Abstract
Industrial micropowders of metals (aluminum, tungsten, hafnium, nickel, titanium, and zirconium) and a semimetal (amorphous boron) have been mechanically treated in a planetary-type ball mill for different time periods. The integral and differential particle size distribution functions have been experimentally determined for all micropowders before and after the mechanical treatment. It has been shown that, in all cases under consideration, the found distribution functions can be represented in a lognormal form. The most informative statistical characteristics (moments) have been determined for the obtained distribution functions. The time correlations of these characteristics have been analyzed. A mathematical ansatz-model has been proposed for the process of multicycle mechanical treatment of metal powders in planetary-type mills. The model enables one to adequately describe the time evolution of the statistical characteristics for an ensemble of micropowder particles.
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Notes
The theoretical and probabilistic justification of this conclusion has been presented in [17].
REFERENCES
German, R.M., Powder Metallurgy and Particulate Materials Processing, Princeton: Met. Powder Ind. Fed., 2005.
Abstracts of Papers, V Int. Conf. “Fundamental Bases of Mechanochemical Technologies”, FBMT-2018, Lyakhov, N., Sepelak, V., Shakhtshneider, T., and Dudina, D., Eds., Novosibirsk: IPC NSU-Publishing, 2018.
Fundamental’nye osnovy mekhanicheskoi aktivatsii, mekhanosinteza i mekhanokhimicheskikh tekhnologii (Fundamentals of Mechanical Activation, Mechanosynthesis, and Mechanochemical Technologies), Av-vakumov, E.G., Ed., Novosibirsk: Izd. Sib. Otd. Ross. Akad. Nauk, 2009.
Khodakov, G.S., Fizika izmel’cheniya (Physics of Dispersion), Moscow: Nauka, 1972.
Streletskii, A.N., Borunova, A.B., Kolbanev, I.V., Sivak, M.V., and Dolgoborodov, A.Yu., Gorenie Vzryv, 2017, vol. 10, no. 2, p. 100.
Smetkin, A.A. and Yarmonov, A.I., Vestn. Povolzh. Gos. Tekhnol. Univ., 2001, no. 7, p. 48.
Ivanov, N.V., Lomaeva, S.F., Elsukov, E.P., and Konygin, G.N., Fiz. Khim. Obrab. Mater., 2003, no. 5, p. 59.
Kurzina, I.A., Bozhko, I.A., Kalashnikov, M.P., Eroshenko, A.Yu., and Sharkeev, Yu.P., Materialovedenie, 2010, no. 5, p. 48.
Malkin, A.I., Klyuev, V.A., Ryazantseva, A.A., and Savenko, V.I., Colloid J., 2019, vol. 81, p. 703.
Malkin, A.I., Aliev, A.D., Klyuev, V.A., Savenko, V.I., Shiryaev, A.A., and Ryazantseva, A.A., Colloid J., 2020, vol. 82, p. 403.
Bogatyreva, E.V., Ermilov, A.G., Sviridova, T.A., Savina, O.S., and Podshibyakina, K.V., Inorg. Mater., 2011, vol. 47, p. 791.
Lomaeva, S.F., Deform. Razrushenie Mater., 2005, no. 3, p. 9.
Dorofeev, R.A., Streletskii, A.N., Povstugar, I.V., Protasov, A.V., and Elsukov, E.P., Colloid J., 2012, vol. 74, p. 675.
Vasil’ev, L.S. and Lomaeva, S.F., Khim. Interesakh Ustoich. Razvit., 2002, no. 10, p. 13.
Grigor'ev, O.K., Kryachko, L.A., Bega, N.D., Laptev, A.V., Golovkova, M.E., Rozhenko, N.N., and Bersudskii, E.I., Elektron. Mikrosk. Prochn. Mater., 2013, no. 19, p. 115.
Malyshev, V.P., Bekturganov, N.S., Makasheva, A.M., and Zubrina, Yu.S., Tsvetn. Met. (Moscow), 2016, no. 2, p. 33.
Malyshev, V.P., Makasheva, A.M., and Zubrina, Y.S., Am. J. Phys. Chem., 2015, vol. 4, p. 42.
Balakrishnan, N. and Chen, W.W.S., Handbook of Tables for Order Statistics from Lognormal Distributions with Applications, Amsterdam: Kluwer, 1999.
Manita, A.D., Teoriya veroyatnostei i matematicheskaya statistika (Probability Theory and Mathematical Statistics), Moscow: Mosk. Gos. Univ., 2001.
