IDENTIFICATION OF THE DISTRIBUTION FUNCTION AND CHARACTERIZATION OF THE NANO– AND MICROPOWDERS SIZES

Ivan S. Bondarchuk, Sergey S. Titov, Sergey S. Bondarchuk
DOI: 10.25699/SSSB.2021.40.6.032 Download PDF
Abstract: The paper proposes two new efficient algorithms, implemented by a short program code in MS Excel, designed to identify and characterize the sizes of nano- and micropowders of particles in the form of generalized gamma or lognormal distributions according to experimental histograms. The proposed method is a new general approach to solving inverse problems of identifying the parameters of differential distribution functions from experimental data based on minimizing the functional that is the coefficient of determination. The algorithm is implemented with formulas (less than 10) of the most common tools (MS Excel spreadsheets without the use of macros), which allow researchers without the skills of professional programmers to easily check and reproduce the presented material, as well as the ability to modify the code to solve a wider range of problems. The text of the article and comments on the worksheets of screenshots represent ready-made instructions for solving problems of identification of distribution functions and characterization of the sizes of nano- and micropowders.
Index terms: particles, powders, distribution function, generalized gamma distribution, lognormal distribution, moment of distribution function, identification of distribution function, characterization of particle sizes, spreadsheets, program code.

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