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Modeling of evolution of growing coating composition

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Abstract

This paper discusses the role of coupling effects between transfer processes, chemical reactions and deformations in the evolution of phase composition of a growing coating and in the formation of a transition zone between coating and substrate. The proposed model of the coating growth is based on the equations of irreversible thermodynamics and accounts for coupling physical and chemical phenomena: diffusion, thermal diffusion, chemical reactions, elastic fields in the diffusion zone and stresses induced by diffusion. The transfer coefficients and kinetic parameters are calculated using classical theories or identified from experiments. As a result, we developed a theory that has direct practical applications and can be specified for a variety of technological and experimental situations. The formulated problem is solved numerically. The phase composition of the coating and residual stresses in the diffusion zone are obtained as a function of time under various technological conditions. The results can be used for prognosis and technology optimization.

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References

  1. Helmersson U. et al.: Ionized physical vapor deposition (IPVD): a review of technology and applications. Thin Solid Films 513, 1–24 (2006)

    Article  Google Scholar 

  2. Veprek, S., Nesladek, P., Niederhofer, A., Mannling, H.: Superhard Nanocrystalline composites presentations of the research and possible industrial applications. In: Kumar, A., Chang, Y-W., Moore, J.J., Sinngeresky J.E.(eds.) Surface Engineering: Science and Technology 1. The Minerals, Metals and Materials Society, pp. 219–230 (1999)

  3. Sarakinos K., Alami J., Konstantinidis S.: High power pulsed magnetron sputtering: a review on scientific and engineering state of the art. Surface Coat. Technol. 204, 1661–1684 (2010)

    Article  Google Scholar 

  4. Bubert H., Jennet H.: Surface and Thin Film Analysis: Principles, Instrumentation, Applications. Wiley-VCH, Weinheim (2002)

    Book  Google Scholar 

  5. Poate J.M., Foti G., Jacobson D.C.: Surface Modification and Alloying by Laser, Ion, and Electron Beams. Plenum Press, New York (1983)

    Book  Google Scholar 

  6. Pelletier J., Anders A.: Plasma-based ion implantation and deposition: a review of physics, technology, and applications. IEEE Trans. Plasma Sci. 33(6), 1944–1959 (2005)

    Article  Google Scholar 

  7. Lotkov, L.I. et al.: Surface Nanoengineering. The Formation of Non-equilibrium States in Surface Layers of Materials in Electron-Ion-Plasma Technologies. Novosibirsk (2008) (in Russian)

  8. Barvinok, V.A., Bogdanovich, V.I.: Physical Basis and Mathematical Modeling of Vacuum Ion-Plasmous Deposition. Mashinostroenie, Moscow (1999) (in Russian)

  9. Andersson J.M., Wallin E., Chirita V., Münger E.P., Helmersson U.: Ab initio calculations on the effects of additives on alumina phase stability. Phys. Rev. 71, 014101 (2005)

    Article  MathSciNet  Google Scholar 

  10. Cho J., Terry S.G., LeSar R., Levi C.G.: A kinetic Monte Carlo simulation of film growth by physical vapor deposition on rotating substrates. Mater. Sci. Eng. 391, 390–401 (2005)

    Article  Google Scholar 

  11. Wadley H.N.G., Zhou X., Johnson R.A.: Mechanisms, model and methods of vapor deposition. Progress in Material Science 46, 329–377 (2001)

    Article  Google Scholar 

  12. Geiser, J., Rohle, R.: Modeling and simulation for physical vapor deposition: multiscale model. World Acad. Sci. Eng. Technol. 2, 425–433 (2008)

  13. Kukshkin S.A., Osipov A.V.: Processes of thin film condensation. Russ. Phys. J. 68(10), 1083–1116 (1999)

    Google Scholar 

  14. Gu S., Lu T.J., Hass D.D., Wadley H.N.G.: Thermal conductivity of zirconia coatings with zig-zag pore microstructures. Acta Mater. 49, 2539–2547 (2001)

    Article  Google Scholar 

  15. Brito R.F., de Carvalho S., de Lima e Silva S.M.M., Ferreira J.R.: Thermal analysis in coated cutting tools. Int. Commun. Heat Mass Trans. 36, 314–321 (2009)

    Article  Google Scholar 

  16. Anishchenko L.M., Lavrenyuk S.Y.: Heat regimes of substrates under thin film coating deposition. Phys. Chem. Mater. Treat. 2, 21–25 (1981) (in Russian)

