519.8 A Diffusion Model of Cluster Evolution in a Heat-Resistant Nickel Alloy Metal Melt
Tyagunov A. G. (Ural Federal University), Zeyde K. M. (Universidad Politècnica Salesiana/University of Genoa), Milder O. B. (Ural Federal University), Tarasov D. A. (Ural Federal University)
NUMERICAL SIMULATION, MOVING BOUNDARY PROBLEM, MOLECULAR DYNAMICS, MELT, ELECTRICAL RESISTANCE
doi: 10.18698/2309-3684-2023-2-332
In this work, a mathematical model of the thermo-temporal evolution of a cluster in the melt of a heat-resistant nickel alloy ZhS6U is constructed. An initial-boundary value problem with a moving boundary is formulated, for the solution of which numerical modeling is used by the particle trajectory method, and a number of classical physical theories are used to describe evolutionary processes. To check the accuracy of the model, a physical experiment is involved in constructing polytherms and isotherms of the electrical resistance of the alloy under consideration. It has been confirmed that the Brownian diffusion model and Drude's theory of conductivity are applicable to describe both the temporal and temperature evolution of a cluster. The approach to modeling based on "hard balls" also justified itself. According to the simulation results, in the time range from 1690 to 1752 K, the number of particles in the cluster varies from 5000 to 2000, the average dynamic viscosity of the cluster varies from 3 to 2 * 1010 Pa * s, however, it is assumed that the central part is much denser than periphery. The cluster radius varies from 24 to 18 A, and the radius of the free zone around the cluster varies from 56 to 43 A. The directions of further development of the model are determined.
Johnston R. L. Atomic and Molecular Clusters. London, Taylor and Francis, 2002, 208 p.
Kotton F. A., Uolton R. Kratnye svyazi metall — metall [Multiple metal-metal bonds]. Moscow, Mir Publischers, 1985, 535 p.
Gubin S. P. Himiya klasterov: Osnovy klassifikacii i stroenie [Chemistry of clusters: Basics of classification and structure]. Moscow, “Nauka” Publishers, 1987, 262 p.
Haberland H. Clusters of atoms and moleculs. Berlin, Heidelberg: Springer-Verlag, 1994, 425 p.
Quinn C.M., McKernan J.G.R., Redmond G.B. Point-group regular representations and the densities of states in finite metal clusters. Faraday Transactions 2: Molecular and Chemical Physics. Journal of the Chemical Society, 1984, vol. 80, no. 12, pp. 1507-1511.
Suzdalev I.P. Nanotekhnologiya: fizikohimiya nanoklasterov, nano-struktur, nanomaterialov [Nanotechnology: physical chemistry of nanoclusters, nanostructures, nanomaterials]. Moscow, URSS, 2005, 589 p.
Frenkel' YA.I. Kineticheskaya teoriya zhidkostej [Kinetic theory of liquids]. Leningrad, “Nauka” Publishers, 1975, 594 p.
Elliott S.R. Medium-Range Structural Order in Covalent Amorphous Solids. Nature, 1991, vol. 354, no. 6353, pp. 445-452.
Lifshic B.G. Metallografiya [Metallography]. Moscow, Metallurgiya [Metallurgy], 1990, 236 p.
ZHukova L.A. Stroenie metallicheskih zhidkostej: Uch. posobie [The structure of metallic liquids: Uch. allowance]. Ekaterinburg, USTU, 2002, 46 p.
Arkharov V.I., Novokhatsky I.A. O kvazipolikristallicheskoj modeli rasplavov [About the quasi-polycrystalline model of melts]. In the collection: Stroenie i svojstva metallicheskih i shlakovyh rasplavov [Structure and properties of metal and slag melts]. Sverdlovsk, 1974, pp. 52-54.
Polukhin V.A., Vatolin N.A., Potemkina E.A. Strukturnye edinicy blizhnego poryadka v amorfnyh metallah i poluprovodnikah [Structural units of short-range order in amorphous metals and semiconductors]. Inorganic Materials: Applied Research. 2002, №2, pp. 8-13.
Turnball D. Kinetics of solidification of supercooled liquid mercury droplets. The Journal of Chemical Physics. 1952, vol. 20, no. 3, pp. 411-424.
