice distances, and with various conventions for inclusion of the charges, leading to possible confusion in their use. Instead, the unambiguous Madelung energy, E(M), is to be preferred in chemistry. An extensive list of Madelung energies is presented. From this data set, it is observed that there is a strong linear correlation between the lattice energies of ionic solids, U(POT), and their Madelung energies: U(POT)/kJ mol(-1) = 0.8519E(M) + 293.9. This correlation establishes that the lattice energy, U(POT), for ionic solids is about 15% smaller than the attractive Madelung energy, the difference arising from the repulsions unaccounted for by the solely coulombic Madelung energy calculation. Correlations of U(POT) against E(M) for alkali metal hydrides and transition metal compounds, each having considerable covalency, show much reduced Madelung contributions to the lattice energy. These correlations permit ready estimation of lattice energies, and are the first to be based on actual data rather than a broad analysis. The independent volume-based thermodynamic (VBT) method, which relies on a separate correlation with the formula unit volume of the ionic material, complements these correlations.

Multichannel Interdiffusion Driven FASnI3 Film Formation Using Aqueous Hybrid Salt/Polymer Solutions toward Flexible Lead‐Free Perovskite Solar Cells

“…[12][13][14][15][16][17][18][19][20][21] The CH 3 NH 3 SnI 3 has been explored in the majority of devices, but there are several important issues: (1) Sn 2+ is easily oxidized to Sn 4+ ; [16,22] (2) Poor quality films tend to form because of rapid crystallization during spin-coating. [16,23] Some have reported more stable devices employing [(NH 2 ) 2 CH]SnI 3 (FASnI 3 ), which presumably results from the enhanced interaction between Sn 2+ and larger sized FA + , making FASnI 3 an attractive candidate. [19,20,24] Mesoporous titanium dioxide (TiO 2 ) scaffold layers have been used to demonstrate Sn-based perovskite solar cells.…”

Generalized Self‐Doping Engineering towards Ultrathin and Large‐Sized Two‐Dimensional Homologous Perovskites

“…[13] Particularly,c haracteristic peaks at low angle decrease consistently as transformation time increases,inaccordance with the XRD evolution of 2DH perovskite thin films with n increasing from 2t o8 .T hus we infer that the increase of transformation time would lead to increased n in 2DH perovskites.M oreover,w hen the transformation time is increased from 1to30min, the absorbance and emission at 407 nm corresponding to (BA) 2 PbBr 4 decrease significantly,a nd novel absorption and emission characteristics at longer wavelength ranging from 434 to 528 nm emerge (Supporting Information, Figure S1). [16] Herein, we suggest that the ability of MA + to mediate intercalation arises from the more stable 2DH structure and smaller steric hindrance than that of BA + .T he intercalation reaction enables the insertion of MA + in the voids between the corner-shared PbBr 6 octahedra. [15] Further increasing the transformation time up to 60 min, only absorption oremission at around 528 nm is retained, suggesting the formation of (BA) 2 (MA) nÀ1 Pb n Br 3n+1 with n!1.…”

Masthead - Full issue pdf

“…The predominant interactive force in ionic materials is the electrostatic (Coulombic or Madelung) interaction, [15] where the charges tend to group themselves so as to balance their overall charge locally, with repulsive van der Waals's forces acting over short distances preventing the collapse of the charge system. These repulsive forces are rather similar, even between diff erent species, and so refl ect volume changes rather similarly, leading to simple volume relationships.…”