Heat-generation behavior of Fe₃O₄ particles in AC magnetic fields: analysis of microstructures through tilting

Abstract

Magnetic field-dependent magnetization of highly crystalline Fe₃O₄ magnetic nanoparticles has been carried out to understand surface canting structures at low and room temperatures. The exchange bias (H_EB) values of ∼18 to 27 Oe at 300 K for three samples prepared from different precursors are observed; and a decrease in value is obtained when the samples are measured at 5 K. However, with a decrease in temperature, coercivity (H_c) increases. This is related to an increase in the percentage of magnetization in the core of the particles and a decrease in the percentage of antiferromagnetic contribution on the surface of the particles when the sample is cooled from 300 K to 5 K. At low concentrations of magnetic particles and low power of the alternating current (AC) magnetic field, heat generation from the three samples is found to vary. In the case of high concentrations of magnetic particles and high power of the AC magnetic field, heat generation from the samples is almost the same. This is due to the saturation of AC magnetic field absorption by the magnetic nanoparticles at such high power and high concentration, irrespective of the samples. These findings are very interesting. The microstructures of the magnetic nanoparticles are studied through tilting from 0° to 14°. Agglomeration, non-agglomeration, porosity, etc. can be distinguished. From dark field (DF) and bright field (BF) images, we were able to resolve many mysterious microstructures, without which many properties would be interpreted wrongly.

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1. Introduction

The quasicrystal was discovered in 1984 by D. Shechtman and his group using the tilting facility in a transmission electron microscope (TEM).¹ When the specimen is rotated with respect to the electron beam, selected-area electron diffraction (SAED) patterns show the six fivefold, ten three-fold, and fifteen two-fold axes (icosahedral symmetry). Using the tilting facility, many microstructures of particles have been characterized. In 2009, Mayoral et al. performed the tilting of polyhedron shaped gold nanoparticles.² In that study, they observed the defects present in the structure. However, it had many drawbacks in the illustration of the face-centered cubic (fcc) structure of gold using the SAED pattern. Also, the systematic dark field (DF) and bright field (BF) images were not recorded. Furthermore, Saverot et al. in 2015 performed a tilting experiment on gold nanoparticles.³ They performed the tilting at angles of 0° and 30°. During this tilting, the different facets of fcc gold nanoparticles were clearly visible. They performed the crystal orientation for confirming the 3D structure of the icosahedral nanoparticles. However, it did not provide the SAED pattern and the DF–BF images, leading to poor confirmation of the 3D structure of the icosahedral nanoparticles. Moreover, Singh et al. in 2016 studied the tilting of gold nanoparticles.^4,5 In that study, they observed forbidden reflections through SAED patterns. These were related to the intrinsic faults present in gold nanoparticles. The foremost drawbacks of this study were that they did not provide studies with variations of large tilting angles. They performed tilting of the gold nanoparticle specimen within a 2–3° angle (very small tilting).

So far, many researchers have focused on metallic and non-metallic systems to understand the microstructures of nanoparticles through tilting of specimens with respect to the electron beam of a TEM. However, the microstructure analysis of magnetic particles has not been much addressed in the literature.

In many papers, it was reported that particles were found to be porous or non-porous after seeing the microstructure without tilting.^6–10 Also, agglomeration or aggregation was elucidated from the observed microstructure without tilting, which can mislead researchers.^11–15

In this article, single crystals of Fe₃O₄ magnetic particles have been prepared using the hydrothermal method. Different precursors have been used to prepare three different particles. Their microstructures are analyzed through tilting from 0 to 14°, high-resolution TEM, SAED patterns, DF and BF images and scanning electron microscopy images. This study provides better visualization of the microstructures of particles (porous or non-porous and agglomerated and/or aggregated through tilting). Simultaneous DF and BF imaging provides information about the microstructures of particles. Our visualization of the microstructure of particles will be useful to those working on the microstructure–property relationship. Induction heating-based hyperthermia has also been studied for these nanostructured materials. The hyperthermia temperature is a temperature (42–43 °C) at which cancer cells can be killed, whereas normal cells remain unaffected.¹⁶

Many papers had been reported in the area of heat generation from magnetic particles, including nanoparticles, under an AC magnetic field (known as induction-based heat generation). This research started in 1950s.¹⁷ These studies have many applications including cancer therapy through hyperthermia. Even though there have been many reports, few have focused on heat generation independent of the types of highly crystalline magnetic particles at higher concentrations and higher powers. Here, this will be discussed. The heat generation is correlated with the respective magnetization data.

