Simulation of the Surface Structure of Ferroelectric Thin Films

  • Olga G. Maksimova
  • Tatiana O. PetrovaEmail author
  • Victor A. Eremeyev
  • Vladislav I. Egorov
  • Alexandr R. Baidganov
  • Olga S. Baruzdina
  • Andrei V. Maksimov
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 109)


Metropolis and Wang-Landau algorithms are described and illustrated on the base two-dimensional Ising model. The influence of the ferroelectric film thickness and the depolarizing field on the spontaneous polarization and the order parameter of the film has been investigated by means of the Monte-Carlo method. Dependences of the polarization of the thin film on the temperature are calculated at different values of its thickness and the potential well depth of the Lennard-Jones potential. To investigate the geometrical and optical properties of textured coatings the anisotropic three-dimensional model based on the fractal plurality of Julia is used. The developed method allows to determine the values of the model parameters for a number of coating samples of steel sheet obtained under different conditions of their formation. The fractal dimension of the objects obtained on the base of this model is determined.



The work is performed within the framework of the project “Methods of microstructural nonlinear analysis, wave dynamics and mechanics of composites for research and design of modern metamaterials and elements of structures made on its base” (grant No. 15-19-10008-P of by the Russian Science Foundation).


  1. 1.
    Wolff, A.: New system for automatic control of colour-coating lines. Stahl und eisen 8, 11 (2003)Google Scholar
  2. 2.
    Gun, G.: Optimization of Technological and Operational Deformation of Products with Coatings. Magnitogorsk, p. 323 (2006)Google Scholar
  3. 3.
    Oura, K.: Introduction to surface physics, M. In: Science, p. 496 (2006)Google Scholar
  4. 4.
    Pratton, M.: Introduction to Surface Physics. Izhevsk, p. 256 (2000)Google Scholar
  5. 5.
    Roldugin, V.: Physical Chemistry of the Surface. Intellect, Dolgoprudny, p. 586 (2008)Google Scholar
  6. 6.
    Vaz, C.: Magnetism in ultrathin film structures. Rep. Prog. Phys. 71, 056501 (2008)CrossRefGoogle Scholar
  7. 7.
    Shilov, S.: Segmental orientation and mobility of ferroelectric liquid crystal polymers. Liq. Cryst. 22(2), 203–210 (1997)CrossRefGoogle Scholar
  8. 8.
    Zentel, R.: Ferroelectric liquid-crystalline elastomers. Adv. Mater. 6(7/6), 598–599 (1994)CrossRefGoogle Scholar
  9. 9.
    Warner, M.: Nematic elastomers—a new state of matter. Prog. Pol. Sci. 21(5), 853–891 (1996)CrossRefGoogle Scholar
  10. 10.
    Saiko, D., Darinskii, B., Yavlyanskaya, I., Budanov, A.: Numerical study of the minima of the thermodynamic potential of a ferroelectric barium titanate. Bull. Voronezh State Univ. Eng. Technol. 2, 125–130 (2016)CrossRefGoogle Scholar
  11. 11.
    Rossetti, G., Maffei Jr., N.: Specific heat study and Landau analysis of the phase transition in PbTiO3 single crystals. J. Phys. Condens. Matter 7(25), 3953–3963 (2005)CrossRefGoogle Scholar
  12. 12.
    Ginsburg, V.: Phase transitions in ferroelectrics. Phys. Usp. 171(10), 1091–1097 (2001)CrossRefGoogle Scholar
  13. 13.
    Dubrovskii, S., Vasil’ev, V.: Computer simulation of the influence of the functionality of nodes on the elasticity of polyacromonomer grids. Polym. Sci. A 53(6), 925 (2011)CrossRefGoogle Scholar
  14. 14.
    Osari, K., Koibuchi, H.: Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer polymer. Polymer 114, 355–369 (2017)CrossRefGoogle Scholar
  15. 15.
    Tepluchin, A.: Simplified accounting of deformations of valence bonds and angles in full-atom modeling of polymers by the Monte-Carlo method. Polym. Sci. C 55(7), 911–919 (2013)Google Scholar
  16. 16.
    Wang, F., Landau, D.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. Am. Phys. Soc. 86(10), 20-50–20-53 (2001)CrossRefGoogle Scholar
  17. 17.
    Wust, T., Landau, D.: Optimized Wang-Landau sampling of lattice polymers: ground state search and folding thermodynamics of HP model proteins. J. Chem. Phys. 137(6), 064903 (2012)CrossRefGoogle Scholar
  18. 18.
    Metropolis, N., et al.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)CrossRefGoogle Scholar
