Chemical Diffusion Coefficient of Lithium

Long-time polarization measurements with the electron-blocking cell provide the steady state voltage from which the ionic conductivity can be calculated. From the transient behavior also the diffusion coefficient is available based on the following equation  

A plot of ln(f/-f/oo) t should give a straight line, with the time constant as a slope. The calculation of yields the chemical diffusion coefficient of lithium  

The short-time behavior was also evaluated and showed consistent values. Since the ionic conductivity in LiFeP04 single crystals was found to be effectively two-dimensional in the b-c plane, a similar behavior for the diffusion coefficient was expected. The results are shown in Fig. 8.6. 

Indeed the transport parameters are almost the same along the b- and c-direction whereas a smaller value was found for the a-direction. Due to the long time needed to reach the steady state long-time polarization measurements were performed at higher temperatures. The extrapolated values for the diffusion coefficient at room temperature are cm /s for b- and c-direction and 

Prosini et al. who used the galvanostatic intermittent titration technique. The chemical diffusion of lithium is activated by ca. 0.7 eV along b- and c-axis and 0.95 eV along a-axis.  

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R P. Prosini, M. Lisi, D. Zanec, and M. PasqnaU [2002] Determination of the Chemical Diffusion Coefficient of Lithium in LiFeP04, Solid State Ionics 148, 45-51. 

K. Kanehori, F. Kirino, T. Kudo, and K. Miyauchi,/. Electrochem. Soc., 138, 2216 (1991). Chemical Diffusion Coefficient of Lithium in Titanium Disulfide Single-Crystals. 

Figure 8.6 Chemical diffusion coefficient of lithium along the three main crystallographic directions of nominally pure LiFeP04...

Prosini, P. R, Lisi, M., Zane, D. Pasquali, M. Determination of the chemical diffusion coefficient of lithium in LiFeP04. Soiid State Ionics, 148,45-51(2002). 

Fig. 9.5 Chemical diffusion coefficient of lithium in d-MoS2 as a function of lithium concentration. The diffusivity parameter is deduced from the potential step polarization method...

Finally, a brief overview was presented of important experimental approaches, including GITT, EMF-temperature measurement, EIS and PCT, for investigating lithium intercalation/deintercalation. In this way, it is possible to determine - on an experimental basis - thermodynamic properties such as electrode potential, chemical potential, enthalpy and entropy, as well as kinetic parameters such as the diffusion coefficients of lithium ion in the solid electrode. The PCT technique, when aided by computational methods, represents the most powerful tool for determining the kinetics of lithium intercalation/deintercalation when lithium transport cannot be simply explained based on a conventional, diffusion-controlled model. 

The chemical diffusion coefficient of the lithium ions, in a solid host lattice, is about 10 cm. s (mean value on different cathodic materials). 

The first example that was demonstrated was the use of the phase with the nominal composition LiisSns as the matrix, in conjxmction with reactant phases in the Hthium-silicon system at temperatures near 400 °C. This is an especially favorable case, due to the high chemical diffusion coefficient or lithium in the LisSns phase. 

It is thus much better to measure the chemical diffusion coefficient directly. Descriptions of electrochemical methods for doing this, as well as the relevant theoretical background, can be found in the literature [33, 34]. Available data on the chemical diffusion coefficient in a number of lithium alloys are included in Table 3. 

Figure 9.5 displays the chemical diffusion coefficient in d-Li MoS2 as a function of the degree of Li insertion. The apparent D in disordered M0S2 at room temperature has been calculated on the assumptirm of uniform Li" distribution at any composition in the solid solution electrode. We observe a continuous decrease of the value of D with the increase of lithium content. The high value 10 cm s of the LF diffusion coefficient at low lithium concentration 0 < ar < 0.2 may result from the smaller diffusion path length of the lithium ion in the disordered phase compared to that of crystalline sample. The variation in the diffusion coefficient can... 

Effect of increasing concentration for lithium lattice occupation on chemical (D) and jump (Dj) diffusion coefficient rates. (Source Bhattacharya, J. and A. Van der Ven. 2011. Physical Reviews B, 83,.l-9. With permission.)... 

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