2. Experimental

2.1 Chemicals

Ferric chloride (FeCl₃, >99%, Sigma-Aldrich), sodium acetate (CH₃COONa, >99%, Sigma-Aldrich), urea ((NH₂)₂C=O, 99.5%, Loba Chem.), ethylene glycol (EG or HO-CH₂-H₂C-OH, 99% SDFCL), ethanol (H₃C-H₂C-OH, 99.9%, Changshu Hongsheng Fine Chem. Co Ltd, China) and acetone (H₃C-CO-CH₃, 99%, Advent Chembio Pvt. Ltd) were used without any further purification.

2.2 Synthesis procedure

Magnetite particles are synthesized using the simple and effective hydrothermal method. In a typical synthesis, FeCl₃ (1 g) was dissolved in ethylene glycol (EG) (30 mL) to form a clear solution, followed by the addition of sodium acetate (3 g) and urea (3 g). The mixture was stirred vigorously for 1 h and then sealed in a Teflon-lined stainless-steel autoclave. The autoclave was heated to 200 °C at a heating rate of 5 °C min⁻¹ and maintained at this temperature for 12 h, and thereafter it was allowed to cool to room temperature. The black products were separated from unwanted materials, such as Fe(OH)₃, using a permanent magnet, washed with ethanol three times and then with acetone once, and finally dried at room temperature for one week. The pH of FeCl₃ dissolved in EG is 6. It is to be noted that EG has reducing properties.¹⁸ Urea has oxidizing properties due to the generation of NH₄OH after decomposition in H₂O.¹⁹ It is likely to increase its pH to > 8 as NH₄OH is basic. Table 1 provides the products or materials obtained using different precursors of urea and sodium acetate at a fixed concentration of FeCl₃ and ethylene glycol. In one case, ethylene glycol is replaced by water.

Table 1 The products or materials obtained by taking different concentrations of urea and sodium acetate at a fixed concentration of FeCl₃ and ethylene glycol (EG). In one case, ethylene glycol is replaced with water. pH values are mentioned before and after hydrothermal treatment

Samples	Precursors				Remarks
	Ferric chloride (g)	Ethylene glycol (mL)	Urea (g)	Sodium acetate (g)
SA	1	30	0	3	Fe3O4 cubic, spherical-shaped particles, before: pH = 6 (FeCl3 + EG), pH = 9 (FeCl3 + EG + sodium acetate), after: pH = 12
SB	1	30	3	0	Fe3O4 cubic, spherical-shaped particles, before: pH = 6 (FeCl3 + EG), pH = 9 (FeCl3 + EG + urea), after: pH = 12
SC	1	30	3	3	Fe3O4 cubic, spherical shaped particles, before: pH = 6 (FeCl3 + EG), pH = 9 (FeCl3 + EG + urea + sodium acetate), after: pH = 12
SD	1	30	0	0	Before: pH = 6 (FeCl3 + EG). after: pH = 12
SE	1 g + 30 mL water	0	0	0	Before: pH = 6 (FeCl3 + water), after: pH = 12

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The possible formation of Fe₃O₄ is described here:

Sample A. With EG and sodium acetate:

Sodium acetate is converted to acetate ions and Na⁺. The Na⁺ ion reacts with H₂O to form NaOH, which is basic.²⁰ It helps in the formation of Fe₃O₄.

Sample B. With EG and urea:

Urea gets decomposed to NH₄OH and CO₂ at 50 °C.¹⁹ NH₄OH helps in the formation of Fe₃O₄.

Sample C. With EG, sodium acetate and urea:

Sample D. With EG:

Here, EG has reducing properties¹⁸ and some of the Fe³⁺ ions are converted to Fe²⁺ ions. It is likely that a mixture of Fe³⁺ and Fe²⁺ ions will form Fe₃O₄. However, as the sample is highly dispersible, it is difficult to recover. It needs further study in the future.

Sample E. With water:

The formation of Fe(OH)₃ is well known.²¹

It is to be noted that since the sample prepared using EG only (step D) is highly dispersible, it is difficult to recover the precipitate even at very high speeds of centrifugation (20 000–40 000 rpm). Steps A–C can form Fe₃O₄ nanoparticles. Step E can form Fe(OH)₃ nanoparticles_. All precipitates obtained from steps A–C and E were recovered by centrifugation at 5000 rpm and washed with ethanol three times. Here, samples (steps A, B and C) have been studied in detail and named sample A, sample B and sample C, respectively (Fig. 1 and Table 1). Variations in pH before and after hydrothermal treatment are also provided. The basicity of the medium generally increases after hydrothermal treatment.

