^{1}

^{*}

^{1}

^{1}

The transmittance (T) and the reflectance (R) were measured for (TMA)
_{2}ZnCl
_{4} single crystals and hence the absorption coefficient (α), extinction coefficient (K
_{ex.}), refractive index (n), real and im-aginary dielectric constants (
*ε'*,
*ε"*) of (TMA)2ZnCl4 crystals were calculated as a function of photon energy. The analysis of the spectra behavior of the absorption coefficient in the absorption region revealed indirect transition. The dispersion of the refractive index is discussed in terms of the sin-gle oscillator Wemple-DiDomenico model. The single oscillator energy (E
_{0}), the dispersion energy (E
_{d}), the lattice dielectric constant (
*ε*
_{L}) and the ratio of free charge carrier concentration to the ef-fective mass (N/m*) were estimated. The FTIR spectra were recorded to study the functional groups of the as grown and annealed samples.

The A_{2}BX_{4} type crystals (with A = K, NH_{4}, Rb; B = Zn, Co; X = Cl, Br) have been interested because of their incommensurately modulated structures and the successive phase transitions [_{2}BX_{4} family [

The compounds belonging to TMA family have attracted much interest because of exhibiting some peculiar characteristics associated with the phase transition. Among them [N(CH_{3})_{4}]_{2}ZnC1_{4} (hereafter (TMA)_{2}ZnCl_{4}) with b-K_{2}SeO_{4} type structure as the normal (or prototype) phase at the high temperature region. (TMA)_{2}ZnCl_{4} exhibits a sequence of structural phase transitions. It turns incommensurate when cooled through a first-order phase transition occurring at T_{INC} = 296 K, becomes ferroelectric by lock-in of the incommensurate modulation at T_{C-F} = 279 K, and at T_{C2} = 276.3 K another first-order ferroelectric phase transition takes place at 181 K is monoclinic, phase V between 181 K and 163 K is monoclinic or triclinic, and phase VI, which is stable below 163 K, is orthorhombic. The highest temperature phase, Phase I, has Pmcn symmetry. In this phase one unit cell contains four formula units consisting of two inequivalent types of tetramethylammonium ions [

Many investigations have been performed on (TMA)_{2}ZnCl_{4} crystals including studies of the effect of electric field and mechanical stress (uniaxial or shear stress) on dielectric permittivity and spontaneous polarization by Styrkowiec and Czapla [_{c1}, (IC) to higher temperature and the transition point T_{c2} (ferroelectric ferroelastic) lower. It is found that the dielectric constant and the shift of the transition point are dependent on the uniaxial stresses and this stress can also induce a change of the crystal symmetry. Linear birefringence (LB) behavior of [N(CH_{3})_{4}]_{2}ZnC1_{4} and [N(CH_{3})_{4}]_{2}CuC1_{4} was studied in the critical region on normal-incommensurate phase transition by Kim et al. [_{3})_{4}]_{2}ZnC1_{4} and [N(CH_{3})_{4}]_{2}CoC1_{4} are measured by Sveleba et al. [_{3})_{4}]_{2}ZnCl_{4} crystals doped with Ni^{2+} in the parent and incommensurate phases. Their temperature dependences obtained are nonlinear in a wide temperature range. It is shown that the nature of this nonlinearity is related to the presence of local spatial regions of the correlated motion of tetrahedral groups. Studies on the behaviour of the modulation wave vector in [(CH_{3})_{4})N]_{2}ZnC1_{4−x}Br_{x} compounds as a function of composition (x) and temperature were performed by Vogels et al. [_{3})_{4}]_{2}ZnC1_{4} crystals was measured at the fixed temperature by Styrkowiec [

Little attention has been paid to the study of optical properties near the absorption edge of (TMA)_{2}ZnCl_{4} crystal. This contribution reports the results of investigation of some optical properties of [N(CH_{3})_{4}]_{2}ZnC1_{4} crystals in the normal phase. Another goal of the present work is to get some information about the vibration bands by Fourier transform infrared (FTIR) spectroscopic studies.