Lemeshko, B.Yu., Lemeshko, S.B., Postovalov, S.N., and Chimitova, E.V., Statisticheskii analiz dannykh, modelirovanie i issledovanie veroyatnostnykh zakonomernostei. Komp’yuternyi podkhod (Statistical Analysis of Data, Modeling, and Study of Probability Principles. Computer Approach), Novosibirsk: Izd. Novosib. Gos. Tekh. Univ., 2011.
Gmurman, V.E., Teoriya veroyatnostei i matemati-cheskaya statistika (Probability Theory and Mathematical Statistics), Moscow: Vysshaya Shkola, 2003.
Kouzov, P.A., Osnovy analiza dispersnogo sostava promyshlennykh pylei i izmel’chennykh materialov (Fundamentals of Analysis of Disperse Composition of Industrial Dust and Dispersing Materials), Leningrad: K-himiya, 1987.
Kolmogorov, A.N., Dokl. Akad. Nauk SSSR, 1941, vol. 31, no. 2, p. 99.
Kolmogorov, A.N., Izv. Akad. Nauk SSSR, Ser. Mat., 1937, no. 3, p. 355.
Belavin, A.A., Kulakov, A.G., and Tarnopol’skii, G.M., Lektsii po teoreticheskoi fizike (Lectures on Theoretical Physics), Moscow: Mosk. Tsentr Nepr. Mat. Obraz., 2015.
Brodskii, R.E. and Virchenko, Yu.P., Nauchn. Vedomosti Belgorod. Univ., Ser. Mat., 2008, no. 13, p. 23.
Romanovskii, B.V., Osnovy khimicheskoi kinetiki (Fundamentals of Chemical Kinetics), Moscow: Ekzamen, 2006.
Gardiner, C.W., Handbook of Stochastic Methods: For Physics, Chemistry and the Natural Sciences, Berlin: Springer, 2004.
Stepanov, S.S., Stochastic World, Heidelberg: Springer, 2013.
Khaken, G., Sinergetika. Printsipy i osnovy, perspektivy i prilozheniya (Synergy. Principles and Fundamentals, Perspectives, and Applications), Moscow: LENAND, 2015.
Sedov, L.I., Metody podobiya i razmernosti v mekhanike (Methods of Similarity and Dimensionality in Mechanics), Moscow: Nauka, 1977.
Gukhman, A.A., Vvedenie v teoriyu podobiya (Introduction to Similarity Theory), Moscow: Vysshaya Shkola, 1973.
Ioffe, A.F., Izbrannye trudy (Selected Works.), vol. 1: Mekhanicheskie i elektricheskie svoistva kristallov (Mechanical and Electrical Properties of Crystals), Leningrad: Nauka, 1974.
Davidenkov, N.N., Izbrannye Trudy (Selected Works), Pisarenko, G.S., Ed., Kyiv: Inst. Probl. Prochn. Akad. Nauk USSR, 1981.
Fridman, Ya.B., Mekhanicheskie svoistva metallov (Mechanical Properties of Metals), Moscow: Mashinostroenie, 3rd ed., 1974.
Lakhtin, Yu.M. and Leont’eva, V.P., Materialovedenie (Materials Science), Moscow: Mashinostroenie, 1990.
Danilov, V.I. and Zuev, L.B., Usp. Fiz. Met., 2008, vol. 9, p. 371.
Pilipenko, N.N., Dolya, I.B., V’yugov, P.N., Lavrinenko, S.D., and Azhazha, R.V., Inorg. Mater., 2006, vol. 42, p. 617.
Ozhigov, L.S., V’yugov, P.N., Savchenko, V.I., Kozhevnikov, O.E., and Rudenko, A.G., Vopr. At. Nauki Tekh., Ser.: Materialoved. Nov. Mater., 2014, no. 1, p. 60.
Chernyaeva, T.P. and Gritsina, V.M., Vopr. At. Nauki Tekh., Ser.: Fiz. Radiats. Povrezhdenii Radiats. Materialoved., 2008, no. 2, p. 15.
Shchukin, E.D. and Savenko, V.I., Mendeleev Commun., 2019, vol. 29, p. 716.
Shchukin, E.D., Savenko, V.I., and Malkin, A.I., Lektsii po fiziko-khimicheskoi mekhanike (Lectures on Physicochemical Mechanics), Moscow: Nobel’ Press, 2015.
ACKNOWLEDGMENTS
We are grateful to N.N. Lozentsova and Yu.P. Toropov for the help in the preparation of powdered materials.
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Savenko, V.I., Klyuev, V.A. & Malkin, A.I. Granulometry of Metal Micropowders Treated in a Planetary-Type Ball Mill. Colloid J 84, 81–92 (2022). https://doi.org/10.1134/S1061933X22010112
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DOI: https://doi.org/10.1134/S1061933X22010112