Influence of preparation method on the structural, linear, and nonlinear optical properties of TiN nanoparticles

In this paper, titanium nitride nanoparticles were prepared in three methods; in the first method, titanium nitride nanoparticles were prepared by the ball milling method; in the second and third methods, the nanoparticles were synthesized by the sol–gel and the co-precipitation methods. The samples were characterized by X-ray diffraction (XRD), energy dispersive spectroscopy (EDS), UV–Vis and Fourier transform infrared spectroscopies, and scanning electron microscopy (SEM), for the study of structural, chemical composition, and linear optical properties, respectively. Moreover, using scanning electron microscopy (SEM), the surface morphology of the samples was investigated. The XRD results showed the effect of calcination in ammonia atmosphere at 1000 °C, obtaining the pure TiN structure. However, because of oxidation in the ambient atmosphere, the titanium oxide phase was created, which was found by EDS spectroscopy and led to the creation of TiN1-xOx\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text {TiN}}_{1-x}{\text {{O}}}_{x}$$\end{document} alloy with two bandgap energy. The nonlinear optical properties of TiN nanoparticles were studied via the Z-scan technique. The nonlinear optical behavior was found as a function of input pump power and concentration of the TiN nanoparticles. Moreover, the nonlinear optical behavior of the TiN nanoparticles shifts from inverse saturation absorption to saturation absorption with the increase in intensity. Overall, the results showed that the TiN nanoparticles give new potentials in nonlinear optical applications.


Introduction
Light control by changing the optical functions leading to the control and manipulation of the lightmatter interactions plays an important and key role in the design and development of optical devices [1][2][3][4]. In fact, with this achievement, a change of the optical parameters is possible, which is an interesting fundamental scientific tool that leads to many advances in technologies related to optics and lasers [5][6][7][8]. Due to the great interest of researchers in this area, the research in the nonlinear optics field has grown significantly [1][2][3][4][9][10][11]. One way to achieve this goal is to make materials with different synthesis methods [12][13][14]. It is also possible to prepare the material in different concentrations and study its nonlinear behavior as a function of concentrations [15,16]. Therefore, the preparation of such materials will improve the optical properties. These materials can replace common metals in optical applications. Nanoscience is becoming increasingly important as a pioneering technology in the production of such materials. These materials have been considered by many researchers due to their use for dual optical and mechanical applications. Among a wide range of these materials, metal nitrides are known as intermetallic materials due to their electronic structure similarity to metals. Titanium nitride (TiN) is an example of such a material [17][18][19][20][21]. Several outstanding features such as high hardness properties (2000 kg / mm 2 ), corrosion resistance and high melting point (2930°C), good compatibility with the body, different production methods, and low manufacturing costs make it a suitable alternative to commonly used metals (gold and silver) in optical applications. Proper electrical conductivity has made it a special electrical ceramic for self-heating plants and a conductor for electronic applications. The properties of titanium nitride generally depend on the stoichiometry (titanium to nitrogen molar ratio), impurities (such as oxygen and chlorine), and the structure that can be controlled by changing the synthesis method and process parameters [22][23][24][25][26]. Various methods have been reported to synthesize titanium nitride in bulk form or thin films using the solid-state method [27][28][29][30][31][32][33][34][35][36][37]. These methods included chemical vapor deposition (CVD) [28] and physical vapor deposition (PVD) [27,29], pulsed laser deposition (PLD) [30], sputtering [27], and chemical methods such as sol-gel [33], and evacuation of electric arc. Most of these methods are performed at high temperatures and high pressures and often require a lot of equipment. Titanium nitride is an intermetallic material with a dark-blue color spectrum. It has different phases: the main phase of TiN is a face-centered cubic structure (FCC), with a lattice parameter of 4.24 o A.
In addition to mechanical and chemical properties, the optical properties of this compound are so important. One of the optical applications of TiN is its utilization in anti-reflective coatings and optical filters [25]. In medical science, it is used to increase quality and characteristics such as lightness, high strength, less abrasion, and more trenchancy of medical instruments. TiN is also used in pigmented solar cells for increasing light absorption and solar cell efficiency [38][39][40][41]. Experimental results have shown that performance of TiN is more efficient than gold at high temperatures and light intensities. Therefore, the use of TiN can be of great interest in nonlinear optics applications [42][43][44][45]. Assistance in photonic development, spectroscopy, fiber optic lines, optical switches, etc., requires knowing the nonlinear optical behavior of materials. Many of the nonlinear optics phenomena result from nonlinear refractive index and nonlinear absorption coefficient. The research community has been looking for nonlinear materials to develop and manufacture lightcontrollable materials. There are many methods for measuring optical parameters accurately. One of the best ways for simultaneous the nonlinear refractive index and the nonlinear absorption coefficient is the Z-scan method [46][47][48][49].
In this paper, titanium nitride was synthesized by different methods to achieve the goal of controlling the interaction of light and matter. Preparation of TiN nanoparticles was performed using simple methods at low temperature and atmospheric pressure. Then, the nonlinear optics behavior of TiN was studied as a function of its concentration in solution and pump laser intensities. Then, from each sample, different concentrations were prepared, and the nonlinear optics behavior of TiN was studied.

