A strategic approach to physico-chemical analysis of bis (thiourea) lead chloride – A reliable semi-organic nonlinear optical crystal

0030-3992/ © 2016 Elsevier Ltd. All rights reserved.

Optics & Laser Technology 89 (2017) 6–15

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A strategic approach to physico-chemical analysis of bis (thiourea) lead chloride – A reliable semi-organic nonlinear optical crystal

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N.R. Rajagopalana,b, P. Krishnamoorthyc, , K. Jayamoorthyb a b c

Research and Development Centre, Bharathiar University, Coimbatore 641046, India Department of Chemistry, St. Joseph's College of Engineering, Chennai 600119, India Department of Chemistry, Dr. Ambedkar Govt. Arts College, Chennai 600039, India

A R T I C L E I N F O

A BS T RAC T

Keywords: Nucleation kinetics UV transmittance SHG efficiency Hyper polarizability Dielectric studies Solid state parameters Hardness

Good quality crystals of bis thiourea lead chloride (BTLC) have been grown by slow evaporation method from aqueous solution. Orthorhombic structure and Pna21 space group of the crystals have been identified by single crystal X-ray diffraction. Studies on nucleation kinetics of grown BTLC has been carried out from which metastable zone width, induction period, free energy change, critical radius, critical number and growth rate have been calculated. The experimental values of interfacial surface energy for the crystal growth process have been compared with theoretical models. Ultra violet transmittance studies resulted in a high transmittance and wide band gap energy suggested the required optical transparency of the crystal. The second harmonic generation (SHG) and phase matching nature of the crystal have been justified by Kurtz-Perry method. The SHG nature of the crystal has been further attested by the higher values of theoretical hyper polarizability. The dielectric nature of the crystals at different temperatures with varying frequencies has been thoroughly studied. The activation energy values of the electrical process have been calculated from ac conductivity study. Solid state parameters including valence electron plasma energy, Penn gap, Fermi energy and polarisability have been unveiled by theoretical approach and correlated with the crystal's SHG efficiency. The values of hardness number, elastic stiffness constant, Meyer's Index, minimum level of indentation load, load dependent constant, fracture toughness, brittleness index and corrected hardness obtained from Vicker's hardness test clearly showed that the BTLC crystal has good mechanical stability required for NLO device fabrication.

1. Introduction

bis (thiourea) zinc chloride [5], and bis (thiourea) strontium chloride [6]. Along this direction we have chosen bis (thiourea) lead chloride (BTLC), for which only crystal structure [7] and a few basic studies have been reported [8]. A thorough knowledge of kinetics parameters are of great value in growing high quality crystals. In the present investigation, crystal growth kinetics parameters of BTLC crystals, including meta-stable zone width, induction period, interfacial energy, critical number, free energy change, critical nucleus radii and nucleation rate have been elucidated. To ensure the required optical quality and electronic structure of single crystal, the UV–visible spectral studies have been performed. The SHG efficiency and phase matching nature of BTLC crystals have been revealed by Kurtz-Perry method. The frequency dependence of dielectric properties gives a clear insight into the material applications. In this regard, the dielectric studies with variable temperature and frequencies have been performed from which various solid state parameters have been deduced. As micro hardness shares a direct correlation with the crystal structure and is sensitive to inter

Non linear optical (NLO) materials are of vital importance for various applications in the domain of frequency conversion, photonics and optoelectronic technology [1]. In the current scenario, material scientists are showing a keen interest on NLO semi-organic complexes owing to their ability to combine the flexibility of organic materials with the mechanical strength and thermal stability of inorganic materials [2]. Synthesis of semi-organic NLO crystals and their subsequent characterization towards device fabrication have attained great impetus in view of their significance in academics and industrial applications. One such semi-organic material class is the metal complex of thiourea. Thiourea molecule, due to its large dipole moment, is capable of forming an extensive network of hydrogen bonds. Although thiourea is a centrosymmetric molecule it becomes non-centrosymmetric on metal coordination which is an essential property for a crystal to exhibit nonlinear optical activity [3]. The well known thiourea complexes reported in the literature include bis (thiourea) cadmium chloride [4],

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Corresponding author. E-mail address: [email protected] (P. Krishnamoorthy).

http://dx.doi.org/10.1016/j.optlastec.2016.10.001 Received 28 February 2016; Received in revised form 27 August 2016; Accepted 1 October 2016

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atomic spacing and lattice perfection [9], the Vickers hardness studies have been extensively done to arrive at the values of important mechanical parameters of BTLC crystals.

induction period is the time taken for forming the critical nuclei at a particular temperature. The correctness of the observed induction period values has been ascertained by repeating the experiments.

