The transmittance (T) and the reflectance (R) were measured for (TMA) 2ZnCl 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 A2BX4 type crystals (with A = K, NH4, Rb; B = Zn, Co; X = Cl, Br) have been interested because of their incommensurately modulated structures and the successive phase transitions [
The compounds belonging to TMA family have attracted much interest because of exhibiting some peculiar characteristics associated with the phase transition. Among them [N(CH3)4]2ZnC14 (hereafter (TMA)2ZnCl4) with b-K2SeO4 type structure as the normal (or prototype) phase at the high temperature region. (TMA)2ZnCl4 exhibits a sequence of structural phase transitions. It turns incommensurate when cooled through a first-order phase transition occurring at TINC = 296 K, becomes ferroelectric by lock-in of the incommensurate modulation at TC-F = 279 K, and at TC2 = 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)2ZnCl4 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 [
Little attention has been paid to the study of optical properties near the absorption edge of (TMA)2ZnCl4 crystal. This contribution reports the results of investigation of some optical properties of [N(CH3)4]2ZnC14 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)2ZnCl4 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 (C4H12NCl) and Zinc chloride (ZnCl2) 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 mm2 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.
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 σopt. | 2.933 ´ 1010 s‒1 |
Electrical conductivity σele. | 16.423 (Ω∙m)‒1 |
Electric susceptibility χc | 0.164 |
Lattice dielectric constant εL | 10.10 |
The ratio of carrier concentration to effective mass N/m* | 2.05 ´ 1059 (m3∙kg)‒1 |
Molar polarizability αp | 1.37 ´ 1021 cm3/mole |
where T is the transmittance and d is the crystal thickness.
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
The reflectance of the surface (R) is written in terms of refractive index (n) [
The optical constants (n, Kex.) were determined from the transmission (T) and reflection (R) spectrum. The absorption coefficient α is related to extinction coefficient Kex. by:
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
[
For further analysis of the experimental results, the electric susceptibility χc can be calculated according to the relation [
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
Lattice dielectric constant εL 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 αp of (TMA)2ZnCl4 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
The dispersion of refractive index of (TMA)2ZnCl4 has been fitted to Wemple and DiDomenico (WDD) model which is based on single oscillator formula [
where E0 is single oscillator energy or average energy gap and Ed is dispersion energy and
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 n0 are also calculated and recorded in
Physical quantity | Value |
---|---|
Single oscillator energy E0 | 6.55 eV |
Dispersion energy Ed | 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 n0 | 1.314 |
Oscillator strength S0 | 2.61 ´ 10‒5 (nm)‒2 |
Oscillator wavelength λ0 | 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 S0 for (TMA)2ZnCl4 crystals. The refractive index is represented by a single Sellmeier oscillator at low energies [
where λ0 is the oscillator wavelength. If we put
S0 is the average oscillator strength. The plotting of
in
and λ0 were determined and listed in
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
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 | CH3 Rocking | ||
1384.66 | 1384.59 | 1384.33 | O-H bending | ||
1415.52 | 1415.58 | 1415.63 | Symmetric bending of CH3 | ||
1483.98 | 1484.89 | 1484.25 | Asymmetric bending of CH3 | ||
2957.35 | 2958.49 | 2957.37 | Symmetric stretching of CH3 | ||
3023.88 | 3025.2 | 3024.71 | Asymmetric stretching of CH3 | ||
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. [
1. Optical transmission studies showed that (TMA)2ZnCl4 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 (sopt. & sele.) and the lattice dielectric constant (εL) and the ratio of free charge carrier concentration to the effective mass (N/m*) were estimated at room temperature for samples of (TMA)2ZnCl4 and listed in
3. The refractive index values have been fitted to the single oscillator Wemple-DiDomenico (WDD) model. The single oscillator energy (E0), the dispersion energy (Ed), Static refractive index n0, Moments of the optical dispersion spectra M‒1 and M‒3, Static refractive index n0 and the Oscillator strength S0 are calculated and presented in
4. FTIR spectra was measured for the as grown and annealed crystals as shown graphically in