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

Abstract

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 TiO_2–x–Co_1–уO oxides in temperature range T = 773 – 1073 К, the values of the individual diffusion coefficients of cobalt D_Co = 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.

References
1. Chebotin V. N. Fizicheskaya khimiya tverdogo tela
[Physical chemistry of a solid state]. Moscow: Khimiya
Publ.; 1982. 320 p. (in Russ.)
2. Tretyakov Yu. D. Tverdofaznye reaktsii [Solid
phase reactions]. Moscow: Khimiya Publ.; 1978. 360 p.
(in Russ.)
3. Afonin N. N., Logacheva V. A. Interdiffusion and
phase formation in the Fe–TiO2 thin-film system.
Semiconductors. 2017;51(10): 1300–1305. DOI:
https://doi.org/10.1134/S1063782617100025
4. Afonin N. N., Logacheva V. A. Cobalt modification
of thin rutile films magnetron-sputtered in vacuum
technical. Technical Physics, 2018;63(4): 605–611. DOI:
https://doi.org/10.1134/S1063784218040023
5. Afonin N. N., Logacheva V. A. Modeling of the
reaction interdiffusion in the polycrystalline systems
with limited component solubility. Industrial
Laboratory. Diagnostics of Materials. 2019;85(9): 35–41.
DOI: https://doi.org/10.26896/1028-6861-2019-85-9-35-41diffusion (In Russ., abstract in Eng.)
6. Afonin N. N., Logacheva V. A. 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.
2019;21(3): 358–365. DOI: https://doi.org/10.17308/kcmf.2019.21/1157 (In Russ., abstract in Eng.)
7. Darken L. S. Diffusion, mobility and their
interrelation through free energy in binary metallic
systems. Trans. AMIE.1948;175: 184–190.
8. Gurov K. P., Kartashkin B. A., Ugaste Yu. E.
Vzaimnaya diffuziya v mnogofaznykh metallicheskikh
sistemakh [Interdiffusion in multiphase metallic
systems]. Moscow: Nauka Publ.; 1981. 350 p. (In Russ.)
9. Kulkarni N. S., Bruce Warmack R. J., Radhakrishnan
B., Hunter J. L., Sohn Y., Coffey K. R., …
Belova I. V. Overview of SIMS-based experimental
studies of tracer diffusion in solids and application to
Mg self-diffusion. Journal of Phase Equilibria and
Diffusion. 2014;35(6): 762–778. DOI: https://doi.org/10.1007/s11669-014-0344-4
10. Aleksandrov O. V., Kozlovski V. V. Simulation
of interaction between nickel and silicon carbide
during the formation of ohmic contacts. Semiconductors.
2009;43(7): 885–891. DOI: https://doi.org/10.1134/S1063782609070100
11. Kofstad P. Nonstoichiometry, diffusion, and
electrical conductivity in binary metal oxides. Wiley-
Interscience; 1972. 382 p.
12. Bak T., Nowotny J., Rekas M., Sorrell C. C. Defect
chemistry and semiconducting properties of titanium
dioxide: II. Defect diagrams. Journal of Physics and
Chemistry of Solids. 2003;64(7): 1057–1067. DOI:
https://doi.org/10.1016/s0022-3697(02)00480-8
13. Iddir H., Öğüt,S., Zapol P., Browning N. D.
Diffusion mechanisms of native point defects in rutile
TiO2: Ab initio total-energy calculations. Physical
Review B. 2007;75(7): DOI: https://doi.org/10.1103/physrevb.75.073203
14. Hoshino K., Peterson N. L., Wiley C. L. Diffusion
and point defects in TiO2–x. Journal of Physics and Chemistry of Solids. 1985;46(12): 1397-1411. DOI:
https://doi.org/10.1016/0022-3697(85)90079-4
15. Fiebig J., Divinski S., Rösner H., Estrin Y.,
Wilde G. Diffusion of Ag and Co in ultrafine-grained
a-Ti deformed by equal channel angular pressing.
Journal of Applied Physics. 2011;110(8): 083514. DOI:
https://doi.org/10.1063/1.3650230
16. Straumal P. B. Stakhanova S. V., Wilde G.,
Divinski S. V. 44Ti self-diffusion in nanocrystalline thin
TiO2 films produced by a low temperature wet chemical
process. Scripta Materialia. 2018;149: 31–35. DOI:
https://doi.org/10.1016/j.scriptamat.2018.01.022
17. Patrick R. Cantwell, Ming Tang, Shen J. Dillon,
Jian Luo, Gregory S. Rohrer, Martin P. Harmer. Grain
boundary complexions. Acta Materialia. 2014;62: 1–48.
DOI: https://doi.org/10.1016/j.actamat.2013.07.037
18. Dillon S. J., Tang M., Carter W. C., Harmer M. P.
Complexion: A new concept for kinetic engineering in
materials science. Acta Materialia, 2007;55(18):
6208–6218. DOI: https://doi.org/10.1016/j.actamat.2007.07.029
19. Grain boundary complexion transitions in
WO3- and CuO-doped TiO2 bicrystals. Acta Materialia.
2013;61(5); 1691–1704. DOI: https://doi.org/10.1016/j.actamat.2012.11.044
20. Nie J., Chan J. M., Qin M., Zhou N., Luo J.
Liquid-like grain boundary complexion and subeutectic
activated sintering in CuO-doped TiO2. Acta
Materialia. 2017;130: 329–338. DOI: https://doi.org/10.1016/j.actamat.2017.03.037