Optical and Thermophysical Characterization of Fe3O4 nanoparticle

The size dependence of optical and, thermophysical properties of Fe3O4 nanoparticle (NPs) has been investigated. Three samples of Fe3O4 NPs with different sizes were prepared by the Co-precipitation method and labeled a, b and c. The UV- vis spectra shifted toward the lower energy with increasing the particles size. The energy bandgaps of the synthesized Fe3O4 NPs are 1.84 ev,1,73 ev, and 1,47 ev for a, b and c respectively. The sizes of the nanoparticles were estimated using the effective mass approximation (EMA) model, and are 10.7 nm, 20.56 nm, and 30.43 nm. These values are comparable to those found by transmission electron microscope (TEM) and X-ray diffraction (XRD). The Photoacoustic (PA) technique was used to research Fe3O4 NPs for thermal diffusivity (α), thermal effusivity (e), and thermal conductivity (k). The determined values of α, e, and k increase as the size of nanoparticles rises and decreases from the bulk by about 33%.

from the gas to the microphone [16]. Therefore, the PA signal contains information about the optical absorption within the sample in addition to the way with which the heat is diffused through the sample. The Rosencwaig and Gersho (RG) theory of the PA effect [17] shows that the pressure variations depend on the optical and thermal parameters of the sample. This study aims to synthesize Magnetite Fe 3 O 4 NPs of various sizes using the process of co-precipitation. The size-dependent UV-vis spectra have been investigated. The energy band gap of Fe 3 O 4 NPs of different sizes was measured. The sizes of nanoparticles have been estimated using effective mass approximation (EMA) [18] and verified by XRD and TEM. Furthermore, thermal diffusivity (α), thermal effusivity (e), and thermal conductivity (k) of different sizes of Fe 3 O 4 NPs have been measured using the nondestructive photoacoustic (PA) technique which attracts great interest because it makes them suitable for many technological applications.

Synthesis of Fe 3 O 4 NPs
Co-precipitation is the most widely and simplest method for synthesis magnetics nanoparticles of controlled sizes by precipitate ferrous and ferric salts. Fe 3 O 4 were prepared under nitrogen (N 2 ) gases bubbling through the solution to protect Fe 3 o 4 against critical oxidation. 20.25 g (FeCl 3 ·6H 2 O), and 10.35 g of (FeCl 2 ·4H 2 O) were dissolved into 250 mL of distilled water. The solution stirring for 80 minutes, chemical precipitation was achieved at 90C under stirring by adding ammonium solution drop by drop at a constant rate until pH ranging between 8 and 14 Completed precipitation of Fe 3 O 4 expected [19]. The system was cooled to room temperature, the precipitates were separated by a magnet and washed with distilled water until pH neutral. Finally, Fe 3 O 4 washed with acetone and dried in an oven at 70-80C for 1.5 h to prepare the nanoparticles of Fe 3 O 4 in powder form, the size and shape depend on the pH value of the solution. We get three different sizes labeled a, b and c. at PH 8-10, 11-12, and 13-14 respectively.

3-Characterizations
The absorption bands of the prepared samples have been measured by the UV-670 Jasco double-beam spectrophotometer utilizes a unique, single monochromator design covering a wavelength range from 190 to 2700 nm. The crystal structure of Fe 3 O 4 NPs was characterized by X-ray Diffraction (XRD) (Shim ADZU diffractometer type XRD 6000. X-ray diffraction (XRD) is a well-known technique for the characterization of bulk and thin film. Transmission Electron Microscope (TEM) is used for characterizing the size of nanoparticles. TEM (JEOL JEM-2100 operated at 200KV with high-resolution Gatan CCD bottom camera, Orius SC200). A highly sensitive (PA) technique has been utilized to investigate the thermal parameters (thermal diffusivity (α), thermal effusivity (e), and thermal conductivity (k) of Fe 3 o 4 NPs of different sizes. The (PA) technique depends on the detection of pressure fluctuations in a sealed closed-cell created by the periodic thermal waves from the sample. The experimental set-up of the PA technique is shown schematically in figure (1). The light beam from Stability 2017 Argon Laser was mechanically modulated by an optical chopper (SR540) and focused onto the sample which was mounted carefully inside a PA cell (MTEC Model 300). The sound wave generated from the sample were subsequently detected as an acoustic signal by a highly sensitive electrical microphone fixed in the PA cell. The PA signal was then amplified by a low noise preamplifier and further processed using a lock-in amplifier (Stanford Research System, Model SR830 DSP [20][21]. The PA signal was recorded for varied frequency for each sample.

TEM analysis
TEM analysis has been used to determine the average particle size of Fe 3 o 4 NPs The TEM micrographs of samples a,b and c are shown in Fig. 2a, 2b, and 2c respectively. The prepared nanoparticles' images show a nearly spherical morphology. The estimated particle size of a, b, and c samples are 10 nm, 20 nm, and 30 nm respectively.

