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We present an experimental study on the etching of detonation nanodiamond (DND) seeds during typical microwave chemical vapor deposition (MWCVD) conditions leading to ultra-thin diamond film formation, which is fundamental for many technological applications. The temporal evolution of the surface density of seeds on Si(100) substrate has been assessed by scanning electron microscopy (SEM). The resulting kinetics have been explained in the framework of a model based on the effect of particle size, according to the Young-Laplace equation, on both chemical potential of carbon atoms in DND and activation energy of reaction. We found that seeds with size smaller than a critical radius, r*, are etched away while those greater than r* can grow. Finally, the model allows to estimate the rate coefficients for growth and etching from the experimental kinetics., Comment: 28 pages; 15 Figures, 3 Tables

The Fokker-Planck (FP) equation has been derived for describing the temporal evolution of the particle size probability density function (PDF) for KJMA (Kolmogorov-Johnson-Mehl-Avrami) transformations. The classical case of transformations with constant rates of both nucleation and growth, in 3D space, has been considered. Integration of the equation shows that the PDF is given by the superposition of one-parameter Gamma distributions with time dependent mean size given by the KJMA theory. The asymptotic behavior of the FP solution offers a demonstration of the conjecture, previously proposed by Pineda et al [E. Pineda, P. Bruna, D. Crespo, Phys. Rev. E 70 (2004) 066119], according to which the set of nuclei formed at the same time are Gamma-distributed, with parameter depending on nucleus birth time. Computer simulations of the transformation with constant nucleation and growth rates, do show that the temporal evolution of the PDF, in the volume domain, is in good agreement with the Johnson-Mehl PDF. The approach based on the FP equations provides a particle size PDF that exhibits such behavior., Comment: 22 pages; 7 figures

We develop a stochastic approach for describing 3D-phase transformations ruled by time-dependent correlated nucleation at solid surfaces. The kinetics is expressed as a series of correlation functions and, at odds with modeling based on Poisson statistics, it is formulated in terms of actual nucleation rate. It is shown that truncation of the series up to second order terms in correlation functions provides a very good approximation of the kinetics. The time evolution of both total amount of growing phase and surface coverage by the new phase have been determined. The theory is applied to describe progressive nucleation with parabolic growth under time dependent hard-disk correlation. This approach is particularly suitable for describing electrochemical deposition by nucleation and growth where correlation effects are significant. In this ambit the effect of correlated nucleation on the behavior of kinetic quantities used to study electrodeposition has also been investigated.

In the electrochemical deposition of thin films the measurement of the current-time curve does not allow for a direct determination of the nucleus growth law, electrode surface coverage and mean film thickness. In this work we present a theoretical approach suitable to gain insight into these quantities from the knowledge of nucleation density, solution parameters and current-time behavior. The model applies to both isotropic and anisotropic growth rates of nuclei and a study on the effect of nucleus shape and aspect ratio on the kinetics is presented. Experimental results from literature are also discussed in the framework of the present approach.

An "experimental" study on the randomness of the fractional digits of $\pi$, $e$ and $\phi$ irrational numbers are presented. This is done by exploiting the $1D$ Poisson-Voronoi tessellation. We employed two approaches and in both cases, within the numerical error, no differences have been detected between the irrational fractional digits and an equivalent random sequence of digits. The number of tested digits is $1.6 \times 10^7$ and $4 \times 10^7$ for the first and second approach, respectively. Although not shown here, we investigated several irrational numbers and all of them have displayed a similar behavior., Comment: 12 pages , 10 figures

The theory of Kolmogorov-Johnson-Mehl-Avrami (KJMA) for phase transition kinetics is subjected to severe limitations concerning the functional form of the growth law. This paper is devoted to side step this drawback through the use of correlation function approach. Moreover, we put forward an easy-to-handle formula, written in terms of the experimentally accessible actual extended volume fraction, which is found to match several types of growths. Computer simulations have been done for corroborating the theoretical approach., Comment: 18 pages ;11 figures

The paper centres on the evaluation of the function n(theta)=N(theta)/N0, that is the normalized number of islands as a function of coverage 0

It has been shown that the KJMA (Kolmogorov-Johnson-Mehl-Avrami) solution of phase transition kinetics can be set as a problem of correlated nucleation [Phys.Rev.B65, 172301 (2002)]. In this paper the equivalence between the standard solution and the approach that makes use of the actual nucleation rate, i.e. that takes into account spatial correlation among nuclei and/or grains, is shown by a direct calculation in case of linear growth and constant nucleation rate. As a consequence, the intrinsic limit of KJMA theory due to the phenomenon of phantom overgrowth is, at last, overcome. This means that thanks to this new approach it is possible, for instance, to describe phase transition governed by diffusion., Comment: 9 pages, 3 figures

The Kolmogorov-Johnson-Mehl-Avrami model, which is a nucleation and growth poissonian process in space, has been implemented by taking into account spatial correlation among nuclei. This is achieved through a detailed study of a system of distinguishable and correlated dots (nuclei). The probability that no dots be in a region of the space has been evaluated in terms of correlation functions. The theory has been applied to describe nucleation and growth in two dimensions under constant nucleation rate, where correlation among nuclei depends upon the size of the nucleus. We propose a simple formula for describing the phase transition kinetics in the presence of correlation among nuclei. The theory is applied to the constant nucleation rate process when correlation depends upon the nucleus-birth time. It is shown that the random sequential adsorption and Tobin process can be analyzed in the framework of the simultaneous nucleation case, admitting a common rationale that is apart from an appropriate re-scaling they represent the same process from the mathematical point of view., Comment: 28 pages, no figures