    Google Scholar 

  17. Wei T., Li Y.S.: An inverse boundary problem for one-dimensional heat equation with a multilayer domain. Eng. Anal. Boundary Elements 33, 225–232 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Rykalin N.N., Zuev I.V., Uglov A.A.: Fundamentals of Electron Beam Processing of Materials. Mashinostroenie, Moscow (1978) (in Russian)

    Google Scholar 

  19. Rykalin N.N., Uglov A.A., Zuev I.V., Kokora A.N.: Laser and Electron Beam Processing of Materials: Handbook. Mashinostroenie, Moscow (1985) (in Russian)

    Google Scholar 

  20. Barvinok V.A., Bogdanovich V.I.: Physical and mathematical modeling of plasma-chemical synthesis of a heterogeneous coating of plasma streams. J. Tech. Phys. 78(1), 68–73 (2008) (in Russian)

    Google Scholar 

  21. Knyazeva A.G., Psakhie S.G.: Thermodynamics of the activated state of materials. J. Appl. Mech. Tech. Phys. 50(1), 118–126 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  22. Montay G., Cherouat A., Nussair A., Lu J.: Residual stress in coating technology. Mater. Sci. Technol. 20, 81–84 (2004)

    Google Scholar 

  23. Breidestein B., Denkena B.: Significance of residual stress in PVD-coated carbide cutting tools. CIRS Ann. Manuf. Technol. 62, 67–70 (2013)

    Article  Google Scholar 

  24. Carneiro J.O., Teixeira V., Portinha A., Vaz F., Ferreira J.A.: A real time scale measurement of residual stress evolution during coating deposition using electric extensometry. Rev. Adv. Mater. Sci 7, 32–40 (2004)

    Google Scholar 

  25. Śliwa A., Dobrzański L.A., Kwaśny W., Sitek W.: Finite element method application for modeling of PVD coatings properties. J. Achiev. Mater. Manuf. Eng. 27(2), 171–174 (2008)

    Google Scholar 

  26. Mackerle J.: Coatings and surface modification technologies: a finite element bibliography (1995–2005). Model. Simul. Mater. Sci. Eng 13, 935–979 (2005)

    Article  Google Scholar 

  27. Arutyunyan, N.K., Drozdov, A.D., Naumov, B.E.: Mechanics of Growing Viscous-Elastic-Plastic Bodies. Moskow (1987) (in Russian)

  28. Meca E., Lowengrub J., Kim H., Mattevi C., Shenoy V.B.: Epitaxial graphene growth and shape dynamics on copper: phase-field modeling and experiments. Nano Lett. 13(11), 5692–5697 (2013)

    Article  Google Scholar 

  29. Deng J., Rokkam S.: A phase field model of surface-energy-driven abnormal grain growth in thin films. Mater. Trans. 52(11), 2126–2130 (2011)

    Article  Google Scholar 

  30. De Groot S.R., Mazur P.: Non-equilibrium Thermodynamics. North-Holland Publishing Company, Amsterdam (1962)

    Google Scholar 

  31. Haase R.: Thermodynamics of Irreversible Process. Addison-Wesley, Massachusetts (1969)

    Google Scholar 

  32. Merzhanov A.G.: Combustion and explosion processes in physical chemistry and technology of inorganic materials. Russ. Chem. Rev. 72(4), 289–310 (2003)

    Article  Google Scholar 

  33. Kovalchenko M.C.: Theoretical Foundation of Hot Treatment by Pressure of Porous Materials. Naukova dumka, Kiev (1980) (in Russian)

    Google Scholar 

  34. Olevsky E., Tikare V., Garino T.: Multi-scale modeling of sintering—a review. J. Am. Ceram. Soc 89(6), 1914–1922 (2006)

    Article  Google Scholar 

  35. Rosovskiy A.Y.: Heterogeneous Chemical Reactions: Kinetics and Macro Kinetics. Nauka, Moscow (1980) (in Russian)

    Google Scholar 

  36. Yablonskii G.S., Bykov V.I., Elokhin V.I., Gorban A.N.: Kinetic Models of Catalytic Reactions. Elsevier, Amsterdam (1991)

