Reactive Interdiffusion of Components in a Non-Stoichiometric Two‑Layer System of Polycrystalline Titanium and Cobalt Oxides

Keywords: modelling, interdiffusion reaction, Kirkendall effect, interphases, polycrystalline films, complex oxides.


We demonstrated the possibility of using the mathematical form of Darken's theory, applied to the description of the Kirkendall effect in binary systems, to the description of reactive interdiffusion in non-stoichiometric polycrystalline film oxide systems with limited solubility. The aim of the study was the simulation of reactive interdiffusion under vacuum annealing of a thin film system consisting of two non-stoichiometric polycrystalline titanium and cobalt oxides. The nonstoichiometric nature of the system assumes the presence of mobile components, free interstitial cobalt and titanium cations in it. Phase formation occurs as a result of reactive interdiffusion and trapping of mobile components of the system
on inter-grain traps. The proposed mechanism describes the formation of complex oxide phases distributed over the depth of the system.
A complex empirical research technique was used, involving Rutherford backscattering spectrometry, X-ray phase analysis and modelling methods. The values of the characteristic parameters of the process were determined by numerical analysis of the experimentally obtained distributions of the concentrations of the components within the developed model. During vacuum annealing of a thin film two-layer system of non-stoichiometric TiO2–x–Co1–уO oxides in temperature range T = 773 – 1073 К, the values of the individual diffusion coefficients of cobalt DCo = 5.1·10–8·exp(–1.0 eV/(kT) cm2/s and titanium
DTi = 1.38·10–13·exp(–0.31 eV/(kT) cm2/s were determined.
It was shown that for T = 1073 K, the phase formation of CoTiO3 with a rhombohedral structure occurs. The extension of the phase formation region of complex cobalt and titanium oxides increases with an increase in the vacuum annealing temperature and at 1073 K it is comparable with the total thickness of the film system.
The model allows predicting the distribution of the concentrations of the components over the depth of multilayer nonstoichiometric systems in which reactive interdiffusion is possible.




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Author Biographies

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

DSc in Chemistry, Research
Fellow, Professor at the Department of Science and
Technology Studies, Voronezh State Pedagogical
University, Voronezh, Russian Federation; e-mail:

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

PhD in Chemistry, Research
Fellow at the Department of General and Inorganic
Chemistry, Voronezh State University, Voronezh,
Russian Federation; e-mail:

How to Cite
Afonin, N. N., & Logachova, V. A. (2020). Reactive Interdiffusion of Components in a Non-Stoichiometric Two‑Layer System of Polycrystalline Titanium and Cobalt Oxides. Condensed Matter and Interphases, 22(4), 430-437.