Beyond the Kolmogorov Johnson Mehl Avrami kinetics: inclusion of the spatial correlation

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 figure

Eliminating overgrowth effects in Poisson spatial process through the correlation among actual nuclei

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 figure

Kinetics of dissolution-precipitation reaction at the surface of small particles: modelling and application

In the framework of the theory of phase transformations with position-dependent nucleation rate, a model has been developed aimed at describing the dissolution-precipitation reaction at the surface of small particles. The precipitation reaction takes place by nucleation and growth processes under time-dependent supersaturation. Depending on the coverage of the particle surface by the new phase, the reaction kinetics exhibits high- and low-rate regimes. The computation is performed for both progressive and simultaneous nucleation. In the case of simultaneous nucleation, closed-form solutions are attained for diffusion- and interface-limited growth modes and for isotropic and anisotropic growths of the nuclei, as well. The scaling properties of the kinetics on particle size are also investigated. The kinetic model is employed for analysing experimental data and makes it possible to estimate the nucleation density on the particle surface and to have an insight into the microscopic growth law of nuclei

Kinetics of phase transformations with heterogeneous correlated-nucleation

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

Kinetics of island growth in the framework of planar diffusion zones and 3D nucleation and growth models for electrodeposition

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

Beyond the constraints underlying Kolmogorov-Johnson-Mehl-Avrami theory related to the growth laws

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 figure

Kinetic theory of cluster impingement in the framework of statistical mechanics of rigid disks

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<theta<1, given N0 initial nucleation centres (dots) having any degree of spatial correlation. A mean field approach has been employed: the islands have the same size at any coverage. In particular, as far as the random distribution of dots is concerned, the problem has been solved by considering the contribution of binary collisions between islands only. With regard to correlated dots, we generalize a method previously applied to the random case only. In passing, we have made use of the exclusion probability reported in [S. Torquato, B. Lu, J. Rubinstein, Phys.Rev.A 41, 2059 (1990)], for determining the kinetics of surface coverage in the case of correlated dots, improving our previous calculation [M. Tomellini, M. Fanfoni, M. Volpe Phys. Rev.B 62, 11300, (2000)].Comment: 10 pages, 3 figure

High Temperature Stability of Onion-Like Carbon vs Highly Oriented Pyrolytic Graphite

Abstract The thermodynamic stability of onion-like carbon (OLC) nanostructures with respect to highly oriented pyrolytic graphite (HOPG) was determined in the interval 765–1030 K by the electromotive force (emf) measurements of solid electrolyte galvanic cell: (Low) Pt|Cr3C2,CrF2,OLC|CaF2s.c.|Cr3C2,CrF2,HOPG|Pt (High). The free energy change of transformation HOPG = OLC was found positive below 920.6 K crossing the zero value at this temperature. Its trend with temperature was well described by a 3rd degree polynomial. The unexpected too high values of LDrHT LT P ~DcPðTÞ jointly to the HR-TEM, STEM and EELS evidences that showed OLC completely embedded in rigid cages made of a Cr3C2/CrF2 matrix, suggested that carbon in the electrodes experienced different internal pressures. This was confirmed by the evaluation under constant volume of dP dT by the a k ratio for OLC (0.5 MPa K21) and HOPG (8 Pa K21) where a and k are the isobaric thermal expansion and isothermal compressibility coefficients, respectively. The temperature dependency of the pressure was derived and utilized to calculate the enthalpy and entropy changes as function of temperature and pressure. The highest value of the internal pressure experienced by OLC was calculated to be about 7 GPa at the highest temperature. At 920.6 K, DrH and DrS values are 95.8 kJ mol21 and 104.1 JK21 mol21, respectively. The surface contributions to the energetic of the system were evaluated and they were found negligible compared with the bulk terms. As a consequence of the high internal pressure, the values of the enthalpy and entropy changes were mainly attributed to the formation of carbon defects in OLC considered as multishell fullerenes. The change of the carbon defect fraction is reported as a function of temperature