2. Experimental procedure

2.3. Crystal growth

2.1. Synthesis and solubility test of BTLC

Single crystals of BTLC have been grown from the saturated aqueous solution by slow evaporation method. The solution has been thoroughly filtered by using Whatman filter paper into a glass beaker, covered well with a perforated polythene cover for restricting the fast evaporation and kept undisturbed in a dust free atmosphere. After a span of 28 days, good quality BTLC crystals have been harvested. The photograph of the grown crystal of BTLC is shown in Fig. 1b.

In the present study, bis (thiourea) lead chloride (BTLC) crystals have been grown by slow evaporation method. Commercially available (AR grade E-Merck) lead chloride and thiourea have been taken in 1:2 ratio and dissolved in deionised water. The resultant solution has been stirred thoroughly by a magnetic stirrer. As thiourea has strong coordinating capacity to form different phases of metal-thiourea complexes, the thorough stirring is needed to avoid co-precipitation of multiple phases. The synthesis has been carried out as per the following chemical reaction.

2.4. Analytical techniques The grown crystals have been characterized by single crystal X-ray diffraction studies using Enraf (Bruker) Nonius CAD4 diffractometer with Mo Kα (λ=0.7170 Å). The optical transmission spectra of BTLC crystals have been recorded in the region of 200–800 nm using Shimadzu UV-106 spectrometer. The SHG and phase matching efficiency of the grown crystals have been measured by Kurtz second harmonic generation (SHG) test using a Quanta ray spectra physics Nd: YAG laser. The dielectric studies on the BTLC crystals have been carried out by the parallel plate capacitor method as a function of temperatures for various frequencies (range of 50 Hz–5 MHz) using Hiocki model 3532-50 LCR Hitester instrument. The mechanical hardness studies have been performed using Leitz–Wetzlar hardness tester fitted with a diamond indenter.

PbCl2 + 2 CS[NH2]2 → Pb[CS(NH2)2 ]2 Cl2 In the view of choosing the proper solvent and optimum temperature to grow high quality crystals, a solubility test has been adopted. The solubility test has been performed using the synthesized BTLC solute and water solvent. The solution was stirred well using a motorized magnetic stirrer and placed in a constant temperature bath maintained at 303 K. When the super-saturation is attained, the equilibrium concentration of the solute has been analyzed using gravimetric technique [10]. The technique has been repeated for temperatures 308, 313, 318 and 323 K. 2.2. Meta-stable zone width and induction period measurements

3. Results and discussion The saturated solution of BTLC has been prepared according to the solubility data. For performing nucleation studies, a constant volume of 100 ml of saturated solution has been taken in a constant temperature bath for five different temperatures (303, 308, 313, 318 and 323 K). As per the poly-thermal method [11], the saturated solution has been carefully cooled from the preheated temperature to the nucleation temperature where the first visible critical nucleus has been observed. The meta-stable zone width has been determined as the difference between nucleation temperature and saturation temperature. In practice, wider meta-stable width is preferred for growing good quality crystals. The solubility and nucleation curves are shown in Fig. 1a. The solubility curve shows a positive solubility gradient. The study of induction period helps to modify and control the nucleation rate for preparing good quality crystals. As per isothermal method [12], the

3.1. X-ray diffraction studies Single crystal X-ray diffraction analysis of BTLC crystal suggests that the BTLC crystal crystallizes in orthorhombic structure with noncentrosymmetric space group Pna21. The obtained axial cell lengths dimensions are a=21.28 Å, b =4.14 Å, c=11.90 Å, Volume V=1048.38 (Å)3, the inter facial angles α=β=γ=90°. The experimental values were in accordance with the reported values [7]. 3.2. Nucleation kinetics 3.2.1. Theoretical approach The interfacial surface energy prevailing between the crystal and its surrounding saturated solution significantly influences the crystal growth and the nucleation rate [13]. Nielson and Sohnel [14] arrived at a relation to find out the interfacial surface energy (γ) which states

γ = ( kT/hd2) × ln (C/C 0)

(1)

where, k is Boltzmann constant, d is the mean diameter of ions, h is the hydration number which varies from 3.4 to 5, C and C0 are the mole fractions of solute in the super saturated and saturated solution respectively at temperature T. Another expression to calculate interfacial surface energy was put forward by Sangwal [15] as

γ = [kT] × [{3– ln (C/C 0)}/8 d2]

(2)

Christoffersen et al. [16] deduced an expression for interfacial surface energy based on the theory of surface nucleation as

γ = 0.282 × ( k T/d2) × ln (C/C 0)

(3)

Using the Eqs. (1–3) the values of interfacial surface energy have been computed and presented in Table 1. 3.2.2. Experimental approach As per the classical theory of homogeneous spherical nucleus

Fig. 1. (a) Meta-stable zone width of bis thiourea lead chloride (b) photograph of bis thiourea lead chloride crystal.

