zldmЗаводская лаборатория. Диагностика материаловIndustrial laboratory. Diagnostics of materials1028-68612588-0187ООО «Издательство «ТЕСТ-ЗЛ»10.26896/1028-6861-2019-85-9-35-41zldm-1060Research ArticleИССЛЕДОВАНИЕ СТРУКТУРЫ И СВОЙСТВ. ФИЗИЧЕСКИЕ МЕТОДЫ ИССЛЕДОВАНИЯ И КОНТРОЛЯTESTING OF STRUCTURE AND PARAMETERS. PHYSICAL METHODS OF TESTING AND QUALITY CONTROLМоделирование реакционной взаимодиффузии в поликристаллических системах с ограниченной растворимостью компонентовModeling of the reaction interdiffusion in the polycrystalline systems with limited component solubilityАфонинН. Н.AfoninN. N.

Афонин Николай Николаевич

394043, г. Воронеж, ул. Ленина 86

Nikolay N. Afonin

ul. Lenina 86, Voronezh, 394043

nafonin@vspu.ac.ruЛогачеваВ. А.LogachevaV. A.

Логачева Вера Алексеевна 

394018, г. Воронеж, Университетская ил. 1

Vera A. Logacheva

Universitetskaya pi. 1, Voronezh, 394018

Воронежский государственный педагогический университетРоссияVoronezh State Pedagogical UniversityRussian FederationВоронежский государственный университетРоссияVoronezh State UniversityRussian Federation2019280920198593541Copyright © Афонин Н.Н., Логачева В.А., 20192019Афонин Н.Н., Логачева В.А.Afonin N.N., Logacheva V.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.zldm.ru/jour/article/view/1060

Синтез многослойных тонкопленочньгх функциональных покрытий предусматривает осаждение материалов и отжиг. При этом возможны процессы взаимодиффузии и фазообразования. Однако моделирование реакционной взаимодиффузии в таких системах, как металл — поликристаллический оксид с ограниченной растворимостью компонентов до последнего времени не осуществляли. Вместе с тем моделирование позволяет выбирать условия отжига (время и температуру), необходимые для включения металла в решетку оксида и его однородного распределения в ней. Представлена количественная модель взаимодействия в слоистой системе металл — поликристаллический оксид другого металла в условиях ограниченной растворимости на основе представлений о взаимной диффузии компонентов и объемных реакций образования сложных оксидов. Модель использовали при исследовании процесса модифицирования тонких пленок оксида титана переходными металлами. Приведены результаты численного анализа экспериментальных концентрационных распределений компонентов в тонкопленочньгх поликристаллических системах Со - ТЮ2 и Fe - Ti02, включая значения индивидуальных коэффициентов диффузии исследуемых металлов и титана в условиях вакуумного отжига. Модель хорошо описывает основные закономерности процесса (появление титана в пленке металла, глубокое проникновение Fe и Со в пленку оксида титана), а также позволяет объяснить образование сложных оксидов не путем послойного роста на границе раздела металл — оксид, а по всей толщине пленки ТЮ2. Полученные данные анализа межфазного взаимодействия в слоистых системах, сопровождающегося реакционной взаимной диффузией, могут использоваться для прогнозирования эволюции фазового состава и управления технологическими процессами получения материалов с заданными свойствами.

that may be accompanied by the processes of mutual diffusion and phase formation. Controlled technological process of forming coatings with the given properties entails the necessity of forecasting the evolution of the phase composition. This in turn requires the development of algorithms and quantitative models of the processes. Reactive mutual diffusion in polycrystalline metal (oxide film systems with limited component solubility) has not been simulated before. The simulation allows selecting the annealing conditions (time and temperature) necessary for the inclusion and uniform distribution of metal in the oxide lattice. A quantitative model of the interaction in a multi-layer system metal — polycrystalline oxide of the other metal under conditions of limited solubility is developed. The model is based on the concepts of mutual diffusion of the components and the bulk reactions of the formation of complex oxides. The developed model was applied to the analysis of the process of modifying thin films of titanium oxide with transition metals. The model allowed us to perform a numerical analysis of the experimental concentrations of the component distributions in polycrystalline Co - Ti02 and Fe - Ti02 thin-film systems. The individual diffusion coefficients of the studied metals and titanium under conditions of vacuum annealing were determined. The model provides a good description of the basic systematic features of the process: the appearance of titanium in the metal film and deep penetration of Fe and Co into the film of titanium oxide. It also explains the fact that complex oxides are formed not by layer-by-layer growth at the metal-oxide interface, but throughout the entire thickness of Ti02 film. The results of analysis of the processes of interracial interaction in layered systems accompanied by the reaction mutual diffusion can be used to predict the evolution of the phase composition, as well as to control the technological processes of obtaining materials with the desired properties.