Fig. 1 Schematic diagram illustrating the products (SA–SE) obtained from different precursors and concentrations through the hydrothermal route.

2.3 Characterization

XRD. The Rigaku diffractometer was used to observe the X-ray diffraction (XRD) pattern of NPs with a copper K_α source, scanning in the range of 2θ = 10–80° at an operating voltage of 40 kV and 30 mA. The average crystallite size (t) of the prepared sample was calculated using the Debye–Scherrer relationship, , where λ is the wavelength of the X-rays, β is the full width at half-maximum (FWHM), and θ is the Bragg angle.

SEM. The scanning electron microscope (SEM) model TESCAN VEGA3 was used to record SEM images and perform elemental analysis through energy-dispersive X-ray spectroscopy (EDX).

TEM. The JEM 2100F transmission electron microscope (TEM), JEOL, operated at an acceleration potential of 200 kV, was used to capture TEM images of the samples.

Induction heating. AC-induction heating was performed in a 2 mL microcentrifuge tube, which was placed in a coil with 4 turns and a 6 cm diameter (Faraday Power System). 280 kHz frequency was applied. 1 mg or 3 mg of the sample was dispersed in 1 mL of water and then sonicated for 10 minutes before any experiment so that a proper homogenous solution would be maintained. Amplitudes of 2, 4 and 6 kW were used, which are equivalent to 211, 422 and 633 Oe, respectively.

3. Results and discussion

3.1 XRD study

Fig. S1 (ESI†) shows the XRD patterns of as-synthesized samples. The presence of impurity phases such as oxide phases, like hematite, remains a challenge for many synthesis methods. Furthermore, the structural characterization of samples is performed using XRD for phase identification of iron oxide in all samples. The XRD patterns of the magnetite nanoparticles synthesized at 200 °C reveal that the 2θ diffraction peaks at 30.38°, 35.72°, 43.40°, 57.28°, and 62.79° can be indexed as the (220), (311), (400), (511), and (440) reflections, respectively, corresponding to the cubic spinel structure of magnetite (Fe₃O₄). These characteristic peaks match well with the standard JCPDS card no. 19–0629, associated with a face-centered cubic (fcc) cell structure with a lattice constant of a = 8.393 Å and the Fd3m space group. Here, half of the tri-valent (Fe³⁺) ions are in the tetrahedral sites, and the other half of the trivalent and all the divalent ions (Fe²⁺) are randomly distributed in the octahedral sites/interstices.²² Magnetic spins in the tetrahedral and octahedral sites of Fe³⁺ cancel each other out. Only the spins of Fe²⁺ provide net magnetization. Thus, the material exhibits ferrimagnetic behavior.

The crystallite sizes of the samples are calculated using the Scherrer formula. Here, we did not subtract the broadening effect from the instrumental factor during the calculation of the full width at half-maximum (FWHM). Usually, the instrumental factor is calculated using standard polycrystalline silicon. The crystallite sizes of samples A, B and C are found to be ∼12, 30, and ∼24 nm, respectively. Sample B prepared using urea as a precursor has higher crystallinity as compared to sample A and/or sample C.

3.2 SEM study

SEM investigations are conducted to examine the morphological conditions and homogeneity of the magnetite particles. SEM images of the Fe₃O₄ nanoparticles are shown in Fig. S2 (ESI†), revealing the formation of spherical particles through this method. The uniform distribution of particles is shown in Fig. S2(A) (ESI†) with a particle size distribution of 500–850 nm for sample SA, prepared using sodium acetate and EG as the precursors. The particles are found to be of agglomerated form. When precursors such as EG and urea are used, the particle size is smaller with a size distribution of 70–350 nm, as shown in Fig. S2(B) ESI.† Interestingly, when the precursors such as urea, sodium acetate and EG are used, the particle size is more uniform, with a particle size distribution of ∼200–600 nm (Fig. S2(C) (ESI†)). Here, every particle is found to be agglomerated. In the literature, Fe₃O₄ and boron-doped Fe₃O₄ particles prepared using ethylene glycol show agglomerated spherical particles.²³ In order to see more clear particles, experiments have been carried out using a high-resolution transmission electron microscope (HRTEM) at an operating voltage of 200 kV.

