Influence of Yb3+on the structural, electrical and optical properties of sol-gel synthesized Ni-Zn nanoferrites

Polycrystalline Yb substituted NiZn nanoferrites with the compositions of Ni0.5Zn0.5YbxFe2-xO4 (x= 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) have been synthesized using sol gel auto combustion technique. Single phase cubic spinel structure has been confirmed by the X ray diffraction (XRD) patterns. Larger lattice constants of the compositions are found with increasing Yb3+ concentration while the average grain size (52 to 18 nm) has noticeable decrease as Yb3+ content is increased. The presence of all existing elements as well as the purity of the samples has also been confirmed from energy dispersive X ray spectroscopic (EDS) analysis. Frequency dependent dielectric constant, dielectric loss, dielectric relaxation time, AC and DC resistivity of the compositions have also been examined at room temperature. The DC resistivity value is found in the order of 10 to power 10 (omega-cm) which is at least four orders greater than the ferrites prepared by conventional method. This larger value of resistivity attributes due to very small grain size and successfully explained using the Verwey and deBoer hopping conduction model. The contribution of grain and grain boundary resistance has been elucidated using Cole Cole plot. The study of temperature dependent DC resistivity confirms the semiconducting nature of all titled compositions wherein bandgap (optical) increases from 2.73 eV to 3.25 eV with the increase of Yb content. The high value of resistivity is of notable achievement for the compositions that make them a potential candidate for implication in the high frequency applications where reduction of eddy current loss is highly required.


Introduction
Spinel ferrites have unique and versatile properties that are very attractive to the researchers.
The prime attention is put on the innovation of novel materials with new and low-cost 0. 20) have not been reported. Therefore, we are intended to uncover the effect of RE ions Yb 3+ substitution for the Fe 3+ ions in the Ni 0.5 Zn 0.5 Yb x Fe 2-x O 4 (x = 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) ferrites for the first time. The electrical, dielectric and optical along with physical properties in detail for the sol-gel auto combustion derived Yb-substituted Ni-Zn nanoferrites at room temperature have been presented in the following sections.

Synthesis route
Nanocrystalline Ni-Zn ferrite with the composition Ni 0.5 Zn 0.5 Yb x Fe 2-x O 4 (x= 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) was synthesized by sol-gel auto combustion technique. To prepare the samples, analytical grade nitrate salts were taken as raw materials. The precursor salts were weighted according to the stoichiometric ratio. Precursor salts were homogeneously dissolved in small amount of ethanol. Then all materials were stirred by a magnetic stirrer until they are dissolved homogeneously. The solution was then heated at 80°C in a magnetic heater until a viscous gel was formed. After the formation of gel, it was dried in a low temperature oven at temperature 250°C for 5 hrs.
Thereafter the dry ash was milled by an agate mortar and pestle. 5% polyvinyl alcohol solution was then mixed with the calcined powder as a binder and samples of desired shapes (pellet and ring) were prepared by applying 10 kN pressure using hydraulic press. Finally, the samples were sintered at 700°C with step of 5°C/min for 5 hrs in air and cooled naturally.

