Modeling the Effect of Oxidation on Magnetic Characteristics of Magnetith Nanoparticles Ilia ILIUSHIN and Leonid AFREMOV

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1 2017 2nd International Conference on Computer, Mechatronics and Electronic Engineering (CMEE 2017) ISBN: Modeling the Effect of Oxidation on Magnetic Characteristics of Magnetith Nanoparticles Ilia ILIUSHIN and Leonid AFREMOV Far Eastern Federal University, Vladivostok, Russia *Corresponding author Keywords: Oxidation processes, Blocking temperature, Nanoparticle, Modeling. Abstraction. The theoretical analysis of the influence of oxidation processes on the blocking temperature and hysteresis characteristics of a system of magnetite nanoparticles was carried out. It is shown that the blocking temperature drops sharply at the initial stage of the maghemization process and practically does not change with an increase in the proportion of maghemite in the region 0,4<<1. In addition, it has been found that the spontaneous saturation magnetization decreases with increasing oxidation state of nanoparticles, while magnetite oxidation leads to an insignificant decrease in the coercive force and the ratio of the residual saturation magnetization to the saturation magnetization. Introduction The study of nanoparticles of iron oxides has a long history. The study of magnetite and maghemite has made a significant contribution both to the foundation of fundamental knowledge and practical applications. The good biocompatibility of superparamagnetic iron oxide nanoparticles makes them very popular for such biomedical technologies as diagnosis (MRI), drug delivery and hyperthermia, as well as popular theranostics [1, 2]. Of interest to these applications are sufficiently small nanoparticles of less than 10 nm in size [3, 4]. However, the complexity of the interpretation of the magnetic properties of nanoparticles is related to the dependence of these properties on the compositional, structural, surface characteristics, as well as interparticle interaction [5-8]. The high level of magnetite instability in the air, since it contains twice as many trivalent ions as divalent ions, leads to partial oxidation of magnetite to maghemite (γ-fe2o3) [9]. With this, a core-shell structure is formed in which the thickness of the oxidized layer depends on the particle size. For example, in the reference [10] results of a study of the effect of maghemisation magnetization process on the magnetic characteristics and blocking temperature of a system of magnetite nanoparticles. Authors showed that increase of the proportion of the oxidized shell (maghemite) lead to decrease of the blocking temperature and have almost no effect on the spontaneous maghemisation of a system of nanoparticles. The oxidation mechanism is well described in the works of O Reilly [11] and Gallagher [12], according to which the oxidation process beginning on the surface, where bivalent iron ions become trivalent. Further, as a result of diffusion processes, the bivalent ions leave vacancies and move from the center of nanoparticle towards the surface and form the oxidized layer. At low temperature [13] and the lowered diffusion threshold, the diffusion gradient abruptly breaks off in an isolated oxide layer. As a result, an oxidized shell is formed around a non-oxidized core, the so-called coreshell structure. However, even though core-shell structures have been studied for more than 50 years [3, 12-15], the effect of such a structure on the magnetic properties of partially oxidized nanoparticles remains insufficiently studied [15]. The aim of this work is to model the effect of the oxidation process on the hysteresis characteristics and the blocking temperature of a system of magnetite nanoparticles. 44