3.3 TEM analysis

Herein, the analyses of Fe₃O₄ nanoparticles synthesized using three different precursors, namely SA prepared from sodium acetate + EG precursors, SB prepared from urea + EG, and SC prepared from sodium acetate + urea + EG, were conducted through the TEM technique.

3.3.1 SA sample

Fig. 2 shows the TEM analysis of the SA sample. A large area with a 100 nm scale bar is shown in Fig. 2(a), and its high magnification with a 50 nm scale bar is provided in Fig. 2(b). Here, the area within the green colored rectangle is magnified. Particles ranging from large (150 nm) to small (50 nm) sizes could be observed. Particles of about 50 nm in size are almost single crystalline. A large sized particle has many small crystallites. However, individual crystallites can show a single crystal nature (Fig. 2(c)), which is supported by the selected area electron diffraction (SAED) pattern. The live FFT (Fast Fourier Transform) is shown in Fig. 2(e), which optimizes the HRTEM image (Fig. 2(d)). The d-spacing is calculated from the HRTEM image using image J software, and its value is found to be 2.6 Å, which matches with the (311) plane of the cubic phase of Fe₃O₄. Fig. 2(f) and (g) show the bright field and dark field images. It is worthwhile to observe that the bright field (BF) image is obtained from the transmitted electron beams passing through the particles and carbon film, whereas the dark field (DF) image is obtained from the scattered or reflected electron beams (I_S) from the particles. It is expressed by I₀ = I_A + I_T + I_S, where I₀ and I_T are the intensities of the electron beam incident on the sample and after passing through the particles and/or the film only, respectively.^22,24I_A is the light intensity absorbed by the particles. It is suggested that the distribution and arrangement of agglomerated crystallites in different sites on the carbon film (over which nanoparticles dispersed in the solvent are dropped in TEM preparation) are not the same. Some of them are thicker or thinner or exhibit different orientations of crystallites in a particle, strain-induced crystallites or grains (marked with green- and purple-colored circles).

Fig. 2 TEM analysis of the SA sample: (a & b) image covering one or more particles, (c) SAED, (d) HRTEM image, (e) live FFT image for HRTEM, (f) BF image, and (g) its DF image.

Fig. 3(a-d) shows the tilting images of a particle along the X-axis with rotation (0°–14°). It is found that some portion of a particle changes from a darker region to a brighter region. This can be shown by an arrow. The amount of electron beam interaction with particles varies at different tilting angles. A gap between neighboring particles could be seen at 0° rotation, but as the angle of rotation increases, neighboring particles appear attached. This can be shown by an arrow (green). Therefore, visualization of particles should be done through proper tilting. Otherwise, wrong interpretations may occur in microstructure analysis.

Fig. 3 TEM analysis of SA: tilting at (a) x = 0°, (b) x = 5°, (c) x = 10°, and (d) x = 14°, respectively. Green arrows demonstrate a gap between neighboring particles at 0° and overlapping between particles appears at 14°.

3.3.2 SB sample

Fig. 4 shows the TEM analysis of the SB sample. In different magnifications (100, 50 and 20 nm scale bars), the microstructures of nanoparticles could be observed (Fig. 4(a–c)). From this, it is observed that there are a few crystallites in a particle, but over-lapping with each other. An agglomerated particle has a size of 500–600 nm. Each crystallite is 50–100 nm in size, but shows a single-crystal nature, which was confirmed by its SAED pattern (Fig. 4(e)). Its HRTEM image is shown in Fig. 4(f) and its live FFT (Fast Fourier Transform) is shown in Fig. 4(g). The value of d-spacing is found to be 4.8 Å, which matches with the (111) plane of the spinel structure of Fe₃O₄. The dark field (DF) image of Fig. 4(c) is shown in Fig. 4(d). Two white spots, marked with circles (green and purple), are observed in a portion of a particle in the DF image, whereas in the bright field (BF) image (Fig. 4(c)), a portion of a particle appears almost unchanged.

Fig. 4 TEM analysis of the SB sample: (a) image covering one or more particles, (b) a single particle, (c) a portion of a particle (BF image), (d) a portion of a particle (DF image), (e) SAED pattern, (f) HRTEM image and (g) its live FFT pattern.