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maximum Gibbs free energy change value is known as critical nucleus. At this critical state, the free energy formation obeys the condition d (ΔG/dr)=0. So, the radius of the critical nucleus (r*) is given by

Table 1 Values of inter facial surface energy (γ) for BTLC crystals (mJ/m2). Saturation temperature (K)

Experimental value

Christoffersen model

NielsonSohnel model

Sangwal model

From graph

303 308 313 318 323

2.233 2.262 2.294 2.323 2.351

2.363 2.402 2.441 2.480 2.519

2.264 2.302 2.339 2.377 2.414

1.619 1.645 1.672 1.699 1.725

1.404 1.435 1.472 1.498 1.523

r* = −2γ/ΔGv

where, Gibbs free energy change for the formation of the critical nucleus (critical free energy barrier, ΔG*) is expressed as,

ΔG* = 16 γ3V3 /3 k2 T2 (lnS)2

J = A exp (−ΔG*/kT)

(11) 30

where A is constant whose value is 10 . The number of molecules in the critical nucleus is considered as the critical number ( i*) of nucleation process which is given by

(4)

where S denotes the super saturation ratio which is the ratio between the mole fractions of solute in the super saturated (C) and saturated solution (C0) at temperature T. τ is the induction period, B is constant, V is molar volume, N is Avogadro's number and R is the gas constant. Since ln B weakly depends on temperature, Eq. (4) can be re-written as,

γ3 = {3R3T3 (lnS)2 ln τ}/{16 π V2NA}

(10)

Rate of nucleation (J) may be defined as the number of critical nuclei formed per unit time per unit volume. It is given by,

formation [17], the relationship between induction period and interfacial surface energy can be given as

ln τ = − lnB + [{16 π γ3V2NA}/{3 R3T3 (lnS)2}]

(9)

i* = 4 π (r*)3 /3 v

(12)

Thus the values of free energy change, critical free energy change, critical radius, critical number and nucleation rate have been calculated and tabulated in Table 2. From the Tables 1 and 2, it has been understood that as the super saturation and temperature were increasing, interfacial surface energy and nucleation rate were favoured by temperature augmentation while free energy change, critical radius and critical number were decreasing with increase in temperature.

(5)

from which the experimental values of interfacial surface energy can be calculated. While assuming Eq. (4) as the equation of a straight line, a plot of ln τ Vs 1/(ln S)2 (Fig. 2) will have a slope (m) such that,

m = {16 π γ3V2NA}/{3 R3T3}

(6)

3.3. UV–visible spectral analysis

γ = [(3R3T3m /16 π V2NA)]1/3

(7)

3.3.1. Transmittance studies The optical transmission study is a pivotal tool to gauge suitability of the synthesized crystal for various NLO applications such as laser frequency doubling, optoelectronic appliances, optical bistability and optical harmonic generation [19]. The optical transmittance spectra of BTLC crystals, recorded in the wavelength range of 200–800 nm are shown in Fig. 3. The UV cut-off wavelength for BTLC is found to be at 285 nm which is sufficiently low to be used for Nd- YAG laser second harmonic generation [20]. The wide range and higher percentage of transmittance (73%) of BTLC crystal in the entire region of study has been established from its UV transmittance spectrum which is a salient feature of materials used in integrated optical devices such as modulators and filters [21]. The absence of the absorption in the visible region, might facilitate to attain microscopic NLO response with non zero hyper-polarizability value [22]. The reduced scattering from crystal point and line effects may be considered as the driving force [23] for the higher percentage of transmittance.

The interfacial surface energy values determined by the experiments have been found to be in accordance with the theoretical values obtained and are presented in Table 1. This confirms that the evaluated nucleation parameters can be used for optimization of the growth of BTLC crystals. The Gibbs free energy change (ΔG) between the crystal and its surrounding mother liquor works as the driving force of BTLC crystallization. As per homogeneous nucleation theory for spherical nucleation, this free energy change is given [18] as

ΔG = (4/3) π r 3ΔGv + 4 π r 2γ

(8)

Where, r is the nucleus radius and ΔGv is the energy change per unit volume which is always a negative quantity. The first term of Eq. (8) points out the formation of new surface and the second term specifies the chemical potential difference between the crystal and its mother liquor. According to classical nucleation theory, as the nucleus grows in size, Gibbs free energy change increases, reaches a maximum value and then starts coming down. The nucleus size which corresponds to

3.3.2. Band gap energy calculation Theoretical value of the band gap energy (Eg) is calculated as 4.33 eV from the equation,

Eg = hC/λ

(13)

where h is the Planck's constant, C is the velocity of light and λ is the wave number. From the transmittance (T), we can deduce the absorption coefficient (α) using the relation,

α = [2.303 log (1/T)]/d

(14)

where d denotes the thickness of the crystal. To calculate the experimental value of band gap energy, Tauc's graph is plotted (Fig. 4) between photon energy (hυ) and (αhυ)2. The linear portion of the resultant curve has been extrapolated towards the x-axis and the point of intersection is taken as the band gap energy. From the Fig. 4, the band gap energy for BTLC has been found to be 4.33 eV. As a result of this wide band gap, the BTLC crystal has exhibited appreciable transmittance in the visible region [24]. Experimentally determined value of band gap energy has been found to be in accordance with that of the theoretical value calculated

Fig. 2. Plot of ln τ Vs 1/(ln S)2.

