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Determination of particle size distributions and transformation enthalpies from the temperature course of a phase transformation

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Abstract

The presented analysis of the temperature course of a phase transformation of nanoparticles offers a powerful tool to obtain data for the particle size distribution and the enthalpy of transformation. The analysis starts with the temperature distribution within an ensemble of nanoparticles and a functional relation between particle size and transformation temperature. In contrast to the Maxwell-Boltzmann distribution, in case of nanoparticles, the distribution of the temperature of the particles follows a normal distribution. Finally a reliable characterization of the specimen and the transformation in question are presented. These results, particularly the particle size distribution, represent – in many cases – a statistically more significant result as compared to the outcome, obtained by evaluation of electron micrographs. Looking at the problems of microcalorimetric determination of reaction enthalpies, one may realize comparable problems. By comparison of the experimental data with the calculated ones, one may obtain additional information about the interaction of the particles within the ensemble.

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Acknowledgments

The author thanks F. D. Fischer and D. Holec for important discussions.

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Correspondence to Dieter Vollath.

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Vollath, D. Determination of particle size distributions and transformation enthalpies from the temperature course of a phase transformation. J Nanopart Res 22, 33 (2020) doi:10.1007/s11051-019-4732-x

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Keywords

  • Energy distribution
  • Phase transformation
  • Particle size distribution
  • Enthalpy of reaction
  • Nanoparticles