1 Introduction

Magnetic nano-particles of the form M x Fe3−x O4 (M = Ni, Co, Zn Cr, etc.) have been an area of research during the recent years as they present many potential applications, such as catalysis [1, 2], targeted drug delivery [3], magnetic data storage [4], contrast agents for magnetic resonance imaging, and heat mediators in magnetic fluid hyperthermia [5–7]. These magnetic nano-particles are useful in order to enhance the biomedical applications because the properties of nano-particles remarkably changed from their bulk counterpart. One of the most interesting properties of magnetic nano-particles is the ability to generate heat under the influence of alternating magnetic field. The heating effect can be obtained from the magnetic hysteresis losses that occur during the magnetization reversal process [8]. Among various magnetic nano-particles, magnetite and cation-substituted magnetite (such as Ni and Co) nano-particles are useful candidates for this purpose. Both of these transition metals can significantly increase the hyperthermic efficiency through a partial or total substitution of high anisotropic Ni2+ or Co2+ ions with Fe2+ ions in the magnetite structure [9].

Magnetite has the inverse spinel cubic structure represented as

$$ [\text{Fe}^{\mathrm{2+}}]_{\text{tet}} [\text{Fe}^{\mathrm{3+}}\text{Fe}^{\mathrm{2+}}]_{\text{oct}}\text{O}_{\mathrm{4} } $$
(1)

It has 8 Fe2+ ions at the octahedral site, and 32 oxygen ions and 16 Fe3+ ions are equally distributed among the tetrahedral and octahedral sites [10]. Magnetism of magnetite is the result of super-exchange interactions between tetrahedral and octahedral cations which result in anti-parallel magnetic moments between them. In the magnetite structure, net magnetization is exhibited by the Fe2+ ions [11]. In the cation-substituted magnetite nano-particles, the divalent ions are replaced by Fe2+ ions which can significantly change their magnetic properties [12]. The nickel- and cobalt-doped magnetite nano-particles also have an inverse spinel cubic structure in which metal ions occupy octahedral site and ferric ions are equally distributed among the tetrahedral and octahedral sites.

A variety of methods have been used for the synthesis of magnetic nano-particles such as sol-gel method [13], co-precipitation [14–16], and hydrothermal [17] and thermal decomposition [18, 19]. Among these, the co-precipitation method is mostly used for preparation of MNPs because it is the simplest and cheapest method [20] and no further heat treatment is required to achieve a structure. In this work, Ni x Fe3−x O4 and Co x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 nano-particles are prepared using the co-precipitation method in order to investigate the effect of Ni and Co doping on structural, thermal, morphological, magnetic, and optical properties of magnetite nano-particles.

2 Experimental Method

2.1 Synthesis of Ni x Fe3−x O4 and Co x Fe3−x O4 Nano-particles

The Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 have been prepared using the co-precipitation method; the block diagram is shown in Fig. 1. Chloride salts (FeCl2, FeCl3, CoCl2, and NiCl2) are used as starting materials. Each salt is dissolved in double-distilled water separately. In the present case, 0.05 M solution of both cobalt and nickel is used in 0.01 and 1.7 M solution of ferrous and ferric chlorides, respectively. Then the previous solution was added to each other, and sodium hydroxide solution (3 M) was added drop wise in this solution. The precipitates were washed with double-distilled water and ethanol several times. The precipitation was dried in an oven at 80∘C for several hours.

Fig. 1
figure 1

Block diagram of co-precipitation method

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2.2 Characterization Techniques

The crystal structures and phase composition of the samples are studied using Philips X-ray diffraction (XRD) with CuK α radiation (λ = 1.5418 Å) at a scanning rate of 2∘/min in the scanning range of 30–140∘. The function goups are analyzed by Perkin Elmer FTIR spectrometer. To investigate the thermal stability of prepared nano-particles, thermogravimetric analysis (TGA) and differential scanning calorimetric (DSC) studies have been carried out. This analysis is done with TGA/DSC (Mettler Toledo Ltd.) instrument at a heating rate of 10∘C/min at room temperature to 1000∘C in nitrogen atmosphere. UV-visible spectra are recorded using a Perkin Elmer Lambda spectrophotometer. SEM are carried out using a Philips Morgagni Scanning Electron Microscope. The magnetic properties of samples are characterized with an Oxford Lake Shore’s Vibrating Sample Magnetometer (VSM) using an applied field of 10 kOe.