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Table 2 Nucleation Parameters of BTLC crystals. Saturation temp. (K)

Nucleation temp (K)

Meta stable zone width

Super saturation ratio (C/C0)

Free energy change (ΔGv) (×106) (J/m3)

Critical Free energy (ΔGc) (×10–20) (J)

Critical radius (r*) (nm)

Critical number (i*)

Nucleation rate (J) (×1027) nuclei/s/Vol)

303

300.3

2.7

1.2 1.3 1.4 1.5

−2.909 −4.186 −5.368 −6.469

2.203 2.044 1.874 1.721

1.535 1.326 1.186 1.083

57.785 37.257 26.638 20.296

5.155 7.540 11.315 16.329

308

304.2

3.8

1.2 1.3 1.4 1.5

−2.957 −4.255 −5.456 −6.575

2.216 2.054 1.875 1.720

1.530 1.321 1.180 1.077

57.201 36.841 26.218 19.961

5.437 7.963 12.144 17.476

313

308.5

4.5

1.2 1.3 1.4 1.5

−3.005 −4.324 −5.545 −6.682

2.240 2.070 1.872 1.725

1.527 1.317 1.173 1.072

56.896 36.530 25.766 19.694

5.590 8.295 13.103 18.448

318

313.8

4.2

1.2 1.3 1.4 1.5

−3.053 −4.393 −5.634 −6.789

2.253 2.088 1.879 1.727

1.522 1.314 1.168 1.067

56.327 36.271 25.445 19.412

5.888 8.581 13.832 19.534

323

319.1

3.9

1.2 1.3 1.4 1.5

−3.101 −4.462 −5.722 −6.896

2.264 2.105 1.883 1.736

1.517 1.311 1.163 1.064

55.726 36.003 25.104 19.215

6.220 8.888 14.646 20.332

Fig. 3. UV–visible transmission spectrum of bis thiourea lead chloride.

Fig. 4. Plot of (αhν)2 Vs hν.

from Eq. (13). The band gap energy acts as an indicator of the crystalline nature of a solid. When the defect concentration is low, it results in the increased gap between valence and conduction bands. Thus, the higher value (4.33 eV) of BTLC indicates the minimum defects concentration present in the lattice [25]. Further, the band gap shares a direct relationship with polarisability nature [26]. As polarisability and SHG are interrelated, the higher value of band gap can be correlated with the possible SHG nature of BTLC crystal.

possible to ascertain the existence of phase matching property of the sample material [28] from the Kurtz and Perry method. The phase matching nature of the crystal can be easily established by measuring its SHG intensity as a function of particle size [29]. If a material owns phase matching nature, the SHG intensity increases with the increase of particle size up to the average coherence length and afterwards remains constant while for a non phase-matchable material, SHG varies inversely with the particle size [30]. In the present investigation, a Quanta Ray Spectra Physics Nd: YAG laser of 1064 nm wavelength,8 ns pulse width, 3 mJ input energy and a repetition rate of 10 Hz has been used. To study and confirm the existence of phase matching nature, the BTLC and standard KDP particles of size ranging from < 63, 63–125, 125–250, 250–345 and > 345 µm have been obtained using standard sieves. The powdered samples have been filled tightly in separate micro-capillary tubes. Using a monochromatic photomultiplier tube, the emitted SHG output (532 nm) has been collected and then converted into voltage output. The results obtained

3.4. Non linear optical studies 3.4.1. Experimental NLO and Phase matching studies A non linear optical effect originates from the interaction of a material with an electromagnetic field of high intensity. The powder SHG test as per Kurtz and Perry method [27] enables one to measure the optical nonlinearity efficiency of new materials with reference to standard urea or potassium dihydrogen phosphate (KDP). It is also 9

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Table 3 Hyper polarisability values of BTLC crystal.

for BTLC and KDP are plotted in Fig. 5. It is evident from the figure that the SHG efficiency of BTLC appreciably increases with particle size up to 250 µm, and the increase is gradual for larger particles. Thus the result gives a strong evidence for the phase matching nature of BTLC. Single crystals of BTLC crystallize in Pna21 which belongs to non-centrosymmetric space group. The non-centrosymmetry is usually accompanied by lacking of an inversion center which fulfils the condition for second order NLO material. The results obtained for BTLC show a powder SHG efficiency of about 1.1 times that of KDP. From the SHG experimental results, it is justified that the BTLC crystal can be used as an efficient alternative for KDP in various optoelectronic applications. This kind of improved SHG efficiency of materials may be due to the presence of appropriate electron sharing groups, responsible for the accentuation of the asymmetric electron distribution leading to enhanced crystallinity, polarisability and hyper polarisability [31].