  19. 19.
    Wolff, U.: Collective Monte Carlo updating for spin systems. Phys. Rev. Lett. 62(4), 361 (1989)CrossRefGoogle Scholar
  20. 20.
    Lee, J.: New Monte Carlo algorithm: entropic sampling. Phys. Rev. Lett. 71(2), 211 (1993)CrossRefGoogle Scholar
  21. 21.
    Wang, F., Landau, D.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86(10), 2050 (2001)CrossRefGoogle Scholar
  22. 22.
    Swendsen, R., Wang, J.-S.: Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57(21), 2607 (1986)CrossRefGoogle Scholar
  23. 23.
    Suzuki, S., et al.: Quantum Ising Phases and Transitions in Transverse Ising Models, vol. 862. Springer, Berlin (2012)Google Scholar
  24. 24.
    Sherrington, D., Kirkpatrick, S.: Solvable model of a spin-glass. Phys. Rev. Lett. 35(26), 1792 (1975)CrossRefGoogle Scholar
  25. 25.
    Cohen, E., Heiman, R., Hadar, O.: Image and video restoration via Ising-like models. In: Image Processing: Algorithms and Systems X; and Parallel Processing for Imaging Applications II, vol. 8295 (2012)Google Scholar
  26. 26.
    Onsager, L.: Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65(3–4), 117 (1944)CrossRefGoogle Scholar
  27. 27.
    Vogel, T., et al.: Scalable replica-exchange framework for Wang-Landau sampling. Phys. Rev. E 90(2), 023302 (2014)CrossRefGoogle Scholar
  28. 28.
    Chan, C.-H., Brown, G., Rikvold, P.: Macroscopically constrained Wang-Landau method for systems with multiple order parameters and its application to drawing complex phase diagrams. Phys. Rev. E. 95(5), 053302 (2017)CrossRefGoogle Scholar
  29. 29.
    Grischenko, A., et al.: Self-organization of polymer molecules at interphase boundaries. SPBU, St. Petersburg (2010)Google Scholar
  30. 30.
    Grischenko, A., Cherkasov, A.: Orientational order in surface layers. Adv. Phys. Sci. 40, 257 (1997)Google Scholar
  31. 31.
    Junquera, J., Ghosez, P.: Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422(3), 506–509 (2003)CrossRefGoogle Scholar
  32. 32.
    Jaita, P., Takeshi, N., Kawazoe, Y., Waghmare, U.: Ferroelectric phase transitions in ultrathin films of BaTiO3. Phys. Rev. Lett. 99, 077601 (2007)CrossRefGoogle Scholar
  33. 33.
    Potapov, A., Bulavkin, V., German, V., Vyacheslavova, O.: The researching of micro structure surfaces with methods of fractal signatures. Tech. Phys. 50(5), 560–575 (2005)CrossRefGoogle Scholar
  34. 34.
    Wang, M., Li, J., Ren, L.: Characteristics of EM scattering on dielectric fractal surface. Chin. Sci. Bull. 42(6), 523 (1997)CrossRefGoogle Scholar
  35. 35.
    Torkhov, N., Bozhkov, V.: Fractal character of the distribution of surface potential irregularities in epitaxial n-GaAs (100). Semiconductors 43(5), 551 (2009)CrossRefGoogle Scholar
  36. 36.
    Kuzmin, O., Malakichev, A.: Geometric fractals modeling through infinite graphs. Mod. Technol. Syst. Anal. Model. 35(3), 79 (2012)Google Scholar
  37. 37.
    Gehani, A., Agnihotri, P., Pujara, D.: Analysis and synthesis of multiband Sierpinski carpet fractal antenna using hybrid neuro-fuzzy model. Prog. Electromagnet. Res. Lett. 68, 59 (2017)Google Scholar
  38. 38.
    Otto, H., Peter, R.: The Beauty of Fractals. Springer, Heidelberg (1986)Google Scholar
  39. 39.
    Zamani, M., Shafiei, F., Fazeli, S., Downer, M., Jafari, G.: Analytic height correlation function of rough surfaces derived from light scattering. Phys. Rev. E. 94, 042809 (2016)CrossRefGoogle Scholar
  40. 40.
    Gozhenko, V., Pinchuk, A., Semchuk, O.: Electromagnetic wave scattering by fractal surface. Ukr. J. Phys. 45(9), 1129 (2000)Google Scholar
  41. 41.
    Semchuk, O., Grechko, L., Vodopianov, D., Kunitska, L.: Features of light scattering by surface fractal structures. Task Q. 13(3), 199 (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Olga G. Maksimova
    • 1
  • Tatiana O. Petrova
    • 2
    Email author
  • Victor A. Eremeyev
    • 2
  • Vladislav I. Egorov
    • 1
  • Alexandr R. Baidganov
    • 1
  • Olga S. Baruzdina
    • 1
  • Andrei V. Maksimov
    • 1
  1. 1.Cherepovets State UniversityCherepovetsRussian Federation
  2. 2.Southern Federal UniversityRostov-on-DonRussian Federation

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