Mathematical modeling of concentration distributions of Fe/Tb-magnetic multilayer media

DOI: 10.31673/2412-4338.2020.011241

Abstract

An important area of resource conservation and enhancement of technological characteristics of materials is the use of nanofilms and nanopores for various purposes. The latter are multilayered nanoscale, characterized by the heterogeneity of physical properties (mechanical, diffusion, electrical, magnetic, optical). They are widely used as structural resource-saving materials in the semiconductor and electronics industries (for new generations of storage devices and circuits), nuclear power, as nanocaps for the working bodies of equipment for the production of fiberglass, microporous filter materials and the like. This has led in recent years to the growth of experimental and theoretical studies of the diffusion kinetics of multilayer nanocomposites, which makes it possible to obtain, on the basis of materials with known properties of new materials, the creation of which is related to structural changes in the aggregation of nanolayers with different properties. In particular, the aggregation of (Fe / Tb) -magnetic multilayer nanofilms revealed significant effects of magnetostriction (sample compression).
In this paper, a mathematical model of diffusion transfer in multi-constituent Fe / Tb magnetic nanofilms is constructed. Numerical diffusion transfer simulation was performed and model adequacy was verified by the results of field experiments. Computer simulation and analysis of the concentration dependences of the diffused components in the layers of the nanofilms as a function of the thickness for different sections of the technological surfaces in the range of change of design and mode parameters.

Keywords: mass transfer, mathematical modeling, nano films, concentration distributions, integral transformation.

References
1. Petryk M.R. (2006) “Matematychne modeliuvannia dyfuziinoho masoperenosu zi spektralnym parametrom dlia n-interfeisnykh neodnoridnykh i nanoporystykh neobmezhenykh seredovyshch”. Naukovyi visnyk Chernivetskoho universytetu: zb. nauk. pr. Chernivtsi: Ruta, 288. P. 90 – 99.
2. Petryk M.R., Vasyliuk P.M., Mykhalyk D.M., Babii N.V. and Petryk O.Iu. (2015) “Modeli protsesiv dyfuziinoho perenosu i metody otsiniuvannia parametriv v bahatokompozytnykh nanoplivkakh”. Monohrafiia. Ternopil: TNTU imeni Ivana Puliuia, 176 p.
3. Petryk M., Vasyliuk M. and Babii N. (2013) “Matematychne modeliuvannia kontsentratsiinykh rozpodiliv bahatosharovykh nanoplivok oksydnoi struktury”. Visnyk TNTU, 2013, Vol. 69, No. 1. P. 231 – 243.
4. Deineka V., Petryk M., Vasyliuk P. and Babii N. (2013) “Matematychne modeliuvannia dyfuziinoho perenesennia v bahatosharovykh nanoplivkakh oksydnoi struktury (doslidzhennia zrazka za tekhnolohiieiu vyrobnytstva bazaltovoho supertonkoho volokna)”. Visnyk TNTU, Vol. 70, No. 2. P. 219 – 231.
5. Deineka V., Petryk M., Vasyliuk P. and Babii N. (2010) “Matematychne modeliuvannia masoperenosu zi zminnymy koefitsiientamy dyfuzii dlia neodnoridnykh obmezhenykh mahnitnykh seredovyshch”. Matematychne ta kompiuterne modeliuvannia. Seriia: Tekhnichni nauky, Kamianets-Podilskyi, No. 4. S. 3 – 17.
6. Leniuk M.P. and Petryk M.R. (2000) Intehralni peretvorennia Furie, Besselia iz spektralnym parametrom v zadachakh matematychnoho modeliuvannia masoperenosu v neodnoridnykh seredovyshchakh. Kyiv, Naukova dumka, 2000. 372 p.
7. Leniuk M.P. and Petryk M.R. (2003) “Matematychne modeliuvannia dyfuziinoho masoperenosu zi spektralnym parametrom dlia n-interfeisnykh neodnoridnykh i nanoporystykh napivobmezhenykh seredovyshch”. Volynskyi matematychnyi visnyk. Seriia prykladna matematyka, Vol. 1. P. 69 − 76.
8. Deineka V.S., Petryk M.R. and Fraissard J. (2011) “Identifying kinetic parameters of mass transfer in components of multicomponent heterogeneous nanoporous media of a competitive diffusion system”. Cybernetics and System Analysis, Springer New York, Vol. 47, No. 5. P. 705 – 723.
9 Dejneka V.S. and Petrik M.R (2012) “Identifikaciya parametrov neodnorodnyh zadach diffuzii v nanomultikompozitah s ispolzovaniem gradientnyh metodov”. Kompyuternaya matematika, No. 1. P. 41 – 51.