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Author: Dreyer, Wolfgang × End date: 2019 × Start date: 2019 × Type: Text × Version: publishedVersion × Subject: hysteresis × Subject: thermodynamics × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Hysteresis and phase transition in many-particle storage systems
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Dreyer, Wolfgang; Guhlke, Clemens; Herrmann, Michael
    We study the behavior of systems consisting of ensembles of interconnected storage particles. Our examples concern the storage of lithium in many-particle electrodes of rechargeable lithium-ion batteries and the storage of air in a system of interconnected rubber balloons. We are particularly interested in those storage systems whose constituents exhibit non-monotone material behavior leading to transitions between two coexisting phases and to hysteresis. In the current study we consider the case that the time to approach equilibrium of a single storage particle is much smaller than the time for full charging of the ensemble. In this regime the evolution of the probability to find a particle of the ensemble in a certain state, may be described by a nonlocal conservation law of Fokker-Planck type. Two constant parameter control whether the ensemble transits the 2-phase region along a Maxwell line or along a hysteresis path or if the ensemble shows the same non-monotone behavior as its constituents.
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    The behavior of a many particle cathode in a lithium-ion battery
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Dreyer, Wolfgang; Guhlke, Clemens; Huth, Robert
    We study the almost reversible storage process of charging and discharging of lithium-ion batteries. That process is accompanied by a phase transition and charging and discharging run along different paths, so that hysteretic behavior is observed. We are interested in the storage problem of the cathode of a lithium-ion battery consisting of a system of many iron phosphate (FePO4) particles. There are mathematical models, see [DGJ08], [DGGHJ09] and [DG09], that describe phase transitions and hysteresis exclusively in a single storage particle and they can describe the observed hysteretic voltage-charge 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. The disappearance of the phase transition in the single particle model implies the disappearance of the hysteresis. However, in the experiment hysteretic behavior survives. 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 by a many particle model. It will be shown that if each of the individual particles is in a homogeneous state, nevertheless the many particle ensemble exhibits phase transition and hysteresis ...
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    Phase transition and hysteresis in a rechargeable lithium battery revisited
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2009) Dreyer, Wolfgang; Gaberscek, Miran; Guhlke, Clemens; Huth, Robert; Jamnik, Janko
    We revisit a model which describes the evolution of a phase transition that occurs in the cathode of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate hysteretic behavior of the voltage
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    Phase transition and hysteresis in a rechargeable lithium battery
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Dreyer, Wolfgang; Gaberšček, Miran; Jamnik, Janko
    We represent a model which describes the evolution of a phase transition that occurs in some part of a rechargeable lithium battery during the process of charging/discharging. The model is capable to simulate the hysteretic behavior of the voltage - charge characteristics. During discharging of the battery, the interstitial lattice sites of a small crystalline host system are filled up with lithium atoms and these are released again during charging. We show within the context of a sharp interface model that two mechanical phenomena go along with a phase transition that appears in the host system during supply and removal of lithium. At first the lithium atoms need more space than it is available by the interstitial lattice sites, which leads to a maximal relative change of the crystal volume of about $6%$. Furthermore there is an interface between two adjacent phases that has very large curvature of the order of magnitude 100 m, which evoke here a discontinuity of the normal component of the stress. In order to simulate the dynamics of the phase transitions and in particular the observed hysteresis we establish a new initial and boundary value problem for a nonlinear PDE system that can be reduced in some limiting case to an ODE system.