Fig. 5(a–d) shows the tilting images of a particle along the X-axis with rotation (0°–14°). A particle consists of many crystallites (i.e., agglomerated particle). At a 0° rotation, a distinct image of gap/porosity within the particle is observed. This is shown by arrows (red). With an increase in tilting angle to 14°, this gap disappears.

Fig. 5 TEM analysis of the SB sample: tilting at (a) x = 0°, (b) x = 5°, (c) x = 10°, and (d) x = 14°. A gap/porous nature is observed at 0° and it disappears at 10° and 14°.

3.3.3 SC sample

Fig. 6(a–e) provides the TEM analysis of the SC sample. The aggregate particle has been observed with size in the range of 300–600 nm recorded at scale bars of 50, 10 and 5 nm (Fig. 6(a–c)). With an increase in magnification, the interface between crystallites can be seen more distinctly. Each crystallite shows a single crystal nature (Fig. 6(d)), which is confirmed by the SAED pattern. Fig. 6(e) shows the HRTEM image of a crystallite and the d spacing is found to be 4.3 Å, which matches with the (111) plane of the spinel structure of Fe₃O₄.

Fig. 6 TEM analysis of the SC sample: images of (a) image covering one or more particles with scale bar = 50 nm, (b) a portion with scale bar = 10 nm and (c) a portion with scale bar = 5 nm. (d) SAED pattern and (e) HRTEM image.

Fig. 7(a–d) shows the tilting images of an aggregate particle along the X-axis with rotation (0°–14°). the particle consists of many crystallites (i.e., an agglomerated particle). At different tilting angles from 0° to 14°, dark and bright spots are different in a particle, which is demonstrated by the green arrows, whereas the variation in overlapping/interface between neighboring particles is indicated by the red arrows.

Fig. 7 TEM analysis of the SC sample: (a) image covering one or more particles, tilting at (a) x = 0°, (b) x = 5°, (c) x = 10°, and (d) x = 14°. The green arrow demonstrates the variation in dark and bright spots in a particle at different tilting angles from 0° to 14°. The red arrow demonstrates the variation in overlapping/interface between neighboring particles at different tilting angles from 0° to 14°.

In addition to microstructure analysis using SEM and TEM, magnetic and heat generation studies for SA, SB and SC samples under AC magnetic fields (induction coils) have been conducted (as discussed in the subsequent section).

The crystallite size calculated from the XRD peaks for the three samples SA, SB and SC is smaller than that determined from the TEM images. This can be explained as follows. The crystallite is the region with a periodically ordered arrangement of atoms or ions, whereas the particle size calculated using TEM represents the region of a group of crystallites present in a particle as well as surface dangling bonds.

3.4 Magnetic study

Magnetization (emu g⁻¹) vs. applied magnetic field (H) plots for the three samples at 5 K and 300 K are shown in Fig. 8(a–f). It is clear that all samples exhibit a hysteresis loop, and the coercivity (H_c) values are given in Table 2. Every sample has two different coercivity values in reverse and forward applied magnetic fields.

Fig. 8 Magnetization vs. applied field of samples (SA (a and b), SB (c and d), and SC (e and f)) measured at two different temperatures (5, 300 K). Inset: Near 0 Oe, the MH curve is provided to observe coercivity (H_c).

Table 2 The parameters such as saturation magnetization and coercivity of the three samples at 5 K and 300 K. Here, H_c1 and H_c2 are the negative and positive magnetic fields, respectively, to bring the magnetic moment to zero. H_C is an average coercivity calculated from eqn (1). H_EB is exchange bias calculated from eqn (2). M_R1 and M_R2 are remanent magnetizations (+ ve and −ve fields, respectively) after bringing magnetic fields to zero. M_S1 and M_S2 are saturation magnetizations measured in +ve and −ve fields, respectively, after applying the maximum magnetic field

Samples	H C (Oe)				M R (emu g^−1)		M S (emu g^−1)
	H c1	H c2	H c	H EB	MR1	MR2	MS1	MS2
SA (300 K)	111	149	130	19	11.94	17.10	84.5	84
SA (5 K)	358	369	364	5	24.32	26.63	87	87.6
SB (300 K)	55	93	74	19	7.89	13.99	82	83.5
SB (5 K)	318	333	325	8	39.5	40.39	85	85.6
SC (300 K)	37	91	64	27	3.24	7.72	49.98	50.05
SC (5 K)	333	368	351	18	22.88	23.89	55.97	56.01