Vatolin N.A., Pastukhov E.A., Lisin V.L., Denisov V.M., Kachin S.V. Difrakcionnye issledovaniya stroeniya vysokotemperaturnyh rasplavov [Diffraction studies of the structure of high-temperature melts]. Ekaterinburg, UB RAS, 2003, 357 p.
Popel S.I., Spiridonov M.A., Zhukova L.A. Atomnoe uporyadochenie v rasplavlennyh i amorfnyh metallah (po dannym elektronografii) [Atomic ordering in molten and amorphous metals (according to electron diffraction data)]. Ekaterinburg, USTU, 1997, 382 p.
Popel P.S. Metastabil'naya mikrogeterogennost' rasplavov evtektikoj i monotektikoj i ee vliyanie na strukturu splava posle zatverdevaniya [Metastable microheterogeneity of eutectic and monotectic melts and its effect on the alloy structure after solidification]. Russian Metallurgy, 2005, no. 1, pp. 22-48.
Popel P.S., Presnyakova E.L., Pavlov V.A., Arkhangelsky E.L. Oblast' sushchestvovaniya metastabil'noj kvazievtekticheskoj struktury v sisteme Sn-Pb[The region of existence of a metastable quasi-eutectic structure in the Sn-Pb system]. Russian Metallurgy (Metally), 1985, no. 4, pp. 198-201.
Gavrilin I.V. Osnovy modeli mikroneodnorodnogo stroeniya zhidkih metallo[Fundamentals of the model of microinhomogeneous structure of liquid metals]. Povyshenie kachestva otlivok i slitkov [Improving the quality of castings and ingots], 1979, no. 2, 5 p.
Gavrilin I.V. Plavlenie i kristallizaciya metallov i splavov [Melting and crystallization of metals and alloys]. Vladimir, VISU, 2000, 260 p.
Skrebtsov A. M. Izuchenie strukturnyh perestroek v zhidkih metallah na model'nom rasplave [Study of structural rearrangements in liquid metals on a model melt]. Reporter of the Priazovskyi state technical university. Section: Technical sciences, 2008, no. 18, pp. 61–65.
Novokhatsky I. A., Yaroshenko A. V. Opredelenie plotnosti metallicheskih zhidkostej v pripoverhnostnyh sloyah s uchetom yavleniya klasternoj adsorbcii [Determination of the Density of Metallic Liquids in Surface Layers Taking into Account the Cluster Adsorption Phenomenon]. Trudy Odesskogo politekhnicheskogo universiteta [Proceedings of the Odessa Polytechnic University], 2002, no. 1 (17), pp. 1–5.
Gay S. L. Osobennosti processa kristallizacii metallov [Features of the process of crystallization of metals]. Vesnik of Yanka Kupala State University of Grodno. Series 6. Engineering Science, 2012, no. 2, pp. 36–43.
Ilyinsky A. G. Osobennosti atomnogo stroeniya metallicheskih materialov v zhidkom i amorfnom sostoyaniyah [Features of the atomic structure of metallic materials in liquid and amorphous states]. Nanosistemi, nanomaterіali, nanotekhnologії [Nanosystems, nanomaterials, nanotechnologies], 2010, vol. 8, no. 3, pp. 483–502.
Li Y., Chen W. Z., Dong B. S., Zhou S. X. Effects of metalloid content on viscosity of Fe-Si-B-P-C alloy melt. Journal of Non-Crystalline Solids, 2018, vol. 490, pp. 31-34.
Zu F. Q., Zhou B., Li X. F., Yi X., Chen Y. Effect of liquid-liquid structure transition on solidification of Sn-Bi alloys. Transactions of Nonferrous Metals Society of China, 2007, vol. 17, no. 5, pp. 893-897.
Rao K.R. Phase transitions in liquids. Current Science, 2001, vol. 80, no. 9, pp. 1098–1100.
Yarger J.L., Wolf G.H. Polymorphism in Liquids. Science, 2004, vol. 306, no. 5697, pp. 820–821.
Tyagunov A., Milder O., Tarasov D., Tyagunov G. LLT Structural Changes in Metal Liquids as a Basis for a Thermal Treatment Technology of Melts: a review. Phase Transitions, 2021, vol. 94, no. 1, pp. 1–22.
Myers T.G., Hennessy M.G., Calvo-Schwarzwälder M. The Stefan problem with variable thermophysical properties and phase change temperature. International Journal of Heat and Mass Transfer, 2020, vol. 149, pp. 118975.
