Empirical Electronic Polarizabilities: Deviations from the Additivity Rule. II. Structures Exhibiting Ion Conductivity

Abstract

Ion conductivity in minerals and compounds is associated with continuous migration paths and leads to negative total electronic polarizability deviations [ = (α obs −α calc )/α obs )] up to 13%. Such deviations can be related to continuous migration paths determined in an earlier Voronoi-Dirichlet Partition (VDP) analysis of fast-ion conductors, that is, compounds such as LiB 3 O 5 with 1D conductivity, Li 4 SiO 4 with 2D conductivity, and Li 2 SO 4 with 3D conductivity. Using the Voronoi-Dirichlet (VD) method in this study, the migration paths and the dimensionality of many more compounds with negative polarizability deviations are identified. Continuous migration paths are found for the confirmed Li-ion conductors LiFePO 4 and Li 3 VO 4 and for the potential Li-ion conductors LiGeBO 4 , CsLiB 6 O 10 , Li 2 Ti 3 O 7 , LiMn 0.8 Fe 0.17 PO 4 , Li 2 NaPO 4 , and LiNaSO 4 . Similarly, continuous migration paths are found for the confirmed

Refractive index and lattice parameter prediction for garnets (A3B2C3X12)

“…Garnet refractive index ( n ) at 589 nm was calculated by methods developed by Shannon and coworkers: 72–74,93 $$$$\begin{equation}{{\bm{n}}}^2 = \frac{{4\pi {{\bm{\alpha }}}_{\bm{T}}}}{{\left( {{\bm{c}} - \frac{{4\pi }}{3}} \right){{\bm{\alpha }}}_{\bm{T}} + {V}_m}} + 1\end{equation}$$$$ $$$$\begin{equation}{{\rm{V}}}_{\rm{m}} = {{\bm{a}}}^3/{\rm{Z}}.\end{equation}$$$$ V m is the molecular volume in Å 3 . Z is the number of formula units per unit cell, which for garnets is 8. α T , the total polarizability (Å 3 ), is: $$$$\begin{equation}{{\bm{\alpha }}}_T = \sum\nolimits_{{\rm{i }} = {\rm{ }}1}^{\rm{N}} {{m}_i{{\bm{\alpha }}}_{ei}} .\end{equation}$$$$…”

“…A complete list of α ei used for calculations is in Table 1. Detailed discussion of α ei for most cations is available in the literature 72–74,93 …”

“…Detailed discussion of α ei for most cations is available in the literature. [72][73][74]93 c is a constant called the electron overlap factor, with a maximum of 4π/3 for strong electron overlap, referred to as the Drude equation, and a minimum of 0 for no electron overlap, referred to as the Lorentz-Lorentz equation. 72 Values of c ranging from 3.69 to 2.19 have been determined for various oxides.…”

Empirical electronic polarizabilities for use in refractive index measurements at 589.3 nm: Hydroxyl polarizabilities

“…The calculated mean values of <α AE > for 54 common minerals and 650 minerals and synthetic compounds differ by less than 3% from the observed values. Using dynamic polarizabilities, we observed systematic deviations in: (1) M 2+ SO 4 •nH 2 O, blödite (Na 2 M 2+ (SO 4 ) 2 •4H 2 O), and kieserite-related minerals (Gagné et al 2018), (2) fast-ion conductors (Shannon et al, 2019), (3) crystal structures containing corner-shared octahedra such as MTiO 3 (M = Ca, Sr, Ba), KNbO 3 , KTaO 3 , Ba .25 Sr .75 Nb 2 O 6 and KTiOPO 4 , and (4) crystal structures containing edge-shared Fe 3+ , Mn 3+ , Ti 4+ , Mo 6+ , and W 6+ octahedra such as MnWO 4 (hübnerite) (Shannon and Fischer, 2016).…”

P3‐Na0.45Ni0.2Mn0.8O2/Na2SeO4 Heterostructure Enabling Long‐Life and High‐Rate Sodium‐Ion Batteries

“…In virtue of strong interactions of heterointerface between NMNO and NSO and the invoking of the built-in electric field in heterointerface, this novel heterostructure NMNO/NSO achieves a synergy function in enhancing structural stability and boosting Na + diffusion and charge transfer kinetics, resulting in a significant enhancement in cycling stability and rate capability. NSO is a potential Na + 2D conductor along the (010) plane according to previously calculated [31] and shows a stable structure. It can be easily in situ grown during NMNO synthesis to form a novel heterostructure NMNO/NSO.…”