3 Results and Discussion

3.1 Structural Analysis

The XRD pattern of the Ni x Fe3−x O4 and Co x Fe3−x O4 where x = 0, 0.05, 0.1, and 0.15 nano-particles is shown in Fig. 2. All the peaks are indexed with JPCD card no.19-0629 which corresponds to an inverse spinel structure of nano-particles. The strong peaks suggested that Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles are highly crystalline. The crystallinity increases with nickel and cobalt doping in magnetite nano-particles. The broadening in the peaks indicates that the particle size is at nano-domain. All XRD patterns show diffraction peaks which correspond to the spinel phase of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles. The parameters extracted from the XRD micrographs are tabulated in Table 1.

Fig. 2
figure 2

XRD patterns of all the samples of a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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Table 1 XRD data of Ni x Fe3−x O4 and Co x Fe3−x O4nano-particles
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The crystallite size of nano-particles is calculated from the FWHM of (311) diffraction peaks using Debye-Scherrer formula [21]:

$$ D_{\mathrm{p}}=\frac{\mathrm{0.94}\lambda}{\beta \text{Cos}\theta} $$
(2)

where β is the full width at half maximum, λ shows the wavelength of CuK α (λ = 1.54 Å), and 𝜃 is the Bragg angle It is observed that particle size decreases with nickel and cobalt doping in magnetite nano-particles which is due to the broadening of the diffracted peaks.

The lattice parameter calculated from the formula [22]:

$$ a = (d (h^{2}+k^{2}+ \text{l}^{2})^{\mathrm{1/2}}) $$
(3)

where h, k, and l are the miller indices. The lattice parameters decrease with increasing nickel and cobalt concentrations, as shown in Fig. 3. This is due to the small ionic radii of Ni (0.69 Å) and Co (0.74 Å) as compared with the ionic radii of Fe2+ (0.77 Å). The X-ray density is calculated using the formula [23]:

$$ d_{\mathrm{x}}= \frac{8M}{\text{Na}^{3}} $$
(4)

where M is the molecular weight and N is the Avogadro number (6.02214 × 1023). The lattice parameters increase with increasing concentration of nickel and cobalt, which is due to the greater molecular weight of nickel (58.6934 g/mol) and cobalt (58.9331 g/mol) as compared with Fe (55.845 g/mol).

Fig. 3
figure 3

Variation of crystallite size and lattice parameters of a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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3.1.1 Diamond Structure

The 3-D structural view of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles is shown in Fig. 4a, b, respectively. The Wyckoff sites and x, y, and z values for all the elements used are listed in Table 2, and parameters obtained from this software are listed in Table 3. The cell volume values are confirmed with the help of the Diamond software using V = a 3. It is evident from the micrographs that there is a slight difference in these structures because of the small variations in the lattice parameters. It is observed from Table 1 that lattice parameter a decreases with increasing nickel and cobalt content, and, therefore, the unit cell volume is small for the highest Ni and Co concentrations, as shown in Fig. 4a, b.

Fig. 4
figure 4

a 3-D structure of Ni x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 nano-particles. b 3-D structure of Co x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 nano-particles

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Table 2 Atomic coordinates of Ni x Fe3−x O4 and Co x Fe3−x O4 (x = 0, 0.05, 0.1, and 0.15) nano-particles
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Table 3 Cell volume and density values for Ni x Fe3−x O4 and Co x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 nano-particles
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3.2 FTIR Analysis

In order to characterize the as-synthesized nano-particles, FTIR spectroscopy was performed in the wavelength range 600–4000 cm−1. The FTIR spectra of Co x Fe3−x O4 and Ni x Fe3−x O4 (x = 0, 0.05, 0.1, and 0.15) nano-particles are shown in Fig. 5a, b, respectively. The obtained spectra are mainly characterized by the presence of organic compounds remaining from the co-precipitation synthesis procedure. The band at 2909.82 cm−1 is attributed to the vibration mode of the O–H bond in the water molecule that remained absorbed in the nano-particle surface during synthesis. The bands at 2359 cm−1 is ascribed to the C–H bond. The band at 1600 cm−1 to 1102 cm−1 are due to the C =O and C–O bonds. The two M–O bonds in the range of 780–890 cm−1 confirms the formation of inverse spinel structure of both types of nano-particles.