Materials and methods
TiN nanoparticles were also prepared by both physical and chemical methods. The ball milling method was used as a physical process, and two chemical processes were used as co-precipitation and sol-gel methods for comparing the results. TiN powder (99.9% Merck) with a particle size of up to 300 lm was used as a reference sample. Titanium isopropoxide (TTIP) with purity down to 97%, hydrazine monohydrate 98%, acetonitrile anhydrous, 99.8%, ethanol 99.8%, and ethylene glycol anhydrous 99.8% were purchased from Sigma-Aldrich and used as a precursor for chemical synthesis methods. All used equipment was washed with ethanol and then with acetone and dried at 120°C. The study of the structure, linear optical properties, and morphology of the samples prepared by physical and chemical methods were performed by X-ray diffraction (XRD), UV-Vis spectroscopy, and scanning electron microscopy (SEM), respectively. Elemental analysis was performed by energy dispersive spectroscopy (EDS) integrated into the SEM system. The samples' chemical bonds and nonlinear optical properties were also investigated using Fourier transform infrared spectroscopy and Z-scan technique, respectively.

Ball mill process
Ball milling was used to grind and pulverize the Merck TiN grains. 10 g of TiN grains were milled for 30 min at 350 and 500 rpm rotation rate of the steel balls in a planetary mill. Figure 1 shows the powder before and after the ball mill process.

Co-precipitation method
Firstly, for preparing titanium nitride by co-precipitation method, needed equipments were washed with deionized water and acetone, thoroughly, and then dried at 120°C. The acetonitrile was added to TTIP as the main precursor solution during 20 min of stirring at 80°C to reach the concentration of 0.339 M. Then hydrazine was added to the solution drop-wise to change its color to creamy (light brown). The solution was refluxed for 12 h in an oil bath at a uniform temperature of 80°C. Finally, using a vacuum desiccator, the solution was dried at 120°C for 15 h and then at room temperature for 5 h. The resulting brown powder was exposed to ammonia gas at 1000°C and 500 SCCM gas flow for 5 h, to obtain and finally, dark brown titanium nitride nanoparticles were obtained. Figure 2 shows the steps of TiN synthesis by the co-precipitation method.

Sol-gel method
For the synthesis of TiN by sol-gel method, TTIP was immersed in nitrogen gas for 10 min; after 20 min stirring at 80°C, ethanol was added to the solution slowly, and ethylene glycol was added drop-wise as a complexing agent. The sol was obtained after 9 h of reflux in an oil bath at 80°C; then the gel was obtained after drying at 120°C for 15 h. TiN nanoparticles were obtained after exposing the powder of an ammonia atmosphere for 5 h at 500 SCCM. Figure 3 shows the steps of TiN synthesis by the co-precipitation method.

