Nanotechnology is considered one of the modern sciences that look for designing the smallest apparatus and it concentrates basically on substituting the particle structures or the atomic parts of the material towards realizing new structures and with the economic cost which should not exceed the raw material   . The Nanotechnology is also regarded as the basic future sciences that will gain an increasing demand in the field of industry, medicine and transferring and transport sector and also in the field of aviation, space and telecommunication   . The biological, chemical and material properties in the Nano-size, differ from the basic shapes and properties of an atom or material itself    . Ferrites are chemical compounds with the formula of AB2O4, where A and B represent various metal cations, usually including iron   . Ferrites are the well-known ferromagnetic materials that consist mainly of ferromagnetic oxides and therefore, are electrically insulating. Ferrites are widely used in high-frequency applications/because an alternating current (AC) field does not induce undesirable eddy currents in an insulating material   . Properties of ferrites are dependent upon several factors such as composition, a method of preparation, substitution and doping of different captions, sintering temperature and time, sintered density, grain size and their distribution. Apart from the fact that they have very complex structures, their physical properties themselves are dependent on a number of valence electrons of the divalent or trivalent metal ions of tetrahedral (A) and octahedral (B) sites. Several attempts have been made to enhance the qualities of ferrites by employing various methods. The most general method is the incorporation of same suitable nonmagnetic/diamagnetic impurities at the A or B sites    . Many of synthesis methods were considered in previous studies for produce the Nano-particles with size in the range of 2 - 100 nm. Among these methods are co-precipitation, hydrothermal and sol-gel methods    .
In this work, Nano-ferrite samples of Zn0.5CuxMg0.5-xFe2O4 were synthesised using co-precipitation method. The structural and optical properties were studied using X-ray diffraction (XRD), Fourier Transform Infrared spectroscopy (FTIR) and UV-Visible spectroscopy. The main purpose is to study the effect of copper substituted magnesium in the Zn0.5CuxMg0.5-xFe2O4 Nano-ferrites.
2. Material and Method
The samples Zn0.5CuxMg0.5-xFe2O4 ferrites nano-crystalline powder with compositions (x = 0.0,0.1,0.2,0.3,0.4) were prepared using high purity (Sigma,98%) of zinc nitrate [Zn(NO3)2∙6H2O(96%)], magnesium nitrate [Mg(NO3)2(99%)] copper nitrate [Cu(NO3)2∙3H2O(99%)] Ferric nitrate [Fe(NO3)2∙9H2O(98%)] and Sodium hydroxide 96% were used as primary components. A Specified amount of Oleic acid was added to the solution as surfactant and coating material. The solution of Fe(NO3)3∙9H2O, 0.4 M (25 ml), Mg(NO3)2∙6H2O, 0.2 M (25 ml), Cu(NO3)2∙3H2O, and Zn(NO3)2∙6H2O were first mixed and then slowly added 3 molarities of NaOH. The PH of the solution was constantly monitored as the NaOH solution was added. The reactant was constantly stirred using magnetic stirrer unit a pH level of (11-12)  . The liquid precipitate was then brought to a reaction temperature of 80˚C and stirred for one hour. At this stage, the product contains some associated water which was removed by heating at 450˚C for 6 hours in temperature controlled muffle furnace Vulcan A-550 at a heating rate 10˚C/min. The final product obtained materials were ground into powder and then made ready for characterization using various techniques.
X-ray diffraction (XRD) data collected by Shimadzu 6000 X-ray diffract meter with Cu-ka radiation of a wavelength of l = 1.5406 Å. At room temperature, with a nickel filter operating at 40 KV, 40 mA the data collected for the 2θ in 0.02-step size and five-second count time in 20˚ - 80˚ range. The MDI jade 0.5 programs used for the XRD date analysis. The crystallite size (D) calculated by Scherer equation  .
At room temperature, the transmittance mode investigated for the sample by a (Satellite FTIR 5000 of the wavelength range of 400 to 4000 cm-1) where the important bands and peaks of spinel structure can be assigned. A Fourier transform infrared spectroscopy collected by KBr pellet method, the material mixed with KBr of ratio 1:100 for FTIR measurement between 400 and 2000 cm-1   .
The UV-Visible absorption was investigated by UV Mini 1240 manufactured by Shimadzu company-Japan. Hydrochloric acid HCl was used as a reference for 100% absorbance  .
3. Results and Discussion
3.1. X-Ray Result
Symmetry is important in the study of structural and optical properties of the nanoparticle ferrites. Figure 1 shows crystalline phases determination of the crystal structure, the lattice parameters and the space group. The spinal of single phase Zn0.5Cu0.4Mg0.1Fe2O4 nano-ferrite, with composition (x = 0.4) after analysing the XRD patterns are well indexed using MDI jade 5 and full proof. The crystal structure is found to be cubic with space group Fd3m.The fined peaks are indexed as the following (220), (311), (400), and (511). The crystallite size, the lattice constant, volume, space group and density are listed in table 1, and the crystal size is calculated using Scherer’s equation   .
where D is the average crystallite size, q is the angle, l is the incident of X-ray wavelength, while b is the (FWHM) of the highest intensity peak (311). The results of X-ray diffraction are listed in table 1.
Figure 2 shows the intensity and 2q for samples with a different concentration of copper crystalline size are found to the scattered in the range 20.94 nm up to 28.33 nm for different compositions. As the concentration of copper increases from x = 0.1 to 0.4, the lattice constant, a, increased from 8.375 Å to 8.397 Å. The increasing in lattice constant is attributed due to the larger ionic radius of
Figure 1. XRD patterns of Zn0.5Cu0.4 Mg0.1Fe2O4.
