Fe elementindekα→γ→δ Katı-Katı Faz Geçişlerinin Moleküler Dinamik Benzetimi ile İncelenmesi

Fe elementinin faz diyagramı incelendiğinde erime sıcaklığının altında farklı sıcaklıklarda farklı kristal yapılara sahip olduğu görülmektedir. Bu çalışmada 4000 atomdan oluşan Fe model sisteminde farklı sıcaklıklarda meydana gelen katı-katı faz dönüşümleri moleküler dinamik benzetim yöntemi kullanılarak incelenmeye çalışıldı. Çok cisim etkileşmelerini içeren Gömülmüş Atom Metodu(GAM) atomlar arasındaki etkileşmeleri hesaplamak için kullanıldı. Fe elementi için erime sıcaklığının altında oluşan α, γ ve δ fazları ve bu fazlar için dönüşüm sıcaklıkları belirlenerek sonuçlar deneysel değerlerle karşılaştırıldı. Model sistemin yapısal analizlerinde radyal dağılım fonksiyonu, termodinamik niceliklerde değişimler ve Ackland-Jones analiz yöntemi kullanıldı. Erime sıcaklığına kadar olan faz geçişlerinin gözlenmesi, hesaplamalarda kullanılan potansiyel fonksiyonunun Fe’nin sistemin modellenmesinde başarılı bir şekilde kullanılabileceğini göstermektedir.

The Investigation with Molecular Dynamic Simulation of α→γ→δ Solid-Solid Phase Transformation in Fe

When the phase diagram of the element Fe is examined, it is seen that it has different crystal structures at different temperatures below its melting temperature. In this study, the solid-solid phase transformations occurring at different temperatures in the Fe model system consisting of 4000 atoms were investigated using molecular dynamic simulation method. The Embedded Atom Method(EAM), which includes many body interactions, was used to calculate interactions between atoms. For the element Fe, the α, γ and δ phases formed below the melting temperature and the transformation temperatures for these phases were determined and the results were compared with the experimental values. Radial distribution function, changes in thermodynamic quantities and Ackland-Jones analysis method were used in the structural analysis of the model system.