Structural properties
The XRD pattern of Yb-substituted Ni-Zn ferrites (NZYF)) with the chemical composition of  [30].
It is perceived from the Fig. 1(b) that the prominent peak (311) first shifts to the higher 2 value and afterward it backs to the lower 2 value. It reveals that the (311) interplaner spacing d initially decreases and then increases with increasing Yb 3+ contents in the composition. The lattice parameter and crystallite size of the compositions have been measured using the XRD   x = 0.20 where D is the average crystallite size, λ is the X-ray wavelength of the source (1.5406Å), β is the full width at half maximum (FWHM) and θ is the Bragg's angle [31,32]. The calculated crystallite sizes are presented in Table 1. The crystallite size decreases from 64 to 11nm with increasing concentration of Yb 3+ is shown in Fig. 2. The crystalline anisotropy induces that produces strain inside the cell volume during the substitution of Yb 3+ ions in place of Fe 3+ due to the difference of ionic radius between the Yb 3+ (0.868 Å) and Fe 3+ (0.67 Å). The sharp declination in the crystallite size is observed from 64 to 25 nm for x = 0 to 0.04 Yb 3+ contents thereafter the declination happen to slow to reach lowest size of 11 nm at x= 0.20 that makes sense from broadening of the intense peaks of (311) plane shown in Fig. 1(b).
It seems that the Yb 3+ ions decrease the degree of crystallinity and lesser the crystal size of the Ni-Zn ferrites. , where D is the average crystallite size and ρ b is the bulk density [33]. The SSA increases with rises the Yb 3+ ions content in the composition while the grain sizes decreases and changes are found to be from 39 to 331 m 2 /gm with grain sizes 64 to 11 nm at x= 0.00 to 0.20 contents in the composition, respectively. This is due to fact that the same volume contains more grain due to the smaller size consequently. Moreover, the grain size reduces almost 17% with increasing x contents and corresponding SSA upsurges 12% which makes sense relation between grain size and the SSA of the compositions.   1). Therefore the a exp declines at x= 0.04 and then increases consequently the R B has also been increased. ( + 0 ) + 1 4 ]. A fair disagreement between a theo and a exp has been observed ( Fig. 3a), however the average a exp value of the composition moderately agrees with the a theo . This can be understood from the following fact that in theoretical calculation, perfect unit cell having cations are in regular arrangement and well-distributed is considered while in the experimental case defects and thermal effects are surely associated therefore an anomaly could be observed.
The following equations [35] are used to calculate the bond lengths of tetrahedral sites (R A ), octahedral sites (R B ), tetrahedral edge length (R), shared and unshared octahedral edge length Rʹ and Rʹʹ, respectively and tabulated in Table 1: where δ= u-u ideal , δ is the inversion parameter that signifies departure from ideal oxygen parameter (u ideal = 0.375 Å) and a is the experimental lattice constant. It is seen from the Table   1 that the average ionic radius of r A is constant while the average size of r B increases with Yb concentration, since a larger ionic radius of Yb 3+ is substituted in place of lower size of Fe 3+ ions. The tetrahedral bond length (R A ) decreases whereas the octahedral bond length (R B ) remains same value at x= 0.04 and then increases with increasing the Yb 3+ concentration. The tetrahedral edge length (R) decreases however both the shared and unshared octahedral edge length increase with increasing concentration of Yb 3+ ions that are in good agreement with Ni substituted Mg-Zn ferrites system [35].
The X-ray density (theoretical density), bulk density and porosity are calculated by using the following equations, respectively:  Table 1. It reveals that the X-ray density (bulk density) increases (decreases) with increasing Yb contents in the composition. This increase is due to the dependency of molecular weight and lattice parameter [1]. The  x is inversely proportional to the a exp ; therefore increasing trend of  x is very usual. It appears that larger ionic radius Yb 3+ ions enter into the cell in the place of smaller radius Fe 3+ ions, which obviously extend the volume of the cell, resulting  b decreases ( b  1/V) with increasing Yb contents.

Microstructure study
The electrical and magnetic properties are strongly inspired by the microstructure of ferrites.
The morphological study of the composition Ni 0.5 Zn 0.5 Yb x Fe 2-x O 4 (x = 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) has been performed using the FESEM and shown in Fig. 4. The FESEM images show the homogeneous, spherical and slightly agglomerated grain size [36].
The average grain size of the compositions has been estimated using ImageJ software shown in to complete grain crystallization and growth, therefore it is evident that the Yb 3+ substituted ferrites are more thermally stable than pure Ni-Zn ferrites.
The energy dispersive X-ray spectroscopic (EDS) analysis has been elucidated to endorse the absence of unwanted elements in the studied compositions. The EDS spectra are depicted in      size is higher than that of the D FESEM that can be explained considering relation between crystallite, grains and particles size in a materials. Crystallite is a single crystal of powder form while grain is single crystal in a bulk/thin film form and a particle is thought as agglomerate which consists of many grains with clear grain boundaries separated each other (inset of Fig. 6b).
Therefore, the D xrd and D FESEM is almost same in a size that is represented inset of Fig. 6a for the NZYF with different Yb contents. Fig. 6b depicts the number of grains contains in a particle (particle size/ D FESEM ) with variation of Yb contents for the NZYF. It is clear that number of grains in a particle increases with increasing Yb content which is consistent with previous discussion (beginning of section 3.2).

