Particles in the size range of 1 - 100 nm possess novel physical and chemical properties as a result of quantum confinement and surface effects that may find many important applications    . Ferrites nanoparticles have the AB2O4 formula, where A and B are as transition metals cations, usually including iron   . Ferrites have known ferromagnetic materials consisting of ferromagnetic oxides consequently, they are insulating materials. Ferrites nanoparticles are used widely in high-frequency applications  . however the Nanoferrite materials are found to use in different physical, chemical and medicine fields, such as semiconductor CoFe2O4 nanoparticles  , ZnFe2O4, NiFe2O4 in solar cell  , magnetic resonance MnFe2O4  , microwave CdxCo1-xFe2O4 (x = 0.0, 0.2, 0.35, 0.5)  and biomedical ZnFe2O4  . In the engineering material science field, ferrite nanoparticles are a unique substance from atoms, and molecules, to build ceramics, or devices  . Nano-Ferrites character makes it an ideal candidate for a technical field such as catalysis, sensors and pigments  . All ferrite nanoparticles properties are dependent on the cations nature, charges and their distribution through the tetrahedral (A) and octahedral (B) sites  . Different preparation methods have been followed to accomplish nanoferrite particles such as solid-state reaction method   , hydrothermal method  , sol-gel method  , co-precipitation route  , and Chemical combustion route  . The chemical co-precipitation route could be the most synthesized method for Mg, Co and Zn Nano-ferrite. It is not very complicated and controlled over crystal structure and extra characters of Substance  . A lot of scholars used the co-precipitation route to synthesize nanoferrite materials because the co-precipitation way is a very simple, quick and low-cost method for synthesis, whereas, the nanoparticles that are consequential from co-precipitation are very harmonious   . Among those, Kumar et al.  used a co-precipitation route to synthesize CoFe2-xGdO4. In this work, Zn0.5Li2xMg0.5-xFe2O4 nanoferrite where (x = 0.0, 0.1, 0.2, 0.3 and 0.4) will be synthesized using co-precipitation methods. X-ray diffraction (XRD) and Fourier Transform Infrared Spectroscopy (FTIR) are used to investigate the structure of B-site substituted magnesium Nano ferrites and to determine the crystal structure of the samples. Ultraviolet-visible spectrometer (UV) is used to investigate the optical properties of crystalline nanoparticles.
2. Material and Method
Zn0.5Mg0.5-xLi2xFe2O4 nanoparticles samples (x = 0.00, 0.10, 0.20, 0.30 and 0.40) were synthesized by use the co-precipitation route. The raw stoichiometric materials are FeCl3, MgCl2∙6H2O, LiCl∙H2O, ZnCl2 with high pure, NaOH was used to found the required solutions with required molarities. Firstly, the solution of MgCl2∙6H2O 0.2 M (25 ml), ZnCl2 and FeCl3 0.4 M (25 ml) mixed, next, slowly added of NaOH solution with stirring to obtain a mixture of pH 11 - 12. The colloid solution kept in a water bath at 80˚C for 1.5 hrs to the removal of NaCl2 and H2O from the powder. The produced powder washed by deionized water until the filtrate had a pH 7. Then the samples were dried and grinned to absolute powder and annealed to 450˚C for 6 hrs in temperature-controlled muffle furnace Vulcan A-550 at a heating rate 10˚C/min. The XRD analysis was carried out to confirm the purity of the synthesized materials using shimadzu 6000. X-ray diffract meter with Cu-kα radiation of a wavelength λ = 1.5406Å source. FTIR measurements were performed using (Mattson, model 960 m 0016) spectra, while the absorption of a solution with different concentrations was calculated using UV min 1240 spectrometer shimadzu.