Figure 2. Comparison of (XRD) pattern for Cu-doped ZnMgFe2O4 spinel samples.
Table 1. Crystallite size (D), Lattice constant (a), volume (v) space group and density of Zn0.5CuxMg0.5-xFe2O4 nano-ferrites: where (X = 0.0, 0.1, 0.2, 0.3, 0.4).
Mg2+ (0.86 Å) compared with Cu2+ (0.73 Å)  . The results showed that the lattice parameter, a, was increased with copper concentration and attributed to the smaller ionic radius of magnesium nanoferrite by co-precipitation. Yue et al.  , worked on the effect of copper on electromagnetic properties of (Mg0.5-xCux Zn0.5)O(Fe2O3)0.98 ferrite and found that the density, grain size, permeability, curie temperature increased. Rezlescu et al.  also reported that the sintered density and resistivity of Mg0.5-xCuxZn0.5 + 0.5MgOFe2O4 ferrite increased up to X = 0.3 whereas, permeability increased up to X = 0.4  . However, in this study; the effect of copper substituted magnesium Nano-ferrites by co-precipitation technique showed the lattice parameter increases from x = 0.1 to 0.4 when the Cu2+concentration was increased.
From table 1 we can observe that the density and volume increase with increasing Cu content. The increase in density and volume may be due to the ionic of constituent ions. After analysing the XRD data, the structural studies showed that all the samples prepared through the co-precipitation method are single phase of a face-centred Cubic (FCC) spinel and the symmetry structures with space group SG: Fd-3m.
Figure 3 shows the relation between lattice parameters and concentration of copper. It can be observed that the lattice constants are increased as the concentration of copper further increase.
3.2. FTIR Analysis
Functional groups of the synthesize Zn0.5CuxMg0.5-xFe2O4are investigated by FTIR spectroscopy in the range of 400 to 4000 cm−1. Figure 4 shows the spectra of all the ferrites has been used to locate the band positions which is listed in Table 2. In the present study the absorption bands v1, v2, v3, v4 and v5 are found to be around 580, 1112, 1382, 1632 and 2920 cm-1.
Figure 3. The relation between lattice parameters and concentration.
Figure 4. FTIR spectra of Zn0.5CuxMg0.5-xFe2o4 Nano ferrites of different concentration of Cu.
Figure 5. Diffused UV-visible spectra of Zn0.5CuxMg0.5-XFe2O4 with varying Cu2+ dopant as (1) X = 0.0, (2) X = 0.1, (3) X = 0.2, (4) X = 0.3 and (5) X = 0.4 showing different band edge absorbance.
Table 2. Wave numbers and band gap energy of the Zn0.5CuxMg0.5-xFe2O4 nano-ferrites samples.
(a) (b) (c) (d)
Figure 6. Plot of (ahn)2 versus hn showing the band gap of Zn0.5Cux Mg0.5-x Fe2O4 with variable Cu2+doping as (a) X = 0.0; (b) X = 0.1; (c) X = 0.2; (d) X = 0.3 and (e) X = 0.4.
Respectively for the all samples; the single-phases spinel structure having two lattices tetrahedral (A) site and octahedral (B) of site   . The band at 2921-2923 cm−1 is attributed to the bending vibrations of methylene (-CH2-). The peaks at 1630 - 1633 cm−1 are due to the plane bending vibration of the (C-H) band bending absorption of COO- Carboxyl group   . The band at 1382 - 1387 cm−1 and is attributed to the C=O stretching vibration of the carboxyl group. In range 1112 - 1117 cm−1, the band is observing and is related to the stretching vibration due to nitrate group   . The frequency band near 576-583 cm−1 and 406 - 428 cm−1 assigned to the tetrahedral and octahedral metal oxygen (M-O) bands in the lattices of the synthesized nanocrystals  ,  . The FTIR frequency bands for various Cu and Mg contents are listed in Table 2.
3.3. UV-Visible Analysis
The diffused UV-visible absorption spectrum is recorded in order to obtain the optical band gap values of Zn0.5CuxMg0.5-xFe2O4 as shown in figure 5. The Maximum absorption displayed for sample 2 Zn0.5Cu0.2Mg0.3Fe2O4 was occurred at 245 Cm−1. However, with the doping of Cu2+ ion, the optical absorption properties of Nano-ferrites follow the band edge of equation (2) (table 2). In addition to that, the band gap energy was calculated for samples by Tauc plot  that shown in figures 6(a)-(d) according to equation (2)   .
where a, h,n, Eg and A are the absorption coefficient, plank constant, light frequency, band gap, and proportionality constant, respectively. The band gap values were found to be 4.67, 4.63, 4.07, 4.29 and 4.04 eV for X = 0.0, 0.1, 0.2, 0.3, and 0.4, respectively. This significant change in the band energies is due to the doping effects of Cu2+ ions crystal lattice  .
Nano-ferrites samples which prepared by co-precipitation were investigated by XRD, FTIR and UV-vis. The lattice parameter was found to increase with copper concentration. Similarly, the size of crystals was found to increase from 15.97 nm to 28.33 nm. The FTIR bending vibration band of the samples confirmed the formation of spinal ferrite structure. The band gap energy calculated using Tauc plot and the absorption edge cut-off indicated that the samples possess insulator behavior.