WIAS Preprint No. 1410, (2009)

Hysteresis in the context of hydrogen storage and lithium-ion batteries


  • Dreyer, Wolfgang
  • Guhlke, Clemens
  • Huth, Robert

2010 Mathematics Subject Classification

  • 74N30 74A15 74F25 74G65

2008 Physics and Astronomy Classification Scheme

  • 82.47.Aa 82.60.Hc 82.60.Qr


  • thermodynamics, phase transitions, hysteresis, chemical potentials, elasticity, hydrogen, lithium-ion batteries


The processes of reversible storage of hydrogen in a metal by loading and unloading and of charging and discharging of lithium-ion batteries have many things in common. The both processes are accompanied by a phase transition and loading and unloading run along different paths, so that hysteretic behavior is observed. For hydrogen storage we consider a fine powder of magnesium (Mg) particles and lithium storage is studied for iron phosphate (FePO$_4$) particles forming the cathode of a lithium-ion battery. The mathematical models that are established in citeDGJ08 and citeDGH09a, describe phase transitions and hysteresis exclusively in a single particle and on that basis they can predict the observed hysteretic plots with almost horizontal plateaus. Interestingly the models predict that the coexistence of a 2-phase system in an individual particle disappears, if its size is below a critical value. However, measurements reveal that this is qualitatively not reflected by the mentioned hysteretic plots of loading and unloading. In other words: The behavior of a storage system consisting of many particles is qualitatively independent of the fact whether the individual particles itself develop a 2-phase system or if they remain in a single phase state. This apparent paradoxical observation will be resolved in this article. It will be shown that if each of the individual particles homogeneously distributes the supplied matter, nevertheless the many particle ensemble exhibits phase transition and hysteresis, because one of the two phases is realized in some part of the particles while the remaining part is in the other phase.

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