Transmission spectrum is very important for any nonlinear optical (NLO) material, because a nonlinear optical material can be of practical use only if it has wide transparency window. Figure 1 shows the variation of the optical transmission (T) and reflectance (R) spectrum as a function of wavelength for (TMA)₂ZnCl₄ single crystal recorded in the range 190 to 900 nm at room temperature. From Figure 1, the lower cut off wavelength is obtained and listed in Table 1. UV-Vis-NIR spectrum, reveal that, (TMA)₂ZnCl₄ crystal is conveniently transparent from 300 to 900 nm with about 60% of transmittance and there is almost a steady transmittance in the visible region. The high transmission or low absorption in the region 300 - 900 nm makes the material to obtain low reflectance and refractive index which is a suitable property for antireflection coating solar thermal devices and nonlinear optical applications.

Electronic transitions between the valence band and the conduction band in crystals starts at the absorption edge that corresponds to the energy difference between the lowest minimum of the conduction band and the highest maximum of the valence band. The value of the energy gap depends in a rather subtle way on the structure and the actual values of the pseudopotential in the crystal. The optical behavior of a material is generally utilized to determine its optical constants for example the absorption coefficient a. The absorption coefficient (a) was calculated by means of the ratio recording technique in order to eliminate the reflection losses. This was achieved by placing a thin crystal in the way of reference beam, and another thicker one in the way of the sam- ple beam. Assuming that the change in reflection with thickness is negligible, the ratio of the transmittance of two samples of different thicknesses is given by [10] :

where T is the transmittance and d is the crystal thickness.

Figure 2(a) shows the spectral response of the total absorption coefficient (α) for (TMA)₂ZnCl₄ crystal. The α-hν dependence exhibits a long tail at the low energy part. It can be seen that the absorption increases slowly with increasing photon energy in the range below = 6.1 eV. At photon energies > 6.1 eV, the spectra showed a steeper increase of the absorption coefficient. It can be assumed that this increase in α(hν) is due to the onset of interband transitions at the fundamental edge.

The relationship between absorption coefficient α and photon energy can be expressed as [11] :

where A is a constant nearly independent of photon energy and is the optical energy gap. Here m repre- sents an index that can take any of the values: 2, 3/2, 1/2 or 3 depending on the type of transition responsible for the absorption. For allowed direct transition m = 1/2 while m = 3/2 for forbidden direct transition. For allowed

indirect transition m = 2 and for forbidden indirect transition m = 3. The range within which this equation is valid is very small and hence it becomes too difficult to determine exactly the value of the exponent m [12] .

In a small energy range, the dependence of on for (TMA)₂ZnCl₄ samples is shown in Figure 2(b). The dependence of on photon energy hν for onset gaps was plotted for different values of m and the best fit was obtained for m = 2. This indicates that the optical absorption obeys Equation (2) with m = 2 which means that (TMA)₂ZnCl₄ crystal is an indirect material and the fundamental edge is due to allowed indirect transitions. By extrapolating the straight lines to the value, where, value of was determined. The obtained value is 5.903 eV. This value has good agreement with those calculated by El-Korashy [13] which reported direct band gap energy value of 5.89 eV at 300 K (the normal paraelectric phase) for this crystal.

The reflectance of the surface (R) is written in terms of refractive index (n) [14] as:

The optical constants (n, K_ex.) were determined from the transmission (T) and reflection (R) spectrum. The absorption coefficient α is related to extinction coefficient K_ex. by:

Figure 3 shows the plot of extinction coefficient (K_ex.) as a function of photon energy (hν). From the graph, it is clear that extinction coefficient (K_ex.) value increases with increase in the photon energy. The dependence of refractive index (n) on the energy is also shown in Figure 3 and it is seen that the refractive index decreases as the photon energy increases. Thus, the extinction coefficient (K_ex.) and refractive index (n) depend on the photon energy. It is understood that the higher value of photon energy will enhance the optical efficiency of the material. Hence, by tailoring the photon energy, one can achieve the desired material for optical device fabrication.

The complex dielectric constant() is related to the refractive index and the extinction coefficient as:

where and are the real and imaginary parts of the complex dielectric constant, respectively.

The variation of the imaginary part of the dielectric constant with photon energy preserves the same dependence of the absorption coefficient while the behavior of, the real part of the dielectric constant, and the refractive index is the same as shown in Figure 4.

The optical conductivity is a measure of the frequency response of the material when irradiated with light is given by the relation [15] :

where c is the velocity of light. The electrical conductivity is related to the optical conductivity by the relation:

The energy dependence of the optical and electrical conductivities is illustrated in Figure 5. The obtained re- sults for extinction coefficient and optical conductivity are in fair agreement with those obtained by Girisun et al.

[15] for tristhiourea zinc sulphate (ZTS) and by Raj et al. [16] for L-Alaninium Malate (LAM) single crystals. The high magnitude of optical conductivity (1.45 ´ 10¹⁰ s^‒1) and the low extinction coefficient (10^‒5) confirms the presence of very high photo response nature of the material. This makes the material more prominent for device applications in information processing and computing.