i≠j

βxxx βxyy βxzz βyyy βyzz βyxx βzzz βzxx βzyy βxyz βtotal (×10–30 esu)

19.72 69.08 49.08 −91.45 23.3 −46.4 −3.1 −7.56 1.44 17.555 1.5507

1/2

βtot = (βx2 + βy2 + βz2 )

(16)

The complete equation for calculating the magnitude of first hyper polarizability is given as follows:

βtot = [(βxxx + βxyy +βxzz)2 + (βyyy +βyzz +βyxx)2 + (βzzz + βzxx + βzyy)2]1/2 (17) As the tensor values of the Gaussian program output will be in the atomic system of unit, they have been converted into electrostatic unit (esu) by using the relation, 1 a.u=8.6393×10–33 esu for hyper polarisability. The values are tabulated in Table 3. As the β value of BTLC (1.55×1030 esu) has been found to be non-zero and higher than that of established NLO material urea (0.3728×10–30 esu), the SHG efficiency of BTLC has been further substantiated. 3.5. Dielectric studies

3.4.2. Theoretical hyper polarizability calculation To serve as a supporting evidence for SHG efficiency of BTLC crystal, its theoretical hyper polarisability values have been calculated by Gaussian-03 program using the Becke3-Lee-Yang-Parr (B3LYP) functional supplemented with the standard 6–31 G (d, p) basis set [32]. As the first step of DFT calculation for hyperpolarizability, the geometry taken from the reported starting structures [7] were optimized (Fig. 6) using which the components of the first hyper polarisability have been calculated as:

∑ (βijj + βjij + βjji )

Values (in atomic units)

In presence of an applied electric field, the hyper-polarizability is indicated by a third rank tensor of 3×3×3 matrix with 27 components. Anyhow, using Kleinmann symmetry [33] the 27 components can be reduced into 10 components (βxxx, βxxy, βxyy, βyyy, βxxz, βxyz, βyyz, βxzz,βyzz and βzzz). The magnitude of the first hyper polarisability tensor can be calculated in terms of x, y, z as

Fig. 5. Variation of SHG with the particle size for BTLC and KDP.

βi =βiii + 1/3

Parameter

3.5.1. Dielectric permittivity Dielectric properties of a material can be correlated with its electro optic properties [34]. For a given crystal, an insight on the structural changes, molecular dynamics, transport phenomenon, defect behaviour, molecular anisotropy and electro-optical molecular responses can be obtained by the study of variance of dielectric properties with temperature and frequency of applied electrical field. Further, the polarization of the crystals due to the applied electric field forms the base for dielectric measurements. [35,36]. For the dielectric measurement studies, polished crystal sample was taken and its parallel

(15)

Fig. 6. Optimized structure of BTLC.

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Fig. 7. Plot of dielectric permittivity Vs log f for bis thiourea lead chloride.

Fig. 8. Plot of dielectric loss Vs log f for bis thiourea lead chloride.

surfaces were coated with silver paint to facilitate proper electrical contact between crystal and the electrodes. The measurements were done at the frequency regions of 50 Hz–5 MHz at 313, 333, 353 and 373 K. The real (εr) and imaginary (εi) parts of dielectric permittivity constant (ε) are given by the expression,

3.5.2. Dielectric loss A plot of variation of dielectric loss with respect to frequency and temperature, as depicted in Fig. 8, shows a similar trend as that of dielectric permittivity. This is because of the fact that the polarization process and conduction process follow similar mechanism. The space charge and macroscopic distortion cause higher tanδ at higher temperature and lower frequencies. With the increasing magnitude of frequency, a point will be attained where the space charge cannot sustain and adhere with the external electrical field. As a result, a dip in polarization will be experienced which may lead to the lowering of. tanδ values [45]. The periodical lowering of tan δ values with increasing frequency attests the defect free nature of the optical quality crystal [46].

ε r = C. d/ε 0 . A

(18)

ε i =ε r tan δ

(19)

