اثر جدایش فازی بر تنش‌های ناشی از نفوذ در ذرات کروی و استوانه‌ای الکترودها
نویسندگان
گروه مهندسی عمران، دانشکده مهندسی عمران و حمل و نقل، دانشگاه اصفهان
چکیده
آزمایش‌های بسیاری نشان داده‌اند جدایش فازی در الکترودها می‌تواند منجر به بروز خرابی‌های مکانیکی و درنتیجه کاهش عمر عملکردی باتری‌های لیتیومی شود. در این تحقیق، به‌کمک یک مدل میدان فازی، به مطالعه اثر پدیده جدایش فازی بر فرایندهای نفوذ یونی، شامل شارژ و دشارژ در ذرات کروی و استوانه‌ای شکل الکترودها پرداخته می‌شود. به این منظور، ابتدا معادلات حاکم بر مسئله استخراج، و پس از گسسته‌سازی به‌کمک روش تفاضل محدود مرکزی، میدان غلظت و سپس میدان تنش از حل عددی معادلات جبری حاصل به‌روش نیوتن- رفسون تعیین می‌شوند. نتایج به‌دست آمده با نتایج تحلیلی حاصل از مدل هسته- پوسته نیز مقایسه و صحت‌سنجی می‌شود. نتایج نشان می‌دهد در محدوده پارامترهای مورد مطالعه، جدایش فازی می‌تواند منجر به افزایش بیش از پنج برابری تنش‌های کششی در سطح ذرات الکترود شود
کلیدواژه‌ها
عنوان مقاله [English]
The Effect of Phase Separation on Diffusion Induced Stresses in Spherical and Cylindrical Electrode Particles
نویسندگان [English]
- S. Esmizade
- H. Haftbaradaran
- F. Mossaiby
Experiments have frequently shown that phase separation in lithium-battery electrodes could lead to mechanical failure, poor cycling performance, and reduced capacity. Here, a phase-field model is utilized to investigate how phase separation affects the evolution of the concentration and stress profiles within the spherical/cylindrical electrode particles, during both insertion and extraction half-cycles. To this end, the governing equations are derived and then discretized using the central finite difference method. The resulting algebraic equations are solved numerically with the aid of the Newton-Raphson method to determine both the concentration and stress fields in the electrode particles. For further verification, the results are compared against predictions of an analytical core-shell model. The results suggest that, within the range of parameters considered here, phase separation could lead to a more than five-fold increase in the maximum tensile stress at the particles surface.
کلیدواژه‌ها [English]
- Lithium-ion batteries
- Phase separation
- Phase-field model
- Diffusion-induced stress
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3. Winter, M., Besenhard, J. O., Spahr, M. E., and Novak, P., “Insertion Electrode Materials for Rechargeable Lithium Batteries”, Advanced Materials, Vol. 10, pp. 725-763, 1998.
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5. Go, J. -Y., and Pyun, S. -I., “Investigation of Stresses Generated During Lithium Transport Through the RF Sputter-Deposited Li1- δ CoO2 Film by a DQCR Technique”, Journal of the Electrochemical Society, Vol. 150, No. 8, pp. A1037-A1043, 2003.
6. Wang, D., Wu, X., Wang, Z., and Chen, L., “Cracking Causing Cyclic Instability of LiFePO4 Cathode Material”, Journal of Power Sources, Vol. 140, No. 1, pp. 125-128, 2005.
7. Arora, P., White, R. E., and Doyle, M., “Capacity Fade Mechanisms and Side Reactions in Lithium‐ion Batteries”, Journal of the Electrochemical Society, Vol. 145, No. 10, pp. 3647-3667, 1998.
8. Cheng, Y. -T., and Verbrugge, M. W., “Diffusion-induced Stress, Interfacial Charge Transfer, and Criteria for Avoiding Crack Initiation of Electrode Particles”, Journal of the Electrochemical Society, Vol. 157, No. 4, pp. A508-A516, 2010.
9. Zhao, K., Pharr, M., Vlassak, J. J., and Suo, Z., “Fracture of Electrodes in Lithium-ion Batteries Caused by Fast Charging”, Journal of Applied Physics, Vol. 108, No. 7, p. 073517, 2010.