Nonlinear optical properties
The nonlinear optical properties, the nonlinear refractive index, n 2 , and the nonlinear absorption coefficient, b, of the samples were investigated experimentally by the Z-scan technique [46][47][48][49]. The Z-scan setup is shown in Fig. 4.
The second harmonic (532 nm) of the Nd-Yag continuous wave (C.W.) laser beam with Gaussian intensity distribution was performed as the light source. The beam power was 150 mW with a beam waist of 6 lm. The intensity of the laser beam was controlled by the neutral density filters. The laser beam converged by a lens with f = 15 cm. The sample moves along the axis of the light beam, near the focal point. Two intensity detectors (Thorlabs, model PM100) are used to investigating the nonlinear refractive index and nonlinear absorption coefficient. The first intensity detector was used to measure the nonlinear refractive index, n 2 , and the second intensity detector was used to measure the nonlinear absorption coefficient, b. In this experiment, first, the intensity of the input light beam was measured without the presence of the sample. The role of the first detector (D1) as a detector is to determine possible fluctuations in the intensity of the laser beam. Then the different samples (TiN nanoparticles), with varying concentrations within a 1 mm thickness quartz cell, were moved by a high-precision optical rail. The samples were displaced along the z-direction of the beam (through the focus of the lens). The optical rail was accurately shifted along the z-direction near the focal point of the lens using a DC stepper motors, automatically. The variations of intensity corresponding to the different positions of the sample were recorded by two intensity detectors (Model PM100) for open and close aperture; these variations were, then, stored in a computer automatically.

Structural study
The XRD patterns were recorded on a Bruker D8 Advance diffractometer (40 kV-40 mA, CuKa radiation, k = 0.15406 nm). Diffractograms were recorded in the range of 2h = 10°-80°with a step size of 0.02°. The nanocrystallites size and microstrain were estimated based on Williamson-Hall method [50] where b is the line broadening at Full Width at Height Maximum (FWHM) of the preferred hkl plane diffraction peak. h hkl is Bragg diffraction angle (peak position), k is a constant, which is about 0.89 for spherical nanoparticles. k is the wavelength of Cu ka peak equal 0.15406 nm, D is crystallite size and is the microstrain. Obviously, using the slope of the fitted lines, the strain can be obtained. For estimating Dislocation density was estimated via the following equation: where D is the crystallites size which is obtained by Scherrer equation (2) [51].
Since the crystal structure of TiN is Face centered cubic (FCC), the lattice parameter, a, can be calculated by the following equation: where h, k, and l are the miller indices, and d is lattice distance obtained from Bragg law: The XRD patterns of different preparation methods are represented in Fig. 5. Based on XRD pattern results, all the crystallographic parameters are reported in Table 1. The linear fitted curves of Eq. 1 are represented in Fig. 6.  , there is oxygen impurity due to oxidation in the ambient air. The oxide phase peak is stronger in the sample prepared at lower rotation rate (350 rpm). By increasing the number of rotations, the rotation rate, and milling process duration, the TiN peaks become stronger, and the TiO 2 peak intensity at 43.64°d ecreases. A fine shift of the peaks to higher angles in the milled samples (see Table 1) could be attributed to a decrease of Bragg planes distance due to fabricating nanoparticles. The slight decrease of FWHM of the peaks is due to an increase of estimated crystallite size for the milled samples. However, the lattice parameter is slightly decreased due to the milling process, which leads to a decrease in Bragg planes distance (d). It is clear that the ball milling process leads to an increase of crystallites sizes generally. Figure 5b represents the XRD patterns of the samples synthesized by the sol-gel method followed by calcining in ammonia atmosphere between 700 and 1000°C

Sol-gel method
. As presented, the pattern of the as-prepared sample (I) corresponds to rutile phase of TiO 2 . The patterns (II, III, and IV) indicate the XRD patterns as a function of calcination temperature. It is observed that after calcining in the ammonia atmosphere, the composition of TiO 2 evolved to TiN. For calcining at  table 1, the sample prepared with the sol-gel method contains smaller nanocrystallites comparing the Merck and ball mill processed samples. The lattice parameter has a fine decrease which could be due to compressive stress in the nanocrystallites that leads to negative microstrain. This is obviously represented in the negative slope of the (W-H) curves (Fig. 6).