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The coercive field H_c of the loop and the displacement EB (exchange bias) can be calculated according to the following relations.²²

where H_c1 and H_c2 are the values of coercivity (the applied field required to bring magnetization to 0) in reverse and forward applied magnetic fields, respectively. A small value of H_c is observed due to slight inhomogeneity in particle size distribution. At 5 K, a value of 364 Oe is found for the SA sample owing to the ferrimagnetic nature at this temperature. Interestingly, the coercivity values for the three samples SA, SB, and SC are found to be 130, 74, and 64 Oe, respectively, at 300 K using eqn (1). Similarly, the coercivity values for the three samples at 5 K are given in Table 2, and their values are more than those obtained at 300 K.

The values of exchange bias, according to eqn (2), for SA, SB and SC samples are found to vary from 5 Oe (5 K) to 18 Oe (5 K), and their values are less than those obtained at 300 K. This can be explained as follows. At 5 K, the magnetization increases significantly compared to that measured at 300 K. Such exchange bias originates due to antiferromagnetic coupling of the surface with the core magnetic domain. Every particle has a magnetic core surrounded by a surface antiferromagnetic layer. With a decrease in particle size, the contribution from the surface antiferromagnetic layer increases due to the increase in surface dangling bonds.²⁵ With a decrease in temperature, the magnetic moment from the core increases, whereas the surface antiferromagnetic contribution decreases. Thereby, exchange bias decreases with a decrease in temperature. The schematic diagram representing the increase in domain size in the core of a particle and the decrease in the antiferromagnetic layer shell with the decrease in temperature from 300 K to 5 K is shown in Fig. 9.

Fig. 9 The schematic diagram representing the increase of domain size in the core of a particle and the decrease of antiferromagnetic layer shell with a decrease of temperature from 300 K to 5 K.

We have recorded the magnetization (ZFC and FC curves) versus temperature curves for the three samples (Fig. 10). The ZFC curve represents the magnetic data recorded in an applied field of 500 Oe during the warming process after cooling from 300 K to 5 K in the absence of an applied magnetic field. The FC curve represents the magnetic data recorded in an applied field of 500 Oe during the cooling process from 300 K to 5 K. Samples SA, SB and SC exhibit ferromagnetic properties from 5 to 300 K. Here, applied magnetic field is 500 Oe, which is high. This magnetic field can overcome the crystalline anisotropic energy of a material. Depending of nature of sample, ZFC and FC curves can merge upon cooling from 300 K to 5 K. In case of sample SA, there is no join in both curves from 300 K to 5 K. In cases of SB and SC, both ZFC and FC curves are starting from same point up to a particular temperature known as irreversible temperature (T_irr) when temperature decreases from 300 K to 5 K. It is understood that the SC sample has lower magnetization than SA or SB, thereby allowing both curves to merge easily when the applied magnetic field dominates over the crystalline anisotropic energy (KV, where K is the anisotropy constant and V is the volume of the particle.^26,27 Smaller-sized particles have lower anisotropy energy. As the size of the SC sample is smaller than that of SA or SB, an irreversible nature of both curves is observed at 125 K. The microstructure and irreversible temperature are related.

Fig. 10 Magnetization versus temperature (ZFC, & FC) curve for 3 samples such as (a) SA, (b) SB and (c) SC at applied magnetic field of 500 Oe.

3.5. Study of induction heating ability

Fig. 11(a–f) shows the heating ability of the different as-prepared samples SA, SB, and SC under increasing power (2, 4, and 6 kW) for 1200 s, in order to understand their heating behavior for potential magnetic hyperthermia applications. Here, two different concentrations of samples (1 mg mL⁻¹ and 3 mg mL⁻¹) and three different powers (2, 4 and 6 kW) are employed to understand their heating behavior up to 1200 s. In Fig. 11(a and b), 2 kW power and two different concentrations of samples are used. For a concentration of 1 mg mL⁻¹, the sample SA has reached a temperature close to the hyperthermia temperature of 40 °C. The sample SB reaches the hyperthermia temperature of 43 °C, but the SC sample shows heating behavior near 35 °C. The SA and SB samples have shown a rise in temperature despite having a lower concentration (1 mg mL⁻¹), and the higher temperature increase is related to their higher values of saturation magnetization, that is, 84 and 83 emu g⁻¹, at 300 K (in Table 2), respectively. For the higher concentration of 3 mg mL⁻¹, samples SA and SB reach the hyperthermia temperature in more than 400 s, but the SC sample reaches 38 °C, which is attributed to its lower magnetization (∼ 50 emu g⁻¹). The samples are highly dispersible in water, as capping agents such as acetate and urea are present on the surface of nanoparticles. These are stable for more than 1 h.