4. 1 DC Resistivity
The temperature dependent resistivity of the samples sintered at 700 C has been carried out by two-probe method in the temperature range from 30 o C to 400 o C, shown in Fig. 8 resistivity may be decreased. By using the Verwey and deBoer hopping conduction model, the variation of resistivity can be explained [41]. The polaron hopping between Fe 3+ and Fe 2+ occurs at the B-site accordingly the conduction takes place. The electron hopping between B-and Asites are very negligible as compared to B-site hopping since the distance between two ions at Bsites is smaller than the distance at different sites (A and B) [42]. The charge carriers hopping of A-sites are not negligible due to the availability of Fe 3+ at the tetrahedral site and throughout the process Fe 2+ ion produced will take the octahedral sites [43].

4. 2 AC Conductivity
Room temperature frequency dependent AC conductivity of Ni 0.5 Zn 0.5 Yb x Fe 2-x O 4 (x= 0.00, 0.04, 0.08, 0.12, 0.16 and 0.20) compositions at a fixed frequency 100 Hz has been illustrated in Fig. 9(a).The ac conductivity demonstrations flat at low frequency region, while it illustrates dispersion at high frequency region. Usually, the total conductivity can be articulated by the band and hopping parts [44], where the first term is DC conductivity or frequency independent while the second term is frequency dependent and associated with the dielectric relaxation, A is a constant, ω is the angular frequency and the frequency exponent n is the dimensionless quantity. Fe 2+ ions hence improves the hopping conduction. The availability of Fe 3+ and Fe 2+ ions at octahedral sites is responsible for conduction [45] as well as dielectric polarization. As the substituent ion Yb 3+ increases, the Fe 3+ decreases at B-sites which reduce the electron exchange between Fe 3+ and Fe 2+ . The plot of log σ ac as a function of log ω 2 is illustrated in Fig. 9 (b). The slope of the curves yields the value of n that provides information regarding the conduction mechanism of the compositions. The value of n indicates i) the conductivity is DC conductivity when n is zero (0), ii) hopping of charge carriers when n is in between 0 and 1 and iii) indicates the hopping between neighboring sites when it is  1,. The calculated values of n are shown in  Fig. 9(b) and found to be less than 1 that recognized the conduction mechanism in our compositions is from the hopping of charge carries at the octahedral sites.

Dielectric constant
The dielectric constant provides the information regarding the relative speed of the electromagnetic signal travels in the material. Dielectric properties are influenced by several factors, such as synthesis method, sintering time and temperature, particle size, type and concentration of substituent atom, cation distribution among different sites, etc. When the electromagnetic signal enters into a dielectric material, the microwave speed decreases approximately equal to the √ε′ [46]. The incident wave absorption of the microwave absorber materials can be enhanced and modified by using the complex permittivity. The dielectric constant i.e., real parts of complex permittivity (ε′) represent the storage of electric energy whether imaginary part (ε″) signifies the loss capability. At room temperature, the frequency dependent real part of complex permittivity of the compositions is shown in Fig. 10(a). The dielectric constant decreases with frequency which is the normal behavior of ferrites that is widely studied by many researchers [1,47]. This dielectric dispersion can be explained based on There is a correlation between AC electrical resistivity and the dielectric constant. Fig. 10(b) demonstrates the variation of √ and ε′ which depicts that they are almost inversely proportional to each other. To relate these two parameters the product of ԑʹ and √ (at 100 Hz) has been calculated and presented in Table 4. Similar trends have also been reported where the conduction mechanism is controlled by the dielectric polarization [50,51].

4. 4 Dielectric loss
The imaginary part of dielectric dispersion () of the compositions has been illustrated in Fig.   11(a). It is clear that the value of  reduces fast at low frequency region and becomes slower at high frequency region showing frequency independent behavior similar trends as real part of dielectric constant,  (Fig. 10a). The dielectric loss (tan) is the loss of electromagnetic radiation in the form of heat due to the collision of atoms in the material during the polarization. The dielectric loss has been determined by the following relation tan = / and represented in Fig.   11 (b). The dielectric loss tangent is the angle of dielectric loss and is very important for total core loss. It is clear that the dielectric loss reveals regular Debye relaxation peaks for all compositions. The peak position of the loss tangent shifted towards higher frequency with the increase in Yb 3+ contents which indicates the increases of jumping probability. The origin of these relaxation peaks can be explicated by the Rezlescu model [52].It tells that the influence of n-type (p-type) carriers in the dielectric loss decline slowly (quickly) as the angular frequency upsurges. The influence of the carriers yields a relaxation peak where the frequency of the external applied field exactly matches with the localized electric charge carrier's jumping frequency [53]. The electron and hole exchange between Fe 3+ , Fe 2+ and Ni 3+ and Ni 2+ , respectively contributes to the electric conduction in the compositions. After a certain frequency (15 MHz), the dielectric parameters do not obey the external applied electric field and the polarization cannot match with the field consequently, the dielectric parameters become nearly constant at higher frequency. Since the value of the dielectric parameters is low, these materials are suggested for high frequency application such as microwave devices.

