Size-dependent microwave absorption properties of Fe₃O₄ nanodiscs

Abstract

Fabrication of uniform magnetic nanodiscs with tunable size is of great importance for the study of their size dependent microwave properties. In this work, uniform Fe₃O₄ nanodiscs with different sizes are successfully synthesized by hydrogen-wet reduction of α-Fe₂O₃ nanodisc templates. The thickness of the Fe₃O₄ discs are around 30 nm and the diameters could be adjusted between 80–500 nm by controlling the amount of water in the reaction. The dynamic permittivity and permeability of Fe₃O₄ nanodisc/paraffin composite (20 vol%) were measured in the frequency range of 0.1–18 GHz. It is found that a larger diameter leads to a higher permittivity, lower permeability and higher resonance frequency as a consequence of stronger shape anisotropy. Moreover, excellent microwave absorption performances are achieved by these nanodiscs, which exhibit wide effective absorption (RL < −10 dB) with wide frequency bandwidth. Furthermore, small nanodiscs show superior microwave absorption properties over large nanodiscs because of lower permittivity which results in a better impedance match. The study not only presents an effective method to fabricate high quality Fe₃O₄ nanodiscs with tunable sizes, but also could be of great help for designing magnetic nanodisc based microwave absorbers.

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1. Introduction

Electromagnetic wave absorption and interference shielding have attracted increased attention due to the wide application of electronic devices in daily life and for military purposes. To suppress electromagnetic interference (EMI), high performance microwave absorbers are in high demand. Magnetic nanoparticles are considered as one of the most promising candidates due to their fascinating magnetic properties which can be well tuned by changing their geometric shape and dimensions. Therefore, considerable efforts have been made in producing different magnetic nanostructures (e.g. discs, rods, hollow structures, etc.).^1–5 Among these, the disc-shaped nanostructure is of great interest because of its higher permeability at a higher frequency range than that of spherical particles, which is beneficial to achieve thinner absorbers.^6,7

Apart from the geometric shape, particle size is also crucial for the magnetic properties of nanoparticles. It has been demonstrated that the particle size could pose a great effect on the microwave permeability and absorption properties of a material.^8–11 However, to our best knowledge, there are limited studies on the size effect of high quality magnetic discs due to the challenge of fabricating high quality nanodiscs with tuneable particle size. Though the mechanical milling method has been used to synthesise flaky particles allowing their microwave absorption properties to be investigated, the poor crystallinity, irregular shape and wide size distribution of the particles can hardly be avoided.^6,12 In comparison, the hydrothermal method is capable of producing uniform disc shapes, particle size and single crystalline structure.^13–15 Recently, our group fabricated high quality Fe₃O₄ nanodiscs via the hydrothermal fabrication of Fe₂O₃ templates and subsequent wet reduction process.¹⁶ It is known that Fe₃O₄ is an important subject of ferrite materials for microwave absorption because of its high magnetization.^17,18 Moreover, the sizes of the final Fe₃O₄ discs are possible to change by adjusting the reaction conditions during the synthesis of the Fe₂O₃ templates.¹⁹ Therefore, it is of great interest to investigate the size effect on the microwave absorption properties of the Fe₃O₄ nanodiscs.

In this paper, Fe₃O₄ nanodiscs with different particle sizes are prepared through a two-step chemical method which includes the hydrothermal fabrication of Fe₂O₃ nanodisc templates and subsequent wet chemical reduction. By changing the amount of tracing water and types of solvent used in the hydrothermal reaction, the sizes of the nanodiscs can be tuned in the range of 80–500 nm with a thickness of about 30 nm. The microwave electromagnetic and absorption properties of the Fe₃O₄ nanodiscs/paraffin composite (20 vol%) are measured in the frequency range of 0.1–18 GHz.

2. Experimental

2.1 Synthesis of Fe₃O₄ nanodiscs

The Fe₃O₄ nanodiscs are fabricated by a two-step chemical method. Fig. 1 illustrates the detailed procedure. In the first step, α-Fe₂O₃ nanodiscs are prepared through a facile alcohol-thermal reaction described elsewhere.¹⁹ In a typical synthesis, a certain amount of FeCl₃·6H₂O, distilled water, sodium acetate (CH₃COONa) and ethanol (or methanol) are mixed together by magnetic stirring. Then the mixture is sealed in a Teflon-lined stainless steel autoclave and maintained at 180 °C for 12 h. After cooling down to room temperature, the red product is collected by centrifuge and washed with distilled water. The sizes of the nanodiscs are controlled by changing the amount of distilled water and the types of solvent used in the first step. Generally, less distilled water would result in thinner nanodiscs with a larger diameter. Additionally, the use of methanol as a solvent could further increase the diameter of the nanodiscs. The reaction conditions for different sizes are listed in Table 1.