Fig. 11 Temperature versus time for magnetic particles under AC magnetic fields (f = 280 khz and different powers). Magnetic particles are SA, SB, and SC. (a and b) 2 kW power and two different concentrations (1 and 3 mg mL⁻¹), (c and d) 4 kW power and two different concentrations (1 and 3 mg mL⁻¹), and (e and f) 6 kW power and two different concentrations (1 and 3 mg mL⁻¹).

In Fig. 11(c and d), 4 kW power and two different concentrations of samples are used. Furthermore, with the increase in power up to 4 kW, samples SA, SB and SC (1 mg mL⁻¹) reach the hyperthermia temperature, but the rise in temperature is greater for samples SA and SB. In the case of a 3 mg mL⁻¹ concentration, all samples reach the hyperthermia temperature in 200 s. The increase in concentration gives rise to an increase in heat generation.

In Fig. 11(e and f), 6 kW power and two different concentrations of samples are employed. All samples reach the hyperthermia temperature, but the rise in temperature is greater in the case of 3 mg mL⁻¹ concentration compared to that for the 1 mg mL⁻¹ concentration. All samples with a concentration of 3 mg mL⁻¹ reach the hyperthermia temperature in 120 s, and their temperatures rise with the same slopes.

For these studies, the following conclusions are drawn: (i) the rise in temperature is dependent on the concentrations of the samples (1, 3 mg mL⁻¹) at lower power (2 kW), (ii) the rise in temperature is dependent on powers (2, 4, 6 kW) at lower concentration (1 mg mL⁻¹), and (iii) the rise in temperature for the higher concentration (3 mg mL⁻¹) is almost the same at higher power (6 kW) because the absorption efficiency of the AC magnetic field by the sample is almost saturated at higher power. The specific absorption rate (SAR) is purely dependent on the heating behavior, and its values for each sample at different powers and concentrations are given in Table 3.

Table 3 Specific absorption rate values of samples at different powers and different concentrations

	SAR (Watt per g)
Induction power (kW) f = 280 kHz	SA		SB		SC
	1 mg mL^−1	3 mg mL^−1	1 mg mL^−1	3 mg mL^−1	1 mg mL^−1	3 mg mL^−1
2	38	140	37	120	32	60
4	126	225	126	224	56	196
6	157	228	144	226	112	225

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The heating behavior at different powers and concentrations has been reported.²⁸Table 4 compares the reported values of the SAR with those of our samples. The heat generation increases with an increase in the applied magnetic field. We have converted our power values to applied magnetic fields for easy comparison. In the case of Fe₃O₄@Au nanoparticles, the SAR of 75 kW per kg-Fe was reported.²⁹ Also, the heating behavior of Fe₃O₄ nanorings under an AC magnetic field has been reported.³⁰

Table 4 Comparison between the reported values of SAR and this work

S. No.	Authors	Materials (mg mL^−1)	f (kHz)	H (Oe)	SAR (W g^−1)	Ref.
1	Sharma et al.	Fe3O4 (5)	280	335	40	31
2	Singh et al.	CaF2:1Eu/Fe3O4 (6)	265	335	122	32
3	Shete et al.	Fe3O4 (6)	280	335	95	33
4	Nikam et al.	Co0.5Zn0.5Fe2O4 (5)	267	251.4	48–164	34
5	Thorat et al.	LSMO (15)	267	300	165	35
6	Dalal et al.	Ni0.3Zn0.4Co0.2Cu0.1Fe2O4 (1)	290	335	200	36
7	Thorat et al.	LSMO (15)	280	500	80	37
8	Mallick et al.	Li0.31Zn0.38Fe2.31O4 (10)	290	335	502	38
9	Ningombam et al.	Mn0.5Fe2.5O4@YVO4:Eu^3+ (10)	242	335	20	39
10	Joshi et al.	Fe3O4 (1)	280	280	26	40
11	Soni et al.	YPO4:Er^3+−Yb^3+ @Fe3O4 (2)	280	300	65	41
Sample SA	Srivastava et al.	Fe3O4 (1 mg mL^−1)	280	211	38	In this study
			280	422	126
			280	633	157
		Fe3O4 (3 mg mL^−1)	280	211	38
			280	422	126
			280	633	157
Sample SB	Srivastava et al.	Fe3O4 (1 mg mL^−1)	280	211	37	In this study
			280	422	126
			280	633	144
		Fe3O4 (3 mg mL^−1)	280	211	120
			280	422	224
			280	633	226
Sample SC	Srivastava et al.	Fe3O4 (1 mg mL^−1)	280	211	32	In this study
			280	422	56
			280	633	112
		Fe3O4 (3 mg mL^−1)	280	211	60
			280	422	196
			280	633	225

