Madelung−Buckingham Model as Applied to the Prediction of Voltage, Crystal Volume Changes, and Ordering Phenomena in Spinel-Type Cathodes for Lithium Batteries

Abstract

Using a Madelung-Buckingham model, we study Li(x)()Mn(2)O(4) and its fluorine-substituted analogue to compute their voltages, lattice volume changes, and ordering phenomena during charge/discharge. The interactions included are the long-range Coulombic, short-range electron-electron repulsion, and the van der Waals. The voltage of the fluorine-substituted spinel is found to be slightly less than that of the unsubstituted. However, the former undergoes a greater crystal volume change than the latter during intercalation and de-intercalation. Investigations of lithium sublattice ordering in this system indicates that during intercalation lithium starts filling exclusively into one sublattice until x = 0.5, and only from x = 0.5 the other sublattice is filled up to x = 1. The models are compared with quantum ab initio and experimental results.

Space-Charge Layers in All-Solid-State Batteries; Important or Negligible?

“…For LCO and LLZO, the formation enthalpy is used as an approximation to the Madelung energy, which appears to be a reasonable approximation since the Madelung energy is the largest contributor to the formation enthalpy in ionic crystals. 43 , 64 In the case of LATP, the Madelung energy and the formation enthalpy are unavailable, and therefore, the formation enthalpy of LLZO was used as an approximation, making it possible to compare the effects of the other material properties of the two solid electrolytes.…”

“…Unfortunately, for many materials, the Madelung constants and energies are not reported in the literature. However, it has been shown that the Madelung constant of a material is closely related to its voltage. , Therefore, the Madelung constants are replaced by the voltages of the material phases, which are filled with ions ( V f ) and emptied of ions ( V e ). The interaction energy between defects is then obtained using where E M is the Madelung energy per Li-equivalent of the structure and ε is the relative permittivity of the material.…”

Soft tilt and rotational modes in the hybrid improper ferroelectric Ca3Mn2O7

“…where A ij and ρ ij denote the strength and the range of the repulsive interaction, respectively, and C ij describes an attractive part with the interatomic distance r. With a well-documented set of data, the shell-model parameters are optimized to reach reasonable agreement with experimental Raman data 18,19 . The resulting shell-model parameters are summarized in Table I.…”

Synthesis Methods and Electrochemical Performance: A Theory on the Valence Disproportionation in LiMyMn2–yO4 (M = Mn, Co) with Interalia Guiding Principles for a Photo-Chargeable Lithium Battery

“…These attributes determine the electrostatic interactions which manifest as the electrochemical properties (OCV, diffusion pathways, diffusion coefficient, electrochemical capacity, etc.). The impact of mixed valency states and atomic coordinates on the electrochemical properties of LiMn 2 O 4−δ Y δ is dealt with in our earlier papers. , The structural phase transitions could initially lead to a slight change in the atomic coordinates of the parent cathode material but could finally cause a collapse in the electrochemical activity. This can be considered quite analogous to a hypothetical collapse of the solar system attributable to a slight displacement in the position of a planet in its orbit.…”

“…Unlike Li x CoO 2 , Li x Mn 2 O 4 does not suffer from Li intercalation, deintercalation problems. Thus, while x in Li x CoO 2 can only vary from 1 to 0.5 due to structural stability issues, x in Li x Mn 2 O 4 can vary through the entire range from 1 to 0. , Assuming an ideal diffusion pathway for lithium in Li x Mn 2 O 4 , this material can serve as a prototype for investigations on valence disproportionation models.…”