Co-precipitation method
Figure 5c shows a sample synthesized by the coprecipitation method. These patterns indicate the effect of calcination of the sample at temperatures of 700-1000°C in an ammonia atmosphere. In this sample, with increasing the calcination temperature, an evolution in the structure from TiO 2 to TiN has occurred. At 700°C, titanium oxide dual phase of anatase and the rutile are observed. As the temperature rises to 800°C, the TiN phase appeared (denoted by *), while the TiO 2 phase (denoted by ?) still exists. However, the TiN peaks are weaker than the   sol-gel prepared sample. At T = 1000°C, the completely purified crystalline the TiN phase is observed without any TiO 2 phase. The preferred peak at (200) is stronger than other samples and the microstrain is negative and lower than other samples. In similarity to sol-gel synthesized sample, the nanocrystallite size is 268.1Å for (200) planes. Lattice parameter is reduced due to compressive stress that is clear in negative slope of the fitted line of the (W-H) curve (Fig. 6).
As presented in Table 1, negative and smaller microstrain in the chemical methods prepared samples contrary of ball milled and Merck samples with positive microstrain. The positive and negative microstrains are due to tensile and compressive stress respectively. According to Hooke's law [52] Eq. (4) describes the linear relationship between microstrain () and stress (r ) in crystals.
where Y is Young's modulus which is approximately 640 GPa for stoichiometric TiN [53]. Hence for different methods prepared samples, the compressive and tensile stress are reported in Table 1. As reported, for physically prepared samples, there is tensile stress with positive microstrains, while in chemically synthesized samples, compressive stress is dominant with negative microstrains.

EDS analysis
EDS analysis spectra and the quantitative analysis results are represented in Fig. 7 and Table 2, respectively. Comparing the spectra with the Merck TiN sample shows equivalent composition in the ball milling process prepared samples. Oxygen impurity in the Merck powder and other samples is attributed to oxidation of the powders in the air. However, for the samples prepared by co-precipitation and sol-gel methods, there is up to 5.5% of carbon in the chemical composition, which could be remained from precursors during synthesis. EDS results describe the chemical composition of TiN 1Àx O x depending on the preparation method.

UV-Visible spectroscopy and bandgap determination
Absorbance measurements were carried out by UV-Vis spectrophotometer model Unico 4802 double-beam in the range of 190-1100 nm, using dispersed nanoparticles in alcohol. The absorption coefficient was obtained using the following equation: where a is the absorption coefficient, and A is the absorbance, and t is the mean nanoparticles diameter. Figure 8 shows the transmittance curves for titanium nitride nanoparticles. As can be seen, the sample synthesized by the co-precipitation method has the highest, and the sample synthesized by the sol-gel method has the lowest transparency in the visible wavelength range compared to other samples, which could be attributed to smaller nanoparticles sizes in the samples prepared by co-precipitation method. Also, the slight shift of absorption edge could be attributed to the bandgap change due to the difference in chemical composition caused by carbon and oxygen impurity (see EDS results). For determining the optical bandgap of the samples, the absorption coefficient (a) may be obtained from Tauc equation for direct bandgaps: [53].
where hm is the energy of the incident photon, C is a constant, and E g is the bandgap energy. The curves of the variation of ðahmÞ 2 versus photon energy, hm, are represented in Fig. 9. According to Eq. 8, the bandgap could be determined by extrapolating the straight portion to the energy axis, i.e., ðahmÞ 2 ¼ 0 [53]. The bandgap of the stoichiometric titanium nitride is reported as direct and equal to 4.3 eV [54]. Based on the absorption edges, the prepared samples have two bandgaps. Depending on the preparation method and concentration of oxygen which leads to forming of TiN 1Àx O x alloy, which is due to oxidation of the samples in the ambient atmosphere, the first bandgap varies from about 1.58 eV for the ball mill method with 350 rpm to 1.95 eV for the ball mill processed sample at 500 rpm. The second bandgap of these samples varies from about 3.25 eV for the ball milled sample at 500 rpm to about 3.94 eV for the ball milled sample at 350 rpm (Fig. 8). The bandgaps of the samples synthesized by chemical methods are between the mentioned values. According to EDS ( Table 2) and FTIR spectroscopy results (Fig. 9)