Koga S., Diagne M., Krstic M. Control and State Estimation of the One-Phase Stefan Problem via Backstepping Design. IEEE Transactions on Automatic Control, 2019, vol. 64, no. 2, pp. 510–525.
Markov S.I. Multiscale Nonconformal Finite Element Methods for Solving Problems with Moving Boundaries. XIV International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering (APEIE), Russia, Novosibirsk, 2018, no. 18303723.
Munjiza A. The combined finite-discrete element method for structural failure and collapse. Engineering fracture mechanics, 2004, vol. 71, no. 4-6, pp. 469-483.
Pestov K.N., Lyubimova O.N., Ostanin M.V. Ob odnom chislennom metode resheniya zadach tipa Stefana [On a numerical method for solving Stefan-type problems]. Vestnik CHGPU. Seriya: Mekhanika predel'nogo sostoyaniya [Bulletin of ChGPU. Series: Limit State Mechanics], 2019, vol. 41, no. 3, pp. 51–60.
He L., Zheng J., Zheng Ya., Chen J., Zhou X., Xiao Z. Parallel algorithms for moving boundary problems by local remeshing. Engineering Computations, 2019, vol. 36, no. 8, pp. 2887–2910.
Grishanov A.N. Эффективный метод построения приближенных решений с применением многосеточных конечных элементов. Doklady Akademii nauk vysshej shkoly Rossijskoj Federacii [Reports of the Academy of Sciences of Higher Education of the Russian Federation], 2018, no. 3(40), pp. 47–57.
Kees C.E., Farthing M.W., Berger R.C., Lackey T.C. A Review of Methods for Moving Boundary Problems. Navigation Systems Research Program, 2009, Vol. ERDC/CHL TR-09-10.
Bowler K.C., Pawley G.S. Molecular Dynamics and Monte Carlo Simulations in Solid-state and Elementary Particle Physics. Proceedings of the IEEE, 1984, vol. 72, no. 1, pp. 42-55.
Unge M. Electron mobility edge in amorphous polyethylene. IEEE International Conference on Dielectrics (ICD), 2016, vol. 2, pp. 828-831.
Baba H., Urano R., Nagai T., Okazaki S. Prediction of self-diffusion coefficients of chemically diverse pure liquids by all-atom molecular dynamics simulations. Journal of Computational Chemistry, 2022, vol. 43, no. 28, pp. 1892–1900.
Gross W.J., Vasileska D., Ferry D.K. A Novel Approach for Introducing the Electron–Electron and Electron–Impurity Interactions in Particle-Based Simulations. IEEE Electron device letters, 1999, vol. 20, no. 9, pp. 463-465.
Zeyde K.M. The Motion of Electrons under the Action of Inertial Forces in the Rarefied Medium. 2022 3rd URSI Atlantic and Asia Pacific Radio Science Meeting (AT-AP-RASC), 2022. DOI: 10.23919/AT-AP-RASC54737.2022.9814326.
Williams J.R., O’Connor R. Discrete Element Simulation and the Contact Problem. Archives of Computational Methods in Engineering, 1999, vol. 6, no. 4, pp. 279—304.
Thornton A., Weinhart T., Luding S., Bokhove O. Modeling of particle size segregation: calibration using the discrete particle method. International Journal of Modern Physics C, 2012, vol. 23, no. 8, pp. 1240014.
Zeyde K.M. Electrodynamic interpretation of the results of electron dynamics modeling using the discrete element method. Ural Radio Engineering Journal, 2020, vol. 4, no. 1, pp. 33-50.
Zeyde K.M. Mercury DPM adaptation for electromagnetic microscopic DEM simulation. 2019 IEEE-APS Topical Conference on Antennas and Propagation in Wireless Communications (APWC 2019), 2019, p. 136-.
Li X., Li D., Yue H., Zhang Z., Liu K., Fan M., Chen D. A high precision particle-moving algorithm for particle-in-cell simulation of plasma. IEEE Transactions on magnetics, 2015, vol. 51, no. 3, pp. 1-4.
Kancleris Z., Šlekas G., Matulis A. Modeling of Two-Dimensional Electron Gas Sheet in FDTD Method. IEEE Transactions on antennas and propagation, 2013, vol. 61, no. 2, pp. 994–996.