моделированиереакционная взаимодиффузияэффект Киркендалламежфазные границытонкие поликристаллические пленкислоистая бинарная система металл — поликристаллический оксидвакуумный отжигmodelingreaction mutual diffusionKirkendall effectinterphase boundariesthin polycrystalline filmslayer polycrystalline metal-oxide binary systemvacuum annealingReferencesSmigelskas A. D., Kirkendall Е. О. Zinc Diffusion in alpha brass / Trans. AIME. 1947. Vol. 171. E 130 - 142.Smigelskas A. D., Kirkendall E. O. Zinc Diffusion in alpha brass / Trans. AIME. 1947. Vol. 171. E 130 - 142.Darken L. S. Diffusion, mobility and their interrelation through free energy in binary Metallic Systems / Trans. AMIE. 1948. Vol. 175. E 184-190.Darken L. S. Diffusion, mobility and their interrelation through free energy in binary Metallic Systems / Trans. AMIE. 1948. Vol. 175. E 184 - 190.Sauer E, Freise V Diffusion in binaren Gemischen mit Volumenanderung / Berichte der Bunsengesellschaft fur physikalische Chemie. 1962. Vol. 66. N 4. E 353 - 362. https://doi.org/ 10.1002/bbpc. 19620660412Sauer E, Freise V Diffusion in binaren Gemischen mit Volumenanderung / Berichte der Bunsengesellschaft fur physikalische Chemie. 1962. Vol. 66. N 4. E 353 - 362. https://doi.org/ 10.1002/bbpc. 19620660412Guy A. G. Reference planes for binary diffusion with variable molar volume / Journal of Materials Science. 1985. Vol. 20. E 4317 - 4328. https://doi.org/10.1007/bf00559320.Guy A. G. Reference planes for binary diffusion with variable molar volume / Journal of Materials Science. 1985. Vol. 20. E 4317 - 4328. https://doi.org/10.1007/bf00559320.Boettinger W. J., Guyer J. E., Campbell С. E., et al. Computation of the Kirkendall velocity and displacement fields in a one-dimensional binary diffusion couple with a moving interface / Froceedings of the Royal Society A: Mathematical, Fhysical and Engineering Sciences. 2007. Vol. 463. N 2088. E 3347 3373. https://doi.org/10.1098/rspa.2007.1904.Boettinger W. J., Guyer J. E., Campbell С. E., et al. Computation of the Kirkendall velocity and displacement fields in a one-dimensional binary diffusion couple with a moving interface / Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2007. Vol. 463. N 2088. E 3347 3373. https://doi.org/10.1098/rspa.2007.1904.Гуров К. П., Карташкин Б. А., Угасте Ю. Э. Взаимная диффузия в многофазных металлических системах. — М.: Наука, 1981. — 350 с.Gurov K. P., Kartashkin B. A., Ugaste Yu. E. Interdiffusion in multiphase metallic systems. — Moscow: Nauka, 1981. — 350 p. [in Russian].Kulkarni N., Warmack R. J. Bruce, Radhakrishnan В., et al. Overview of SIMS-Based Experimental Studies of Tracer Diffusion in Solids and Application to Mg Self-Diffusion / J. Fhase Equilib. Diffusion. 2014. Vol. 35. N 6. E 762 - 778. https://doi.org/10.1007/sll669-014-0344-4.Kulkarni N., Warmack R. J. Bruce, Radhakrishnan В., et al. Overview of SIMS-Based Experimental Studies of Tracer Diffusion in Solids and Application to Mg Self-Diffusion / J. Phase Equilib. Diffusion. 2014. Vol. 35. N 6. E 762 - 778. https://doi.org/10.1007/sll669-014-0344-4.Tsuji S. Multiphase binary diffusion in infinite and semi-infinite media: Fart I. On the determination of interdiffusion coefficients / Metallurgical and Materials Transactions A. 1994. Vol. 25. N 4. E 741 - 751. https://doi.org/10.1007/bf02665451.Tsuji S. Multiphase binary diffusion in infinite and semi-infinite media: Part I. On the determination of interdiffusion coefficients / Metallurgical and Materials Transactions A. 1994. Vol. 25. N 4. E 741 - 751. https://doi.org/10.1007/bf02665451.Paul A., Kodentsov A., van Loo F. J. J. Intermetallic growth and Kirkendall effect manifestations in Cu/Sn and Au/Sn diffusion couples / Zeitschrift fur Metallkunde. 