1,721,081 research outputs found
Kinetics of island density in thin film growth in the framework of statistical mechanics of rigid disks
No full textThe paper centers on the evaluation of the function n(Theta)=N(Theta)/N-0, that is the normalized number of islands as a function of coverage Theta is an element of[0,1], given N-0 initial nucleation centers (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, and 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, and M. Volpe, Phys. Rev. B 62, 11300 (2000)]
Spatial distribution of nuclei in progressive nucleation: Modeling and application
No full textPhase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article an analytical approach is presented for computing pair-correlation function of nuclei in progressive nucleation. This quantity is further employed for characterizing the spatial distribution of nuclei through the nearest neighbor distribution function. The modeling is developed for nucleation in 2D space with power growth law and it is applied to describe electrochemical nucleation where correlation effects are significant. Comparison with both computer simulations and experimental data lends support to the model which gives insights into the transition from Poissonian to correlated nearest neighbor probability density. (C) 2018 Elsevier B.V. All rights reserved
Fokker-Planck equation for the particle size distribution function in KJMA transformations
Full text linkThe 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 figure
Interface evolution in phase transformations ruled by nucleation and growth
No full textAn analytical model for the evolution of the boundary of the new phase in transformations ruled by nucleation and growth is presented. Both homogeneous and heterogeneous nucleation have been considered: The former includes transformations in 2D and 3D space and the latter nucleation and growth on flat solid substrate. The theory is formulated for the general case of spatially correlated nuclei, arbitrary nucleation rate and power growth law of nuclei. In the case of heterogeneous nucleation, spheroidal nuclei have been assumed and the dependence of the kinetics on contact angle investigated. The validity of the present approach is deemed through comparison with experimental data from literature which also comprise oxide growth by ALD (Atomic Layer Deposition) metal electrodeposition at solid substrate and alloy recrystallization. (C) 2020 Elsevier B.V. All rights reserved
Mean field rate equation for diffusion-controlled growth in binary alloys
No full textA system of rate equations is developed for modeling the kinetics of diffusional phase transitions in binary alloys. By employing a mean field assumption and the quasi static approximation a novel expression for the growth law of the nuclei is obtained in terms of supersaturation and diffusion length of component in the parent phase. The mean field rate equations are integrated for the model case of a transformation ruled by simultaneous nucleation and the behaviour of both Avrami's exponent and rate constant investigated as a function of the initial value of the supersaturation. The expression of the activation energy, as extracted by the Arrhenius plot of the rate constant, is determined and is shown to be a function of the activation energies for nucleation and diffusion, and of the initial value of the supersaturation. The limiting case of infinite diffusion length is also analysed and discussed. (C) 2002 Elsevier Science B.V. All rights reserved
On the grain size distribution function in KJMA compliant growth
No full textnucleation and growth has been computed by means of Kolmogorov’s second equation. The transformation is
modeled in accord with the classical KJMA (Kolmogorov-Johnson-Mehl-Avrami) theory for linear growth of
nuclei and either simultaneous or progressive nucleation. For 3D growth, it is shown that for progressive
nucleation, second order term can be neglected in the differential equation for the PDF of grain volume. For sitesaturated
nucleation the variance of the distribution increases with time to attain the value of the Gamma distribution
at the end of the transformation. It is demonstrated that in this case the PDF is given by convolution of
Gaussian-like solutions of Kolmogorov’s equation with Gamma distribution. The validity of the model is checked
by computer simulations available in literature
A model kinetics for nucleation and diffusion-controlled growth of immiscible alloys
No full textA system of mean field rate equations is employed for describing the kinetics of solid-solid phase separation within the immiscibility gap of binary alloys. The system allows us to study the time evolution of both supersaturation and diffusion length of the components in the metastable phase. It is shown that in the case of simultaneous nucleation the system of differential equations leads to a simple formula for the characteristic time of the transformation in terms of material parameters and initial supersaturation. The nucleation rate is computed on the basis of the classical nucleation theory and the alloy is assumed to behave as a regular solution. It turns out that for low values of the initial supersaturation the nucleation process can be considered as simultaneous. It is also found that thermally activated nucleation takes place for supersaturation values lower than about 0.21. The assumption of a concentration-independent diffusion coefficient and the effect of nucleus curvature on interface composition have been analyzed and discussed
Soft impingement in diffusion-controlled growth of binary alloys: moving boundary effect in one-dimensional system
No full textThe impact of soft impingement on the kinetics of diffusion-controlled growth of binary alloys is investigated. An analytical approach is developed which takes into account the process of island growth, that is the time dependence of the position of the nucleus/parent phase interface. The concentration profile, the growth law, and the kinetics of the fraction of transformed phase are computed and compared with those attained for point islands. At odd with the point island approach the local kinetics of growth depends on initial supersaturation. On the other hand, the whole transformation kinetics is in good agreement with that of the point island model with an Avrami exponent close to the theoretical value n = 0.5. The concentration profile is well described by a polynomial function in the whole spatial domain, with an exception for the initial stage of the phase separation. The effect of the spatial distribution of the nuclei on the kinetics is also studied in the model case of hard-core correlation among nuclei
Steady state energy distribution function of adatoms in reactive adsorption
No full textThe interplay between the energy distribution function of adatoms and the rate of diatom formation in catalytic reaction is studied by means of mean field rate equations. The recombination of adatoms is described as a multi-channel process where adatom desorption arises from several energy levels. It is shown that the distribution function can be computed, analytically, as a function of the ratio between recombination probability and rate constant for energy disposal to the solid. This parameter is the key quantity of the kinetics since it governs both reaction rate and the shape of the energy distribution function. It is found that, in order to obtain steady state conditions, the control parameter is constrained within a well defined interval of values which result lower than unity. It is shown that a kinetic transition takes place for the highest value of the parameter, which entails hyperthermal reaction rate
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