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Stutensee, Germany

Vollath D.,NanoConsulting | Fischer F.D.,University of Leoben
Progress in Materials Science | Year: 2011

Based on the definition of fluctuation in connection to phase transformations, structural fluctuations are spontaneous transitions from an equilibrium phase to a non-equilibrium phase, followed by a back-transformation into the equilibrium phase, criteria for the fluctuation of isolated single particles and ensembles of nanoparticles are developed. It is important to realize that, in case of ensembles, the probability for fluctuation depends on the number of transformed particles. Especially the latter criteria are deduced from a statistical model describing fluctuation processes. Furthermore, this statistical model leads to the conclusion that the equilibrium state of fluctuation processes is characterized by a minimum of the free enthalpy. Interestingly, this equilibrium state is independent of the character of the nanoparticles either being conventional particles or ones characterized by indistinguishability. A detailed thermodynamic analysis, studying isothermal and adiabatic processes, of the behavior of a single isolated particle and an ensemble under isothermal and adiabatic conditions allows formulating a set of seven theorems. In the adiabatic case, the calculations indicate the existence of bistability or hysteresis in the temperature range of transformation. Experimentally, these phenomena are well documented, however, in most cases, attributed to activation phenomena. As a result of this study, at least connected to nanoparticles, the interpretation of these experiments needs thorough examination. Furthermore, a complete or partial adiabatic enclosure of the specimen, which is in experimental reality unavoidable, causes a shift of the transformation temperatures. This result enforces a new view on phase diagrams, especially on those for nanoparticles. © 2011 Elsevier Ltd. All rights reserved. Source

Vollath D.,NanoConsulting | Fischer F.D.,University of Leoben
Journal of Nanoparticle Research | Year: 2010

A thermodynamic analysis of phase transformations of nanoparticles under hydrostatic pressure has revealed important differences between phase transformations under isothermal or adiabatic conditions. This presuppositionless analysis fully explains a hysteresis with respect to the phase fraction and the pressure observed experimentally. It is important to mention that the results of this analysis may be transferred to the role of any external volumetric field acting on phase transforming nanoparticles. Typical examples are phase transformations of ferromagnetic intermetallics subjected to the influence of magnetic fields. Source

Vollath D.,NanoConsulting | Fischer F.D.,University of Leoben
Journal of Materials Chemistry | Year: 2011

A statistical model delivering average equilibrium concentrations and indications for the time evolution of ensembles of phase transforming nanoparticles, showing fluctuations, gives clues for a new approach. It is shown that the temporal evolution of transformation of the ensemble depends on the distinguishability of the particles. However, the equilibrium configuration of fluctuating ensembles does not depend on the distinguishability of the particles. The outcome of the presuppositionless statistical fluctuation model is the proof that any fluctuations connected to phase transformations occur in the minimum of the free enthalpy. Additionally, the analysis allows drafting a new fluctuation condition for ensembles. © 2011 The Royal Society of Chemistry. Source

Vollath D.,NanoConsulting
International Journal of Materials Research | Year: 2012

Phase transformations of freestanding nanoparticles are well analyzed. The situation is different for particles embedded in a second matrix. The special case of melting and crystallizing of nanoparticles in a rigid matrix is the topic of this study based on the energy balance, resulting in a size dependency of these phase transformations primarily on variation of the materials properties with the particle size. Therefore, an important outcome of this study is the result that thermodynamic data of bulk materials are insufficient to describe phenomena connected to nanoparticles. The differences may be significant. © 2012 Carl Hanser Verlag, Munich, Germany. Source

Fischer F.D.,University of Leoben | Leindl M.,University of Leoben | Dirschmid H.,Vienna University of Technology | Vollath D.,NanoConsulting | Clemens H.,University of Leoben
ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik | Year: 2010

Heat can be released or consumed in particles in a nearly adiabatic way due to phase transformation, thermal fluctuation, etc. In this case a temperature field, strongly varying in space and time, develops in the particle in addition to the global temperature field. Analytical as well as numerical solutions for this additional temperature field are presented for identical and different thermal properties of both the particle and its environment. The case of heat conduction and of heat transfer is dealt with. Consequences for nanoparticles are discussed. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim. Source

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