where, C is the capacitance, d is the thickness of the material, ε0 is the absolute permittivity of the free space, A is the area and tanδ is the tangent loss. A graph plotted between dielectric permittivity and log frequency at various temperatures is shown in Fig. 7. From the figure, it has been observed that for all the temperatures, at lower frequencies the dielectric permittivity values are higher. The observed higher dielectric permittivity values at low frequency indicate the charge accumulation at the interface between the sample and electrode resulting in space charge polarization [37]. Moreover, at low to moderate frequencies, it is easy for dipoles to respond and orient themselves with the applied electric field. On increasing the frequency, dielectric constant is decreasing and become saturated. This phenomenon can be ascribed to the high occurrence of periodic reversal of the electric field at the interface which suppresses the contribution of charge carriers. It causes the dearth of excessive ion diffusion in the direction of electric field [38]. As a result, the dipole orientation is disturbed which weakens the interaction prevailing between the external electric field and dipoles. So the dielectric permittivity value is decreasing [39]. This low dielectric permittivity at high frequency values suggest the possible SHG conversion efficiency of BTLC crystal and are in good agreement with Miller rule [40]. The microelectronics industry needs low dielectric constant materials as an interlayer dielectric which surrounds and insulates the inter connecting wiring [41]. Moreover, lowering the dielectric constant value causes reduced delay, reduced power consumption and a minimal crosstalk between nearby interconnects. The materials with low dielectric permittivity lead to a small resistor-capacitor (RC) constant, permitting a higher bandwidth in the range of 1012 Hz for light modulation and hence are of special interest in the high-speed electro-optic modulating applications [42]. While analyzing about the temperature effects, it is established that the dielectric permittivity values are increasing appreciably with rise in temperature. This trend is caused by the thermal activation of charge carrier exchange in the lattice sites [43]. The values do not show any discontinuity, and abnormalities signaled the lack of phase transitions [44] in the BTLC crystal in the entire temperature range on which the experiment has been carried out.

3.5.3. Ac conductivity and energy of activation The alternating current conductivity σac is calculated by the relationship,

σac = ω ε 0 ε r tan δ

(20)

where, angular momentum ω=2πf, f is the frequency of applied field. On plotting a graph between σac and log ω at different temperatures, as shown in Fig. 9, a frequency independent plateau at lower frequency regions and dispersion behaviour at higher frequency portions was observed. The activation energy (Ea) of the electrical process is derived from an Arrhenius plot using the relation,

Fig. 9. Plot of ac conductivity Vs log ω for bis thiourea lead chloride.

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Table 4 Solid state parameters of BTLC crystals. Parameters

Values for BTLC crystals

Plasma energy (eV) Penn gap (eV) Fermi energy (eV) Polarisability by Penn gap (cm3) Polarisability by Clausius–Mossotti equation (cm3) Polarisability by band gap energy (cm3)

18.62 3.54 14.55 5.21×10−23 5.29×10−23 3.05×10–23

ship between the polarisability and band gap energy [50] is given as

α p = [ 1−( Eg /4.06)] × (M /ρ)x0.396 × 10 –24

From the Eqs. (23–29), the important solid state parameters which are required to interpret SHG efficiency have been elucidated and presented in Table 4. As the SHG efficiency depends on the polarisability, the higher values of polarisability readily indicate that BTLC will have more SHG efficiency. These observations serve as a supporting evidence for the obtained SHG results (Section 3.4.1) from Kurtz powder technique.

Fig. 10. Variation of log σac Vs T−1 for bis thiourea lead chloride.

σac = σ0 exp (−Ea /kT)

(21)

where σ0 denotes the conductivity at temperature T and k is Boltzmann constant. The plot of ln σac Vs 1000/T is presented in Fig. 10. From the linear fit graph, the slope has been measured and the activation energy was deduced from the formula,

Ea = (− Slope) × 1000 × Boltzmann constant

3.7. Mechanical studies 3.7.1. Determination hardness number and Meyer's index One of the most sought after properties of any device material is its mechanical strength, represented by its hardness. The hardness of the crystal can be considered as the ratio of applied load to the surface area of indentation. The hardness of the crystal provides an in-depth idea about the strength, molecular bindings, elastic constants and yield strength of the material [51]. The Vicker's hardness value is one of the significant deciding factors in selecting the cutting, grinding, polishing and processing steps of crystals in the fabrication of NLO devices [52]. In the present work, Vickers hardness indentations (Fig. 11a) have been made on the BTLC crystals at room temperature for 25, 50 and 100 g, maintaining the time of indentation as 10 s for all trials. For each load, five well defined indentations have been made and the average diagonal length has been used to calculate the micro-hardness number. The Vickers hardness numbers (HV) at different loads have been deduced from the formula,

(22)

The activation energy calculations resulted in the values of 0.079, 0.070, 0.062, 0.056 and 0.054 eV at frequencies of 1 kHz, 5 kHz, 10 kHz, 50 kHz and 100 kHz respectively. The low value of activation energy is an indicator of the ordered state and lesser number of defects prevailing in the sample [47]. 3.6. Solid state parameters Elucidation of solid state parameters is one of the interesting method to analyze second harmonic generation efficiency of a compound. For BTLC, the single crystal XRD data revealed the molecular weight (M) as 430.35 and density was measured as 2.7262 g cm−3. From dielectric studies, it is learnt that the dielectric constant was saturated (ε∞) for 1 MHz at a value of 17.3. Using Clausius–Mossotti equation, the polarisability (αp) can be calculated [48].

