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The magnetic properties of SrFe12O19 (SFO) hard hexaferrite are controlled by the complex relationship of its microstructure, which determines their relevance to permanent magnet applications. Select a group of SFO nanoparticles obtained by sol-gel spontaneous combustion synthesis, and perform in-depth structural X-ray powder diffraction (XRPD) characterization by G(L) line profile analysis. The obtained crystallite size distribution reveals the obvious dependence of the size along the [001] direction on the synthesis method, leading to the formation of flaky crystallites. In addition, the size of SFO nanoparticles was determined by transmission electron microscopy (TEM) analysis, and the average number of crystallites in the particles was estimated. These results have been evaluated to illustrate the formation of single domain states below the critical value, and the activation volume is derived from time-dependent magnetization measurements, aimed at elucidating the reverse magnetization process of hard magnetic materials.
Nano-scale magnetic materials have great scientific and technological significance, because their magnetic properties exhibit significantly different behaviors compared with their volume size, which brings new perspectives and applications1,2,3,4. Among nanostructured materials, M-type hexaferrite SrFe12O19 (SFO) has become an attractive candidate for permanent magnet applications5. In fact, in recent years, a lot of research work has been done on customizing SFO-based materials on the nanoscale through a variety of synthesis and processing methods to optimize size, morphology, and magnetic properties6,7,8. In addition, it has received great attention in the research and development of exchange coupling systems9,10. Its high magnetocrystalline anisotropy (K = 0.35 MJ/m3) oriented along the c-axis of its hexagonal lattice 11,12 is a direct result of the complex correlation between magnetism and crystal structure, crystallites and grain size, morphology and texture . Therefore, controlling the above characteristics is the basis for meeting specific requirements. Figure 1 illustrates the typical hexagonal space group P63/mmc of SFO13, and the plane corresponding to the reflection of the line profile analysis study.
Among the related characteristics of ferromagnetic particle size reduction, the formation of a single domain state below the critical value leads to an increase in magnetic anisotropy (due to a higher surface area to volume ratio), which leads to a coercive field14,15. The wide area below the critical dimension (DC) in hard materials (typical value is about 1 µm), and is defined by the so-called coherent size (DCOH)16: this refers to the smallest volume method for demagnetization in the coherent size (DCOH) , Expressed as the activation volume (VACT) 14. However, as shown in Figure 2, although the crystal size is smaller than DC, the inversion process may be inconsistent. In nanoparticle (NP) components, the critical volume of reversal depends on the magnetic viscosity (S), and its magnetic field dependence provides important information about the switching process of NP magnetization17,18.
Above: Schematic diagram of the evolution of the coercive field with particle size, showing the corresponding magnetization reversal process (adapted from 15). SPS, SD, and MD stand for superparamagnetic state, single domain, and multidomain, respectively; DCOH and DC are used for coherence diameter and critical diameter, respectively. Bottom: Sketches of particles of different sizes, showing the growth of crystallites from single crystal to polycrystalline. <DXRD> and <DTEM> indicate crystallite and particle size, respectively.
However, on the nanoscale, new complex aspects have also been introduced, such as strong magnetic interaction between particles, size distribution, particle shape, surface disorder, and the direction of the easy axis of magnetization, all of which make the analysis more challenging19,20 . These elements significantly affect the energy barrier distribution and deserve careful consideration, thereby affecting the magnetization reversal mode. On this basis, it is particularly important to correctly understand the correlation between the magnetic volume and the physical nanostructured M-type hexaferrite SrFe12O19. Therefore, as a model system, we used a set of SFOs prepared by a bottom-up sol-gel method, and recently conducted research. The previous results indicate that the size of the crystallites is in the nanometer range, and it, together with the shape of the crystallites, depends on the heat treatment used. In addition, the crystallinity of such samples depends on the synthesis method, and more detailed analysis is required to clarify the relationship between crystallites and particle size. In order to reveal this relationship, through transmission electron microscopy (TEM) analysis combined with the Rietveld method and line profile analysis of high statistical X-ray powder diffraction, the crystal microstructure parameters (ie, crystallites and particle size, shape) were carefully analyzed. XRPD) mode. Structural characterization aims to determine the anisotropic characteristics of the obtained nanocrystallites and to prove the feasibility of line profile analysis as a robust technique for characterizing peak broadening to the nanoscale range of (ferrite) materials. It is found that the volume-weighted crystallite size distribution G(L) strongly depends on the crystallographic direction. In this work, we show that supplementary techniques are indeed needed to accurately extract size-related parameters to accurately describe the structure and magnetic characteristics of such powder samples. The process of reverse magnetization was also studied to clarify the relationship between morphological structure characteristics and magnetic behavior.
