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A nonlinear and nonadditive composition-dependent change of the ionic conductivity in mixed glass-former (MGF) glasses when one glass former, such as PS(5/2), is replaced by a second glass former, such as GeS2, at constant alkali modifier concentrations, such as Na2S, is known as the mixed glass-former effect (MGFE). Alkali ion conducting glasses are of particular interest for use as solid electrolytes in alkali-based all-solid-state batteries because sulfide amorphous materials have significantly higher alkali ion conductivities than their oxide glass counterparts. In this study of the ternary MGF system Na2S + GeS2 + PS(5/2), we report the careful structural characterization of these glasses using a combination of vibrational, infrared (IR), Raman, and nuclear magnetic resonance (NMR) spectroscopies. Our measurements of the 0.5Na2S + 0.5[xGeS2 + (1-x)PS(5/2)] MGF system show that this glass system exhibits a strongly negative MGFE and non-Arrhenius ionic conductivities. While this negative MGFE in the Na(+) ion conductivity makes these glasses less attractive for use in solid-state Na batteries, the structural origin of this effect is important to better understand the mechanisms of ion conduction in the glassy state. For these reasons, we have examined the structures of ternary 0.5Na2S + 0.5[xGeS2 + (1-x)PS(5/2)] glasses using Raman, IR, and (31)P MAS NMR spectroscopies. In these studies, it is found that the substitution of PS(5/2) by GeS2, that is, increasing x, leads to unequal sharing of the Na(+) in these glasses. Thus, in all MGF compositions, phosphorus groups are associated with a disproportionately larger fraction, f(Na(P)) > 0.5(1 - x), of the Na(+) ions while the germanium groups are found to be Na(+)-deficient relative to the total amount of Na(+) present in the glass, that is, f(Na(Ge)) < 0.5x. From the spectroscopic study of these glasses, a short-range order (SRO) structural model is developed for these glasses and is based on the germanium and phosphorus SRO groups in these glasses as a first step in understanding the unique negative MGFE and non-Arrhenius behavior in the Na(+) ion conductivity in these glasses.

Previously observed non-Arrhenius behavior in fast ion conducting glasses [Phys. Rev. Lett. 76, 70 (1996)] occurs at temperatures near the glass transition temperature, Tg, and is attributed to changes in the ion mobility due to ion trapping mechanisms that diminish the conductivity and result in a decreasing conductivity with increasing temperature. It is intuitive that disorder in glass will also result in a distribution of the activation energies (DAE) for ion conduction, which should increase the conductivity with increasing temperature, yet this has not been identified in the literature. In this paper, a series of high precision ionic conductivity measurements are reported for 0.5Na2S + 0.5] glasses with compositions ranging from 0 ≤ x ≤ 1. The impact of the cation site disorder on the activation energy is identified and explained using a DAE model. The absence of the non-Arrhenius behavior in other glasses is explained and it is predicted which glasses are expected to accentuate the DAE effect on the ionic conductivity.

A negative mixed glass former effect (MGFE) in the Na(+) ion conductivity of glass has been found in 0.5Na2S + 0.5[xGeS2 + (1 - x)PS5/2] glasses where the Na(+) ion conductivity is significantly smaller for all of the ternary glasses than either of the binary end-member glasses. The minimum conductivity of ∼0.4 × 10(-6) (Ω cm)(-1) at 25 °C occurs for the x = 0.7 glass. Prior to this observation, the alkali ion conductivity of sulfide glasses at constant alkali concentration, but variable ratio of one glass former for another (x) ternary mixed glass former (MGF) glasses, has always produced a positive MGFE in the alkali ion conductivity; that is, the ternary glasses have always had higher ion conductivities that either of the end-member binary glasses. While the Na(+) ion conductivity exhibits a single global minimum value, the conductivity activation energy exhibits a bimodal double maximum at x ≈ 0.4 and x ≈ 0.7. The modified Christensen-Martin-Anderson-Stuart (CMAS) model of the activation energies reveals the origin of the negative MGFE to be due to an increase in the dielectric stiffness (a decrease in relative dielectric permittivity) of these glasses. When coupled with an increase in the average Na(+) ion jump distance and a slight increase in the mechanical stiffness of the glass, this causes the activation energy to go through maximum values and thereby produce the negative MGFE. The double maximum in the conductivity activation energy is coincident with double maximums in CMAS calculated strain, ΔES, and Coulombic, ΔEC, activation energies. In these ternary glasses, the increase in the dielectric stiffness of the glass arises from a negative deviation of the limiting high frequency dielectric permittivity as compared to the binary end-member glasses. While the CMAS calculated total activation energies ΔEact = ΔES + ΔEC are found to reproduce the overall shape of the composition dependence of the measured ΔEact values, they are consistently smaller than the measured values for all compositions x. The new concept of an effective Madelung constant for the Na(+) ions in glass is introduced, MD(Na(+)), to account for the difference. Calculated MD(Na(+)) values necessary to bring the CMAS and experimental ΔEact values into agreement are in excellent agreement with nominal values for typical oxide crystals containing Na(+). New MD simulations of oxide glasses were performed and were used to calculate MD(Na(+)) values for Na2O + SiO2 glasses for the first time and were found to agree quite well with the values for the sulfide glasses studied here. Insights from the current study have been used to predict and design new MGF systems that may lead to a positive MGFE in the ionic conductivity.