Romanczuk P., Bär M., Ebeling W., Lindner B., Schimansky-Geier L. Active Brownian particles. From individual to collective stochastic dynamics. The European Physical Journal. Special Topics, 2012, vol. 202, pp. 1–162.
Melkikh A.V., Povzner A.A., Shumikhina K.A. Molekulyarnaya fizika. Uchebnoe posobie [Molecular physics. Tutorial]. Ekaterinburg, UrFU, 2006, 242 p.
Andrade-Neto A.V. Dielectric function for free electron gas: comparison between Drude and Lindhard model. Revista Brasileira de Ensino de F´ısica, 2017, vol. 39, no. 2, pp. 1-8.
Chang T., Mukherjee S., Watkins N.N., Stobbe D.M., Mays O., Baluyot E.V., Pascall A.J., Tringe J.W. In situ monitoring for liquid metal jetting using a millimeter wave impedance diagnostic. Scientific Reports, 2020, vol. 10, no. 22325, pp. 1-9.
Wang L. Atomistics of self-diffusion in liquid metals. EPJ Web of Conferences, 2017, vol. 151, no. 02004, pp. 1-9.
Rizvi S.M.H., Mazhari B. An Analytical Approach to Model the Effects of Diffusion in Space-Charge-Limited Current in Organic Semiconductor Films. 2018 4th IEEE International Conference on Emerging Electronics (ICEE), 2019, art. no. 19256716. DOI: 10.1109/ICEE44586.2018.8937967.
Kim M., Zydney A.L. Effect of electrostatic, hydrodynamic, and Brownian forces on particle trajectories and sieving in normal flow filtration. Journal of Colloid and Interface Science, 2004, vol. 269, no. 2, pp. 425–431.
Abgaryan K.K., Eliseev S.V., Zhuravlev A.A., Reviznikov D.L. Нigh-speed penetration. Discrete-element simulation and experiments. Computer research and modeling, 2017, vol. 9, no. 6, pp. 937–944.
Heitzinger C., Ringhofer C., Ahmed S., Vasileska D. Accurate three-dimensional simulation of electron mobility including electron-electron and electron-dopant interactions. Proceedings - Electrochemical Society, 2005, vol. PV 2004-13, pp. 165-183.
Bird R.B., Stewart W.E., Lightfoot E.N. Transport Phenomena. Hoboken, John Wiley & Sons, 2007, 905 p.
Ojovan M.I. Viscous flow and the viscosity of melts and glasses. Physics and Chemistry of Glasses, 2012, vol. 53, no. 4, pp. 143–150.
Varshneya A.K. Fundamentals of Inorganic Glasses. New York, Academic Press, 1994, 570 p.
Povadator A.M., Vyuhin V.V., Tsepelev V.S., Tyagunov A.G. Sposob beskontaktnogo izmereniya elektricheskogo soprotivleniya metallicheskogo tverdogo obrazca ili ego rasplava metodom vrashchayushchegosya magnitnogo polya i ustrojstvo dlya ego osushchestvleniya [A method for non-contact measurement of the electrical resistance of a metallic solid sample or its melt by the method of a rotating magnetic field and a device for its implementation]. Invention Patent№2299425, May 20, 2007.
Tyagunov G.V., Tsepelev V.S., Tyagunov A.G., Baryshev E.E., Vyuhin V.V., Driver A.M. Ustrojstvo dlya opredeleniya intensivnosti strukturnoj perestrojki rasplavov zharoprochnyh splavov [Device for determining the intensity of structural rearrangement of melts of heat-resistant alloys]. Patent RUS no. 157157, 20.11.2015.
Tyagunov G.V., Tsepelev V.S., Povodator A.M., Baryshev E.E., Vyuhin V.V., Tyagunov A.G., Mushnikov V.S. Ustrojstvo ocenki ravnovesnosti metallicheskih rasplavov [Device for evaluating the equilibrium of metal melts]. Utility model patent RUS 182131, 26.12.2017
Тягунов А.Г., Зейде К.М., Мильдер О.Б., Тарасов Д.А. Диффузионная модель эволюции кластера в металлическом расплаве жаропрочного никелевого сплава. Математическое моделирование и численные методы, 2023, № 2, с. 3–32.
Download article
Количество скачиваний: 364