2004. Vol. 95. N 10. E 913-920.Paul A., Kodentsov A., van Loo F. J. J. Intermetallic growth and Kirkendall effect manifestations in Cu/Sn and Au/Sn diffusion couples / Zeitschrift fur Metallkunde. 2004. Vol. 95. N 10. E 913-920.Александров О. В., Козловский В. В. Моделирование взаимодействия никеля с карбидом кремния при формировании омических контактов / ФТП. 2009. Т. 43. № 7. С. 917 923.Aleksandrov O. V., Kozlovsky V V. Simulation of interaction between nickel and silicon carbide during the formation of ohmic contacts / Semiconductors. 2009. Vol. 43. N 7. E 885 891. https://doi.org/10.1134/S1063782609070100 [in Russian].Молохина Л. А., Рогалин В. Е., Филин С. А. и др. Математическая модель роста фаз в двухкомпонентных многофазных системах при изотермическом отжиге / Журнал физической химии. 2017. Т. 91. № 9. С. 1468 - 1475.Molokhina L. A., Rogalin V E., Kaplunov I. A., et al. Mathematical model for the growth of phases in binary multiphase systems upon isothermic annealing / Russian Journal of Physical Chemistry A. 2017. Vol. 91. N 9. E 1635 - 1641. https://doi.org/10.1134/s0036024417090217.Zheng J., Ни X., Ren Z., et al. Solid-state reaction studies in A1203 - Ti02 system by diffusion couple method / ISIJ International. 2017. Vol. 57. N 10. E 1762 - 1766. https://doi.org/ 10.2355/isijinternational.isijint-2017-042.Zheng J., Hu X., Ren Z., et al. Solid-state reaction studies in A1203 - Ti02 system by diffusion couple method / ISIJ International. 2017. Vol.57. N10. E 1762-1766. https://doi.org/ 10.2355/isijinternational.isijint-2017-042.Ren Z. S., Ни X. J., Li S. Y., et al. Interdiffusion in the Fe203 - Ti02 system / Int. J. Miner. Metall. Mater. 2013. Vol. 20. N 3. E 273. https://doi.org/10.1007/sl2613-013-0723-6.Ren Z. S., Hu X. J., Li S. Y, et al. Interdiffusion in the Fe203 - Ti02 system / Int. J. Miner. Metall. Mater. 2013. Vol. 20. N 3. E 273. https://doi.org/10.1007/sl2613-013-0723-6.Mangum J., Podowitz-Thomas S., Nikkei J., et al. Investigating Pb diffusion across buried interfaces in Pb(Zr0.2Ti0.8)O3 thin films via time-of-flight secondary ion mass spectrometry depth profiling / Surf. Interface Anal. 2017. Vol. 49. N 116. E 973 - 977. https://doi.org/10.1002/sia.6255.Mangum J., Podowitz-Thomas S., Nikkei J., et al. Investigating Pb diffusion across buried interfaces in Pb(Zr0 2Ti0 8)03 thin films via time-of-flight secondary ion mass spectrometry depth profiling / Surf. Interface Anal. 2017. Vol. 49. N 116. E 973 - 977. https://doi.org/10.1002/sia.6255.Silva C., Costa A. R. G., da Silvac R., et al. Magnetic and electrical characterization of Ti02 single crystals co-implanted with iron and cobalt / Journal of Magnetism and Magnetic Materials. 2014. Vol.364. E 106-116 https://doi.org/10.1016/ j.jmmm.2014.04.022.Silva C., Costa A. R. G., da Silvac R., et al. Magnetic and electrical characterization of Ti02 single crystals co-implanted with iron and cobalt / Journal of Magnetism and Magnetic Materials. 2014. Vol.364. E 106-116 https://doi.org/10.1016/ j.jmmm.2014.04.022.Dholam R., Patel N., Ad ami M., et al. Hydrogen production by photocatalytic water-splitting using Cr- or Fe-doped Ti02 composite thin films photocatalyst / International Journal of Hydrogen Energy. 