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Subject: phase transitions ×

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Now showing 1 - 10 of 28
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    Simulation der Strahlhärtung von Stahl mit WIAS-SHarP
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2002) Buchwalder, A.; Hömberg, D.; Jurke, Th.; Spies, H.-J.; Weiss, W.
    Die Software WIAS-SHarP zur Simulation der Oberflaechenhaertung von Stahl mit Laser- und Elektronenstrahl wurde im Rahmen eines zweijaehrigen interdisziplinaeren Forschungsprojektes entwickelt. Das zugrunde liegende mathematische Modell besteht aus einem System gewoehnlicher Differentialgleichungen zur Beschreibung der Gefuegeumwandlungen, gekoppelt mit einer nichtlinearen Waermeleitungsgleichung sowie Komponenten zur Beschreibung der Energieeinkopplung. Um eine moeglichst breite Anwendbarkeit der Software zu gewaehrleisten, wurden werkstoffspezifische Kennwerte zum Umwandlungsverhalten fuer eine grosse Anzahl praxisrelevanter Staehle bereitgestellt. Zur Modellverifikation wurden experimentelle Untersuchungen bei beteiligten Industriepartnern durchgefuehrt und mit den entsprechenden Simulationsrechnungen verglichen.
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    Stochastic model for LFP-electrodes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Dreyer, Wolfgang; Friz, Peter K.; Gajewski, Paul; Guhlke, Clemens; Maurelli, Mario
    In the framework of non-equilibrium thermodynamics we derive a new model for porous electrodes. The model is applied to LiFePO4 (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by surface fluctuations leading to a system of stochastic differential equations. The model is capable to derive an explicit relation between battery voltage and current that is controlled by thermodynamic state variables. This voltage-current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltagecharge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.
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    Dynamical phase transitions for flows on finite graphs
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Gabrielli, Davide; Renger, D. R. Michiel
    We study the time-averaged flow in a model of particles that randomly hop on a finite directed graph. In the limit as the number of particles and the time window go to infinity but the graph remains finite, the large-deviation rate functional of the average flow is given by a variational formulation involving paths of the density and flow. We give sufficient conditions under which the large deviations of a given time averaged flow is determined by paths that are constant in time. We then consider a class of models on a discrete ring for which it is possible to show that a better strategy is obtained producing a time-dependent path. This phenomenon, called a dynamical phase transition, is known to occur for some particle systems in the hydrodynamic scaling limit, which is thus extended to the setting of a finite graph.
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    On a thermomechanical model of phase transitions in steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2007) Chełminski, Krzysztof; Hömberg, Dietmar; Kern, Daniela
    We investigate a thermomechanical model of phase transitions in steel. The strain is assumed to be additively decomposed into an elastic and a thermal part as well as a contribution from transformation induced plasticity. The resulting model can be viewed as an extension of quasistatic linear thermoelasticity. We prove existence of a unique solution and conclude with some numerical simulations.
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    A revisited Johnson-Mehl-Avrami-Kolmogorov model and the evolution of grain-size distributions in steel
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2016) Hömberg, Dietmar; Patacchini, Francesco Saverio; Sakamoto, Kenichi; Zimmer, Johannes
    The classical Johnson-Mehl-Avrami-Kolmogorov approach for nucleation and growth models of diffusive phase transitions is revisited and applied to model the growth of ferrite in multiphase steels. For the prediction of mechanical properties of such steels, a deeper knowledge of the grain structure is essential. To this end, a Fokker-Planck evolution law for the volume distribution of ferrite grains is developed and shown to exhibit a log-normally distributed solution. Numerical parameter studies are given and confirm expected properties qualitatively. As a preparation for future work on parameter identification, a strategy is presented for the comparison of volume distributions with area distributions experimentally gained from polished micrograph sections.
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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.
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    Electrical and optical properties of epitaxial binary and ternary GeTe-Sb2Te3 alloys
    (London : Nature Publishing, 2018) Boschker, Jos E.; Lü, Xiang; Bragaglia, Valeria; Wang,Ruining; Grahn, Holger T.; Calarco, Raffaella
    Phase change materials such as pseudobinary GeTe-Sb2Te3 (GST) alloys are an essential part of existing and emerging technologies. Here, we investigate the electrical and optical properties of epitaxial phase change materials: α-GeTe, Ge2Sb2Te5 (GST225), and Sb2Te3. Temperature-dependent Hall measurements reveal a reduction of the hole concentration with increasing temperature in Sb2Te3 that is attributed to lattice expansion, resulting in a non-linear increase of the resistivity that is also observed in GST225. Fourier transform infrared spectroscopy at room temperature demonstrates the presence of electronic states within the energy gap for α-GeTe and GST225. We conclude that these electronic states are due to vacancy clusters inside these two materials. The obtained results shed new light on the fundamental properties of phase change materials such as the high dielectric constant and persistent photoconductivity and have the potential to be included in device simulations.
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    Sub-nanometre resolution of atomic motion during electronic excitation in phase-change materials
    (London : Nature Publishing, 2016) Mitrofanov, Kirill V.; Fons, Paul; Makino, Kotaro; Terashima, Ryo; Shimada, Toru; Kolobov, Alexander, V.; Tominaga, Junji; Bragaglia, Valeria; Giussani, Alessandro; Calarco, Raffaella; Riechert, Henning; Sato, Takahiro; Katayama, Tetsuo; Ogawa, Kanade; Togashi, Tadashi; Yabashi, Makina; Wall, Simon; Brewe, Dale; Hase, Muneaki
    Phase-change materials based on Ge-Sb-Te alloys are widely used in industrial applications such as nonvolatile memories, but reaction pathways for crystalline-to-amorphous phase-change on picosecond timescales remain unknown. Femtosecond laser excitation and an ultrashort x-ray probe is used to show the temporal separation of electronic and thermal effects in a long-lived (>100 ps) transient metastable state of Ge2Sb2Te5 with muted interatomic interaction induced by a weakening of resonant bonding. Due to a specific electronic state, the lattice undergoes a reversible nondestructive modification over a nanoscale region, remaining cold for 4 ps. An independent time-resolved x-ray absorption fine structure experiment confirms the existence of an intermediate state with disordered bonds. This newly unveiled effect allows the utilization of non-thermal ultra-fast pathways enabling artificial manipulation of the switching process, ultimately leading to a redefined speed limit and improved energy efficiency and reliability of phase-change memory technologies.
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    Mayer and virial series at low temperature
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Jansen, Sabine
    We analyze the Mayer pressure-activity and virial pressure-density series for a classical system of particles in continuous configuration space at low temperature. Particles interact via a finite range potential with an attractive tail. We propose physical interpretations of the Mayer and virial series' radius of convergence, valid independently of the question of phase transition: the Mayer radius corresponds to a fast increase from very small to finite density, and the virial radius corresponds to a cross-over from monatomic to polyatomic gas. Our results have consequences for the search of a low density, low temperature solid-gas phase transition, consistent with the Lee-Yang theorem for lattice gases and with the continuum Widom-Rowlinson mode.