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However, our results suggest that the heat generation or power dissipation (P) of the system in an AC magnetic field is dependent on the variation of the amplitude of frequency (f) and fields (H). The parameter likely to affect induction heating is discussed in brief. The power dependence can be expressed by the following equation:⁴²

P = μ₀πχ′′fH_o² (3)

where μ_o is the permeability of free space and χ′′ is the imaginary part of magnetic susceptibility (χ). Magnetic susceptibility is calculated by dividing the magnetization by the applied magnetic field (χ = M/H); and it has two parts: real (χ′) and imaginary (χ′′).

The imaginary part (χ′′) is related to the heat dissipation of the system, which is defined as

where τ is the total relaxation contributed by Brownian motion (τ_B) and Néel's spin (τ_N) and ω = 2πf (in s⁻¹ unit).

The density of the particles is related to the loss power density P or the specific absorption rate (SAR), which can be calculated using the following relation

where C is the specific heat capacity of the solvent (for water, C is 4.18 J g⁻¹ K⁻¹). In most cases, 1 to 3 mg of particles is dispersed in 1 mL of water. ΔT/Δt represents the slope of the time-dependent temperature curve in the heat generation curve.⁴³m_magn is the ratio of the amount of sample to the total of amount of the sample and solvent (water) and it is unitless.

4. Conclusions

Fe₃O₄ single crystal nanoparticles were prepared using the hydrothermal method. Different precursors such as ethylene glycol, sodium acetate and urea were used to prepare Fe₃O₄ particles. There is a variation in pH before and after hydrothermal treatment. In the SEM study, it is difficult to distinguish the particles in samples SA, SB and SC. In the TEM study, we were able to distinctly visualize agglomerated particles, aggregated particles, interfaces between crystallites or particles, and gaps/porosity in a particle. Verification of the microstructure could be performed well through tilting of the sample with respect to the electron beam and using dark field and bright field imaging in the TEM experiment. Also, the magnetic study has been performed. SA and SB show higher magnetization compared to SC. With a decrease of temperature, the coercivity increases, whereas exchange bias decreases. In this context, induction studies of samples have been carried out to evaluate their heating ability. The specific absorption rate (Watt g⁻¹) has been calculated to estimate the heating capacity of these nanostructure materials. Several conclusions on heat generation at low and high concentrations of magnetic nanoparticles and at low and high powers of AC magnetic fields have been provided. Our SAR values are compared with many reported values. Smaller-sized particles have lower magnetization and lower SAR values compared to larger particles.

Author contributions

Manas Srivastava: data collection; formal analysis; investigation; methodology; writing – original draft, and funding acquisition; Ruchi Agrawal: data curation; investigation; and methodology. Atom Rajiv Singh: data curation; investigation; methodology, and writing – original draft. Leishangthem Sanatombi Devi: investigation; formal analysis; and writing – original draft. Rashmi Joshi: investigation; methodology; and writing – original draft. Bheeshma Pratap Singh: writing, review and editing; and supervision. D. Sarkar: investigation and writing – review and editing. Rakesh Kumar Singhal: review, editing and writing original draft. Raghumani Singh Ningthoujam: conceptualization, supervision, investigation; and writing – review and editing.

Data availability

All data supporting this article are included in the manuscript and/or included as part of the ESI.†

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

One of the authors, M. Srivastava, acknowledges the award from CSIR, New Delhi (CSIR-SRA; 9146-A). We highly acknowledge Dr Niharendu Choudhury, Head, Chemistry Division, BARC, for his support and encouragement during this work. We also highly appreciate SAIF, IIT Bombay, Mumbai, for providing the TEM facility.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4dt02448f

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