(TMA)_{2}ZnCl_{4} single crystals were grown using the solution growth technique from saturated solutions by slow cooling from 45˚C to 35˚C instead of isothermal evaporation. The raw material used for growth was obtained by mixing aqueous solutions of tetramethylammonium chloride (C_{4}H_{12}NCl) and Zinc chloride (ZnCl_{2}) in stoichiometric amounts. Typically the growth runs lasted from 30 - 50 days. During this period the average cooling and growth rates were 0.2˚C/day and 0.3 mm/day, respectively. After an initial capping period, the crystal grew clear to heights ranging from 10 to 15 mm each. From the as grown crystals specimens were formed into b-plates with size of about 0.8 mm in thickness and 36 mm^{2} in area using a wet thread saw. The specimens used for optical measurements were clear, transparent and free from any noticeable defects. More details about the grown crys- tals are shown elsewhere [

The optical transmittance was recorded at room temperature using Shimadzu UV-VIS dual beam scanning spectrophotometer in the energy range 2.1 - 6.4 eV. The incident unpolarized light was nearly perpendicular to (010) plane. The surrounding medium was air. The relative specular reflectance was measured at an incident angle of 5˚, while the sample was placed horizontally facing downward and was illuminated from the bottom.

The FTIR spectra were recorded in the range 400 - 4000 cm^{−1} employing a NICOLET FTIR 6700 spectrometer by the KBr pellet method to study the functional groups of the samples.

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. _{2}ZnCl_{4} single crystal recorded in the range 190 to 900 nm at room temperature. From _{2}ZnCl_{4} 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 [

Physical quantity | Value |
---|---|

Optical energy gap | 5.903 eV |

Cut off wavelength | 195.016 nm |

Optical conductivity σ_{opt}_{.} | 2.933 ´ 10^{10} s^{‒1 } |

Electrical conductivity σ_{ele}_{.} | 16.423 (Ω∙m)^{‒1} |

Electric susceptibility χ_{c} | 0.164 |

Lattice dielectric constant ε_{L} | 10.10 |

The ratio of carrier concentration to effective mass N/m^{*} | 2.05 ´ 10^{59} (m^{3}∙kg)^{‒1} |

Molar polarizability α_{p} | 1.37 ´ 10^{21} cm^{3}/mole |

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

_{2}ZnCl_{4} 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

The relationship between absorption coefficient α and photon energy

where A is a constant nearly independent of photon energy and

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 [

In a small energy range, the dependence of _{2}ZnCl_{4} samples is shown in _{2}ZnCl_{4} crystal is an indirect material and the fundamental edge is due to allowed indirect transitions. By extrapolating the straight lines to the value, where

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

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:

_{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 _{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(

where

The variation of the imaginary

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

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

[^{10} 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 [

where ɛ_{0} 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 _{c}-hν relationship is depicted in _{c} calculated near the energy gap at 5.9 eV is listed in

Lattice dielectric constant ε_{L} and contribution of charge carriers (N) can be calculated by the fitting of the linear part of the relation [

where e is electronic charge, c is the velocity of light and

The molar polarizability α_{p} of (TMA)_{2}ZnCl_{4} single crystals can be deduced according to the Clausius-Mos- sotti local-field polarizability model [

where L is the Avogadro’s number, ρ is the density of material and M molecular weight. The photon energy dependence of _{p} value is deduced and listed in

The dispersion of refractive index of (TMA)_{2}ZnCl_{4} has been fitted to Wemple and DiDomenico (WDD) model which is based on single oscillator formula [

where E_{0} is single oscillator energy or average energy gap and E_{d} is dispersion energy and _{d} depends on the imaginary part of dielectric constant _{0} does not. Due to this reason E_{d} is very nearly independent of E_{0}, and E_{0} is related to the bond energy of chemical bonds present in the system. Oscillator parameters calculated from the linear fit of _{0}/E_{d}) and the slope (1/E_{0}E_{d}), the dispersion parameters E_{d} and E_{0} are calculated and given in _{0}) have been calculated by extrapolating the WDD dispersion equation for