Rietveld analysis of X-ray powder diffraction (XRPD) data shows that the crystallite size along the c-axis can be adjusted by suitable heat treatment. It specifically shows that the peak broadening observed in our sample is likely to be due to the anisotropic crystallite shape. In addition, the consistency between the average diameter analyzed by Rietveld and the Williamson-Hall diagram (<DXRD> and <DXRDWH> in Table S1) shows that the crystallites are almost strain-free and there is no structural deformation. The evolution of the crystallite size distribution along different directions focuses our attention on the obtained particle size. The analysis is not simple, because the sample obtained by sol-gel spontaneous combustion is composed of agglomerates of particles with a porous structure6,9 ,twenty one. TEM is used to study the internal structure of the test sample in more detail. Typical brightfield images are reported in Figure 3a-c (for a detailed description of the analysis, please refer to section 2 of the supplementary materials). The sample consists of particles with the shape of small pieces. The platelets join together to form porous aggregates of different sizes and shapes. In order to estimate the size distribution of platelets, the area of ​​100 particles of each sample was manually measured using ImageJ software. The diameter of the equivalent circle with the same particle area as the value is attributed to the representative size of each measured piece. The results of samples SFOA, SFOB and SFOC are summarized in Figure 3d-f, and the average diameter value is also reported. Increasing the processing temperature increases the size of the particles and their distribution width. From the comparison between VTEM and VXRD (Table 1), it can be seen that in the case of SFOA and SFOB samples, the average number of crystallites per particle indicates the polycrystalline nature of these lamellae. In contrast, the particle volume of SFOC is comparable to the average crystallite volume, indicating that most of the lamellae are single crystals. We point out that the apparent sizes of TEM and X-ray diffraction are different, because in the latter, we are measuring the coherent scattering block (it may be smaller than the normal flake): In addition, the small error orientation of these scattering domains will be calculated by diffraction .
The bright-field TEM images of (a) SFOA, (b) SFOB and (c) SFOC show that they are composed of particles with a plate-like shape. The corresponding size distributions are shown in the histogram of the panel (df).
As we have also noticed in the previous analysis, the crystallites in the real powder sample form a polydisperse system. Since the X-ray method is very sensitive to the coherent scattering block, a thorough analysis of the powder diffraction data is required to describe the fine nanostructures. Here, the size of the crystallites is discussed through the characterization of the volume-weighted crystallite size distribution function G(L)23, which can be interpreted as the probability density of finding crystallites of assumed shape and size, and its weight is proportional to it. Volume, in the sample analyzed. With a prismatic crystallite shape, the average volume-weighted crystallite size (average side length in the [100], [110] and [001] directions) can be calculated. Therefore, we selected all three SFO samples with different particle sizes in the form of anisotropic flakes (see Reference 6) to evaluate the effectiveness of this procedure to obtain accurate crystallite size distribution of nano-scale materials. In order to evaluate the anisotropic orientation of the ferrite crystallites, line profile analysis was performed on the XRPD data of the selected peaks. The tested SFO samples did not contain convenient (pure) higher order diffraction from the same set of crystal planes, so it was impossible to separate the line broadening contribution from the size and distortion. At the same time, the observed widening of the diffraction lines is more likely to be due to the size effect, and the average crystallite shape is verified through the analysis of several lines. Figure 4 compares the volume-weighted crystallite size distribution function G(L) along the defined crystallographic direction. The typical form of crystallite size distribution is lognormal distribution. One characteristic of all obtained size distributions is their unimodality. In most cases, this distribution can be attributed to some defined particle formation process. The difference between the average calculated size of the selected peak and the value extracted from the Rietveld refinement is within an acceptable range (considering that the instrument calibration procedures are different between these methods) and is the same as that from the corresponding set of planes by Debye The average size obtained is consistent with the Scherrer equation, as shown in Table 2. The trend of the volume average crystallite size of the two different modeling techniques is very similar, and the deviation of the absolute size is very small. Although there may be disagreements with Rietveld, for example, in the case of the (110) reflection of SFOB, it may be related to the correct determination of the background on both sides of the selected reflection at a distance of 1 degree 2θ in each direction. Nevertheless, the excellent agreement between the two technologies confirms the relevance of the method. From the analysis of peak broadening, it is obvious that the size along [001] has a specific dependence on the synthesis method, resulting in the formation of flaky crystallites in SFO6,21 synthesized by sol-gel. This feature opens the way for the use of this method to design nanocrystals with preferential shapes. As we all know, the complex crystal structure of SFO (as shown in Figure 1) is the core of the ferromagnetic behavior of SFO12, so the shape and size characteristics can be adjusted to optimize the design of the sample for applications (such as permanent magnet related). We point out that crystallite size analysis is a powerful way to describe the anisotropy of crystallite shapes, and further strengthens the previously obtained results.