FTIR spectroscopy study
FTIR spectroscopy was effectuated for investigating the type of chemical bonds in the synthesized samples. Figure 10a represents the IR transmittance of the titanium nitride sample purchased from Merck Company, Fig. 10b represents the ball milled sample by 350 rpm rotation rate, and Fig. 10c corresponds to the same sample at 500 rpm. Figure 10d also represents the synthesized sample by sol-gel method, and Fig. 10e corresponds to the sample synthesized by the co-precipitation method. In all of the spectra, the absorbance in the range of 3200 to 3700 cm À1 , corresponds to O À H bond due to the presence of water and alcohol solvents in the sample remained from synthesis process. In the range of 1570 cm À1 , a double carbon bond is observed as C=C, which is due to carbonyl bonds. Absorbance at 1406 cm À1 , is related to the C-H 3 bond chain in the  samples. At 1343 cm À1 , a weak absorbance attributed to C bond is observed, which is a sign of a unique carbon bond. The absorbance around 1122 cm À1 is related to C-O bond, corresponding to carbon dioxide in the chamber atmosphere. Moreover, it could be attributed to carbon and oxygen bond due to epoxy bond. Absorbance at 1017 cm À1 , corresponds to Ti À N bond, which confirms the formation of a titaniumnitride bond in the process. In the range of 649 cm À1 , Ti À O bonds show oxygen and titanium bonds [31,54]. As presented, all of the synthesized samples contain the Ti À N bonds confirming the synthesis of TiN after calcining in ammonia atmosphere.

Study of surface morphology of titanium nitride nanoparticles
Scanning Electron Microscope (SEM) images were obtained via TESCAN VEGA3 Model equipped with EDS microanalysis system for chemical composition analysis. SEM images of the reference (Merck TIN) and samples prepared by different methods are represented in Fig. 11. Figure 11a shows the surface morphology of the TiN particles purchased from Merck. The images show the particles with homogeneous size, polyhedron, and irregular morphology. Figure 11b shows the particles prepared by ball mill process at 350 rpm. It is observed pseudospheric and aggregated grains with decreased size. The particles size is nonuniform and irregularly multifaceted. Figure 11c shows the SEM images of the particles prepared by the ball milling at 500 rpm. The particles are nonuniform and irregularly multifaceted. SEM images of the ball mill processed samples (Fig. 11b, c) revealed the porous structure with an average particles size around 100 nm with an increase in porosity after processing. Figure 11d shows the sample synthesized by the sol-gel method annealed at 1000°C. The surface morphology shows the more aggregated particles with higher size than ball mill method, while the porosity was decreased. Figure 11e shows the images of the sample synthesized by the co-precipitation method annealed at 1000°C in ammonia atmosphere. Spherical aggregated particles in ball-shaped grains with a size up to 100 nm and smaller than other samples.