___

  • [1] Engin C., Urbassek H.M., Molecular-dynamics investigation of the fcc-bcc phase transformation in Fe. Computational Materials Science 2008, 41: 297–304.
  • [2] Weissavach W., Malzeme Bilgisi ve Mayenesi, Birsen Yayın evi. 5. Baskı, İstanbul, 2009.
  • [3] Karewar S., Sietsma J., Santofimia M.J., Effect of pre-existing defects in the parent fcc phase on atomistic mechanisms during the martensitic transformation in pure Fe: A molecular dynamics study. Acta Materialia 2018, Vol.142: 71-81.
  • [4] Singh S.B., Mechanisms of bainite transformation in steels. Phase Transformations in Steels 2012; Vol 1: 385-416.
  • [5] Porter D.A., Easterling K.E., Phase Transformations in Metals and Alloys, 2nd ed., Chapman & Hall, London, 1992.
  • [6] Pepperhoff W., Acet M., Constitution and Magnetism of Iron and its Alloys, Springer, Berlin, 2001.
  • [7] Pereloma E., Edmonds D. V., Phase transformations in steels: Vol. 2 Diffusionless transformations, high strength steels, modelling and advanced analytical techniques. Oxford: Woodhead, 2012.
  • [8] Gandhi K.R.K., Singru R.M., Effect of bcc-fcc phase transition on the compton profiles of iron. Appl. Phys. A 1982, 28: 119–122.
  • [9] Cuenya B.R., et al., Observation of the fcc-to-bcc Bain transformation in epitaxial Fe ultrathin films on Cu3Au(001), Surface Science, 2001, vol. 493(1–3): pages 338-360.
  • [10] Haasen P., Physikalische Metallkunde, 3rd ed., Springer Berlin,1994.
  • [11] Entel P., Meyer R., Kadau K., Herper H.C., Hoffmann E., Martensitic transformations: first-principles calculations combined with molecular-dynamics simulations. Eur. Phys. J. B 1998, vol.5: 379-388.
  • [12] Porter D.A., Easterling K.E., Phase transformations in metals and alloys (2nd ed.), Chapman & Hall, London, 1992.
  • [13] Pepperhoff W., Acet M., Constitution and magnetism of iron and its alloys, Springer, Berlin, 2001.
  • [14] Pereloma E., Edmonds D.V. (Eds.), Phase transformations in steels, Diffusionless transformations, high strength steels, modelling and advanced analytical techniques, vol. 2, Woodhead Publishing Limited, Cambridge, 2012.
  • [15] Lee B., Shim J., Baskes M.I., Semiempirical atomic potentials for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, Al, and Pb based on first and second nearest-neighbor modified embedded atom method. Phys. Rev. B, 2003, 68B: 144112.
  • [16] Tateyama S., Shibuta Y., Kumagai T., Suzuki T., A Molecular Dynamics Study of Bidirectional Phase Transformation between bcc and fcc Iron. ISIJ Int. 2011, vol.51(10): 1710-1716.
  • [17] Lee T., et al, Atomistic modeling of thermodynamic equilibrium and polymorphism of iron. J. Phys.: Condens. Matter 2012, vol.24: 225404.
  • [18] Finnis M.W., Sinclair J.E., A simple empirical N-body potential for transition metals. Philosophical Magazine A 1984, vol.50(1): 45-55.
  • [19] Johnson R., Oh D., Analytic embedded atom method model for bcc metals. Journal of Materials Research 1989, vol.4(5), 1195-1201.
  • [20] Etesami S.A., Asadi E., Molecular dynamics for near melting temperatures simulations of metals using modified embedded-atom method. Journal of Physics and Chemistry of Solids, 2018, vol.112: 61–72.
  • [21] Chamati H., et al., Embedded-atom potential for Fe and its application to self-diffusion on Fe(100). Surface Science 2006, vol.600: 1793–1803.
  • [22] Mendelev M. I., et al., Development of new interatomic potentials appropriate for crystalline and liquid iron. Philosophical Magazine 2003, vol. 83, No. 35: 3977–3994.
  • [23] Cagin T., Dereli G., Uludogan M., Tomak, M., Thermal and mechanical properties of some fcc transition metals. Phys. Rev. B 1999, vol.59(4): 3468-3472.
  • [24] Zhang X.J., Chen C.L., Phonon dispersion in the Fcc metals Ca, Sr and Yb. J. Low Temp. Phys. 2012, vol.169: 40-50.
  • [25] Tolpin K.A., Bachurin V.I., Yurasova, V.E., Features of energy dependence of NiPd sputtering for various ion irradiation angles. Nucl. Instrum. Methods Phys. Res. B 2012, vol.273: 76-79.
  • [26] Louail L., Maouche D., Roumili A., Hachemi, A., Pressure effect on elastic constants of some transition metals. Mat. Chem. Phys. 2005, vol.91: 17-20.
  • [27] Daw, M.S., Hatcher, R.D., Application of the embedded atom method to phonons in transition metals. Solid State Comm. 1985, vol.56: 697-699.
  • [28] Voter A.F., Chen S.P.. Accurate Interatomic Potentials for Ni, Al, and Ni3Al. Mat. Res. Soc. Symp. Proc. 1987, vol.82: 175.
  • [29] Finnis M.W., and Sinclair, J.E. 1984. A simple empirical N-body potential for transition metals. Philosophical Magazine, 1984; 50: 45-55.
  • [30] Sutton, A.P., Chen, J.. Long-range Finnis-Sinclair potentials. J. Philosophical Magazine Letter, 1990; 61: 139-146.
  • [31] Parrinello, M., and Rahman, A.. Crystal Structure and Pair Potentials: A Molecular-Dynamics Study. Phys. Rev. Lett., 1980; 45: 1196-1201.
  • [32] Parrinello M., and Rahman, A.. Polymorphic transitions in single crystals: A new molecular dynamics method. J. Appl. Phys., 1981; 52: 7182-7190.
  • [33] http://lammps.sandia.gov/.LAMMPS Molecular Dynamics Simulator (Access Date:10.09.2020)
  • [34] Rigby, M., Smith, E. B., Wakeham, W. A., Maitland, G. C., The Forces Between Molecules, 144, Oxford University Press, Clarendon Press, 1986.
  • [35] Ackland G. J., and Jones A. P., Applications of local crystal structure measures in experiment and simulation. Physical Review B, 2006, vol.73: 054104.
  • [36] Karimi M., Stapay G., Kaplan T., Mostoller M., Temperature dependence of the elastic constants of Ni: reliability of EAM in predicting thermal properties. Modelling Simul. Mater. Sci. Eng. 1997, vol.5: 337.