Fig. 5
figure 5

FTIR micrographs of a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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3.3 DSC/TGA Analysis

The thermal characterization of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 are performed by DSC/TGA analysis. The experiments were carried out in nitrogen atmosphere. The TGA curve of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles is shown in Fig. 6a, b, respectively. As the temperature increases from 30 to 150∘C, 2.5% weight loss is observed in both nickel- and cobalt-doped magnetite nano-particles. This is due to the moisture which is absorbed during the experiment.

Fig. 6
figure 6

Variation in percent weight loss as a function of temperature (TGA curve) for a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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The DCS graphs of as-synthesized Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 nano-particles is shown in Fig. 7a, b, respectively. The graphs shows the variation of heat flow as a function of temperature. The change in enthalpy is calculated by using the formula [24]:

$$ {\Delta} H =\frac{Q_{2}\mathrm{-}Q_{1}}{T_{2}\mathrm{-}T_{1}} $$
(5)
Fig. 7
figure 7

Variation in heat flow as a function of temperature (DSC curve) for a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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First, calculate Q 2– Q 1 from y-axis and then T 2– T 1 from x-axis and then divide both values. The values of enthalpy change of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 nano-particles with increasing transition temperature is shown in Table 3. A sharp exothermic peak was observed in magnetite nano-particles at ∼336∘C temperature due to the phase transition from γ-Fe2O3 to α-Fe2O3 [25]. The peak starts at T 1 (207∘C) and ends at T 2 (339∘C) with an enthalpy change of −6.8 J/g. When the concentration of nickel and cobalt is increased, the value of enthalpy decreases and is listed in Table 4. The variation of enthalpy change and transition temperature as a function of the cobalt and nickel concentrations is shown on Fig. 8a, b, respectively. It is observed that when the concentration of nickel increases, the transition temperature increases and enthalpy decreases.

Fig. 8
figure 8

Variation in enthalpy and transition temperature of a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles as a function of cobalt and nickel concentrations

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Table 4 Values of enthalpy and phase transition temperature of a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles
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3.4 SEM Analysis

The surface topography and morphology of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 nano-particles are shown in Figs. 9–d and 10a–d, respectively. The SEM specimens are prepared by dispersing the powdered compounds in deionized water and sonicating them for 30 min [26]. One drop of the sonicated solution is placed on the silicon wafer and then dried with the help of a hot plate. The figures indicate that the shape of both nickel- and cobalt-doped magnetite nano-particles are spherical with little agglomeration.

Fig. 9
figure 9

SEM micrographs of a Fe3O4, b Co0.05Fe2.95O4, c Co0.05Fe2.9O4, and d Co0.05Fe2.85O4 nano-particles at 50 μm resolution

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Fig. 10
figure 10

SEM micrographs of a Fe3O4, b Ni0.05Fe2.95O4, c Ni0.05Fe2.9O4, and d Ni0.05Fe2.85O4 nano-particles at 50 μm resolution

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3.5 Magnetic Properties

The hysteresis loops for Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 are shown in Fig. 11a, b, respectively. The values of coercivity (H c), saturation magnetization (M s), remanence (M r), anisotropy, and magnetic moment are tabulated in Table 5. It is observed that the value of magnetization is decreased with increasing nickel and cobalt concentrations, because Ni2+ and Co2+ ions replace the Fe2+ ions on the octahedral sites. The magnetic moment of Ni2+ (2μ B) Co2+ (3μ B) [27] is less than that of Fe2+ (4μ B). This is in accordance with the Neel’s sublattice model; firstly, Ni2+ and Co2+ ions cause the shifting of Fe3+ ions from tetrahedral to octahedral site, but when the concentration of nickel and cobalt ions increases, the tetrahedral-octahedral interactions decrease and the octahedral-octahedral interactions increase. As a result, the total magnetic moment of the system is decreased and therefore magnetization also decreased.