2 The Oxidation Model of Magnetite Nanoparticle Study of the effect of single-phase oxidation on the magnetic properties of materials of titanomagnetites conducted within the framework of the model [16, 17]. Figure 1. Illustration for the oxidation model of magnetite nanoparticle. Distribution of the oxidation parameter z shown in the upper part of picture. Distribution is calculated within the framework of the model described in the reference [17]. Lower part of this picture is an illustration of core-shell nanoparticle with homogeneously oxidized core z and inhomogeneously oxidized shell ( z z 1). According to this model, the oxidation of magnetite can be considered as two mutually complementary processes that ensure the formation of a core-shell nanoparticle: the growth of a heterogeneously oxidized shell and a simultaneous increase in the oxidation state z of a homogeneously oxidized core of a nanoparticle (fig. 2). At the first stage of the simulation, it is assumed that the magnetite nanoparticle is not oxidized (z=0). Further, two phases are formed in the particle, an inhomogeneously oxidized shell of thickness, and a partially oxidized core of magnetite with a degree of oxidation z. At the k-th stage, the thickness of the inhomogeneously oxidized shell increases to k, and the degree of oxidation of the core to k z. We use the core-shell nanoparticle model for oxidized nanoparticles of magnetite described in reference [18]: 1. We assume a uniformly magnetised ellipsoidal nanoparticle with volume V=4πQB /3 and elongation Q (phase 1) containing uniformly magnetised ellipsoidal core with volume v = εv = 4πqb /3 and elongation q (phase 2). 2. Crystallographic anisotropy axes of both phases and major axes are parallel to each other and spontaneous maghemisation vectors I () and I () are located in same plane with the external magnetic field H; 3. External magnetic field (=0) and thermal fluctuations (=0), nanoparticle will be in one of four states: magnetic moments of both phases are parallel first state «( )» and third state «( )»; magnetic moment of phase is oriented the opposite side between them self second state «( )» and fourth state «( )». 4. If temperature is not equal to zero then population (the probability of finding nanoparticle in one of four states) of four magnetic states can be determined with the help of matrix exponential [19]: ()=exp( ) (0)+ exp( ( )), (1) Where the matrix elements,, and vectors (), (0) expressed through and () respectively: =,, (),=,=,()= (),(0)= (2) () 45

3 Here = ( В ) are the elements of a transition matrix from th equilibrium state to th state, =10 is the frequency factor, potential barriers separating i- th and k-th states. Equations (1) and (2) allows one to calculate maghemisation of a system of nanoparticles: (t)=с(1 ε)i () + εi () (,) (,)+ +(1 ε)i () εi () (,) (,)(). (3) Where = is the volume concentration of nanoparticles, () stands for the size distribution function of nanoparticles. During the calculations influence of oxidation on the magnetic characteristics of a system of magnetite nanoparticles we used the approximation of the experimentally established dependence of the spontaneous magnetization on the sizes of the nanoparticles [20] and the degree of oxidation z [21] was approximated by the following expressions: (,)=4801 ( ) Гс, = см. (4) Approximation of the experimental results [22] made it possible to determine the dependence of the magnetic crystallographic anisotropy constant on the degree of oxidation: (,)= ()( ). (5) The dependence of the magnetic crystallographic anisotropy constant on the degree of oxidation was determined with the help of [22] ()= +, (6) where, according to [23, 24] crystallographic anisotropy constants of magnetite are = 1,06 10 erg/cm 3, =0,029 erg/cm 2. During the calculations of various types of remanent magnetization, it was assumed that as a result of oxidation of magnetite in a spherical nanoparticle, =2 in size, a spherical magnetite core with radius covered by a maghemite shell is formed. The size distribution function was taken from the distribution presented in the reference [15].]. Blocking Temperature The spectrum of the relaxation times is determined by the frequency matrix = ( ). Since the eigenvalues of the transition matrix are the inverse times of the transition from one state to another one 1, we will use the maximum of them,, to estimate the transition time to the equilibrium state, if transitions with a shorter relaxation time have already been completed. Then, to estimate the blocking temperature, we can use ( )=. Calculation time is 1 second. When calculating the dependence of blocking temperature of the system of nanoparticles on the oxidation state, the experimental values [10] of the particle characteristics presented in Table 1 were used. The results of modeling the effect of oxidation on the blocking temperature, it was shown Figure 2. That is suggested the process of maghemization leads to a decrease in. And in the region of small values of the share of maghemite =1 <0,4 a sudden drop in the blocking Table 1. Particle characteristics of the system of nanoparticles [10] Diameter of the core, nm Shell thickness, nm Magnetite share,

