1,721,126 research outputs found
Effect of the impingement on the kinetics of island aggregation in the post-nucleation stage of film growth at solid surfaces
No full textThe kinetics of island aggregation in the post-nucleation stage, for a model case system where the impingement mechanism among the islands dominates the film growth, has been measured using scanning electron microscopy (SEM). A theoretical model previously developed is found to be in accordance with the experimental kinetics [M. Fanfoni, M. Tomellini, Appl. Surf. Sci,, 136 (1998) 338.]. (C) 1999 Elsevier Science B.V. All rights reserved
The influence of steps on the island distribution function in thin solid film formation
No full textThe gamma distribution has been shown to be the simplest function for describing the universal size distribution function of InAs quantum dots on GaAs(001) substrate (Fanfoni et al 2007 Phys. Rev. B 75 245312), although there is no reason to believe that it could not be applied to any film growth where the principal feeding of the islands occurs through surface diffusion as proposed, after numerical simulations in the two-dimensional case, by Mulheran and Blackman (1995 Phil. Mag. Lett. 72 55). As far as InAs/GaAs(001) quantum dots are concerned, by fitting the data of Ebiko et al (1999 Phys. Rev. B 60 8234) and Krzyzewski et al (2002 Phys. Rev. B 66 201302(R)) to the gamma function, beta = 4.5 and 2.9 are the respective returned values. The latter value appears anomalous because for a Poissonian distribution of points (centers of islands), beta = 3.5-3.6. Moreover, the greater the spatial correlation the greater the beta value. We prove that the presence of steps alters the distribution of nucleation centers throughout the substrate in such a way that its variance increases with respect to the substrate without steps and, as a consequence, beta decreases
L'analogia in fisica come strumento di indagine: il moto casuale e l'interferenza tra onde incoerenti
No full textThe Johnson-Mehl-Avrami-Kolmogorov model: A brief review
No full textThe kinetics of isothermal phase transformations have been described by the Johnson-Mehl-Avrami-Kolmogorov (JMAK) phenomenological model since the 40's. Although many theoretical investigators have given a fundamental contribution to extend the range of applicability of the model, the experimentalists keep using the model in its original form, owing to its simplicity, at times risking to overinterpret the experimental results. The early attempts to apply the JMAK model to surface science date back to the 70's, but it has been systematically applied only in the last fem years. There is not enough space here to review thoroughly the model and its applications. For this reason, after a historic introduction, we describe here in some detail the model and finally we review in brief its application to surface science
Connection between phantom and spatial correlation in the Kolmogorov–Johnson–Mehl–Avrami-model: a brief review
No full textThe goal of this minireview is restricted to describe how the theoretical basis of
Kolmogorov (1937)–Johnson-Mehl (1939) –Avrami (1939–41) model has evolved from
its birth up to the present day. The model, which dates back to the late of 1930s, has the
purpose of describing the kinetics of a phase transformation. Given the nature of this
article, although there are hundreds (if not thousands) of experimental data concerning
the most disparate topics, which are interpreted on the basis of the KJMA model, no
arguments relating to these, will be touched upon.
Starting from the ingenious concept of phantom nuclei, firstly introduced by Avrami
to get the exact kinetics, we review theoretical approaches which overcome such
concept. We will show how spatial correlation among nuclei plays a fundamental role
in these modelings
Avrami's kinetic approach for describing Volmer Weber growth mode at solid surfaces studied via PES and AES
No full textA model is presented for describing the time dependence of the photoelectron and/or Auger signals during the overlayer formation in the case of Volmer Weber growth mode, i.e. 3D island formation. The impingement among clusters has been taken into account in the framework of Avrami's statistical approach. A first system has been considered in which nucleation occurs at a given number of preexisting sites randomly distributed throughout the whole surface. The results obtained by numerical computations indicate that particular conditions can be indeed realized for which the PES signal is chiefly related to the kinetics of the surface fraction that is covered by islands. A more involved system has been also modeled where nucleation does not occur at preexisting sites but through the formation of stable dimers. Under this circumstance, Avrami's treatment of island impingement can be still retained although now a system of integral differential equations has to be solved to get the kinetics. Such a modelling should be suitable for describing the metallic film growth studied by PES
Order and randomness in Kolmogorov-Johnson-Mehl-Avrami-type phase transitions
No full textThe distribution of points on a 2D domain influences the kinetics of its coverage when a growth law is attached at each point. This implies that the kinetics of space filling can be adopted as a descriptor of the degree of order of the initial point distribution. In this paper, the degree of order of an initial array of points has been changed following two paths: (i)from a regular square lattice, through increasing displacement assigned to each point, towards Poissonian disorder; (ii)from a Poissonian distribution, by introducing a hard core potential with increasing correlation lengths, towards a more ordered lattice. A linear growth law has been attached to the points of the initial array and the kinetics X(X e), where X e is the extended coverage as defined in the Kolmogorov-Johnson-Mehl-Avrami model, has been monitored. The quantitative analysis has been performed by fitting the kinetics to an equation which we propose for the first time and which has proved to be, in fact, highly suitable for the purpose. The results demonstrate that the gross of variation from order to disorder is obtained for point displacements, u, of the order of a, the latter being the constant of a square lattice. Vice versa, the introduction of a correlation distance in a random distribution provokes at most an order limited to the first neighbors and no real order can ever be reached. Others descriptors have been investigated, all confirming our results. We also developed an analytical description based on the use of the f-functions, as have been defined by Van Kampen, up to the second order terms. Such a description has been shown to work well for u/a<1 within an interval ΔX e which depends on the value. © 2012 IOP Publishing Ltd
Phase transition kinetics in the case of nonrandom nucleation
No full textA theoretical model is developed for describing phase transition kinetics occurring by nucleation and growth processes. The model treats the case of spatially correlated nuclei and applies to any kind of nucleation function. A stochastic approach is employed that gives the fraction of transformed phase as a function of a series in terms of the m-dots correlation functions. Truncation of the expansion up to the second order in the correlation functions leads to an analytical solution. Computer simulations based on the hard core model have been also performed confirming the goodness of the analytical approach
Perché il logaritmo della somma non è uguale alla somma dei logaritmi: gli operatori lineari
No full textQuesto articolo vuole offrire uno spunto di riflessione su come alcune regole matematiche possano essere comprese ad un livello concettuale più alto e dunque più generale. Tra le molteplici possibilità abbiamo scelto le funzioni logaritmiche come esempio paradigmatico
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