Fig. 11
figure 11

Hysteresis loops of a Ni x Fe3−x O4 and b Co x Fe3−x O4 (x = 0, 0.05, 0.1, and 0.15) nano-particles

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Table 5 Magnetic properties of Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles
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It is also revealed that the coercivity increases with increasing quantity of nickel and cobalt substitution. This is because of the decrease in crystallite size by the doping of nickel and cobalt ions. As the crystallite size decreases, the number of domain walls decreases and the chances of magnetization and demagnetization of a material decreases. The anisotropy constant K is calculated using the following the relation [28].

$$ K = \frac{M_{s}{ \times} H_{\mathrm{c}}}{\mathrm{0.98}} $$
(6)

where H c and M s are the coercivity and saturation magnetization, respectively. Anisotropy constant K depends on the substituted ion concentration. This means that the anisotropy constant increases with increasing nickel content and therefore the magnitude of H c also increases. This effect appears largest for the highest cobalt-concentrated sample that shows a highest value of coercivity.

The magnetic moment (n B) is calculated from the following formula [29]:

$$ n_{\mathrm{B}}=\frac{M{ \times} M_{\mathrm{s}}}{5588} $$
(7)

where M is molecular weight. The values of magnetic moments show that all the samples are ferromagnetic in nature.

3.6 Optical Properties

The optical properties of Ni x Fe3−x O4 and Co x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 are determined using UV-visible spectroscopy. For this purpose, the samples are prepared by dissolving each sample in 10 ml of DMF solution. Figure 12a, b shows the absobance versus wavelength curves of all the samples. The shifting in wavelength for Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles reveals the blue shift in absorption edge which is the confirmation of the formation of nano-particles [30].

Fig. 12
figure 12

UV-Vis absorption spectra for a Ni x Fe3−x O4 and b Co x Fe3−x O4 nano-particles

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The band gap of the samples is evaluated from the Tauc relation[31]:

$$ (\alpha h\nu )^{n}=A(h\nu -E_{\mathrm{g}})^{n} $$
(8)

where E g is the optical band gap energy and h is the planks constant (6.62 × 10−34). The value of n for direct, indirect, allowed, and forbidden transitions is, 2, 1/2, and 3/2, respectively. The optical band gap energy of all the samples is estimated by extrapolating a straight line on x-axis which cuts the axis at some point; that point indicates the value of the optical band gap energy. The graph of E g for all the samples is plotted in Fig. 13a, b, respectively. It is revealed that when the concentration of nickel and cobalt increases, the optical band gap energy increases. This may be due to the decrease in particle size, as shown in Fig. 14. When the crystallite size reaches the nano-scale where every element is made up of only a finite number of atoms, the electron hole pairs become very close together that the columbic force is no longer neglected and gives the overall higher kinetic energy. Hence, the larger band gap means that a large energy is required to excite an electron from valance to conduction band [32–35]. Optical band gap may also be increased because when the particle size decreases, the number of atoms becomes finite, the energy levels or overlapping orbitals decrease, and the width of the band starts to narrow. This narrowing of the band results in an increase in the optical band gap. The values of the optical band gap energy of all the samples are tabulated in Table 6.

Fig. 13
figure 13

Determination of optical band gap for a Ni x Fe3−x O4 and b Co x Fe3−x O4

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Fig. 14
figure 14

Variation in band gap energy and crystallite size as a function of a nickel and b cobalt concentrations

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Table 6 The absorption wavelength, band gap energy, and crystallite size values for Ni x Fe3−x O4 and Co x Fe3−x O4 with x = 0, 0.05, 0.1, and 0.15 nano-particles
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4 Conclusion

Ni x Fe3−x O4 and Co x Fe3−x O4 nano-particles with x = 0, 0.05, 0.1, and 0.15 have been prepared by co-precipitation method. The structural characterization displays that all the samples are composed of highly crystalline single-phase inverse spinel structure. FTIR analysis confirms the single phase with the major band at 887 cm−1, which is due to the stretching vibrations of metal-oxide bond. SEM analysis revealed that the particles are spherical in shape. Thermal analysis shows that stability increases with the increasing Ni and Co concentrations in magnetite nano-particles. The magnetic measurement enlightens that the coercivity and anisotropy highly increase with cobalt doping in magnetite nano-particles as compared with nickel-doped magnetite nano-particles. This result has a great interest for magnetic fluid hyperthermia application. UV-visible analysis indicates the blue shift in the absorption edge of both nickel- and cobalt-doped magnetite nano-particles which also confirms the formation of nano-particles.