210 research outputs found
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
Evidence for vibrational excitation of the adlayer in exoergic processes at metal surfaces: H-atom abstraction and recombination and adsorption-stimulaterd desorption of CO
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
~DcPĂ°TĂž 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
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