Nonlinear optics studies
By the Z-scan method, the nonlinear optical properties of the titanium nitride with different synthesis methods were performed. The Z-scan technique has the advantages of simplicity and high sensitivity; therefore, it is an increasingly popular method to measure optical nonlinearities of materials [47]. Using the Z-scan setup, two important nonlinear optics parameters can be determined, both size and sign [46]. This technique is used to measure both the nonlinear absorption coefficient and the nonlinear refractive index. The Z-scan theory can exhibit either a minimum in back focal(valley) followed by a maximum in front focal(peak) or a maximum in back focal (peak) followed by a minimum in the front focal (valley), indicating the positive or negative sign of nonlinear refractive index.
The nonlinear refractive index of materials is defined as follows: where n 0 is the linear refractive index, I is the intensity of beam, and n 2 is the nonlinear refractive index.
where DU 0 is related to the peak to valley of the normalized transmittance obtained through the following equation: where S ' 0. Also, k is the wave number, I 0 is the beam intensity in the focal point, L eff ¼ ð1 À expðÀa 0 LÞÞ=a 0 , L is the cell thickness, and a 0 is the linear absorption coefficient. The nonlinear refractive index n 2 ðcm 2 =WÞ is obtained from the best fitting performed on the experimental data using Eq. 10. If n 2 [ 0 self-focusing effect, and if n 2 \0 selfdefocussing effects will appear in the sample. In other words, in the closed aperture setup, n 2 is positive, when the sample movie in the ?z-direction from left to right, the transmittance curve, T (z), has a valley-peak. Also, when n 2 is negative, the light intensity increased, and the transmittance curve, T (z), has a peak-valley.
Also, the nonlinear absorption coefficient, b, is obtained using [47] b where T(0) is open-hole transmittance. When b [ 0, it is saturable absorption (SA); when b\0, it is reverse saturable absorption (RSA) or two-photon absorption.
In this study, changes in sample synthesis, sample concentration change, light-material interaction are manipulated. By installing different neutral density filters, the samples are illuminated with laser powers of 70 mW, 85 mW, 100 mW, and 120 mW. Also, different weight percentages 0.3%, 0.6%, and 1.2% were prepared from the sample. In the first study, by changing the power of the laser beam, using the neutral density filter, and at a constant concentration of the sample, the nonlinear optical behavior was determined for the synthesized nanoparticles in different methods. In the second study, by changing the concentration of the sample with different weight percentages, the nonlinear behavior of the synthesized nanoparticles by different methods was investigated. The nonlinear properties of TiN prepared by the ball mill (350 rpm), ball mill (500 rpm) co-precipitation, and sol-gel methods in different intensities and concentrations are shown in Figs. 12, 13, 14, and 15. The results show well the change in the nonlinear behavior of TiN nanoparticles by changing the concentration, laser beam intensity, and synthesis of nanoparticles. In each figure, up is the close aperture results, and down is the open aperture data results. The valley, followed by a peak normalized transmittance obtain from the closed aperture Z-scan data, indicates that the sign of the refraction index nonlinearity is positive (i.e., self-focusing). This behavior is observed in all data. Also, The valley at the focal point obtain from the open aperture Z-scan data in the intensity of 85 mW, 100 mW, and 120 mW indicates that the sign of the nonlinear absorption coefficients is positive (i.e., saturable absorption). But the open aperture Z-scan nonlinear optical curves at 70 mW, shows a peak at the focal point, which indicates that the nonlinear absorption coefficient is negative (i.e., reverse saturable absorption). Therefore, as the figures show, with the increase of the input beam power in the open aperture Z-scan diagrams, we have a change from peak to valley, which shows the change from reverse saturation absorption to saturation absorption.
In the process of absorbing saturation with laser beam radiation to TiN nanoparticles, the electrons in the valence band of this material receive energy and are excited, causing it to go to the conduction band. These electrons continue this process until the conduction band becomes saturated. After the conduction band is saturated, the band electrons do not absorb the energy capacity, which increases the light passing through the material. The reverse saturation absorption process occurs through the ESA excited state absorption process, in which the electrons of the valence band receive energy and are excited and sent to the conduction band. They go to higher energy states in the conduction band. In the interaction of  light with TiN, the nonlinear absorption process of this material takes place through a two-photon absorption (TPA) process, in which the electrons of the capacitance band go to a virtual plane by absorbing one photon and by absorbing a second photon. They go to the delivery bar. In the open aperture curve, TiN sample with increasing the power of the incident beam to the material, a state change from peak to valley was observed, which is due to the conversion of saturation absorption behavior to reverse saturation absorption matter.
Using Eq. 10 and 12 and determining the peaks and valleys in closed and open aperture diagrams, all the nonlinear refractive index and the nonlinear absorption coefficients of the studied samples were determined separately. The results are given in Tables 3, 4, 5, and 6.
According to Tables 3, 4, 5, and 6, at a concentration of 0.3%, with increasing the intensity of the input beam, the nonlinear refractive index decreases and the nonlinear absorption coefficient decreases. At a concentration of 0.6%, with decreasing the intensity of the input beam, the nonlinear refractive index increases, and also the nonlinear absorption coefficient increases. At a concentration of 1.2%, with decreasing the intensity of the input beam, the nonlinear refractive index increases, and the nonlinear absorption coefficient also increases. At the lowest intensity (70 mW), the value of the nonlinear absorption coefficient is negative, which indicates a change to the reverse saturation absorption mode. At 120 mW intensity, the nonlinear refractive index and nonlinear absorption coefficient decrease with increasing concentration. At an intensity of 100 mW, the nonlinear refractive index, and nonlinear absorption coefficient decrease with increasing concentration. At 85 mW intensity, the nonlinear refractive index, and nonlinear absorption coefficient decrease with increasing concentration. At 70 mW, the nonlinear refractive index decreased with increasing concentration, and the nonlinear absorption coefficient increased. The results show that due to the nonlinear behavior of titanium nitride in 70 mW is reverse saturation absorption can be to protect the eyes and optical instruments against high intensity laser in low power. Also, due to the nonlinear behavior of titanium nitride at all intensities is selffocusing, can play an important role in the manipulation and correction of the shape of laser pulses.
For further comparison with other various nonlinear optical parameters, the nonlinear refractive index(n 2 ) and the nonlinear absorption coefficient(b) reported in the literature are listed in Table 7.
Comparison between measurements obtained, the nonlinear refractive index (n 2 ) parameter obtained for the TiN shows a larger value than most other data. Also, the nonlinear absorption coefficient is much larger than all the results. Table 7 clearly shows that the TiN is an appropriate case for nonlinear optics applications. The results in Fig. 16 show that the synthesis and concentration functions are a significant help in controlling and manipulating lightmatter interactions, provide a very effective way to improve optical properties, and thus play an important role in designing and manufacturing new materials for use in optical processes.

