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Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

ABSTRACT: Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion coefficient and ionic conductivity deviate from the random walk case, with this deviation quantified by single-particle and collective correlation factors, f and fI, respectively. These factors vary between materials, and depend on the concentration of mobile particles, the nature of the interactions, and the host lattice geometry. Here, we study these correlation effects for the garnet lattice using lattice-gas Monte Carlo simulations. We find that, for non-interacting particles (volume exclusion only), single-particle correlation effects are more significant than for any previously studied three-dimensional lattice. This is attributed to the presence of two-coordinate lattice sites, which causes correlation effects intermediate between typical three-dimensional and one-dimensional lattices. Including nearest-neighbour repulsion and on-site energies produces more complex single-particle correlations and introduces collective correlations. We predict particularly strong correlation effects at xLi=3 (from site energies) and xLi=6 (from nearest-neighbour repulsion), where xLi=9 corresponds to a fully occupied lithium sublattice. Both effects are consequences of ordering of the mobile particles. Using these simulation data, we consider tuning the mobile-ion stoichiometry to maximize the ionic conductivity, and show that the 'optimal' composition is highly sensitive to the precise nature and strength of the microscopic interactions. Finally, we discuss the practical implications of these results in the context of lithium garnets and other solid electrolytes.

SUBMITTER: Morgan BJ

PROVIDER: S-EPMC5717647 | biostudies-literature | 2017 Nov

REPOSITORIES: biostudies-literature

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Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

Morgan Benjamin J BJ

Royal Society open science 20171101 11

Ionic transport in solid electrolytes can often be approximated as ions performing a sequence of hops between distinct lattice sites. If these hops are uncorrelated, quantitative relationships can be derived that connect microscopic hopping rates to macroscopic transport coefficients; i.e. tracer diffusion coefficients and ionic conductivities. In real materials, hops are uncorrelated only in the dilute limit. At non-dilute concentrations, the relationships between hopping frequency, diffusion c ...[more]

PMID: 29291073

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Project description:Traditional multiple-group confirmatory factor analysis (multiple-group CFA) is usually criticized for having too restrictive model assumption, namely the scalar measurement invariance. The new multiple-group analysis methodology, alignment, has become an effective alternative. The alignment evaluates measurement invariance and more importantly, permits factor mean comparisons without requiring scalar invariance which is usually required in traditional multiple-group CFA. Some simulation studies and empirical studies have investigated the applicability of alignment under different conditions, but some areas remain unexplored. Based on the simulation studies of Asparouhov and Muthén and of Flake and McCoach, this current simulation study is broken into two sections. The first study investigates the minimal group sizes required for alignment in three-factor models. The second study compares the performance of multiple-group CFA, multiple-group exploratory structural equation model (multiple-group ESEM), and alignment by including different proportions and magnitudes of cross-loadings in the models. Study 1 shows that when the model has no noninvariant parameters, the alignment requires relatively lower group sizes. Explicitly, the minimal group size required for alignment was 250 when the amount of groups was three, the minimal group size was 150 when the amount of groups was nine, and 200 when the amount of groups was 15. When there are noninvariant parameters in the model and the amount of groups is low, a group size of 350 is a safe rule of thumb. When there are noninvariant parameters in the model and the amount of groups is high, a group size of 250 is required for trustworthy results. The magnitude of noninvariance and the noninvariance rate do not affect the minimal group size required for alignment. Study 2 shows that multiple-group CFA provides accurate factor mean estimates when each factor had 20% factor loading (1 factor loading) with small-sized cross-loading. Multiple-group ESEM provides accurate factor mean estimates when the magnitude of cross-loading is small or when each factor had 20% factor loading (1 factor loading) with medium-sized cross-loading. Alignment provides accurate factor mean estimates when there are only small-sized cross-loadings in the model. The parameter estimates, coverage rates and ratios of average standard error to standard deviation for each methodology are not influenced by the amount of groups. Recommendations are concluded for using multiple-group CFA, multiple-group ESEM, traditional alignment and aligned ESEM (AESEM) based on the results. Multiple-group CFA is more suitable for use when scalar invariance is established. Multiple-group ESEM works best when there are small-sized or only a few medium-sized cross-loadings in the model. Traditional alignment allows for small-sized cross-loadings and a few noninvariant parameters in the model. AESEM integrates the advantages of alignment and ESEM, can provide accurate estimates when noninvariant parameters and cross-loadings both exist in the model. Compared to multiple-group CFA, multiple-group ESEM, the alignment methodology performs well in more situations.

Dataset Information

Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

Publications

Lattice-geometry effects in garnet solid electrolytes: a lattice-gas Monte Carlo simulation study.

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