Analysis of Spherical Particles Size Distribution – Theoretical Basis

• Autorzy: Gurgul D. , Burbelko A. , Wiktor T.

Identyfikatory

DOI

10.24425/118807

• Języki publikacji: EN

Abstrakty

EN

The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.

Słowa kluczowe

EN

alloy crystallisation; mathematical models; analysis of spherical; planimetric analysis; linear analysis

PL

krystalizacja stopów; modele matematyczne; analiza sferyczna; analiza planimetryczna; analiza liniowa

• Wydawca: Komisja Odlewnictwa Polskiej Akademii Nauk Oddział w Katowicach
• Czasopismo: Archives of Foundry Engineering
• Rocznik: 2018
• Tom: Vol. 18, iss. 1
• Strony: 29--34
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Gurgul D.

• AGH University of Science and Technology, 30-059 Krakow, Poland

autor

Burbelko A.

• AGH University of Science and Technology, 30-059 Krakow, Poland

autor

Wiktor T.

• AGH University of Science and Technology, 30-059 Krakow, Poland

Bibliografia

• [1] Wicksell, S.D. (1925). The Corpuscle Problem: A Mathematical Study of a Biometric Problem. Biometrika. 17(1/2), 84-99.
• [2] Więcek, K., Skowronek, K. & Khatemi, B. (2005). Graphite particles size distribution in nodular cast iron. Metallurgy and Foundry Engineering. 31(2), 167-173.
• [3] Sheil, E. (1935). Statistische Gefügeuntersuchungen I. Zeitschrift für Metallkunde. 27(9), 199-208.
• [4] Schwartz, H.A. (1934). The Metallographie Determination of the Size Distribution of Temper Carbon Nodules. Metals and Alloys. 5, 139-140.
• [5] Saltykov, S.A. (1952). Stereometric Metallurgy. Moscow: Metallurgizdat.
• [6] Saltikov, S.A. (1967). The determination of the size distribution of particles in an opaque material from the measurement of the size distribution of their sections. In the Second International Congress for Stereology, Chicago 8-13 April 1967 (pp. 163-173). Berlin-Heidelberg-New York: Springer Verlag.
• [7] Li, T., Shimasaki, S., Taniguchi, Sh. & Narita, Sh. (2016). Reliability of Inclusion Statistisc in Steel Stereological Methods. ISIJ International. 56(9), 1625-1633.
• [8] Kong, M., Bhattacharya, R.N., James, C. & Basu, A. (2005). A statistical approach to estimate the 3D size distribution of spheres from 2D size distributions. GSA Bulletin. 117(1/2), 244-249. DOI: 10.1130/B25000.1.
• [9] Jakeman, A.J. & Anderssen, R.S. (1975). Abel type integral equations in stereology. I. General discussion. Journal of Microscopy. 105(2), 121-133.
• [10] Ohser, J. & Sandau, K. (2000). Considerations About the Estimation of the Size Distribution in Wicksell’s Corpuscle Problem. Lecture Notes in Physics. 554, 185-202.
• [11] Hielbroner, R. (2002, May). How to derive size distributions of particles from size distributions of sectional areas. Retrived July 4, 2017, from https://earth.unibas.ch/ micro/support/PDF/grainsize.pdf
• [12] Cahn, J.W., & Fullman R.L. (1956). On the use of lineal analysis for obtaining particle-size distribution functions in opaque samples. Transactions, American Institute of Mining, Metallurgical, and Petroleum Engineers. 206, 610-612.
• [13] Lord, C.W. & Willis, T.F. (1951). Calculation of air bubble distribution from results of a Rosiwal traverse of aerated concrete. ASTM Bulletin. 177, 177-187.
• [14] Spektor, A.G. (1950). Analysis of distribution of spherical particles in non-transparent structures. Zavodsk. Lab. 16, 173-177.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018)