Study of the Phase Composition of Fe 2 O 3 Nanoparticles

Transcription

1 WDS'9 Proceedings of Contributed Papers, Part III, , 29. ISBN MATFYZPRESS Study of the Phase Composition of Fe 2 O 3 Nanoparticles V. Valeš, J. Poltierová-Vejpravová, A. Mantlíková, and V. Holý Charles University, Faculty of Mathematics and Physics, Department of Condensed Matter Physics, Prague, Czech Republic. P. Brázda Charles University, Faculty of Science, Department of Inorganic Chemistry, Prague, Czech Republic. Abstract. The changes of the phase composition of iron oxide samples prepared by solgel method using single precursor both for nanoparticles and the matrix were studied by x-ray diffraction. Obtained were analyzed by an approach using the Debye formula which is suitable for the size of particles up to about 1 nm. The phase composition of the nanoparticles was described by a core-shell model corresponding to the assumed inward movement of the phase interface between two phases. First results of the phase composition of Fe 2 O 3 nanoparticles have already been obtained. Introduction Important physical properties of nanoparticles are determined mainly by their atomic structure, especially by their phase composition and the presence of structure defects. X-ray diffraction is a good tool for studying the structure of the nanoparticles, its application for very small particles is however limited by very small intensity of the scattered wave. For this reason special experimental setups, like e.g. diffraction with small incidence angle, are used and many experiments have to be done at synchrotrons. Standard methods of the measured analysis based on the description of the diffraction using instrumental functions and functions of physical broadening of the lines fail in the case of very small particles. An ab-initio calculation method (based on the Debye formula [Cervellino et al., 24; Cervellino et al., 23]) has to be used instead. In this work the Debye formula is used for the description of the diffraction of iron oxide samples measured at ANKA synchrotron in Karlsruhe. Using this approach we determine basic parameters of the particles such as lattice parameters and the size of the particles, as well as the presence of different phases. During annealing, subsequent phase transitions from γ-fe 2 O 3 to ε-fe 2 O 3 and to α-fe 2 O 3 take place. New phases nucleate probably at the surface of the nanoparticles and the phase transformation proceeds towards the particle center ([Woo et al., 28; Gich et al., 26]), so that the structure of the nanoparticles can be described by a core-shell model; this model was used in the Debye-formula based simulation. From the analysis of the experimental we determined the kinetic parameters of the phase transitions and their dependence on the nanoparticle sizes. Measured samples The great interest in Fe 2 O 3 nanoparticles is caused mainly by magnetic properties of these particles, namely extremely high room temperature coercivity of epsilon phase of these iron oxide nanoparticles. The samples were prepared by ex-situ annealing of organic precursors and then measured at ANKA synchrotron in Karlsruhe with incidence angle 5º and the wavelength of.97 Å. The primary beam was monochromatized by a 2x111Si monochromator, the diffracted radiation was measured by a point detector equipped with a narrow entrance slit and a filter suppressing the Fefluorescence. The series of samples was prepared with the final annealing temperature from 9 ºC to 115 ºC with the step of 5 ºC. To the temperature of 9 ºC all the samples were heated at the speed 1 ºC per minute and stayed at this temperature for 4 hours. As for the sample with the final temperature 9 ºC this was the whole procedure. The other samples were then with the same speed heated to their final annealing temperature with the 4-hour waiting each 5 ºC up to their final heating This procedure causes the creation of Fe 2 O 3 nanoparticles in the amorphous SiO 2 matrix. From the literature [Brázda et al., 29] it is known that the particles created at the lowest final temperature should be in the form of maghemite and with increasing final temperature the phase of Fe 2 O 3 particles should change to ε and hematite. 28

2 Theoretical description Debye formula in Eq. (1), which has been used for the x-ray analysis describes the intensity distribution of the samples consisting of the same randomly oriented particles, knowing the positions of the atoms in one such a particle. sin( Qr ) * ij I ( Q) = fi f j, (1) i, j Qrij where the double sum goes over all atoms in the particle, Q is the length of the scattering vector, f i is the atom form factor of the i-th atom and r ij is the distance between i-th and j-th atom. The formula is valid for any arrangement of atoms in any particle; no lattice is needed; only exact positions of atoms in the particle are important. The only technical limit of using of this equation is the number of terms in the double sum. For instance, a particle of Fe 2 O 3 of diameter of 13 nm contains about 1 5 atoms, which means that there are 1 1 interatomic distances that have to be taken into account for every Q. For this reason, the distribution function of atomic pairs was calculated and a histogram of all interatomic distances was created; an example of such histogram is shown in Fig. 1 corresponding to a spherical particle with the radius of 4 Å, the histogram has been constructed using the step width of.1 Å. Since we introduced the histogram of interatomic distances, we can rewrite the Eq. (1) using calculated from the histogram, i.e. we know the multiplicity of each of interval of distances. The rewritten form of Debye formula in equation (2) enables us to perform calculations for much larger samples. For the intensity we can write 2 ( ) sin( Qri ) I Q = mi f, (2) i Qri where m i is the multiplicity factor for the i-th interval of distances. The expression in Eq. (2) is valid only for one type of atoms in the particle, which is not our case (because of different atom form factors). This fact requires only some technical changes, which do not affect the fundamental meaning of Eq. (2). The phase transition from one phase to the other is supposed to take place from the particle surface to its center. For this reason the core-shell model of the particle (particle consisting of two different phases) has been introduced to the Debye formula program. In order to have a brief look in to the behavior of the simulated calculated by our model, diffraction curves for different phases m 3,x1 5 2,5x1 5 2,x1 5 1,5x1 5 1,x maghemite R maghemite =4nm ε-fe 2 O 3 5,x1 4, r[a] Figure 1. Calculated histogram of interatomic distances in a spherical Fe 2 O 3 particle of radius of 4 Å. The histogram step is.1 Å Figure 2. Calculation of diffraction curves for different phases of Fe 2 O 3. The full line corresponds to the pure maghemite particle of radius of 5 Å; the dotted one to the pure ε-fe 2 O 3 particle of the same radius; and the dashed line represents the diffraction from the particles of radius 5 Å, which consist of the core (radius 4 Å) of maghemite and the shell of ε-fe 2 O 3. 29