Fig. 1 Scheme for the fabrication of Fe₃O₄ nanodiscs.

Table 1 Chemical amounts for the synthesis of α-Fe₂O₃ nanodiscs with different sizes

Sample name	D1	D2	D3
CH3COONa (g)	5	5	5
FeCl3·6H2O (g)	1.09	1.09	1.09
Distilled water (ml)	5.3	2.8	2.8
Solvent (40 ml)	Ethanol	Ethanol	Methanol

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In the second step, the α-Fe₂O₃ nanodisc templates with different particle sizes were reduced into the Fe₃O₄ phase through a wet chemical reduction method as reported earlier.²⁰ In a typical reduction process, 100 mg of the α-Fe₂O₃ templates and 20 g of trioctylamine (TOA) were mixed using sonication. With the addition of 1 g of oleic acid, the mixture was refluxed at 340 °C under a sufficient flow of H₂ (5%) and Ar (95%) for about 30 min. When the reaction was completed, the colour of the mixture changed from red to black. The black product was then collected, washed with toluene and dried at 60 °C for characterization.

2.2 Characterization

The products were characterized using powder X-ray diffraction (PXRD; Bruker, Advance D8). The morphology and size of the magnetite nanodiscs were determined on a Hitachi S-4800 field emission scanning electron microscopy (FESEM). Room-temperature magnetostatic properties were measured using a vibrating sample magnetometer (VSM; Lakeshore, Model 7404). The microwave properties of the Fe₃O₄ nanodiscs/paraffin composite were studied in an APC7 coaxial line mode at room temperature with an Agilent PNA E8363B network analyzer. The complex permeability (μ_r = μ′_r − jμ′′_r) and permittivity (ε_r = ε′_r − jε′′_r) of the mixture in the 0.1–18 GHz frequency range were evaluated by measuring the reflection coefficient S₁₁ and the transmission coefficient S₂₁. The absorption characteristics were evaluated by simulating the reflection loss of the composite backed by a metal plate. The reflection loss (RL) curves were calculated from the relative permeability and permittivity at a given frequency and absorber thickness, according to the following equations:

RL = 20 log|(Z_in − Z₀)/(Z_in + Z₀)| (1)

Z₀ = (μ₀/ε₀)^1/2 (2)

Z_in = (μ₀μ_r/ε₀ε_r)^1/2  tan h [j2πf(μ₀μ_rε₀ε_r)^1/2d] (3)

where Z_in is the impedance of the composite backed by the ground plane, Z₀ is the intrinsic impedance of free space, d is the thickness of the absorber, f is the frequency of incident electromagnetic waves, μ_r is the complex permeability and ε_r is the complex permittivity.

3. Results and discussion

Fig. 2 shows the SEM images of the synthesized iron oxide nanodiscs before and after reduction. As shown in low-magnification images (Fig. 2a–c), uniform disc-like particles with different sizes are successfully fabricated on a large scale. It can be seen from high-magnification images (Fig. 2e–f) that the thickness of the three sets of nanodiscs are about 28, 26 and 38 nm with the diameter ranging from around 84, 228 and 490 nm, respectively, by means of changing the amount of water and types of solvent used in the alcohol-thermal reaction, as summarized in Table 1. For convenience, the three samples are named as D1, D2 and D3 for later discussion. The sizes of the three sets of nanodiscs are summarized in Table 2. It can be seen that the diameter to thickness ratio (aspect ratio) of D1, D2 and D3 is about 3, 8.7 and 12.6, respectively. The selected area electron diffraction (SAED) patterns acquired from single nanodiscs are also provided in the top-right corner of each figure. It is apparent that D1 and D2 show hexagonal-symmetry diffraction dots, indicating a perfect single crystalline structure (Fig. 2d–e). In contrast, the SAED pattern of D3 is composed by more than one set of diffraction patterns (Fig. 2f), implying the existence of different crystalline orientations in a single disc. This can be confirmed from the SEM images of D3. It is noticed that the D3 sample appears like a stacking of several thin layers. These thin layers may possess different crystalline orientations, resulting in more than one diffraction pattern, as observed in Fig. 2f.