3. Results and Discussion
3.1. XRD Result
The crystal structure of samples studied using a Philips PW1700 X-ray diffract meter (operated at 40 kV and current of 30 mA) and the XRD data of all samples were collected between 10O and 80O with 0.06 C/s speed of using Cu Kα radiation with λ = 1.5418 Å. The representative XRD charts of all five Zn0.5Li2xMg0.5-xFe2O4 samples as shown in Figure 1. The XRD data was displayed in Figure 1 for all powders of Zn0.5Li2xMg0.5-xFe2O4 samples. All crystallites with cubic crystal structure with the Fd-3 m space group    . Table 1 showed the XRD parameters of Zn0.5Li2xMg0.5-xFe2O4 nanopowder, also it described the relation between the rated molar of lithium concentration and structure parameters of samples, that noticed the increase of lattice parameter(a) from 8.379 to 8.408 Å of a sample by increasing the molar of lithium cations, whereas Li1+ ionic radius is less than Mg2+ cations radii. The crystallite size of samples was calculated by Debye-Scherrer equation   .
That result showed that the samples were crystallite in the nanoscale and that decreased from 116 to 96 nm for series with substitution increasing of Mg2+ with Li1+ cations.
3.2. FTIR Result
The infrared spectra of synthesized nanoferrite powders were recorded by Mattson Fourier Transform Infrared Spectrophotometer in the range of 400 to 4000 which shown in Figure 2. In the present study, the absorption bands are found to be around 420, 580, 1111, 1380 and 1635 cm−1, respectively for all the compositions. The transmittance bands within these specific limits reveal the formation of a single-phase spinel structure having two sub-lattices tetrahedral (A) site and octahedral (B) site. The 420 cm−1 band due to the vibrational band of a metal ion at a tetrahedral site with oxygen ions  . The band around 582 is caused by the metal-oxygen vibration in the tetrahedral sides. This difference in the spectral positions is due to the different values of metal ion-distances for octahedral and tetrahedral sites. The band around 1111 is due to C-C stretch and C-C-H bending. The 1375 band is associated with the O-H bending vibration. The band around 1639 is due to C=C stretching. The 2621 band is due to the stretching mode of (H-O-H) vibration mode of free or absorbed water which implies that the hydroxyl groups are retained in ferrites   .
Figure 1. XRD spectrum of Zn0.5Li2xMg0.5-xFe2O4 series.
Figure 2. The Fourier Transform Infrared Spectrophotometer of Zn0.5Li2xMg0.5-xFe2O4 samples.
Table 1. The crystal structure parameters of Zn0.5Li2xMg0.5-xFe2O4 samples.
3.3. UV. Visible Result
The absorption spectra of was showed in Figure 3 high absorption of all samples noticed at 340 nm. The Tauc plot  was used to calculate the bandgap energy Eg of samples. The absorption coefficient α near the band edge in many Nano ferrites shows an exponential upon photon energy usually obeying the relation  .
Figure 3. The relation between absorbance and wavelengths of Zn0.5Li2xMg0.5-xFe2O4 samples.
Figure 4. The optical energy bandgab of Zn0.5Li2xMg0.5-xFe2O4 samples.
(α) coefficient of absorption, (A) edge width parameter, Eg is the energy bandgap, (n) is a constant related to the transition degree and ( ) is incident photon energy. Figure 4 showed the Tauc plot method for samples. The energy band gap is founded in the range 3.28 to 3.12 eV for samples with different concentration (x = 0.0, 0.1, 0.2, 0.3 and 0.4), respectively, it was shoed decreased with substations ratio increasing that may be related to change in the electronic transition levels and occurrence new center transition levels between the conduction and valence bands of molecular.
Nanocrystalline, Zn0.5Mg0.5-xLi2xFe2O4 Nano ferrites (x = 0.00, 0.10, 0.20, 0.30 and 0.40) samples are successfully prepared by sol-gel approach. The XRD pattern showed a cubic spinel structure for each sample. The lattice parameter is found an increase from 8.379 to 8.408 Å with Li1+ concentration increasing. Also, the crystallite size (D) decreased from 116 to 96 nm with substitution ratio increasing. A Lattice parameter increased with Li1+ concentration increasing as a result of the larger ionic radius of the Li1+ ion. The FTIR spectrum of the synthesized samples proved the cubic spinel formation. UV-visible spectroscopy showed that the bandgap energy of the samples computed to be 3.28, 3.24, 3.19, 3.15 and 3.12 eV, for Li1+ concentration increased for the samples, respectively. This study was limited to the preparation and study of the composition and photometric properties. It is also recommended to study the rest of the physical and chemical properties, especially magnetic properties in order to classify these materials and determine their applications.