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Simulation of the Surface Structure of Ferroelectric Thin Films

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Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 109))

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Abstract

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.

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References

  1. Wolff, A.: New system for automatic control of colour-coating lines. Stahl und eisen 8, 11 (2003)

    Google Scholar 

  2. Gun, G.: Optimization of Technological and Operational Deformation of Products with Coatings. Magnitogorsk, p. 323 (2006)

    Google Scholar 

  3. Oura, K.: Introduction to surface physics, M. In: Science, p. 496 (2006)

    Google Scholar 

  4. Pratton, M.: Introduction to Surface Physics. Izhevsk, p. 256 (2000)

    Google Scholar 

  5. Roldugin, V.: Physical Chemistry of the Surface. Intellect, Dolgoprudny, p. 586 (2008)

    Google Scholar 

  6. Vaz, C.: Magnetism in ultrathin film structures. Rep. Prog. Phys. 71, 056501 (2008)

    Article  Google Scholar 

  7. Shilov, S.: Segmental orientation and mobility of ferroelectric liquid crystal polymers. Liq. Cryst. 22(2), 203–210 (1997)

    Article  CAS  Google Scholar 

  8. Zentel, R.: Ferroelectric liquid-crystalline elastomers. Adv. Mater. 6(7/6), 598–599 (1994)

    Article  CAS  Google Scholar 

  9. Warner, M.: Nematic elastomers—a new state of matter. Prog. Pol. Sci. 21(5), 853–891 (1996)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  12. Ginsburg, V.: Phase transitions in ferroelectrics. Phys. Usp. 171(10), 1091–1097 (2001)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Osari, K., Koibuchi, H.: Finsler geometry modeling and Monte Carlo study of 3D liquid crystal elastomer polymer. Polymer 114, 355–369 (2017)

    Article  CAS  Google Scholar 

  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. 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)

    Article  CAS  Google Scholar 

  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)

    Article  Google Scholar 

  18. Metropolis, N., et al.: Equation of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)

    Article  CAS  Google Scholar 

  19. Wolff, U.: Collective Monte Carlo updating for spin systems. Phys. Rev. Lett. 62(4), 361 (1989)

    Article  CAS  Google Scholar 

  20. Lee, J.: New Monte Carlo algorithm: entropic sampling. Phys. Rev. Lett. 71(2), 211 (1993)

    Article  CAS  Google Scholar 

  21. Wang, F., Landau, D.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86(10), 2050 (2001)

    Article  CAS  Google Scholar 

  22. Swendsen, R., Wang, J.-S.: Replica Monte Carlo simulation of spin-glasses. Phys. Rev. Lett. 57(21), 2607 (1986)

    Article  CAS  Google Scholar 

  23. Suzuki, S., et al.: Quantum Ising Phases and Transitions in Transverse Ising Models, vol. 862. Springer, Berlin (2012)

    Google Scholar 

  24. Sherrington, D., Kirkpatrick, S.: Solvable model of a spin-glass. Phys. Rev. Lett. 35(26), 1792 (1975)

    Article  Google Scholar 

  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. Onsager, L.: Crystal statistics. I. A two-dimensional model with an order-disorder transition. Phys. Rev. 65(3–4), 117 (1944)

    Article  CAS  Google Scholar 

  27. Vogel, T., et al.: Scalable replica-exchange framework for Wang-Landau sampling. Phys. Rev. E 90(2), 023302 (2014)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  29. Grischenko, A., et al.: Self-organization of polymer molecules at interphase boundaries. SPBU, St. Petersburg (2010)

    Google Scholar 

  30. Grischenko, A., Cherkasov, A.: Orientational order in surface layers. Adv. Phys. Sci. 40, 257 (1997)

    Google Scholar 

  31. Junquera, J., Ghosez, P.: Critical thickness for ferroelectricity in perovskite ultrathin films. Nature 422(3), 506–509 (2003)

    Article  CAS  Google Scholar 

  32. Jaita, P., Takeshi, N., Kawazoe, Y., Waghmare, U.: Ferroelectric phase transitions in ultrathin films of BaTiO3. Phys. Rev. Lett. 99, 077601 (2007)

    Article  Google Scholar 

  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)

    Article  CAS  Google Scholar 

  34. Wang, M., Li, J., Ren, L.: Characteristics of EM scattering on dielectric fractal surface. Chin. Sci. Bull. 42(6), 523 (1997)

    Article  Google Scholar 

  35. Torkhov, N., Bozhkov, V.: Fractal character of the distribution of surface potential irregularities in epitaxial n-GaAs (100). Semiconductors 43(5), 551 (2009)

    Article  CAS  Google Scholar 

  36. Kuzmin, O., Malakichev, A.: Geometric fractals modeling through infinite graphs. Mod. Technol. Syst. Anal. Model. 35(3), 79 (2012)

    Google Scholar 

  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. Otto, H., Peter, R.: The Beauty of Fractals. Springer, Heidelberg (1986)

    Google Scholar 

  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)

    Article  CAS  Google Scholar 

  40. Gozhenko, V., Pinchuk, A., Semchuk, O.: Electromagnetic wave scattering by fractal surface. Ukr. J. Phys. 45(9), 1129 (2000)

    CAS  Google Scholar 

  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 

Download references

Acknowledgements

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).

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Authors and Affiliations

  1. Cherepovets State University, 5 Lunacharskii Av., Cherepovets, 162600, Russian Federation

    Olga G. Maksimova, Vladislav I. Egorov, Alexandr R. Baidganov, Olga S. Baruzdina & Andrei V. Maksimov

  2. Southern Federal University, 105/42 Bolshaya Sadovaya Str., Rostov-on-Don, 344006, Russian Federation

    Tatiana O. Petrova & Victor A. Eremeyev

Authors
  1. Olga G. Maksimova
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  2. Tatiana O. Petrova
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  3. Victor A. Eremeyev
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  4. Vladislav I. Egorov
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  5. Alexandr R. Baidganov
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  6. Olga S. Baruzdina
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  7. Andrei V. Maksimov
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Correspondence to Tatiana O. Petrova .

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Editors and Affiliations

  1. Institute for Mathematics, Mechanics and Computer Science, Southern Federal University, Rostov-on-Don, Russia

    Mezhlum A. Sumbatyan

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Maksimova, O.G. et al. (2019). Simulation of the Surface Structure of Ferroelectric Thin Films. In: Sumbatyan, M. (eds) Wave Dynamics, Mechanics and Physics of Microstructured Metamaterials. Advanced Structured Materials, vol 109. Springer, Cham. https://doi.org/10.1007/978-3-030-17470-5_4

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