Advertisement

Powder Metallurgy and Metal Ceramics

, Volume 56, Issue 5–6, pp 253–263 | Cite as

Potential Size-Dependent Temperature Hysteresis of the First-Order Phase Transition in a Nanoscale Metallic Powder

  • A. S. Shirinyan
  • Yu. S. Bilogorodsky
  • V. A. Makara
NANOSTRUCTURED MATERIALS
  • 21 Downloads

The paper describes the evolution of a nanoscale powder in the cyclic heat treatment process that induces first-order phase transition. Transformation α-Fe ↔ γ-Fe in the temperature cycling range 800 ↔ 1450 K is used as an example to obtain a thermal hysteresis (temperature difference between the forward and inverse transformations). The existence of a thermodynamic hysteresis is justified in conditions when the ergodic hypothesis is not valid for nanosystems, resulting in the difference between forward and inverse transformations α-Fe ↔ γ-Fe because of the difference in their energy barriers. The thermal hysteresis is determined by the superposition of size-dependent kinetic hysteresis and size-dependent thermodynamic hysteresis. Three different cases of size dependence of the hysteresis loop width for the volume content of the new phase are identified. A potential weak size effect or zero size effect in a wide nanosize range resulting from the compensation of kinetic and thermodynamic hystereses is justified for the first time. The correlations between the size of nanopowder particles, cycling rate, and hysteresis loop width for the volume content of the new phase exhibit logarithmic dependence.

Keywords

thermal cycling nanoscale powder iron polymorphic transition size effect thermodynamic hysteresis kinetic hysteresis loop width 

