Sıvı Vanadyumun Kristalizasyon Sürecine Soğutma Oranı Etkisinin Moleküler Dinamik Benzetim Metodu ile İncelenmesi

Isıtma ve soğutma süreçlerinde vanadyumun mikro yapısal değişimleri ve soğutma hızının kristalizasyon süreci üzerine etkileri gömülü atom metodu kullanılarak moleküler dinamik benzetim yöntemi ile araştırıldı. Soğutma oranın etkisi sekiz farklı soğutma oranı (Q=0.05-10 K/ps) kullanılarak araştırıldı ve sonuçlar çiftler dağılım fonksiyonu, Honeycutt-Andersen ve Voronoi mozaikleme analiz yöntemleri kullanılarak analiz edildi ve ayrıntılı bir şekilde tartışıldı. Erime noktası civarında hesaplanan çiftler dağılım fonksiyonu ve yapı faktörünün deneysel sonuçlarla tutarlı olduğu gözlenmiştir. Daha yavaş soğutma oranları için kristalizasyon sıcaklığından başlayarak ideal bcc kristal yapıyı temsil eden 1441 ve 1661 bağlı çiftlerinin ve <0,6,0,8> kümelerinin ani ve bir o kadar keskin bir artışı izlenmiştir. Daha düşük sıcaklıklarda söz konusu bağlı çiftlerin ve kümelerin dağılımlarının ısıtma sürecinde elde edilen sonuçlarla neredeyse üst üste olduğu gözlenmiştir. Bu sonuçlar yavaş soğutma oranları için sistemin sıvı yapıdan ideal bcc kristal yapıya geçiş yaptığının açık delilidir. Sistem daha hızlı soğutulduğunda, bcc kümelerin yanı sıra başka kristal kümelerin de oluştuğu gözlenmiştir.

Anahtar Kelimeler:

Kristalizasyon, Gömülü Atom Metodu, Çiftler Analiz, Voronoi Mozaikleme

Investigation of Cooling Rate Effect of Liquid Vanadium on the Crystallization Process with Molecular Dynamic Simulation Method

The microstructural changes of vanadium in the heating and cooling processes and the effects of the cooling rate on the crystallization process were investigated by the molecular dynamics simulations method using the embedded atom method. The effect of the cooling rate was investigated using eight different cooling rates (Q=0.05-10 K/ps), and the results were analyzed and discussed in detail using the pair distribution function, Honeycutt-Andersen and Voronoi tessellation analysis methods. It was observed that the pair distribution function and structure factor calculated around the melting point were consistent with the experimental results. Starting from the crystallization temperature point for slower cooling rates, there was a sudden and sharp increase in the number of 1441 and 1661 bounded pairs and <0,6,0,8> clusters representing the ideal bcc crystal structure. It was observed that the distributions of these bonded pairs and clusters at lower temperatures were nearly overlapping with the results obtained during the heating process. These results are clear evidence that the system transition from liquid to ideal bcc crystal structure for slow cooling rates. When the system was cooled faster, it was observed that it formed in other crystal clusters besides bcc clusters.

Keywords:

Crystallization, Embedded Atom Method, Voronoi Tessellation, Pair Analysis,

PDF

___

Alder, B. J., Wainwright, T. E. 1957. "Phase Transition for a Hard Sphere System", The Journal of Chemical Physics, 27(5), 1208–1209.
Alexander, S., McTague, J. 1978. "Should All Crystals Be bcc? Landau Theory of Solidification and Crystal Nucleation", Physical Review Letters, 41(10), 702–705.
Ashkenazy, Y., Averback, R. S. 2010. "Kinetic stages in the crystallization of deeply undercooled body-centered-cubic and face-centered-cubic metals", Acta Materialia, 58(2), 524–530.
Bolef, D. I., Smith, R. E., Miller, J. G. 1971. "Elastic Properties of Vanadium. I. Temperature Dependence of the Elastic Constants and the Thermal Expansion", Physical Review B, 3(12), 4100–4108.
Celik, F. A. 2012. "Molecular dynamics simulation of crystallization of amorphous aluminium modelled with EAM", Bitlis Eren University Journal of Science and Technology, 2, 44–48.
Celtek, M., Sengul, S. 2018a. "The characterisation of atomic structure and glass-forming ability of the Zr–Cu–Co metallic glasses studied by molecular dynamics simulations", Philosophical Magazine, 98(9), 783–802.
Celtek, M., Sengul, S. 2018b. "Thermodynamic and dynamical properties and structural evolution of binary Zr 80 Pt 20 metallic liquids and glasses: Molecular dynamics simulations", Journal of Non-Crystalline Solids, 498, 32–41.
Çeltek, M., Şengül, S. 2019. "Effects of cooling rate on the atomic structure and glass formation process of Co90Zr10 metallic glass investigated by molecular dynamics simulations", Turkish Journal of Physics, 43(1), 11–25.
Celtek, M., Sengul, S., Domekeli, U. 2017. "Glass formation and structural properties of Zr50Cu50-xAlx bulk metallic glasses investigated by molecular dynamics simulations", Intermetallics, 84, 62–73.
Çeltek, M., Şengül, S., Dömekeli, Ü. 2019. "Hızlı Soğutma Sürecinde Dörtlü Zr48Cu36Ag8Al8 İri Hacimli Metalik Camının Atomik Yapısının Gelişimi", Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 23(3), 954–962.
Celtek, M. 2019. "The effect of atomic concentration on the structural evolution of Zr100-xCox alloys during rapid solidification process", Journal of Non-Crystalline Solids, 513, 84–96.
Chung, H. M., Loomis, B. A., Smith, D. L. 1996. "Development and testing of vanadium alloys for fusion applications", Journal of Nuclear Materials, 239, 139–156.
Daw, M. S., Baskes, M. I. 1984. "Embedded atom method: derivation and application to impurities,surfaces and other defects in metal", Phsical Review B, 29(12), 6443–6453.
Debela, T. T., Wang, X. D., Cao, Q. P., Zhang, D. X., Jiang, J. Z. 2014. "The crystallization process of liquid vanadium studied by ab initio molecular dynamics", Journal of Physics: Condensed Matter, 26(15), 155101.
Debela, T. T., Wang, X. D., Cao, Q. P., Zhang, D. X., Wang, S. Y., Wang, C. Z., Jiang, J. Z. 2014. "Atomic structure evolution during solidification of liquid niobium from ab initio molecular dynamics simulations", Journal of Physics Condensed Matter, 26(5), 055004
Egry, I., Holland-Moritz, D. 2011. "Levitation methods for structural and dynamical studies of liquids at high temperatures", European Physical Journal: Special Topics.
Ganesh, P., Widom, M. 2006. "Signature of nearly icosahedral structures in liquid and supercooled liquid copper", Physical Review B, 74(13), 134205.
Greiner, J. D., Carlson, O. N., Smith, J. F. 1979. "Single‐crystal elastic constants of vanadium and vanadium with oxygen additions", Journal of Applied Physics, 50(6), 4394–4398.
Haynes, W. M. 2015. "CRC Handbook of Chemistry and Physics 95th Edition", CRC Press LLC, Boca Raton.
Honeycutt, J. D., Andersen, H. C. 1987. "Molecular Dynamics Study of Melting and Freezing of Small Lennard- Jones Clusters", Journal of Physical Chemistry, 91(24), 4950–4963.
Hoyt, J. J., Asta, M., Sun, D. Y. 2006. "Molecular dynamics simulations of the crystal–melt interfacial free energy and mobility in Mo and V", Philosophical Magazine, 86(24), 3651–3664.
Itami, T., Munejiri, S., Masaki, T., Aoki, H., Ishii, Y., Kamiyama, T., Hoshino, K. 2003. "Structure of liquid Sn over a wide temperature range from neutron scattering experiments and first-principles molecular dynamics simulation: A comparison to liquid Pb", Physical Review B, 67(6), 064201.
Jakse, N., Pasturel, A. 2003. "Local Order of Liquid and Supercooled Zirconium by Ab Initio Molecular Dynamics", Physical Review Letters, 91(19), 195501.
Jakse, N., Pasturel, A. 2004. "Ab initio molecular dynamics simulations of local structure of supercooled Ni", The Journal of Chemical Physics, 120(13), 6124–6127.
Kelton, K. F., Lee, G. W., Gangopadhyay, A. K., Hyers, R. W., Rathz, T. J., Rogers, J. R., Robinson, D. S. 2003. "First X-Ray Scattering Studies on Electrostatically Levitated Metallic Liquids: Demonstrated Influence of Local Icosahedral Order on the Nucleation Barrier", Physical Review Letters, 90(19), 195504.