Fig. 2 (a)–(c) Low-magnification and (d)–(f) high-magnification SEM images of the Fe₃O₄ nanodiscs. The insets in (d)–(f) are the SAED images acquired on a single nanodisc.

Table 2 Dimensions and the static magnetic properties of the Fe₃O₄ nanodiscs: AR denotes the aspect ratio (diameter/thickness). M_s and H_c are the saturation magnetization and coercivity, respectively

Sample name	D1	D2	D3
Diameter (nm)	84	225	479
Thickness (nm)	28	26	38
Aspect ratio	3	8.7	12.6
Ms (emu g^−1)	82	80	87
Hc (Oe)	236	267	245

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Fig. 3 presents the PXRD spectra and room-temperature hysteresis loops of the fabricated Fe₃O₄ nanodiscs. It is shown in Fig. 3a that before reduction the raw products exhibit a typical rhombohedral α-Fe₂O₃ phase (JPCDS no. 33-0664), which is in good agreement with the results reported elsewhere.¹⁹ After the reduction process, the patterns of the three sets of nanodiscs could be well indexed to the inverse spinel structure of Fe₃O₄ (JPCDS no. 11-0614), agreeing well with the results in our recent work.¹⁶ It confirms the successful conversion from rhombohedral α-Fe₂O₃ to spinel Fe₃O₄. The room-temperature hysteresis loops of the Fe₃O₄ nanodiscs are provided in Fig. 3b. Similar ferrimagnetic hysteresis behaviours are revealed for the Fe₃O₄ nanodiscs. Typical magnetic parameters, namely saturation magnetization (M_s) and coercivity (H_c), of the nanodiscs are listed in Table 2 for comparison. As shown in the table, the M_s values of D1, D2 and D3 are about 82, 80, 87 emu g⁻¹, respectively, which are quite close to the bulk value of Fe₃O₄ (92 emu g⁻¹).²¹ Meanwhile, the H_c values are about 236, 267 and 245 Oe, respectively. They are obviously larger than the reported values of spherical Fe₃O₄ nanoparticles,²² which is attributed to the large shape anisotropy of the nanodiscs.

Fig. 3 (a) XRD and (b) room-temperature hysteresis loops of the Fe₃O₄ nanodiscs.

Fig. 4a shows the real part (ε′_r) and imaginary part (ε′′_r) of the complex permittivity of the Fe₃O₄ nanodiscs/paraffin composite (20 vol%) in the frequency range of 0.1–18 GHz. It can be seen that the ε′_r is almost constant in the 0.1–10 GHz range for the three samples. However, it is noticeable that there is a resonance peak at around 10 GHz for the ε′′_r of D3. This might result from the interface relaxation.²³ As mentioned earlier, sample D3 is composed by several thin layers stacked together. The interfacial polarization between these thin layers would lead to the resonance peak at 10 GHz.²⁴ Meanwhile, the ε′_r increases as the nanodiscs get larger. Among the three sets of nanodiscs, D1 shows the lowest ε′_r of about 13, while it increases to 25 for D3. It agrees well with the trend reported for Fe₉₀Al₁₀ micro-flakes.²⁵ Fig. 4b presents the real part (μ′_r) and imaginary part (μ′′_r) of the frequency dependent complex permeability. In contrast to the ε′_r, the μ′_r decreases with increasing diameter. The initial permeability (μ′₀) of D1 is about 2.0 at 0.1 GHz, while it decreases to 1.9 and 1.8 for D2 and D3, respectively. The decrease is reasonable because the μ′₀ is inversely proportional to the anisotropy, including the shape anisotropy, crystalline anisotropy and any other kinds of anisotropy.²⁶ For the nanodisc with larger diameter (i.e. higher aspect ratio), the shape anisotropy is stronger than that of the smaller one, leading to the reduction of μ′₀. Furthermore, the μ′′_r–f curve reveals an obvious resonance peak for the three sets of nanodiscs with a slight difference in the resonance frequency (f_r). It is about 2.8 GHz for D1 and about 3.3 GHz for D2 and D3. In order to verify the above values, the f_r is calculated by using Kittle’s formula which gives the nature resonance frequency of anisotropic magnetic nanostructures. According to Kittle’s formula,