References

  1. 1.
    A. S. Shirinyan and V. A. Makara, Size-Dependent Physicochemical Phenomena in Nanosized Solid Systems: Monograph [in Ukrainian], in 2 parts, Kyivsky Universytet, Kyiv (2014), p. 319.Google Scholar
  2. 2.
    T. Sarkar, S. Roy, J. Bhattacharya, et al., “Thermal hysteresis of some important physical properties of nanoparticles,” J. Colloid Interface Sci., 327, 224–232 (2008).CrossRefGoogle Scholar
  3. 3.
    A. Atitoaie, R. Tanasa, and C. Enachescu, “Size dependent thermal hysteresis in spin crossover nanoparticles reflected within a Monte-Carlo based Ising-like model,” J. Magn. Magn. Mater., 324, 1596–1600 (2012).CrossRefGoogle Scholar
  4. 4.
    T. Krenke, M. Acet, E. F. Wassermann, et al., “Martensitic transitions and the nature of ferromagnetism in the austenitic and martensitic states of NiMn–Sn alloys,” Phys. Rev. B, 72, 014412(1)–014412(9) (2005).CrossRefGoogle Scholar
  5. 5.
    P. J. Shamberger and F. S. Ohuchi, “Hysteresis of the martensitic phase transition in magnetocaloric effect Ni–Mn–Sn alloys,” Phys. Rev. B, 79, 144407(1)–144407(9) (2009).CrossRefGoogle Scholar
  6. 6.
    A. Neimark, P. I. Ravikovitch, and A. Vishnyakov, “Adsorption hysteresis in nanopores,” Phys. Rev. B, 65, R1493–R1496 (2002).Google Scholar
  7. 7.
    W. A. Jesser, R. Z. Shneck, and W. W. Gille, “Solid-liquid equilibria in nanoparticles of Pb–Bi alloys,” Phys. Rev. B, 69, 144121(1)–144121(13) (2004).CrossRefGoogle Scholar
  8. 8.
    D. Michel, B. F. Borisov, E. V. Charnaya, et al., “Phase transitions for gallium microparticles in a porous glass,” Nanostruct. Mater., 12, 515–518 (1999).CrossRefGoogle Scholar
  9. 9.
    V. V. Kokorin and L. E. Kozlova, “Effect of nanoparticles on structural states of martensitic phases in Fe and Cu alloys,” Nanosyst. Nanomater. Nanotekhnol., 2, No. 2, 645–673 (2004).Google Scholar
  10. 10.
    K. Jacobs, D. Zaziski, E. C. Scher, et al., “Activation volumes for solid–solid transformations in nanocrystals,” Science, 293, 1803–1806 (2001).CrossRefGoogle Scholar
  11. 11.
    D. R. Knittel, S. P. Pack, S. H. Lin, and L. Eyring, “A thermodynamic model of hysteresis in phase transitions and its application to rare earth oxide systems,” J. Chem. Phys., 67, No. 1, 134–142 (1977).CrossRefGoogle Scholar
  12. 12.
    A. S. Shirinyan and Y. S. Bilogorodskyy, “Size-induced thermal thermodynamic hysteresis in nanopowder undergoing structural transitions––from particular case to general behavior,” J. Phase Trans., 82, No. 7, 551–565 (2009).CrossRefGoogle Scholar
  13. 13.
    S. S. Kiparisov, A. A. Nuzhdin, and S. V. Strelova, “Some characteristics of the reverse polymorphic transformations of sintered iron and cobalt,” Powder Metall. Met. Ceram., 23, No. 7, 546–550 (1984).Google Scholar
  14. 14.
    F. J. Shackelford and W. Alexander (eds.), CRC Materials Science and Engineering Handbook, 3rd ed., CRC Press LLC Inc. Boca Raton, London–New York–Washington–Florida (2001), p. 1949.Google Scholar
  15. 15.
    B. Ya. Lyubov, Kinetic Theory of Phase Transitions [in Russian], Metallurgiya, Moscow (1969), p. 264.Google Scholar
  16. 16.
    B. S. Gudkov, A. N. Subbotin, and V. I. Yakerson, “Temperature hysteresis in heterogeneous catalysis,” Priroda, No. 6, 16–21 (2001).Google Scholar
  17. 17.
    W. S. Lai and X. S. Zhao, “Strain-induced elastic moduli softening and associated fcc<–>bcc transition in iron,” Appl. Phys. Lett., 85, No. 19, 4340–4342 (2004).CrossRefGoogle Scholar
  18. 18.
    L. H. Liang and Q. Jiang, “Size and interface effects on critical temperatures of ferromagnetic, ferroelectric and superconductive nanocrystals,” Acta Mater., 53, 3305–3311 (2005).CrossRefGoogle Scholar
  19. 19.
    J. W. Christian, The Theory of Transformations in Metals and Alloys. Part 1: Equilibrium and General Kinetic Theory, Pergamon Press, Oxford (1975).Google Scholar
  20. 20.
    R. C. Weast, M. J. Astle, and W. H. Beyer (eds.), 1986-1987 CRC Handbook of Chemistry and Physics, 67th ed., CRC Press Inc., Florida (1987), p. 2000.Google Scholar
  21. 21.
    W. Matienseen and H. Warlimont (eds.), Springer Handbook of Condensed Matter and Materials Data, Springer, Berlin–Heidelberg–New York (2005), p. 1120.Google Scholar
  22. 22.
    L. Vitos, A. V. Ruban, H. L. Skriver, et al., “The surface energies of metals,” Surf. Sci., 411, 186–202 (1998).CrossRefGoogle Scholar
  23. 23.
    G. A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca–London (1981), p. 570.Google Scholar
  24. 24.
    A. S. Shirinyan, Y. S. Bilogorodskyy, and J. W. P. Schmelzer, “Influence of nanopowder particle sizes on competition and growth of different crystallographic phases during temperature cycling,” Acta Mater., 57, 5771–5781 (2009).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • A. S. Shirinyan
    • 1
  • Yu. S. Bilogorodsky
    • 1
    • 2
  • V. A. Makara
    • 1
    • 3
  1. 1.Scientific Training Center for Physicochemical Materials ScienceTaras Shevchenko National University of Kyiv and National Academy of Sciences of UkraineKyivUkraine
  2. 2.Cherkassy Regional Center for Ecological and Naturalistic CreativityMinor Academy of Sciences of UkraineCherkassyUkraine
  3. 3.Taras Shevchenko National University of KyivKyivUkraine

Personalised recommendations