(a) SFOA, (b) SFOB, (c) SFOC selected reflection (100), (110), (004) volume weighted crystallite size distribution G(L).
In order to evaluate the effectiveness of the procedure to obtain the precise crystallite size distribution of nano-powder materials and apply it to complex nanostructures, as shown in Figure 5, we have verified that this method is effective in nanocomposite materials (nominal values). The accuracy of the case is composed of SrFe12O19/CoFe2O4 40/60 w/w %). These results are fully consistent with the Rietveld analysis (see the caption of Figure 5 for comparison), and compared to the single-phase system, SFO nanocrystals can highlight a more plate-like morphology. These results are expected to apply this line profile analysis to more complex systems in which several different crystal phases can overlap without losing information about their respective structures.
The volume-weighted crystallite size distribution G(L) of selected reflections of SFO ((100), (004)) and CFO (111) in nanocomposites; for comparison, the corresponding Rietveld analysis values ​​are 70(7), 45(6) and 67(5) nm6.
As shown in Figure 2, the determination of the size of the magnetic domain and the correct estimation of the physical volume are the basis for describing such complex systems and for a clear understanding of the interaction and structural order between magnetic particles. Recently, the magnetic behavior of SFO samples has been studied in detail, with special attention to the reversal process of magnetization, in order to study the irreversible component of magnetic susceptibility (χirr) (Figure S3 is an example of SFOC)6. In order to gain a deeper understanding of the magnetization reversal mechanism in this ferrite-based nanosystem, we performed a magnetic relaxation measurement in the reverse field (HREV) after saturation in a given direction. Consider \(M\left(t\right)\proptoSln\left(t\right)\) (see Figure 6 and supplementary material for more details) and then obtain the activation volume (VACT). Since it can be defined as the smallest volume of material that can be coherently reversed in an event, this parameter represents the “magnetic” volume involved in the reversal process. Our VACT value (see Table S3) corresponds to a sphere with a diameter of approximately 30 nm, defined as the coherent diameter (DCOH), which describes the upper limit of the system’s magnetization reversal by coherent rotation. Although there is a huge difference in the physical volume of particles (SFOA is 10 times larger than SFOC), these values ​​are quite constant and small, indicating that the magnetization reversal mechanism of all systems remains the same (consistent with what we claim is the single domain system) 24 . In the end, VACT has a much smaller physical volume than XRPD and TEM analysis (VXRD and VTEM in Table S3). Therefore, we can conclude that the switching process does not only occur through coherent rotation. Note that the results obtained by using different magnetometers (Figure S4) give quite similar DCOH values. In this regard, it is very important to define the critical diameter of a single domain particle (DC) in order to determine the most reasonable reversal process. According to our analysis (see supplementary material), we can infer that the obtained VACT involves an incoherent rotation mechanism, because the DC (~0.8 µm) is very far from the DC (~0.8 µm) of our particles, that is, the formation of domain walls is not Then received strong support and obtained a single domain configuration. This result can be explained by the formation of the interaction domain25, 26. We assume that a single crystallite participates in an interaction domain, which extends to interconnected particles due to the heterogeneous microstructure of these materials27,28. Although X-ray methods are only sensitive to the fine microstructure of domains (microcrystals), magnetic relaxation measurements provide evidence of complex phenomena that may occur in nanostructured SFOs. Therefore, by optimizing the nanometer size of the SFO grains, it is possible to prevent switching to the multi-domain inversion process, thereby maintaining the high coercivity of these materials.
(a) The time-dependent magnetization curve of SFOC measured at different reverse field HREV values ​​after saturation at-5 T and 300 K (indicated next to the experimental data) (magnetization is normalized according to the weight of the sample); for clarity, The inset shows the experimental data of 0.65 T field (black circle), which has the best fit (red line) (magnetization is normalized to the initial value M0 = M(t0)); (b) the corresponding magnetic viscosity (S) is the inverse of SFOC A function of the field (the line is a guide for the eye); (c) an activation mechanism scheme with physical/magnetic length scale details.
Generally speaking, magnetization reversal may occur through a series of local processes, such as domain wall nucleation, propagation, and pinning and unpinning. In the case of single-domain ferrite particles, the activation mechanism is nucleation-mediated and is triggered by a magnetization change smaller than the overall magnetic reversal volume (as shown in Figure 6c)29.