Kim, T. H., Lee, G. W., Sieve, B., Gangopadhyay, A. K., Hyers, R. W., Rathz, T. J., Goldman, A. I. 2005. "In situ High-Energy X-Ray Diffraction Study of the Local Structure of Supercooled Liquid Si", Physical Review Letters, 95(8), 085501.
Kittel, C. 1986. "Introduction to Solid State Physics", John Wiley Sons Inc, New York.
Lou, H., Wang, X., Cao, Q., Zhang, D., Zhang, J., Hu, T., Jiang, J.-Z. 2013. "Negative expansions of interatomic distances in metallic melts", Proceedings of the National Academy of Sciences, 110(25), 10068–10072.
Mandell, M. J., McTague, J. P., Rahman, A. 1977. "Crystal nucleation in a three‐dimensional Lennard‐Jones system. II. Nucleation kinetics for 256 and 500 particles", The Journal of Chemical Physics, 66(7), 3070–3075.
Mauro, N. A., Bendert, J. C., Vogt, A. J., Gewin, J. M., Kelton, K. F. 2011. "High energy x-ray scattering studies of the local order in liquid Al", The Journal of Chemical Physics, 135(4), 044502.
Morishita, K., Diaz De La Rubia, T. 1995. "A Molecular Dynamics Simulation Study of Defect Production in Vanadium", MRS Proceedings, 396, 39.
Olsson, P. A. T. 2009. "Semi-empirical atomistic study of point defect properties in BCC transition metals", Computational Materials Science, 47(1), 135–145.
Ori, G., Montorsi, M., Pedone, A., Siligardi, C. 2011. "Insight into the structure of vanadium containing glasses: A molecular dynamics study", Journal of Non-Crystalline Solids, 357(14), 2571-2579.
Pan, S.-P., Feng, S.-D., Qiao, J.-W., Wang, W.-M., Qin, J.-Y. 2015. "Crystallization pathways of liquid-bcc transition for a model iron by fast quenching", Scientific Reports, 5(1), 16956.
Plimpton, S. 1995. "Fast Parallel Algorithms for Short-Range Molecular Dynamics", Journal of Computational Physics, 117(1), 1–19.
Schenk, T., Holland-Moritz, D., Simonet, V., Bellissent, R., Herlach, D. M. 2002. "Icosahedral Short-Range Order in Deeply Undercooled Metallic Melts", Physical Review Letters, 89(7), 075507.
Schöpe, H. J., Bryant, G., van Megen, W. 2006. "Two-Step Crystallization Kinetics in Colloidal Hard-Sphere Systems", Physical Review Letters, 96(17), 175701.
Schuh, C., Hufnagel, T., Ramamurty, U. 2007. "Mechanical behavior of amorphous alloys", Acta Materialia, 55(12), 4067–4109.
Sengul, S. 2020. "Evolution of local structure during melting of Zr0.7Pd0.3 nanowires by molecular dynamics simulations", Vacuum, 174, 109197.
Sengul, S., Celtek, M., Domekeli, U. 2020. "The structural evolution and abnormal bonding ways of the Zr80Pt20 metallic liquid during rapid solidification under high pressure", Computational Materials Science, 172, 109327.
Sengul, S, Celtek, M. 2018. "Pressure Effects on the Structural Evolution of Monatomic Metallic Liquid Hafnium", BEU Journal of Science, 7(1), 144–158.
Shuleshova, O., Löser, W., Holland-Moritz, D., Herlach, D. M., Eckert, J. 2012. "Solidification and melting of high temperature materials: In situ observations by synchrotron radiation", Journal of Materials Science, 47, 4497–4513.
Silvestrelli, P. L., Ambrosetti, A. 2019. "Liquid-glass transition in monoatomic vanadium: A first-principles study", Physical Review B, 99(9), 094201.
Sorkin, V., Polturak, E., Adler, J. 2003a. "Molecular dynamics study of melting of the bcc metal vanadium. I. Mechanical melting", Physical Review B - Condensed Matter and Materials Physics., 68, 174102.
Sorkin, V., Polturak, E., Adler, J. 2003b. "Molecular dynamics study of melting of the bcc metal vanadium. II. Thermodynamic melting", Physical Review B, 68(17), 174103.
Stukowski, A. 2010. "Visualization and analysis of atomistic simulation data with OVITO-the Open Visualization Tool", Modelling and Simulation in Materials Science and Engineering, 18(1), 015012.
Thakor, P. B., Sonvane, Y. A., Jani, A. R. 2011. "Structural properties of some liquid transition metals", Physics and Chemistry of Liquids, 49(4), 530–549.
Todorov, I. T., Smith, W., Trachenko, K., Dove, M. T. 2006. "DL_POLY_3: new dimensions in molecular dynamics simulations via massive parallelism", Journal of Materials Chemistry, 16(20), 1911.
Voronoi, G. 1908. "New Parametric Applications Concerning the Theory of Quadratic Forms - Second Announcement", J. Reine Angew. Math., 134, 198–287.
Waseda, Y. 1981. "The Structure of Non-Crystalline Materials-Liquids and Amorphous Solids", London: McGraw-Hill, New York.
Wu, S., Fang, X. W., Wang, S. Y., Wang, C. Z., Yao, Y. X., Ho, K. M., Chen, L. Y. 2011. "Fluctuation between icosahedral and body-centered-cube short-range orders in undercooled Zr liquid", Journal of Applied Physics, 110(10), 103518.
Zhang, L., Huang, H. 2006. "Young’s moduli of ZnO nanoplates: Ab initio determinations", Applied Physics Letters, 89, 183111.
Zinkle, S., Matsui, H., Smith, D., Rowcliffe, A., Van Osch, E., Abe, K., Kazakov, V. 1998. "Research and development on vanadium alloys for fusion applications", Journal of Nuclear Materials, 258–263, 205–214.