Conclusion
In the present study, the titanium nitride nanoparticles were produced by several methods. The XRD, FTIR, SEM, and UV-Vis techniques were employed to characterize the TiN nanoparticles. The X-ray diffraction pattern revealed the removal of the titanium oxide phase after annealing at 1000°C in ammonia. However, due to oxidation in ambient air, EDS results showed the oxygen impurity in all the b Fig. 14 Nonlinear optical properties of titanium nitride prepared by the co-precipitation method. The closed aperture Z-Scan data with different concentration and laser beam power of a 70 mW, b 85 mW, c 100 mW, and d 120 mW; the open aperture Z-Scan data with different concentration and laser beam power of e 70 mW, f 85 mW, g 100 mW, and h 120 mW samples that caused the creation of TiN 1Àx O x alloy and change in bandgap energy. SEM images confirmed the particles aggregation and increase of porosity in the milled samples, due to the decrease in particle size. The Z-scan arrangement was utilized to study the nonlinear optical properties of the samples as a function of laser beam power and concentration of the nanoparticles in dispersed solution. The results show that with increasing concentration and laser beam power, nonlinear refractive index and nonlinear absorption coefficient decrease. As the input intensity increased in the nonlinear absorption of the samples, a transition from saturation to reverse saturation was observed. In other words, the value of the nonlinear absorption coefficient at the lowest investigated intensity (70 mW) results in a negative value which decreases the absorption coefficient. This coefficient was obtained at higher power (120 mW, 100 mW, 85 mW), which increased the absorption coefficient. Therefore, the results showed that the nonlinear refractive index behavior of the samples is always similar and has self-focusing behavior, but the