The moments of optical dispersion spectra

The zero-frequency refractive index (static refractive index) is obtained using Equation (13), by putting

Furthermore the values of static refractive index zero-frequency refractive index n_{0} are also calculated and recorded in

Physical quantity | Value |
---|---|

Single oscillator energy E_{0} | 6.55 eV |

Dispersion energy E_{d} | 2.06 eV |

Moment of the optical dispersion spectra M_{‒1} | 0.314 (eV)^{2} |

Moment of the optical dispersion spectra M_{‒3} | 7.323 ´ 10^{‒3} (eV)^{‒2} |

Static refractive index n_{0} | 1.314 |

Oscillator strength S_{0} | 2.61 ´ 10^{‒5} (nm)^{‒2 } |

Oscillator wavelength λ_{0} | 157.87 nm |

The values of dispersion parameters and the optical moments gathered in

The refractive index n can also be analyzed to determine the oscillator strength S_{0} for (TMA)_{2}ZnCl_{4} crystals. The refractive index is represented by a single Sellmeier oscillator at low energies [

where λ_{0} is the oscillator wavelength. If we put

S_{0} is the average oscillator strength. The plotting of

in _{0}

and λ_{0} were determined and listed in

FTIR spectra carried out in the range 400 - 4000 cm^{−1} of as grown (TMA)_{2}ZnCl_{4} crystals and crystals annealed for 1 and 2 hours in the paraelectric phase at 150˚C have been assigned in ^{−1} is assigned to C-N stretching mode of vibration. The rocking of CH_{3} 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 CH_{3} and the out-of-plane bending is assigned to the band at 1487 cm^{−1}. Symmetric and asymmetric stretching of CH_{3} 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. [

The FTIR spectra for specimens annealed at different temperatures in the normal phase (

Wavenumber (cm^{−}^{1}) | Assignment | ||||
---|---|---|---|---|---|

As grown | Annealed at 150˚C for 1 h | Annealed at 150˚C for 2 h | |||

457.05 | 456.62 | 454.16 | C-N-C (skeletal bending) | ||

458.02 | |||||

949.78 | 949.78 | 949.78 | Symmetric stretching of C-N | ||

1287.27 | 1287.31 | 1286.89 | CH_{3} Rocking | ||

1384.66 | 1384.59 | 1384.33 | O-H bending | ||

1415.52 | 1415.58 | 1415.63 | Symmetric bending of CH_{3} | ||

1483.98 | 1484.89 | 1484.25 | Asymmetric bending of CH_{3} | ||

2957.35 | 2958.49 | 2957.37 | Symmetric stretching of CH_{3} | ||

3023.88 | 3025.2 | 3024.71 | Asymmetric stretching of CH_{3} | ||

3476.12 | 3477.09 | 3443.77 | O-H Vibration of water molecule | ||

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. [_{3})_{4}]_{2}ZnC1_{4} 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.

1. Optical transmission studies showed that (TMA)_{2}ZnCl_{4} crystal was optically transparent in the entire visible region with a lower cut-off below 256 nm. From the data the absorption coefficient (α) and the optical band gap

2. The refractive index (n) was calculated as a function of photon energy. Values of the optical and electrical conductivities (s_{opt}. & s_{ele.}) and the lattice dielectric constant (ε_{L}) and the ratio of free charge carrier concentration to the effective mass (N/m^{*}) were estimated at room temperature for samples of (TMA)_{2}ZnCl_{4} and listed in

3. The refractive index values have been fitted to the single oscillator Wemple-DiDomenico (WDD) model. The single oscillator energy (E_{0}), the dispersion energy (E_{d}), Static refractive index n_{0}, Moments of the optical dispersion spectra M_{‒1} and M_{‒3}, Static refractive index n_{0} and the Oscillator strength S_{0} are calculated and presented in

4. FTIR spectra was measured for the as grown and annealed crystals as shown graphically in _{3}, C-N and C-N-C groups are identified (