A simple and most promising oxide-assisted catalyst-free method is used to prepare silicon nitride nanowires that give rise to high yield in a short time. After a brief analysis of the state of the art, we reveal the crucial role played by the oxygen
partial pressure: when oxygen partial pressure is slightly below the threshold of passive oxidation, a high yield inhibiting the formation of any silica layer covering the nanowires occurs and thanks to the synthesis temperature one can control nanowire dimensions.
The synthesis of Si3N4 nanowires from the reaction of silicon nanoparticles with N2 in the 1200-1440 C temperature range is reported. The nitridation conditions are such that the reaction with nitrogen is favoured by the presence of silicon oxide in
the particles and by the active oxidation of silicon without a catalyst. It is shown that the Si to Si3N4 conversion rate depends on the amount of silicon particles used in the experiments and that, in general, the reaction slows down for greater amounts. This trend is explained by particle stacking, which restricts the exchange of gases between the furnace atmosphere and the atmosphere around the inner particles. In a first stage, local oxygen partial pressure increases around the inner particles and inhibits nitridation locally. If the amount of reactant Si nanoparticles is small enough, this extrinsic effect is avoided and the intrinsic nitridation kinetics can be measured. Experiments show that intrinsic kinetics does not depend on temperature.
A simple numerical model which calculates the kinetics of crystallization involving randomly distributed nucleation and isotropic growth is presented. The model can be applied to different thermal histories and no restrictions are imposed on the time
and the temperature dependencies of the nucleation and growth rates. We also develop an algorithm which evaluates the corresponding emerging grain size distribution. The algorithm is easy to implement and particularly flexible making it possible to simulate several experimental conditions. Its simplicity and minimal computer requirements allow high accuracy for two- and three-dimensional growth simulations. The algorithm is applied to explore the grain morphology development during isothermal treatments for several nucleation regimes. In particular, thermal nucleation, pre-existing nuclei and the combination of both nucleation mechanisms are analyzed. For the first two cases, the universal grain size distribution is obtained. The high accuracy of the model is stated from its comparison to analytical predictions. Finally, the validity of the Kolmogorov-Johnson-Mehl-Avrami model is verified for all the cases studied.
The kinetics and microstructure of solid-phase crystallization under continuous heating conditions and random distribution of nuclei are analyzed. An Arrhenius temperature dependence is assumed for both nucleation and growth rates. Under these circum
stances, the system has a scaling law such that the behavior of the scaled system is independent of the heating rate. Hence, the kinetics and microstructure obtained at different heating rates differ only in time and length scaling factors.Concerning the kinetics, it is shown that the extended volume evolves with time according to alpha_ex=[exp(kappa Ct)]^m+1, where t is the dimensionless time. This scaled solution not only represents a significant simplification of the system description, it also provides new tools for its analysis. For instance, it has been possible to find an analytical dependence of the final average grain size on kinetic parameters. Concerning the microstructure, the existence of a length scaling factor has allowed the grain-size distribution to be numerically calculated as a function of the kinetic parameters.
In this paper, we develop a method for obtaining the approximate solution for the evolution of single-step transformations under non-isothermal conditions. We have applied it to many reaction models and obtained very simple analytical expressions for
the shape of the corresponding transformation rate peaks. These analytical solutions represent a significant simplification of the systems description allowing easy curve fitting to experiment. A remarkable property is that the evolutions of the transformed fraction obtained at different heating rates are identical when time is scaled by a time constant. The accuracy achieved with our method is checked against several reaction models and different temperature dependencies of the transformation rate constant. It is shown that its accuracy is closely related with that of the Kissinger method.
Avramis model describes the kinetics of phase transformation under the assumption of spatially random nucleation. In this paper we provide a quasi-exact analytical solution of Avramis model when the transformation takes place under continuous heating
. This solution has been obtained with different activation energies for both nucleation and growth rates. The relation obtained is also a solution of the so-called Kolmogorov-Johnson-Mehl-Avrami transformation rate equation. The corresponding non-isothermal Kolmogorov-Johnson-Mehl-Avrami transformation rate equation only differs from the one obtained under isothermal conditions by a constant parameter, which only depends on the ratio between nucleation and growth rate activation energies. Consequently, a minor correction allows us to extend the Kolmogorov-Johnson-Mehl-Avrami transformation rate equation to continuous heating conditions.
The space subdivision in cells resulting from a process of random nucleation and growth is a subject of interest in many scientific fields. In this paper, we deduce the expected value and variance of these distributions while assuming that the space
subdivision process is in accordance with the premises of the Kolmogorov-Johnson-Mehl-Avrami model. We have not imposed restrictions on the time dependency of nucleation and growth rates. We have also developed an approximate analytical cell size probability density function. Finally, we have applied our approach to the distributions resulting from solid phase crystallization under isochronal heating conditions.