2009. Vol. 34. N 13. E 5337 - 5346. https:// doi.org/10.1016/j.ijhydene.2009.05.011.Dholam R., Patel N., Ad ami M., et al. Hydrogen production by photocatalytic water-splitting using Cr- or Fe-doped Ti02 composite thin films photocatalyst / International Journal of Hydrogen Energy. 2009. Vol. 34. N 13. E 5337 - 5346. https:// doi.org/10.1016/j.ijhydene.2009.05.011.Sobczyk-Guzendaa A., Owczareka S., Szymanowskia H., et al. Iron doped thin Ti02 films synthesized with the RF PECVD method / Ceramics International. 2015. Vol. 41. N 6. E 7496 - 7500. https://doi.Org/10.1016/j.ceramint.2015.02.071.Sobczyk-Guzendaa A., Owczareka S., Szymanowskia H., et al. Iron doped thin Ti02 films synthesized with the RF PECVD method / Ceramics International. 2015. Vol. 41. N 6. E 7496 - 7500. https://doi.Org/10.1016/j.ceramint.2015.02.071.Самарский А. А. Теория разностных схем. — M.: Наука, 1977. — 656 с.Samarsky A. A. Theory of differential schemes. — Moscow: Nauka, 1977. — 656 p. [in Russian].Ни W., Hayashi К., Fukumura Т., et al. Spontaneous formation of suboxidic coordination around Co in ferromagnetic rutile Ti095Co005O2 film /Applied Physics Letters. 2015. Vol. 106. N 22.' E 222403-1 - 222403-5. https://doi.org/10.1063/ 1.4921847.Hu W., Hayashi K., Fukumura Т., et al. Spontaneous formation of suboxidic coordination around Co in ferromagnetic rutile Tiog5Cooo502 film / Applied Physics Letters. 2015. Vol. 106. N 22. E 222403-1 - 222403-5. https://doi.org/10.1063/ 1.4921847.Dai G., Liu S., Liang Y., et al. Synthesis and enhanced photoelectrocatalytic activity of p-n junction Co304/Ti02 nanotube arrays / Applied Surface Science. 2013. Vol. 264. E 157 - 161. https://doi.Org/10.1016/j.apsusc. 2012. 09. 160.Dai G., Liu S., Liang Y., et al. Synthesis and enhanced photoelectrocatalytic activity of p-n junction Co304/Ti02 nanotube arrays / Applied Surface Science. 2013. Vol. 264. E 157 161. https://doi.Org/10.1016/j.apsusc. 2012. 09. 160.Matsumoto Y., Murakam M., Shono Т., et al. Room-temperature ferromagnetism in transparent transition metal-doped titanium dioxide / Science. 2001. Vol. 291. E 854 - 856. https:// doi.org/10.1126/science.1056186.Matsumoto Y., Murakam M., Shono Т., et al. Room-temperature ferromagnetism in transparent transition metal-doped titanium dioxide / Science. 2001. Vol.291. E 854-856. https:// doi.org/10.1126/science.1056186.Sooda S., Umar A., Mehta S., et al. Highly effective Fedoped Ti02 nanoparticles photocatalysts for visible-light driven photocatalytic degradation of toxic organic compounds / J. of Colloid and Interface Science. 2015. Vol. 450. E 213 - 223. https://doi.org/10.1016/jjcis.2015.03.018.Sooda S., Umar A., Mehta S., et al. Highly effective Fedoped Ti02 nanoparticles photocatalysts for visible-light driven photocatalytic degradation of toxic organic compounds / J. of Colloid and Interface Science. 2015. Vol. 450. E 213 - 223. https://doi.org/10.1016/jjcis.2015.03.018.Афонин H. H., Логачева В. А., Герасименко Ю. В. и др. Взаимодействие кобальта и титана с тонкими пленками их оксидов в процессе вакуумного отжига / Конденсированные среды и межфазные границы. 2013. Т. 15. № 3. С. 232 - 237.Afonin N. N., Logacheva V A., Gerasimenko Yu. V, et al. Interaction of cobalt and titanium with a thin films of their oxides during vacuum annealing / Condensed matter and interphases. 2013. Vol. 15. N 3. E 232 - 237 [in Russian].