Tracer diffusion coefficients D* of lithium ions in Li x Mn2O4 (0.2 < x < 1) thin films were measured as a function of the composition x by using secondary ion mass spectrometry. For this purpose, a new “step-isotope-exchange method” was developed to observe the time dependence of the 6Li isotope concentration ratio in the Li x Mn2O4 film which is in contact with a 6Li-enriched electrolyte to exchange Li+ ions. A steep decrease in D* depending on the Li composition was observed for Li x Mn2O4, with D* = 8 × 10–13 cm2 s–1 for x = 0.2 and decreasing to 1.5 × 10–17 cm2 s–1 for x = 1.0 (bulk diffusion coefficient, D b *). This behavior is well explained by a vacancy diffusion model for the α phase on Li x Mn2O4 (0.77 < x < 1.0). Chemical diffusion coefficients D̃ were also measured in the range of 0.2 < x < 1.0 by an electrochemical method, which was compared with the D* to evaluate the effect of thermodynamic factors. The thermodynamic factors and interactions between Li+ ions were found to strongly influence the chemical diffusion coefficient. The tracer diffusion measurements are important to understand the charge–discharge mechanism in the electrodes of lithium-ion batteries.

SUMMARYThe reference signals used in a multichannel system are usually strongly crosscorrelated. Preprocessing is normally added to reduce the crosscorrelation between the reference signals because this correlation makes estimating the adaptive filter coefficients difficult. However, this preprocessing is equivalent to warping the reference signals. The transmission of these warped reference signals to an unknown system hinders the essential system operation. On the other hand, it is necessary for uncorrelated components between the reference signals to exist when estimating the adaptive filter coefficients. Preprocessing that increases the ratio of these components is important in improving the convergence characteristics. In this paper, we propose an algorithm that does not transmit preprocessed reference signals to an unknown system, but only uses them to estimate the adaptive filter coefficients, and explain the design conditions needed to implement this algorithm. In other words, with the condition of not increasing the estimation errors, we derive the optimum values of the coefficients that reduce the correlation between the reference signals, which is a feature of this algorithm, and verify its effectiveness in simulations. By employing the proposed algorithm, improvements in the convergence characteristics can be designed without affecting the essential operation of the system.

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