Complex electric modulus spectra
Complex electric modulus conveys the information regarding the electrical response of the materials that whether polycrystalline samples are homogeneous or inhomogeneous in nature.
Frequency dependent real (M) and imaginary (M) part of complex electric modulus at room temperature is illustrated in Fig. 12. The complex electric modulus can be expressed by M  = M + iM = /( 2 +  2 ) + i/( 2 +  2 ) [54]. It is seen from the Fig. 12(a), at lower frequency region, the value of M shows small value indicating the comfort of polaron hopping. The value of M reveals a dispersive maximum in the higher frequency region (not show full spectra due to frequency limitation of our machine).
In Fig. 12(b), the imaginary part of electric modulus (M) demonstrations that the curves shifts at higher frequency region considerably with significant broadening with increasing Yb contents as well. The peaks shift and broadening at higher frequency are related to the correlation between ion charges and the spread of relaxation time, respectively. The relaxation time (τ M ) has been calculated from the peak position of frequency dependent M″ curve (Fig. 12b) and presented in Table 3. The relaxation time is connected with the jumping probability per unit time P by the relation, τ = 1/P [55]. In the lower region (f  f m ) of maximum peak frequency, the charge carriers are mobile and move over long distances accompanying the hopping conduction process.
However, in the higher region (f  f m ), the charge carriers are restricted to potential wells and are movable over short distances accompanying the relaxation polarization process. So the appearance of maximum peak value in the electric modulus indicates the conductivity relaxation (transition from long range to short range mobility with rise of frequency) [54]. be persuaded by the grain effect which arises from smaller capacitance dominating the electric modulus. Two semicircles in the plot suggest significant influences of grain and grain boundary contribution in the studied compositions. It is bit difficult to observe two complete semicircles due to huge resistance alteration between grain and grain boundary since the electric modulus represents the smallest capacitance while the impedance plot demonstrates the largest resistance.

Diffuse reflectance spectroscopy (DRS)
The optical band gap of all the compositions of Ni 0.5 Zn 0.5 Yb x Fe 2-x O 4 has been measured from the Tauc's plot using UV-Vis diffuse reflectance spectroscopy shown in Fig. 14. The Tauc's relation is given as [56], is the Kubelka-Munk function, R ∞ is the ratio of diffuse reflectance between the sample and the reference material, A is a constant, hν is the incident photon energy. A graph has been plotted of [F(R ∞ )hν] 2 against hν (Fig. 14). From the extrapolating of the linear part of the plot to the energy axis (intercepting value) provides the value of the energy band gap (E g ). The value of E g is found to be 2.73 eV to 3.25 eV. Our calculated parent composition (Ni 0.5 Zn 0.5 Fe 2 O 4 ) E g value (2.73 eV) is in good agreement with the reported value of 2.56 eV [57]. It shows that the E g value increases with the increase in the Yb content. It is suggested that the value of E g can be changed by different factors such as crystallite size, structural parameter, and presence of impurities. The increase of E g in this case may be ascribed to the smaller crystallite size with increasing Yb contents in the composition.
The particle size, average crystallite and grain size have been estimated in the range of 183 to 343 nm , 64 to 11 nm and 52 to 18 nm for different Yb 3+ content by the dynamic light scattering (DLS) technique, XRD spectra and FESEM images, respectively and correlation between them is successfully explained. Two expected vibration bands are found to be at 595 cm -1 corresponds  The estimated relaxation time is found to be in the range of 4 to 0.5 micro seconds. Energy band gap escalates (2.73 eV to 3.25 eV) with rising substituted Yb contents that is attributed from the UV-Vis spectroscopy. It is remarkable that the estimated high dc resistivity value is found to be in the range of 2.2  10 9 -cm to 2.6  10 10 -cm for different Yb 3+ substitution (x= 0.0 to x= 0.20 in step of 0.04) is the silent feature of these ferrites, thereby lowering dielectric loss makes them suitable candidate for implication in high frequency applications such as microwave devices.