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Subject: nucleation and growth ×

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    The metal-insulator transition in disordered solids: How theoretical prejudices influence its characterization A critical review of analyses of experimental data
    (London : Taylor and Francis, 2019) Möbius, Arnulf
    In a recent experimental study, Siegrist et al. [Nature Materials 10, 202–208 (2011)] investigated the metal-insulator transition (MIT) induced by annealing in GeSb 2 Te 4 . The authors concluded that this phase-change material exhibits a discontinuous MIT with finite minimum metallic conductivity. The striking contrast between their work and reports on many other disordered substances from the last decades motivates the present in-depth study of the influence of the MIT criterion used on the character of the MIT derived. First, we discuss in detail the inherent biases of various approaches to locating the MIT. Second, reanalyzing GeSb 2 Te 4 data, we show that this material resembles other disordered solids to a large extent: according to a widely-used approach, its temperature dependences of the conductivity, σ(T), may likewise be interpreted in terms of a continuous MIT. Third, examining previous experimental studies of crystalline Si:As, Si:P, Si:B, Ge:Ga, CdSe:In, n-Cd 0:95 Mn 0:05 Se, Cd 0:95 Mn 0:05 Te 0:97 Se 0:03 :In, disordered Gd, and nanogranular Pt-C, we detect substantial problems in the interpretations of σ(T) in numerous studies which claim the MIT to be continuous: Evaluating the logarithmic derivative d ln σ/d ln T highlights serious inconsistencies. In part, they are common to all such studies and seem to be generic, in part, they vary from experiment to experiment. Fourth, for four qualitatively different phenomenological models of the temperature and control parameter dependence of the conductivity, we present the respective flow diagrams of d ln σ/d ln T. In consequence, the likely generic inconsistencies seem to originate from the MIT being discontinuous, in contradiction to most of the original interpretations. Because of the large number and diversity of the experiments considered, these inconsistencies provide overwhelming evidence against the common, localization theory motivated interpretations. The primary challenges now lie in improving measurement precision and accuracy, rather than in extending the temperature range, and in developing a microscopic theory which explains the seemingly generic features of d ln σ/d ln T. © 2018, © 2018 The Author(s). Published with license by Taylor & Francis. © 2018, © Arnulf Möbius.
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    Parameter identification in non-isothermal nucleation and growth processes
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Hömberg, Dietmar; Lu, Shuai; Sakamoto, Kenichi; Yamamoto, Masahiro
    We study non-isothermal nucleation and growth phase transformations, which are described by a generalized Avrami model for the phase transition coupled with an energy balance to account for recalescence effects. The main novelty of our work is the identification of temperature dependent nucleation rates. We prove that such rates can be uniquely identified from measurements in a subdomain and apply an optimal control approach to develop a numerical strategy for its computation.
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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.