10. Gabrisch, H., Wilcox, J., and Doeff, M., “TEM Study of Fracturing in Spherical and Plate-like LiFePO4 Particles”, Electrochemical and Solid-State Letters, Vol. 11, No. 3, pp. A25-A29, 2008.
11. Xia, Y., and Yoshio, M., “An Investigation of Lithium Ion Insertion into Spinel Structure Li‐Mn‐O Compounds”, Journal of the Electrochemical Society, Vol. 143, No. 3, pp. 825-833, 1996.
12. Sun, C. -F., Karki, K., Jia, Z., Liao, H., Zhang, Y., Li, T., Qi, Y., Cumings, J., Rubloff, G. W., and Wang, Y., “A Beaded-string Silicon Anode”, Acs Nano, Vol. 7, No. 3, pp. 2717-2724, 2013.
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20. Hao, F., and Fang, D., “Reducing Diffusion-induced Stresses of Electrode-Collector Bilayer in Lithium-ion Battery by Pre-strain”, Journal of Power Sources, Vol. 242, pp. 415-420, 2013.
21. Cheng, Y. -T., and Verbrugge, M. W., “Evolution of Stress Within a Spherical Insertion Electrode Particle under Potentiostatic and Galvanostatic Operation”, Journal of Power Sources, Vol. 190, No. 2, pp. 453-460, 2009.
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23. Deshpande, R., Cheng, Y. -T., and Verbrugge, M. W., “Modeling Diffusion-induced Stress in Nanowire Electrode Structures”, Journal of Power Sources, Vol. 195, No. 15, pp. 5081-5088, 2010.
24. Zhang, X., Shyy, W., and Sastry, A. M., “Numerical Simulation of Intercalation-induced Stress in Li-ion Battery Electrode Particles”, Journal of the Electrochemical Society, Vol. 154, No. 10, pp. A910-A916, 2007.
25. Deshpande, R., Cheng, Y.-T., Verbrugge, M. W., and Timmons, A., “Diffusion Induced Stresses and Strain Energy in a Phase-transforming Spherical Electrode Particle”, Journal of The Electrochemical Society, Vol. 158, No. 6, pp. A718-A724, 2011.
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28. Cahn, J. W., and Hilliard, J. E., “Free Energy of a Nonuniform System. I. Interfacial Free Energy”, The Journal of Chemical Physics, Vol. 28, No. 2, pp. 258-267, 1958.
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31. Haftbaradaran, H., Maddahian, A., and Mossaiby, F., “A Fracture Mechanics Study of the Phase Separating Planar Electrodes: Phase Field Modeling and Analytical Results”, Journal of Power Sources, Vol. 350, pp. 127-139, 2017.
32. Crank, J., The Mathematics of Diffusion, Oxford University Press, 1979.
33. Levi, M., and Aurbach, D., “Frumkin Intercalation Isotherm-a Tool for the Description of Lithium Insertion Into Host Materials: A Review”, Electrochimica Acta, Vol. 45, No. 1, pp. 167-185, 1999.
34. Burch, D., and Bazant, M. Z., “Size-dependent Spinodal and Miscibility Gaps for Intercalation in Nanoparticles”, Nano Letters, Vol. 9, No. 11, pp. 3795-3800, 2009.
35. Burch, D., “Intercalation Dynamics in Lithium-ion Batteries”, Ph.D. Desertation Massachusetts Inst of Tech Cambridge Dept of Mathematics, 2009.
36. Doyle, M., Fuller, T. F., and Newman, J., “Modeling of Galvanostatic Charge and Discharge of the Lithium/polymer/insertion Cell”, Journal of the Electrochemical Society, Vol. 140, No. 6, pp. 1526-1533, 1993.
37. Bazant, M. Z., “Theory of Chemical Kinetics and Charge Transfer Based on Nonequilibrium Thermodynamics”, Accounts of Chemical Research, Vol. 46, No. 5, pp. 1144-1160, 2013.
38. Timoshenko, S., and Goodier, J., Theory of Elasticity, McGraw-Hill book Company, 1951.
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