4 Temperature is realized. Further development of the maghemization process (0,4<<1) ractically does not affect the value of. 400 T b, K W Figure 2. Dependence of the blocking temperature on the fraction of maghemite W for nanoparticles. The points indicate the experimental values of [10]. The results of the calculations agree qualitatively with the experimental values of the blocking temperature, given in [10]. Hysteresis Characteristics For study the effect of oxidation on the hysteresis characteristics of a system of core-shell nanoparticles, hysteresis loops were constructed. Figure 3. Dependence of the saturation maghemisation of magnetite I on the degree of oxidation z. The points indicate the experimental values of the saturation magnetisation presented in the reference [15]. Dependence of the saturation maghemisation of magnetite I on the degree of oxidation z. shows on the fig. 3. As was to be expected, because of the linear dependence of the spontaneous maghemisation [12] on the oxidation state z, the saturation maghemisation decreases linearly with increasing z. The obtained result agrees well with the experimental data [15]. The dependence of the coercive field of magnetite nanoparticles on the degree of oxidation is presented on the fig. 4a. It can be seen that the theoretical curve passes somewhat lower than the experimental curve. This is due to the fact that in modeling we did not include particles with a size larger than 100 nm in the distribution function, assuming their number to be negligible. While a certain fraction of particles smaller than 100 nm can be in the superparamagnetic state, which led to lower theoretical values of 47

5 not only the coercive field but also the ratio of the remanent saturation maghemisation to the saturation maghemisation of magnetite (fig. 4b). Figure 4. Dependences of: the coercive field (a), remanent saturation magnetization to saturation magnetization ratio (b) on the degree of oxidation z of magnetite. The points indicate the experimental values presented in the reference [15]. Conclusion Theoretical analysis of the influence of oxidation processes on the hysteresis characteristics of a system of magnetite nanoparticles carried out within the framework of a core-shell nanoparticle model [18] showed that: the blocking temperature is changed sharply at the initial stage of the maghemite magnetite process, with an increase in the proportion of maghemite =1 in the area <0,4 and practically does not be changed at 0,4<<1, that coincides with the experimental results [10]; Saturation magnetization decreases with increasing degree of oxidation of nanoparticles, at the same time oxidation of magnetite slightly affects the coercive field and the ratio. The results of the modeling are in good agreement with experimental data [15]. Acknowledgement This research was financially supported by the the Ministry of Education and Science of the Russian Federation No / 8. 9" Reference [1] Reddy, L. H.; Arias, J. L.; Nicolas, J.; Couvreur, P. Chem. Rev. 2012, 112, [2] Levy, M.; Quarta, A.; Espinosa, A.; Figuerola, A.; Wilhelm, C.; Garcia-Hernandez, M.; Genovese, A.; Falqui, A.; Alloyeau, D.; Buonsanti, R.; Cozzoli, P. D.; Garcia, M. A.; Gazeau, F.; Pellegrino, T. Chem. Mater. 2011, 23, [3] Gazeau, F.; Levy, M.; Wilhelm, C. Nanomedicine 2008, 3 (6), [4] Roca, A. G.; Costo, R.; Rebolledo, A. F.; Veintemillas-Verdguer, S.; Tartaj, P.; Gonzalez- Carreno, T.; Morales, M. P.; Serna, C. J. J. Phys. D: Appl. Phys. 2009, 42, [5] Salazar, J. S.; Perez, L.; de Abril, O.; Phuoc, L. T.; Ihiawakrim, D.; Vazquez, M.; Greneche, J.-M.; Begin-Colin, S.; Pourroy, G. Chem. Mater. 2011, 23, [6] Roca, A. G.; Niznansky, D.; Polierova-Vejpravova, J.; Bittova, B.; Gonzalez-Fernandez, M. A.; Serna, C. J.; Morales, M. P. J. Appl. Phys. 2009, 105, [7] Kim, T.; Shima, M. J. Appl. Phys. 2007, 101, 09M516. [8] Daou, T. J.; Grenèche, J. M.; Pourroy, G.; Buathong, S.; Derory, A.; Ulhaq-Bouillet, C.; Donnio, B.; Guillon, D.; Begin-Colin, S. Chem. Mater. 2008, 20, [9] Colombo, U.; Fagherazzi, G.; Gazzarrini, S.; Lanzavecchia, G.; Sroni, G. Nature 1968, 219,

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