journal article·2015Open access

A Unifying View of the Constant-Phase-Element and Its Role as an Aging Indicator for Li-Ion Batteries

Eduardo Cuervo-Reyes, Christian Philipp Scheller, Marcel Held, Urs Sennhauser

Abstract

Various materials display a constant phase impedance, Z ∝[ i ω] − u , over a wide frequency range. In this paper, we show that this behavior is a natural consequence of charge transport in the macroscopic limit, and that in contrast to the common belief, no assumptions on the "relaxation functions" are required. Our unifying view of the constant-phase-element (CPE) is then employed for analyzing impedance spectra that were recorded during the aging of Li x FePO 4 cells. We find and explain a significant correlation between their capacity loss and changes in the exponent ( u ) of the CPE describing cathodic Li-intercalation. Changes in u with the state of charge are also discussed. CPE exponents are shown to be valuable performance indicators for Li-ion batteries.
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Research context

OpenAlex topics: Advancements in Battery Materials · Advanced Battery Technologies Research · Advanced Battery Materials and Technologies

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References (43)

Show source-provided references
1. 10.1016/j.jpowsour.2005.01.00610.1016/j.jpowsour.2005.01.006 ↗
2. 10.1016/j.jpowsour.2007.03.07110.1016/j.jpowsour.2007.03.071 ↗
3. 10.1149/1.216246710.1149/1.2162467 ↗
4. 10.1149/1.210843010.1149/1.2108430 ↗
5. 10.1016/j.jpowsour.2010.09.12110.1016/j.jpowsour.2010.09.121 ↗
6. 10.1149/1.296422010.1149/1.2964220 ↗
7. 10.1149/2.029211jes10.1149/2.029211jes ↗
8. 10.1149/2.0061501eel10.1149/2.0061501eel ↗
9. 10.1149/2.053304jes10.1149/2.053304jes ↗
10. 10.1016/j.electacta.2005.02.02610.1016/j.electacta.2005.02.026 ↗
11. 10.1149/1.221356810.1149/1.2213568 ↗
12. 10.1088/0305-4470/30/21/00610.1088/0305-4470/30/21/006 ↗
13. 10.1016/j.cnsns.2006.07.00810.1016/j.cnsns.2006.07.008 ↗
14. 10.1016/j.cnsns.2011.03.02710.1016/j.cnsns.2011.03.027 ↗
15. Macdonald J. R. , Impedance Spectroscopy Theory, Experiment, and Applications (John Wiley & Sons, Inc., Hoboken, New Jersey, 2005), ISBN 0-471-64749-7.
16. 10.3390/en607357110.3390/en6073571 ↗
17. 10.1149/1.349956510.1149/1.3499565 ↗
18. 10.1016/S0022-0728(00)00497-610.1016/S0022-0728(00)00497-6 ↗
19. 10.1016/j.corsci.2006.06.02710.1016/j.corsci.2006.06.027 ↗
20. 10.1007/s10008-005-0084-910.1007/s10008-005-0084-9 ↗
21. 10.1021/jp712066k10.1021/jp712066k ↗
22. 10.1088/1751-8113/42/5/05500410.1088/1751-8113/42/5/055004 ↗
23. 10.1016/j.ssi.2009.04.00210.1016/j.ssi.2009.04.002 ↗
24. 10.1149/2.033306jes10.1149/2.033306jes ↗
25. From here on i = − 1 .
26. We follow the convention in the electrochemical society and use the term cathode for the positive (metal-oxide) electrode, despite the reversed role of anode and cathode during the battery charging process.
27. 10.1007/BF0101684310.1007/BF01016843 ↗
28. 10.1103/PhysRevB.12.245510.1103/PhysRevB.12.2455 ↗
29. 10.1080/0001873900010150110.1080/00018739000101501 ↗
30. 10.1142/p03610.1142/p036 ↗
31. Gnedenko B. V. Kolmogorov A. N. , Limit distributions for sums of independent random variables. (Addison-Wesley Mathematics Series. Addison-Wesley, Cambridge, MA, 1954), ISBN 0201024209.
32. Although the generalized central limit theorem is often phrased referring to the convergence of PDFs with power law tail toward stable PDFs, it actually implies the convergence of generic PDFs. By generic, one refers to most commonly found PDFs ψ(t), which are analytic functions of their variable t in the limit t → ∞. Therefore, a generic PDF admits a Taylor expansion around infinity, in powers of 1/t. From this point, there are two possibilities; either some coefficients of the expansion are non-zero, or all coefficients are zero. The first case results in a power-law asymptotic behavior. The second case implies that all moments are finite (and the more restricted central limit theorem applies).
33. 10.1103/PhysRevLett.75.358910.1103/PhysRevLett.75.3589 ↗
34. Since we defined p ( r , t ) as a probability density normalized to 1, j ( r , t) is a probability current. The conversion from p ( r , t ) to particle density n ( r , t ) (and also from probability current to current density) is simply a pre-factor equal to the number of particles N; e.g. n ( r , t ) = N p ( r , t ) .
35. Tikhonov A. N. Samarskiǐ A. A. , Equations of Mathematical Physics (Dover Publications, New York, NY, 1990), ISBN 0486664228.
36. 10.1088/0034-4885/29/1/30610.1088/0034-4885/29/1/306 ↗
37. AHR32113M1Ultra-B high power cylindrical cell, purchased from A123 systems: http://www.a123systems.com.
38. 10.1149/2.029305jes10.1149/2.029305jes ↗
39. 10.1016/j.jpowsour.2005.03.17210.1016/j.jpowsour.2005.03.172 ↗
40. 10.1149/1.304342910.1149/1.3043429 ↗
41. 10.1149/1.164460110.1149/1.1644601 ↗
42. 10.1016/S0378-7753(01)00588-210.1016/S0378-7753(01)00588-2 ↗
43. 10.1002/andp.1935416070510.1002/andp.19354160705 ↗