scholarly journals Wagner-Vengrenovich Distribution

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Bohdan V. Ivanskii ◽  
Anatolii V. Moskalyuk ◽  
Sergey V. Yarema ◽  
Igor I. Panko ◽  
Miroslav O. Stasyk
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Chemical Reaction ◽  
Size Distribution Function ◽  
Cluster Growth ◽  
Total Flow ◽  
Cluster Surface ◽  
Rate Of Growth

The process of coarsening of nanoclusters or nanocrystals (NCs) is investigated for the case when cluster growth (dissolution) is governed simultaneously by both diffusion along dislocation pipes and the rate of formation of chemical connections (chemical reaction) at cluster surface, namely, Wagner’s growing mechanism. For that, the total flow of atoms to (from) a cluster is represented by two parts, namely, diffusion part and the Wagner (kinetic) one. The dependence of the rate of growth of NC on the ratio of the parts of the total flow has been determined as well as the NC’s size distribution function referred to as the Wagner-Vengrenovich distribution. Computed distribution is compared with experimentally obtained histograms.

Informational Measures of the Shape of the Amoroso Distributions for the Research of Dispersed Materials

2021 ◽  
Vol 1031 ◽  
pp. 58-66
Author(s):  
Vitaly Polosin
Keyword(s):  
Particle Size ◽  
Distribution Function ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Applied Research ◽  
Particle Distribution ◽  
Size Distribution Function ◽  
Distribution Model ◽  
Information Uncertainty ◽  
Particle Size Distribution Function

For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. For the particle size distribution function various forms of exponential models are used to construct models of the properties of dispersed substance. The most difficult stage of applied research is to determine the shape of the particle distribution model. The article proposes a uniform model for setting the interval of information uncertainty of non-symmetric particle size distributions. Based on the analysis of statistical and information uncertainty intervals, new shape coefficients of distribution models are constructed, these are the entropy coefficients for shifted and non shifted distributions of the Amoroso family. Graphics of dependence of entropy coefficients of non-symmetrical distributions show that distributions well-known are distinguish at small of the shapes parameters. Also it is illustrated for parameters of the form more than 2 that it is preferable to use the entropy coefficients for the unshifted distributions.The material contains also information measures for the well-known logarithmic normal distribution which is a limiting case of distribution Amorozo.

Analysis of Nanopowders by Small-Angle X-Ray Scattering Method’s

2012 ◽  
Vol 7 (4) ◽  
pp. 107-116
Author(s):  
Sergey Bardakhanov ◽  
Ludmila Vikulina ◽  
Vladimir Lysenko ◽  
Andrey Nomoev ◽  
Sergey Poluyanov ◽  
...  
Keyword(s):  
Distribution Function ◽  
Size Distribution ◽  
Small Angle ◽  
Electron Accelerator ◽  
Size Distribution Function ◽  
X Ray ◽  
X Ray Scattering ◽  
Ray Scattering

The possibility of application of small-angle X-ray scattering (SAXS) for nanopowders analysis was studied. The research for eight silica powders (including four powders obtained by the authors with help of electron accelerator) was conducted. The possibility of application of small angle X-ray scattering for determination of size distribution function of nanoparticles was shown

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