Keywords: modeling,, reaction interdiffusion,, Kirkendall effect,, interphase boundaries,, polycrystalline films,, complex oxides


Purpose. A model of reactive interdiffusion in a bilayer system of polycrystalline oxides of two metals with moving and stationary components in each phase is proposed. The model develops Darken theory of interdiffusion in a binary system with unlimited solubility.
Results. The model provides for the existence of an immobilized metal in two states – in the composition of the traps of its phase and in the form of the oxide of another metal trapped in the trap in the phase. The interdiffusion of the mobile component of metals into phases of neighboring oxides with subsequent capture to trap centers serves as the basis for the formation of phases of complex oxides. The formulation of the boundary-value problem of the model is considered.
Conclusions. Within the framework of the model, a numerical analysis of the experimental concentration distributions of titanium and cobalt in the TiO2-x – Co1-yO thin-fi lm system obtained by the Rutherford backscattering method was performed. The analysis revealed the dominant role of the diffusion of mobile cobalt into the TiO2-x phase compared with the diffusion of mobile titanium into the Co1-yO phase and the region of localization of the formation of complex oxide phases in the vicinity of the TiO2-x–Co1-yO interface.




  1. Chebotin V. N. Fizicheskaya khimiya tverdogo tela [Physical chemistry of a solid body]. M.: Khimiya Publ., 1982, 320 p. (in Russ.)
  2. Tretyakov Yu. D. Tverdofaznye reaktsii [Solid phase reactions]. M.: Khimiya Publ., 1978, 360 p. (in Russ.)
  3. Afonin N. N., Logacheva V. A. Interdiffusion and phase formation in the Fe–TiO2 thin-fi lm system. Semiconductors, 2017, v. 51(10), pp. 1300–1305.
  4. Afonin N. N., Logacheva V. A. Cobalt modifi cation of thin rutile fi lms magnetron-sputtered in vacuum technical. Technical Physics, 2018, v. 63(4), pp. 605–611.
  5. Kofstad P. Nonstoichiometry, diffusion, and electrical conductivity in binary metal oxides. Wiley-Interscience, 1972, 382 p.
  6. Smigelskas A. D., Kirkendall E. O. Zinc Diffusion in alpha brass. Trans. AIME, 1947, v. 171, pp. 130–142.
  7. Chambers S. A., Thevuthasan S., Farrow R. F. C., Marks R. F., Thiele J. U., Folks L., Samant M. G., Kellock A. J., Ruzycki N., Ederer D. L., Diebold U. Epita xial growth and properties of ferromagnetic co-doped TiO2 anatase. Appl. Phys. Lett., 2001, v. 79, pp. 3467–3469.
  8. Matsumoto Y., Murakami M., Shono T., Hasegawa T., Fukumura T., Kawasaki M., Ahmet P., Chikyow T., Koshihara S., Koinumaet H. Room-temperature ferromagnetism in transparent transition metal-doped titanium dioxide. Science, 2001, v. 291, pp. 854–856.
  9. Darken L. S. Diffusion, mobility and their interrelation through free energy in binary metallic systems. Trans. AMIE, 1948, v. 175, pp. 184–190.
  10. Samarsky A. A. [Theory of difference schemes]. M.: Nauka Publ., 1977, 656 с. (in Russ.)
  11. Afonin N. N., Logacheva V. A., Gerasimenko Yu. A., Dolgopolova E. A., Khoviv A. M. Interaction of cobalt and titanium with thin fi lms of their oxides during vacuum annealing // [Condensed Matter and Interphase], 2013, v. 15 (3), p. 232-237. URL: (in Russ.)


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Author Biographies

Nikolay N. Afonin, Voronezhs State Pedagogical University 86, Lenina str., 394043 Voronezh, Russian Federation

Dr. Sci. (Chem.), Professor, Voronezh State Pedagogical University, Voronezh, Russian Federation; e-mail: ORCID iD 0000-0002-9163-744X.

Vera A. Logacheva, Voronezh State University 1, Universitetskaya pl., 394018 Voronezh, Russian Federation

Cand. Sci. (Chem.), Researcher, Voronezh State University, Voronezh, Russian Federation; e-mail: ORCID iD 0000-0002-2296-8069.

How to Cite
Afonin, N. N., & Logacheva, V. A. (2019). MODELING OF INTERDIFFUSION AND PHASE FORMATION IN THE THIN-FILM TWO-LAYER SYSTEM OF POLYCRYSTALLINE OXIDES TITANIUM AND COBALT. Kondensirovannye Sredy I Mezhfaznye Granitsy = Condensed Matter and Interphases, 21(3), 358-365.