The gap between the critical magnetism and the physical diameter implies that the incoherent mode is a concomitant event of magnetic domain reversal, which may be due to material inhomogeneities and surface unevenness, which become correlated when the particle size increases 25, resulting in a deviation from uniform magnetization state.
Therefore, we can conclude that in this system, the magnetization reversal process is very complicated, and the efforts to reduce the size in the nanometer scale play a key role in the interaction between the microstructure of the ferrite and the magnetism. .
Understanding the complex relationship between structure, form and magnetism is the basis for designing and developing future applications. The line profile analysis of the selected XRPD pattern of SrFe12O19 confirmed the anisotropic shape of the nanocrystals obtained by our synthesis method. Combined with TEM analysis, the polycrystalline nature of this particle was proved, and it was subsequently confirmed that the size of the SFO explored in this work was lower than the critical single domain diameter, despite the evidence of crystallite growth. On this basis, we propose an irreversible magnetization process based on the formation of an interaction domain composed of interconnected crystallites. Our results prove the close correlation between the particle morphology, crystal structure and crystallite size that exist at the nanometer level. This study aims to clarify the reversal magnetization process of hard nanostructured magnetic materials and determine the role of microstructure characteristics in the resulting magnetic behavior.
The samples were synthesized using citric acid as a chelating agent/fuel according to the sol-gel spontaneous combustion method, reported in Reference 6. The synthesis conditions were optimized to obtain three different sizes of samples (SFOA, SFOB, SFOC), which were obtained by appropriate annealing treatments at different temperatures (1000, 900, and 800°C, respectively). Table S1 summarizes the magnetic properties and finds that they are relatively similar. The nanocomposite SrFe12O19/CoFe2O4 40/60 w/w% was also prepared in a similar way.
The diffraction pattern was measured using CuKα radiation (λ = 1.5418 Å) on the Bruker D8 powder diffractometer, and the detector slit width was set to 0.2 mm. Use a VANTEC counter to collect data in the 2θ range of 10-140°. The temperature during data recording was maintained at 23 ± 1 °C. The reflection is measured by step-and-scan technology, and the step length of all test samples is 0.013° (2theta); the maximum peak value of the measurement distance is-2.5 and + 2.5° (2theta). For each peak, a total of 106 quanta are calculated, while for the tail there are about 3000 quanta. Several experimental peaks (separated or partially overlapped) were selected for further simultaneous analysis: (100), (110) and (004), which occurred at the Bragg angle close to the Bragg angle of the SFO registration line. The experimental intensity was corrected for the Lorentz polarization factor, and the background was removed with an assumed linear change. The NIST standard LaB6 (NIST 660b) was used to calibrate the instrument and spectral broadening. Use LWL (Louer-Weigel-Louboutin) deconvolution method 30,31 to obtain pure diffraction lines. This method is implemented in the profile analysis program PROFIT-software32. From the fitting of the measured intensity data of the sample and the standard with the pseudo Voigt function, the corresponding correct line contour f(x) is extracted. The size distribution function G(L) is determined from f(x) by following the procedure presented in Reference 23. For more details, please refer to the supplementary material. As a supplement to the line profile analysis, the FULLPROF program is used to perform Rietveld analysis on XRPD data (details can be found in Maltoni et al. 6). In short, in the Rietveld model, the diffraction peaks are described by the modified Thompson-Cox-Hastings pseudo Voigt function. LeBail refinement of the data was performed on the NIST LaB6 660b standard to illustrate the instrument’s contribution to peak broadening. According to the calculated FWHM (full width at half the peak intensity), the Debye-Scherrer equation can be used to calculate the volume-weighted average size of the coherent scattering crystalline domain:
Where λ is the X-ray radiation wavelength, K is the shape factor (0.8-1.2, usually equal to 0.9), and θ is the Bragg angle. This applies to: the selected reflection, the corresponding set of planes and the entire pattern (10-90°).
In addition, a Philips CM200 microscope operating at 200 kV and equipped with a LaB6 filament was used for TEM analysis to obtain information about particle morphology and size distribution.
Magnetization relaxation measurement is performed by two different instruments: Physical Property Measurement System (PPMS) from Quantum Design-Vibrating Sample Magnetometer (VSM), equipped with 9 T superconducting magnet, and MicroSense Model 10 VSM with electromagnet. The field is 2 T, the sample is saturated in the field (μ0HMAX:-5 T and 2 T, respectively for each instrument), and then the reverse field (HREV) is applied to bring the sample into the switching area (near HC), and then the The magnetization decay is recorded as a function of time over 60 minutes. The measurement is performed at 300 K. The corresponding activation volume is evaluated based on those measured values ​​described in the supplementary material.
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