Логачева В. А., Афонин Н. Н., Вахтель В. М. и др. Взаимодействие компонентов в двухслойной пленочной системе Fe - Ti02, полученной методом магнетронного распыления / Конденсированные среды и межфазные границы. 2016. Т. 18. № 3. С. 345 - 355.Logacheva V A., Afonin N. N., Vakhtel V M., et al. Interection of components in bilayer film system Fe - Ti02, obtained by magnetron sputtering / Condensed matter and interphases. 2016. Vol. 18. N 3. E 345 - 355 [in Russian].Chambers S., Thevuthasan S., Farrow R. F. C, et al. Epitaxial growth and properties of ferromagnetic co-doped Ti02 anatase / Appl. Fhys. Lett. 2001. Vol. 79. E 3467 - 3469. https://doi.Org/10.1063/l.1420434.Chambers S., Thevuthasan S., Farrow R. F. C, et al. Epitaxial growth and properties of ferromagnetic co-doped Ti02 anatase / Appl. Phys. Lett. 2001. Vol. 79. E 3467 - 3469. https:// doi.org/10.1063/1.1420434.Cordishi D., Burriesci N., D'Alba E, et al. Structural characterization of Fe/Ti oxide photocatalysts by X-ray, ESR, and Mossbauer methods / J. Solid State Chem. 1985. Vol. 56. E 182 190. https://doi.org/10.1016/0022-4596(85)90055-6.Cordishi D., Burriesci N., D'Alba E, et al. Structural characterization of Fe/Ti oxide photocatalysts by X-ray, ESR, and Mossbauer methods / J. Solid State Chem. 1985. Vol. 56. E 182 190. https://doi.org/10.1016/0022-4596(85)90055-6.Sasaki J., Peterson N., Hoshino K. Tracer impurity diffusion in single-crystal rutile (Ti02_I) / J. Fhys. Chem. Solids. 1985. Vol.46. N11. E 1267-1283. https://doi.org/10.1016/ 0022-3697(85)90129-5.Sasaki J., Peterson N., Hoshino K. Tracer impurity diffusion in single-crystal rutile (Ti02_I) / J. Phys. Chem. Solids. 1985. Vol.46. N11. E 1267-1283. https://doi.org/10.1016/ 0022-3697(85)90129-5.Cyuan-You S., Hwan-Wen L., Hong-Yang L. Kirkendall porosity in barium titanate-strontium titanate diffusion couple / Ceramics International. 2009. Vol. 35. N 7. E 2951 - 2958. https://doi.Org/10.1016/j.ceramint.2009.04.009.Cyuan-You S., Hwan-Wen L., Hong-Yang L. Kirkendall porosity in barium titanate-strontium titanate diffusion couple / Ceramics International. 2009. Vol. 35. N 7. E 2951 2958. https://doi.Org/10.1016/j.ceramint.2009.04.009.Wang X., Feng J., Bai Y., et al. Synthesis, properties, and applications of hollow micro-/nanostructures / Chem. Rev. 2016. Vol. 116. E 10983-11060. https://doi.org/10.1021/acs.chemrev 5b00731.Wang X., Feng J., Bai Y., et al. Synthesis, properties, and applications of hollow micro-/nanostructures / Chem. Rev. 2016. Vol. 116. E 10983-11060. https://doi.org/10.1021/acs.chemrev 5b00731.Klingera L., Rabkinab E. On the nucleation of pores during the nanoscale Kirkendall effect / Materials Letters. 2015. Vol. 161. E 508 - 510. https://doi.Org/10.1016/j.matlet.2015. 09.004.Klingera L., Rabkinab E. On the nucleation of pores during the nanoscale Kirkendall effect / Materials Letters. 2015. Vol.161. E 508-510. https://doi.0rg/lO.lOl6/j.matlet. 2015.09.004.Zhang D., Jin C, Li Z., et al. Oxidation behavior of cobalt nanoparticles studied by in situ environmental transmission electron microscopy / Science Bulletin. 2017. Vol. 62. N 11. E 775 778. https://doi.Org/10.1016/j.scib.2017.05.003.Zhang D., Jin C, Li Z., et al. Oxidation behavior of cobalt nanoparticles studied by in situ environmental transmission electron microscopy / Science Bulletin. 2017. Vol. 62. N 11. E 775 - 778. https://doi.Org/10.1016/j.scib.2017.05.003.

The authors declare that there are no conflicts of interest present.