ω_r = γ{[H_e + (N_x − N_z)M_s]·[H_e + (N_y − N_z)M_s]}^1/2 (4)

where ω_r = 2πf_r is the angular resonance frequency, H_e is the external field which equals to zero in this case, N_i (i = x, y, z) is the demagnetizing factor which is related to the shape anisotropy. The demagnetizing factor can be derived from stoner’s equation if the nanodiscs are considered as thin ellipsoids.²⁷ The results are given in Table 3. It is apparent that the resonance frequency calculated from Kittle’s formula (f^Kittel_r) is in good agreement with the value measured experimentally (f^exp_r), indicating that the experimental results are reliable. Moreover, it confirms that D2 and D3 show almost the same resonance frequency. This could be attributed to their large aspect ratios (D2, 8.7; D3, 12.6) which result in very close demagnetization factor values, as shown in Table 3. It also worth noting from Fig. 4b that at low frequency (i.e. 0.1 GHz) all three samples show non-zero μ′′_r. This would be ascribed to the vortex core dynamics related resonance. As reported before,^16,28 the Fe₃O₄ nanodiscs possess a vortex domain structure, where the spin in the nanodisc aligns circularly except the vortex core in the centre.²⁹ The vortex core could lead to resonance and non-zero μ′′_r at low frequency.³⁰

Fig. 4 (a) Complex permittivity and (b) permeability of Fe₃O₄ nanodiscs/paraffin composite (20 vol%) measured in the frequency range of 0.1–18 GHz.

Table 3 Demagnetizing factor (N_z) and resonance frequency of Fe₃O₄ nanodisc/paraffin composites (20 vol%). f^exp_r and f^Kittel_r denote the resonance frequency derived from experiment and Kittel’s equation, respectively

	D1	D2	D3
Nz	0.446	0.487	0.493
f^expr (GHz)	2.8	3.3	3.3
f^Kittelr (GHz)	1.9	3.0	3.1

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Fig. 5 shows the calculated reflection loss (RL) as a function of frequency and absorber thickness for the three nanodisc/paraffin composites. As shown in Fig. 5a, D1 exhibits effective microwave absorption (RL < −10 dB) in a wide frequency bandwidth of about 2–18 GHz. Meanwhile, several RL minima are observed. They are about −35.6, −31.8 and −37.0 dB at 8.7 GHz, 14.4 GHz and 2.6 GHz with a thickness of 2.5 mm, 4.4 mm and 5.9 mm, respectively. Such multiple minima would greatly enlarge the frequency bandwidth for effective absorption, which is a great advantage for practical applications. In comparison, D2 also exhibits similar wide absorption bandwidth (Fig. 5b). The minimum RL is about −29.7 dB at 3.1 GHz with 4.5 mm thickness, which is lower than for D1. Besides, several RL local minima (<−20 dB) are also found at around 9.4 GHz with a thickness of about 2.1 mm. Compared with D1 and D2, D3 also shows multiple RL minima in a similar area, while the minimum RL values are reduced. They are about −24.7 dB and −16.4 dB at 2.5 GHz and 9.8 GHz with a 4.4 mm and 1.6 mm thickness, respectively. The reduction in RL value is mainly attributed to the change in permittivity. It is shown in Fig. 4a that the ε′_r increases obviously when the nanodiscs get larger. Consequently, the increase in ε′_r leads to a poor impedance match compared with the small nanodiscs (i.e. D1 and D2), leading to a decreased RL value.³¹ Therefore, small nanodiscs with relatively low permittivity could benefit the microwave absorption properties by improving the impedance match.

Fig. 5 Calculated reflection loss (RL) as a function of frequency and absorber thickness (<10 mm) for the Fe₃O₄ nanodiscs/paraffin composite (20 vol%). The color in the figure indicates the value of RL according to the color bar on the right side. The contours in the projection indicate the area of RL < −10 dB.

4. Conclusions

In summary, we fabricated uniform Fe₃O₄ nanodiscs with different sizes by a two-step chemical method. These nanodiscs exhibit wide effective absorption bandwidth because of multiple RL minima. Moreover, it is found that the particle size is crucial for the microwave electromagnetic and absorption properties of the nanodiscs. With an increase in the disc diameter, the permittivity increases, while the permeability decreases accompanied by an increase in the resonance frequency. Moreover, small nanodiscs exhibit better microwave absorption properties than large ones due to better impedance match.

Acknowledgements

The project is financially supported by A-Star SERC R284-000-103-305.

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