α p = (3 M /4πN ρ) × (ε∞−1 /ε∞+2)

Hv = 1.8544 P/d2,

(23)

(24)

where ħ=h/2π, ωp is the plasma angular frequency and Z is the total number of valence electrons. There are 66 valence electrons available in the case of BTLC. Once we know the valence electron plasma energy, the Penn gap (Ep), Fermi energy (EF) and polarisability (αp) are calculated [49] by the expressions

EP = ħω p /(ε∞−1)½

(25)

EF = 0.2948(ħω p)4/3

(26)

α p = [(ħω p)2 S0 /{(ħω p)2S0 + 3 EP 2}] × (M/ρ)x0.396 × 10 –24

(27)

where S0 is a material specific constant such that,

S0 = 1− {(EP /4 EF)} + {1/3} (EP /4 EF)1/2

(30)

where P is the applied load in Kg and d is the average diagonal length of indentation impression in mm. From the plot of hardness values Vs corresponding loads for BTLC

where N is Avogadro number. The polarisability value can also be obtained from the values of valence electron plasma energy and Penn gap. The valence electron plasma energy (ħωP) is given as,

ħω p = 28.8[(Z. ρ)/M]½

(29)

(28)

Yet another method to calculate the polarisability is making use of the band gap energy of the crystal. From UV spectral Tauc's plot, the band gap energy of the crystal was measured as 4.33 eV. The relation-

Fig. 11. (a) Crack pattern (b) Plot of Hv Vs P for bis thiourea lead chloride.

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Fig. 12. Plot of log P Vs log d for bis thiourea lead chloride. Fig. 13. Plot of P Vs d2 for bis thiourea lead chloride.

crystal as shown in Fig. 11b, it is learnt that hardness number increases with increasing load indicating the reverse indentation size effect (RISE) [53]. In RISE, the material undergoes a relaxation, accompanying a release of the indentation stress along the surface away from the indentation site, which may be due to the crack formation, dislocation activity and elastic deformation of the tip of the indenter. Meyer's work hardening coefficient (Meyer's index) can be calculated from the Meyer's law [54]. By this law, the load and the size of indentation can be related as

P = k1dn

The elastic stiffness constant C11 is calculated using Wooster's formula [58]

C11 = (Hv)7/4

This elastic stiffness constant value gives an idea of bonding toughness between the adjacent atoms. High value of C11 signifies that the binding forces between the atoms are quite strong [59]. The tendency of a material containing cracks to resist the fracture may be explained by fracture toughness (KC) analysis [60]. KC explains how much fracture stress is exerted on the materials under consistent loading. The cracks developed on a crystal determine the fracture toughness. Based on c/a value, Proton and Rawling [61] classified the cracks as Median cracks (c/a≥2.5) and Palmqvist cracks (c/a < 2.5) where a=d/2 and c is the crack length in μm, measured from the center of indentation mark to the crack end. The title compound shows c/a < 2.5 and hence the developed cracks may be considered as Palmqvist type. For Palmqvist crack system, the fracture toughness is given by,

(31)

where k1 is the material constant and n is Meyer's index. In the form of a straight line equation, the Eq. (28) can be written as,

log P = logk1 + n log d

(32)

A graph drawn between log P Vs log d is shown in Fig. 12. The n value is obtained from the slope of this line and it is found to be 3.12. For a material, if n > 2, the hardness increases with load and if n < 2, the hardness decreases with the load [53]. In the case of BTLC, n value has been found to be 3.12 and the result supports RISE pattern. According to Onitsch [55], n should lie between 1 and 1.6 for harder materials and above 1.6 for softer materials. So BTLC crystal comes under softer material category. The Hays and Kendall resistance pressure theory defines the resistance pressure as a minimum level of indentation load (W) below which there is no plastic deformation occurs [56]. As per this theory,

P–W = k2d2

K C = k P a/l1/2

(37)

Where, l=c−a, the mean Palmqvist crack length and k is the constant whose value is equal to 1/7 for the Vickers indenter. Brittleness index (Bi) of the crystal determines its fracture without any appreciable deformation. Brittleness index can be calculated from fracture toughness from the relation [62],

Bi = HV /K C

(33)

(38)

The values of Vickers's micro hardness number and other related mechanical parameters have been calculated and given in Table 5. When the hardness number is high, greater the stress required to form dislocation and hence the crystal will be of higher crystalline perfection. The higher mechanical strength and lower defects increases the laser damage threshold of the crystal and make the material more competent functional materials towards the laser technology and SHG applications [52]. The obtained hardness parameter values clearly attest the mechanical stability of BTLC crystal to act as a candidate for fabricating various opto-electronic devices such as laser driven fusion setup, medical and spectroscopic processor and optical communication devices [63].

where W is the minimum load to initiate plastic deformation (Newtonian resultant pressure) and k2 is a load dependent constant. The values of W and k2 have been calculated from the graphs plotted between P vs. d2 as depicted in Fig. 13. The plot turns out to be a straight line, where W (−30.75 g) is the intercept along the load axis and k2 (0.061) is the slope. The negative intercept is an indication of RISE pattern. From the k2 value, it is possible to calculate the corrected hardness (H0) of the material from the relation,

H 0 = 1854.4 × k2.

