Calculation of the Thermodynamic Characteristics of Fe–P System by the Molecular Dynamics Method

  • 5 Accesses


The problem of dephosphorization of iron-carbon alloys is relevant for the metallurgical industry, since a high concentration of phosphorus contributes to the appearance of a number of extremely undesirable phenomena. A lot of experimental work has been devoted to solving this problem, but it has still not been completely possible to cope with it. Any field experiments aimed at studying the process of phosphorus removal require considerable material and time costs, but at the same time do not guarantee getting the desired result. Therefore, to search for new approaches to solving this problem, it is much more rational to use numerical simulation methods involving the computational capabilities of modern computers. At present, computer experiments are the same recognized research method as theoretical research and real experiment. To study the behavior of phosphorus atoms in iron using a numerical experiment, it is necessary to build a computational model and test it by calculating various characteristics whose values are known in advance. In this paper, the method of molecular dynamics was chosen as the method of computer simulation. Using this method, one can conduct experiments with given atomic velocities and describe dynamics of the studied processes. To describe the interparticle interaction, we used the potential calculated in the framework of the immersed atom method. The study was conducted on a computational cell simulating α-iron crystal with phosphorus substitution atoms. The constructed model demonstrated satisfactory results when calculating the known characteristics of the simulated system. Dependencies of changes in such characteristics as temperature coefficient of linear expansion, melting point, latent heat of melting and heat capacity on the concentration of phosphorus atoms, as well as in some cases on magnitude of the applied external pressure, were established. Calculations showed that, for example, the phosphorus concentration of 0.5% leads to an increase in the average thermal coefficient of linear expansion by 9%, a decrease in temperature and latent heat of fusion by 5% and a heat capacity by 7%.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.


  1. 1

    Daud, A.D., Semin, A.E., Kotel’nikov, G.I., and Shchukina, L.E., Dephosphorization of high-chromium steels by using rare earth oxides, Izv. Vyssh. Uchebn. Zaved., Chern.Metall., 2017, vol. 60, no. 1, pp. 54–59.

  2. 2

    Robei, R. and Uaitkhed, M., Ladle treatment of pig iron at specific production conditions, MRT. Metall. Proizvod. Tekhnol. Metall. Protsess., 2014, no. 1, pp. 16–24.

  3. 3

    Georgadze, A.G., Gerner, V.I., Elashvili, M.I., Nikiforov, P.A., Pletnev, A.N., and Smirnov, S.A., Conditions for dephosphorization of liquid metal in a casting ladle, Lit’e Metall., 2012, vol. 67, no. 3, pp. 117–119.

  4. 4

    Starostenkov, M.D., Potekaev, A.I., Grinkevich, L.S., Kulagina, V.V., and Markidonov, A.V., Dynamics of edge dislocations in a low-stability FCC-system irradiated by high-energy particles, Russ. Phys. J., 2017, vol. 59, no. 9, pp. 1446–1453.

  5. 5

    Markidonov, A.V., Starostenkov, M.D., and Smirnova, M.V., Self-diffusion process in an FCC crystal caused by the passage of a shock wave, Russ. Phys. J., 2015, vol. 58, no. 6, pp. 828–832.

  6. 6

    Markidonov, A.V., Starostenkov, M.D., and Poletaev, G.M., Transformation of nanopores in gold under conditions of thermoactivation and the effects of acoustic and shock waves, Bull. Russ. Acad. Sci.: Phys., 2015, vol. 79, no. 9, pp. 1089–1092.

  7. 7

    Markidonov, A.V., Starostenkov, M.D., and Tabakov, P.Y., Splitting vacancy voids in the grain boundary region by a post-cascade shock wave, Mater. Phys. Mech., 2013, vol. 18, no. 2, pp. 148–155.

  8. 8

    Andersen, H.C., Molecular dynamics simulations at constant pressure and/or temperature, J. Chem. Phys., 1980, vol. 72, no. 4, pp. 2384–2393.

  9. 9

    Daw, M.S. and Baskes, M.I., Embedded-atom method: Derivation and application to impurities and other defects in metals, Phys. Rev. B, 1984, vol. 29, no. 12, pp. 6443–6453.

  10. 10

    Foiles, S.M., Baskes, M.I., and Daw, M.S., Embedded-atom-method functions for the FCC metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Phys. Rev. B, 1986, vol. 33, no. 12, pp. 7983–7991.

  11. 11

    Biersack, J.P. and Ziegler, J.F., Refined universal potentials in atomic collisions, Nucl. Instrum. Methods, 1982, vol. 194, pp. 93–100.

  12. 12

    Ackland, G.J., Mendelev, M.I., Srolovitz, D.J., Han, S., and Barashev, A.V., Development of an interatomic potential for phosphorus impurities in α-iron, J. Phys.: Condens. Matter, 2004, vol. 16, pp. 2629–2642.

  13. 13

    Ko, W.-S., Kim, N.-J., and Lee, B.-J., Atomistic modeling of an impurity element and a metal–impurity system: pure P and Fe–P system, J. Phys.: Condens. Matter, 2012, vol. 14, pp. 225002–225016.

  14. 14

    Grigor’ev, I.S. and Meilikhov, E.Z., Fizicheskie velichiny: spravochnik (Physical Quantities: Handbook), Moscow: Energoatomizdat, 1991.

  15. 15

    Belonoshko, A.B., Skorodumova, N.V., Rosengren, A., and Johansson, B., Melting and critical superheating, Phys. Rev. B, 2006, vol. 73, pp. 0122011–0122013.

  16. 16

    Mazhukin, V.I., Shapranov, A.V., Perezhigin, V.E., Koroleva, O.N., and Mazhukin, A.V., Kinetic melting and crystallization stages of strongly superheated and supercooled metals, Math. Models Comput. Simul., 2017, vol. 9, no. 4, pp. 448–456.

  17. 17

    Yang, H., Lu, Y., Chen, M., and Guo, Z., A molecular dynamics study on melting point and specific heat of Ni3Al alloy, Sci. China, Ser. G: Phys.,Mech. Astron., 2007, vol. 50, no. 4, pp. 407–413.

  18. 18

    Tablitsa fizicheskikh velichin: spravochnik (Table of Physical Quantities: Handbook), Kikoin, I.K., Ed., Moscow: Atomizdat, 1976.

  19. 19

    Zaitsev, I.D., Zozulya, A.F., and Aseev, G.G., Mashinnyi raschet fiziko-khimicheskikh parametrov neorganicheskikh veshchestv (Automated Calculation of Physicochemical Parameters of Inorganic Substances), Moscow: Khimiya, 1983.

  20. 20

    Zinov’ev, V.E., Teplofizicheskie svoistva metallov pri vysokikh temperaturakh: spravochnik (Thermophysical Properties of Metals at High Temperatures: Handbook), Moscow: Metallurgiya, 1989.

Download references

Author information

Correspondence to A. V. Markidonov.

Additional information

Translated by K. Gumerov

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Markidonov, A.V., Lubyanoi, D.A., Kovalenko, V.V. et al. Calculation of the Thermodynamic Characteristics of Fe–P System by the Molecular Dynamics Method. Steel Transl. 49, 606–611 (2019).

Download citation


  • crystal
  • impurity
  • molecular dynamics
  • potential
  • EAM
  • temperature
  • pressure
  • heat
  • enthalpy