    Google Scholar 

  37. Karlov, N.V., Kirichenko, N.A., Lukyanchuk, B.S.: Laser Thermal Chemistry. Moscow (1992) (in Russian)

  38. Mayer K.U., Frind E.O., Blowes D.W.: Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resourc. Res. 38(9), 13-1–13-21 (2002)

    Article  Google Scholar 

  39. Spanos T.J.T.: The Thermophysics of Porous Media. A CRC Press Company, Boca Raton (2002)

    MATH  Google Scholar 

  40. Knyazeva A.G., Dyukarev E.A.: Model of autowave propagation of solid-state low-temperature chlorination of butyl chloride. Combust. Explos. Shock Waves 34(5), 556–565 (1998)

    Article  Google Scholar 

  41. Kryukova O.N., Knyazeva A.G.: Critical phenomena in particle dissolution in the melt during electron-beam surfacing. J. Appl. Mech. Tech. Phys. 48(1), 109–118 (2007)

    Article  Google Scholar 

  42. Knyazeva A.G., Chashchina A.A.: Numerical study of the problem of thermal ignition in a thick-walled container. Combust. Explos. Shock Waves 40(4), 432–437 (2004)

    Article  Google Scholar 

  43. Sorokova S.N., Knyazeva A.G.: Numerical study of the influence of the technological parameters on the composition and stressed-deformed state of a coating synthesized under electron-beam. Theor. Found. Chem. Eng. 44(2), 172–185 (2010)

    Article  Google Scholar 

  44. Karapetiync M.K.: Chemical Thermodynamics. Khimiya, Moskow (1975) (in Russian)

    Google Scholar 

  45. Knyazeva A.G.: Connected equations of heat and mass transfer in a chemically reacting solid mixture with allowance for deformation and damage. J. Appl. Mech. Tech. Phys. 37(3), 381–390 (1996)

    Article  Google Scholar 

  46. Knyazeva A.G., Demidov V.N.: Transfer coefficients for three component deformable alloy. Vestnik PermGTU Mechanika 3, 84–99 (2011) (in Russian)

    Google Scholar 

  47. Stark J.P.: Solid State Diffusion. Wiley, New York (1976)

    Google Scholar 

  48. Gurov K.P.: Phenomenological Thermodynamics of Irreversible Processes (Physical basis). Nauka, Moscow (1978) (in Russian)

    Google Scholar 

  49. Kondepudi D., Prigogine I.: Modern Thermodynamics. From Heat Engines to Dissipative Structures. Wiley, Chichester (1999)

    Google Scholar 

  50. Barvinok V.A.: Controlling of Stressed State and Properties of Plasmatic Coatings. MIR, Moscow (1964) (in Russian)

    Google Scholar 

  51. Timoshenko S.P., Goodier J.N.: Theory of Elasticity, 3rd edn. MeCraw-Hill, New York (1970)

    Google Scholar 

  52. Kudinov, V.A., Kartashov, E.M., Kalashnikov, V.V.: Analytical solutions of heat and mass transfer and thermal elastic problems for multi layer constructions. Vysshaya shkola, Moscow (2005) (in Russian)

  53. Grigoriev, I.C., Meylikhov, E.Z. (eds.): Physical Values. Reference Book. Energoatomizdat, China (1991) (in Russian)

  54. Ryabinin, G.A. (ed.): Reference book of physical values. St. Petersnurg (2001) (in Russian)

  55. Zephirov, A.P. (ed.): Thermodynamical Properties of Inorganic Substances. Reference Book. Atomizdat, Moscow (1965) (in Russian)

  56. Knyazeva A.G.: Regimes of development of initial nucleus in solid phase reaction limited by diffusion. Combust. Explos. Shock Waves 32(4), 72–76 (1996)

    Article  Google Scholar 

  57. Knyazeva A.G.: Modeling of irreversible processes with high area of internal surfaces. Physical mesomechanics 6(5), 11–27 (2003) (in Russian)

    Google Scholar 

  58. Knyazeva A.G.: Nonlinear models of deformable media with diffusion. Phys. Mesomech. 6, 35–51 (2011)

    MathSciNet  Google Scholar 

  59. Kuiken G.D.C.: Thermodynamics of Irreversible Processes: Applications to Diffusion and Rheology. Wiley, New York (1994)

    Google Scholar 

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Knyazeva, A.G., Shanin, S.A. Modeling of evolution of growing coating composition. Acta Mech 227, 75–104 (2016). https://doi.org/10.1007/s00707-015-1430-3

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