UV-Vis absorption
Optical absorption spectra of samples show a broad absorbance (no sharp absorbance peaks) for all different sizes fig (3), which is mainly due to the half-metallic behavior of Fe 3 O 4 NPs [22]. The visible absorption is mainly because of the mixture of the ligand near-infrared absorption is assigned to the inter valence field transition and charge-transfer transition, while the charge-transfer transition between the metal ions. The absorption edges are 372 nm,383 nm, and 404 nm for the samples a, b, and c respectively The electronic transitions are the essential parameter of the optical absorption. These transitions are controlled by certain selection rules, which can be expressed by using Tauc's equation [23].

(1)
where hν is the energy of the incident photons, α is the absorption coefficient, A is a constant, h is Planck's constant, and n is a constant with allowed values of 1/2 and 2 and not allowed values of 3/2 and 3 for direct and indirect transitions correspondingly. The values of n were detected in the range (0.925-1.083) which predicts the electronic allowed direct transition. The values of band-gap are determined by the Tauch-plot curve of αhʋ 2 value on hʋ. The interception of the extrapolation of this linear part to the energy axis gives energy bandgap E g Figure 4 shows the difference of ( αhν) 2 with photon energy hν for the three samples (a,b, and c). The values of E g for Fe 3 o 4 NPs are 1.84, 1,73, and 1,47ev.
Using the calculated bandgap and the "Effective Mass Approximation" model (EMA) the size of Fe 3 O 4 NPS is calculated. The EMA model is given by [24].

X-Ray diffraction analysis.
XRD measurements were used to recognize the crystalline structure of the products. Fig (5) showed that the XRD peaks can match fine with the characteristic peaks of the inverse cubic spinel (reflection peak at 2θ=35.6°) structure (JCPDS 19-629), which shows the crystalline structure of Fe 3 O 4 NPs. The average crystalline size calculated using the Debye-Scherrer equation [25].
Where β is the full-width at half-maximum (FWHM) value of XRD diffraction lines, the wavelength λ= 0.15405 nm and θ is the half diffraction angle of 2θ [26][27][28]

Thermal measurements
The thermal properties of Fe 3 O 4 nanoparticles were studied with the Photoacoustic (PA) technique. The samples in powder form were compressed into disks (under a hydraulic pressure 30 Ton/inch) with the thickness (0.62 mm). For each appropriate (depth profile analysis) the PA signal amplitude was reported at different chopping frequencies (f). Fig 6 shows the plots of ln PA signal amplitude versus lnf for synthesized samples (a), (b), and (c) respectively. A distinct slope transition is observed at a frequency f c (the sample transitions from thermally thick to thermally thin) where the crossover occurs. The thermal diffusivity (α), for all samples, was then calculated using the relation [29].   (4) where L is the thickness of the sample. The measured values of α are shown in Table 1. It easily observes that as the size of Fe 3 o 4 NPs increase the thermal diffusivity increase.
The thermal effusivity (e) of the samples was also calculated using the PA technique, where the PA signal amplitude q is given for optically opaque and thermally thick samples by [30][31][32]   ,(I 0 ) is the incident light strength, (Υ) is the specific heat ratio, (P 0 ) is the ambient pressure, (α g ) is the gas thermal diffusivity, (Ɩ g ) is the length of the gas column, (T 0 ) is the ambient temperature and (f) is the modulation frequency. Using Si as a reference sample, with 15670 Ws 1/2 m -2 K -1 thermal effusivity [29]. The Si reference sample is used to extract the B constant.  . The values of (α.e and k) are increasing as the size of nanoparticles increases and decreases from its bulk value. The value of (k) for sample c is about 66 % from bulk value (9.7W/mK) [33]. Such decreases in (k) of Fe 3 O 4 NPs from the bulk value are agreement with N. Rajkumar et al [33]. In their work, they obtained a decrease in (k) about 59 % for particles size 10 nm from the bulk value. In such a study, they explained the decrease of k of Fe 3 O 4 NPs from the bulk value based on phonon. When the particles are small, phonon confinement increases, and thus the collision rate increases (mean free path decreases) resulting in reduced thermal conductivity. Moreover, As the size of the nanomaterial decrease, the surface-to-volume ratio increases, and the presence of increased surfaces due to roughness additionally provides the phonon with a scattering mechanism. This additional scattering decreases the mean free path of the phonon which causes the resistance in the heat flow resulting in a reduction of the thermal diffusivity and conductivity [34 -35].

Conclusion
Magnetite nanoparticles synthesized by chemical co-precipitation method. The prepared Fe 3 O 4 (NPs) nanoparticles were characterized by TEM, UV-vis, and XRD. The average particle sizes estimated by TEM images are 10 nm,20 nm, and 30 nm. The UV-vis absorption spectra of Fe 3 O 4 shifted toward the visible region and the redshift of broad an absorbance spectrum to longer wavelength with increasing particle size. The particle sizes are confirmed by an effective mass approximation model and XRD data. Furthermore, the Photoacoustic (PA) technique has been used to study the thermal diffusivity (α), thermal effusivity (e), and thermal conductivity (k) of Fe 3 O 4 NPs. The values of (α.e and k) are increasing as the size of nanoparticles increases and decreases from its bulk value. The value of (k) for sample c is about 66 % of the bulk value it decreases with a decrease in particle size. The decrease in thermal conductivity as the particle size decreased is due to the increase in phonon containment and thus the increase in collision rate (mean decrease in the free path) leading to a decrease in thermal conductivity.