3 were calculated (Fig. 2). From this picture the difference between the maghemite and ε phases of Fe 2 O 3 can be seen as well as the effect of the core-shell structure of these two phases, which causes some mixture of the diffraction pattern of both phases. Data analysis Several samples from the series described above were analysed by the Debye-formula approach using the core-shell model, assuming that the interface of the two phases moves from the surface to the center of the particle. The from the Figs. 3 5 (samples A C) were ted by hand and the results are summarized in Table 1; the errors were estimated from this too. The background was approximated ad-hoc by a polynomial of the third power. The broad peak around 13º is caused by the amorphous SiO 2 matrix and for our ting is not important. The s describe the measured well and the parameters of the core-shell model were obtained. The sample D (Fig. 6) could not have been ted because of a too large size of the particles that made the simulation extremely time-consuming θ (deg) Figure 3. Sample A. Measured and of the sample annealed at the 9 ºC as the highest Figure 5. Sample C. Measured and of the sample annealed at the 1 ºC as the highest Figure 4. Sample B. Measured and of the sample annealed at the 95 ºC as the highest Figure 6. Sample D. Measured of the sample annealed at the 11 ºC as the highest Table 1. Results obtained from the measured ting. The errors of the rate of both phases are roughly estimated. The error of the total radius is not mentioned; the value of the total radius means the lower estimate of the real radius. Sample Total radius (Å) Maghemite (%) ε-fe 2 O 3 (%) A 4 34 ± 6 66 ± 6 B 5 26 ± 4 74 ± 4 C 58 ± 8 1 ± 8 21

4 Discussion As we showed in the previous section, the calculated describes well the measured. However, the question of the uniqueness of the model is still open. For instance, we assumed that the new phase is being created at the surface of the particle; i.e., that the shell is represented by the new phase while the old one is in the core, as we have assumed in our model. If this assumption is not valid we have to change the phase of the core to the phase of the shell and vice versa. This possibility has to be taken into account as well as the situation when there is no core-shell structure and for example some particles consist of one phase and the others of the second one. The difference between the interchange of core and shell in sample A is shown in the Fig. 7. In this case there are slight differences which could be observable, but the question is if by the hand ting we can get better agreement. In the Fig. 8, where the difference between core-shell particle model and the mixture of particles consisting of single phase is shown, one can see that the difference between both cases is much smaller and it is impossible to distinguish between them. Both calculations have been made using the same ratio of present phases. Since the peak corresponding to certain phase is created only by the atoms in the particle belonging to this phase, the total size of the whole particle has to be larger for the core-shell model then for the model consisting of single phase particles. This can be seen from the Fig. 8, where the widths of diffraction peaks for both models are approximately the same and for the calculation using mixture model, particles were about 3 % smaller then particles used for core-shell model calculation. It could be possible to determine the size of the particles using other methods (TEM) and decide which model this size corresponds to. From the work [Bráza et al., 29] it follows that the average radius of the particles annealed up to 1 ºC is 6 Å, what is just in between both model cases (mixture model, core-shell model; Fig. 8) so it has to be investigated more R tot =4 A 28 A of maghemite in ε 3 A of ε in maghemite Figure 7. Analysis of sample A. The difference of the diffraction pattern when exchanging the phase composition in the core and in the shell. The total radius of the particle is 4 Å mixture of separate phases, radius 5 A core-shell, ε around maghemite, radius 44.8/7 A Figure 8. Analysis of sample B. The difference of the diffraction pattern between the core-shell structure model (maghemite in the core, radius 7 Å) and the mixture of one-phase particles (radius 5 Å) mixed in the same ratio that corresponds to the ratio in the core-shell model. Conclusion From the ting of the measured we obtained the total size of analyzed samples (A C) and the fraction of the maghemite and ε phase assuming the core-shell model with maghemite as a core. It can be seen that the size of the particles increase with increasing annealing temperature and that the fraction of maghemite decreases and it completely vanishes at the temperature of 1 ºC. This corresponds to the assumption presented above. As for the sample D, which has not been analysed, the hematite diffraction peaks appear. Both he core-shell model of the nanoparticles and the Debye formula are suitable tools for the analysis of our samples. In the future we have to investigate, whether it is possible to distinguish between the core and the shell, i.e., whether we can determine which phase is in the core and which

5 one is in the shell. A method, which would enable us to analyze larger particles, has to be implemented as well. References A. Cervellino, C. Giannini, A. Guagliardi and D. Zanchet, Eur. Phys. J. B 41, 485, 24. A. Cervellino, C. Giannini and A. Guagliardi, J. Appl. Cryst. 36, 1148, 23. Chang-Woo Lee, Sung-Soo Jung and Jai-Sung Lee, Materials Letters 62, 561, 28. M. Gich, C. Frontera, A. Roig et al, Chemistry of Materials 18, 3889, 26. P. Brázda, D. Nižňanský, J.-L. Rehspringer, J. Poltierová Vejpravová, J. Sol-Gel Sci. Technol., 51, 78-83,