(36)

(34)

The corrected hardness value of the crystal has been calculated as 113.09 kg/mm2 for the BTLC crystal.

4. Conclusion 3.7.2. Determination yield strength, elastic stiffness constant, fracture toughness and brittleness index From the hardness value, the yield strength (σV) can be calculated [57] using the relation

σV = {HV/2.9} × {[ 1 – (n−2)] × [12.5(n−2)/1−(n−2)]n−2 }

The good quality single crystals of bis (thiourea) lead chloride have been grown by the slow solvent evaporation method. A positive solubility gradient has been established by the solubility graph. The values of critical size of the nucleus, critical number, growth rate and free energy changes have been calculated from the study of nucleation

(35) 13

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Table 5 Mechanical parameters of BTLC crystals. Load, P (gm)

Hardness number, Hv (Kg/mm2)

Elastic stiffness constant, C11 (GPa)

Yield strength σV (Gpa)

c/a value

Type of crack

Fracture toughness (KC) (g/μm1/2)

Brittleness index (Bi) (103 μm−1/2)

25 50 100

53.13 65.65 87.49

10.25 14.85 24.54

4.45 5.50 7.33

1.35 1.86 2.17

Palmqvist Palmqvist Palmqvist

23.07 33.34 63.31

2.30 1.97 1.38

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kinetics. Experimentally attained values of interfacial surface energy (ranging from 2.2 to 2.4 mJ/m2) have been found to be in good agreement with the values obtained from various theoretical models. Results from single crystal XRD analysis indicated that the BTLC crystal crystallized in orthorhombic structure with space group Pna21. The ultra violet and visible spectral studies revealed the cut off wavelength, transmittance and band gap energy 285 nm, 73% and 4.33 eV respectively. These values guaranteed the required optical quality of the title crystal. Further, the higher transmittance in the visible region might have facilitated the attainment of microscopic NLO response. The higher band gap energy indicated the crystalline nature of the sample. From the Kurtz-Perry method, the SHG efficiency of BTLC has been found to be 1.1 times as that of KDP reference sample. The test has indicated the phase matching nature of BTLC. The SHG efficiency has further been authenticated by the non zero value (1.5507×10–30 esu) of theoretical hyper polarizability. At higher temperature and higher frequencies, it has been observed that the dielectric measurements of BTLC crystals exhibited very low dielectric constant and less power dissipation which in turn suggested fewer defects in the samples. AC conductivity study has been employed to arrive at the values of activation energy of electrical process and it resulted in 0.079, 0.070, 0.062, 0.056 and 0.054 eV at frequencies of 1, 5, 10, 50 and 100 kHz respectively. These low activation values are an indication that the sample has more ordered crystallinity. The solid state parameters viz. plasma energy, Penn gap, Fermi energy and Polarisability, determined in this work unveiled the possible higher SHG efficiency of the title crystal. The Vicker's hardness study findings in terms of Meyer's index, stiffness constant, yield strength, fracture toughness and brittleness index strongly supported the mechanical stability of BTLC. The higher hardness values (53.13–87.49 kg/mm2) suggested that the BTLC will act as a competent material in laser technology. Thus the cumulative influence of all the discussed advantageous properties of BTLC proves its aptness to be considered as a reliable semi-organic NLO material and its high prospect to be prolifically utilized in various NLO and opto-electronic applications such as laser frequency doubling, laser driven fusion setup, optical harmonic generation and high speed electro optic filtration and modulation. Acknowledgements The authors thank Sophisticated Analytical Instrument Facility at Indian Institute of Technology (Chennai), Indian Institute of Science (Bengaluru), University of Madras (Guindy campus), St. Joseph College (Trichy), Mechanical department Research centre of St. Joseph's College of Engineering, (Chennai), PG and research department of Chemistry, Dr. Ambedkar Govt. Arts College (Chennai) for providing various lab facilities towards the research studies. References [1] P.N. Prasad, D.J. Williams, Introduction to Nonlinear Optical Effects in Molecules and Polymers, John-Wiley and Sons Inc, New York, 1991. [2] S.M. Ravi kumar, N. Melikechi, S. Selvakumar, P. Sagayaraj, Phys. B 403 (2008) 4160–4163. [3] J.G.S. Lopes, L.F.C. de Oliveira, H.G.M. Edwards, P.S. Santos, J. Raman Spectrosc. 35 (2004) 131–139. [4] S. Selvakumar, J.P. Julius, S. Rajasekar, A. Ramanand, P. Sagayaraj, Mater. Chem.

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