For further analysis of the experimental results, the electric susceptibility χ_c can be calculated according to the relation [17] :

where ɛ₀ is the dielectric constant in the absence of any contribution from free carriers. The energy dependence of the electric susceptibility is similar to that of the imaginary part of the dielectric constant. χ_c-hν relationship is depicted in Figure 6, then the value of electric susceptibility χ_c calculated near the energy gap at 5.9 eV is listed in Table 1.

Lattice dielectric constant ε_L and contribution of charge carriers (N) can be calculated by the fitting of the linear part of the relation [18] ;

where e is electronic charge, c is the velocity of light and is the ratio of carrier concentration to effec- tive mass, Figure 7 shows the fitting of Equation (11) near the absorption edge. When the carrier concentration increases, the energy gap decreases, then the refractive index increases [19] .

The molar polarizability α_p of (TMA)₂ZnCl₄ single crystals can be deduced according to the Clausius-Mos- sotti local-field polarizability model [20] from the relation:

where L is the Avogadro’s number, ρ is the density of material and M molecular weight. The photon energy dependence of is shown in Figure 8. From the extrapolation, the molar polarizability α_p value is deduced and listed in Table 1.

The dispersion of refractive index of (TMA)₂ZnCl₄ has been fitted to Wemple and DiDomenico (WDD) model which is based on single oscillator formula [21] [22] .

where E₀ is single oscillator energy or average energy gap and E_d is dispersion energy and is the photon energy. Factor E_d depends on the imaginary part of dielectric constant whereas E₀ does not. Due to this reason E_d is very nearly independent of E₀, and E₀ is related to the bond energy of chemical bonds present in the system. Oscillator parameters calculated from the linear fit of and around the absorption edge as depicted in Figure 9. From the intercept (E₀/E_d) and the slope (1/E₀E_d), the dispersion parameters E_d and E₀ are calculated and given in Table 2. The dispersion plays a significant role with respect to optical communication and spectral dispersion [23] . The values of static refractive index (n₀) have been calculated by extrapolating the WDD dispersion equation for and listed in Table 2.

The moments of optical dispersion spectra and, can be evaluated using the relationships [24] :

The zero-frequency refractive index (static refractive index) is obtained using Equation (13), by putting, i.e. based on the expression:

Furthermore the values of static refractive index zero-frequency refractive index n₀ are also calculated and recorded in Table 2.

The values of dispersion parameters and the optical moments gathered in Table 2, are strongly agree with Wemple [21] and DiDomenico [22] .

The refractive index n can also be analyzed to determine the oscillator strength S₀ for (TMA)₂ZnCl₄ crystals. The refractive index is represented by a single Sellmeier oscillator at low energies [25] :

where λ₀ is the oscillator wavelength. If we put. We can rewrite Equation (17) as:

S₀ is the average oscillator strength. The plotting of versus shows linear part edge as shown

in Figure 10. The intersection with axis is and the slope is. Hence, the values of S₀

and λ₀ were determined and listed in Table 2.

FTIR spectra carried out in the range 400 - 4000 cm⁻¹ of as grown (TMA)₂ZnCl₄ crystals and crystals annealed for 1 and 2 hours in the paraelectric phase at 150˚C have been assigned in Table 3 and the functional groups have been identified (Figure 11). The band observed at 950 cm⁻¹ is assigned to C-N stretching mode of vibration. The rocking of CH₃ is assigned to the bands observed at 1071 and 1280 cm⁻¹. The band at 1415 cm⁻¹ is assigned to the in-plane bending mode of CH₃ and the out-of-plane bending is assigned to the band at 1487 cm⁻¹. Symmetric and asymmetric stretching of CH₃ is observed at 2952 and 3022 cm⁻¹ respectively. The band observed around 3435 cm⁻¹ and 1635 cm⁻¹ are assigned to the O-H stretching and bending vibration of water molecule present in the KBr compound. The values assigned were in close agreement with the assignments made by Ganguly et al. [26] , as shown in Table 3.

The FTIR spectra for specimens annealed at different temperatures in the normal phase (Figure 11), shows the same peaks assigned for the as grown crystal have been observed (Table 3). There is a slight shift in the peak positions because of the hydrogen bonding. There is no significant variation in the vibration frequencies with thermal annealing. With increasing annealing duration, the absorption peaks centered at 949.78, 1287.27,

1415.52 and 3023.88 cm⁻¹ decreases in intensity, while the peaks at 1597 and 1636 cm⁻¹ increase in intensity. Another significant spectral feature observed is the transformation of sharp peaks as at 457.05, 1287.27 and near 3470 cm⁻¹ to a broad hump with increasing the annealing duration. Also there is a complete removal of some peaks such as the peaks centered at 2366 cm⁻¹ and 2758 cm⁻¹ which decrease in intensity and then vanish completely.

Sveleba et al. [6] showed that, the temperature dependences of the birefringence δ(Δnc) for [N(CH₃)₄]₂ZnC1₄ crystal specimen annealed at 370 K for 1.5 h brought about a reduction of the rate of nonlinear variation of δ(Δnc) with the temperature. Also deviations from linear temperature dependences are observed in the dielectric permittivity temperature dependence measurements. They attribute this behavior to fluctuation processes and/or the appearance of a new phase state of the crystal.