- Email: [email protected]
Refractive index, band gap energy, dielectric constant and polarizability calculations of ferroelectric Ethylenediaminium Tetrachlorozincate crystal
Author’s Accepted Manuscript Refractive index, band gap energy, dielectric constant and polarizability calculations of ferroelectric Ethylenediaminium Tetrachlorozincate crystal S. Kalyanaraman, .Vijayalakshmi
P.M.
Shajinshinu,
S www.elsevier.com/locate/jpcs
PII: DOI: Reference:
S0022-3697(15)30012-3 http://dx.doi.org/10.1016/j.jpcs.2015.07.007 PCS7585
To appear in: Journal of Physical and Chemistry of Solids Received date: 25 February 2015 Revised date: 22 May 2015 Accepted date: 6 July 2015 Cite this article as: S. Kalyanaraman, P.M. Shajinshinu and S .Vijayalakshmi, Refractive index, band gap energy, dielectric constant and polarizability calculations of ferroelectric Ethylenediaminium Tetrachlorozincate crystal, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2015.07.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Refractive index, Band gap energy, Dielectric constant and Polarizability calculations of Ferroelectric Ethylenediaminium Tetrachlorozincate crystal S.Kalyanaramana,*, P.M.Shajinshinua,b,S.Vijayalakshmia a
PG& Research Department of Physics, Sri Paramakalyani College, Alwarkurichi -627 412, India b
Department of Physics, Sun College of Engineering and Technology, Nagercoil -629 902 ,
India
Abstract Single crystal of Ethylenediaminium Tetrachlorozincate has been grown by slow evaporation method. The single crystal XRD study confirms the orthorhombic structure of the crystal. The presence of functional group vibrations are ascertained through FTIR and Raman studies. In optical studies, the insulating behaviour of the material is established by Tauc plot. The refractive index and the real dielectric constant of the crystal are calculated. The electronic polarizability in the high frequency optical region is also calculated from the dielectric constant values by using the Clausius-Mossotti equation. The large value of dielectric constant is identified through dielectric studies and it points to the ferroelectric behaviour of the material. Further an experimental study confirms the ferroelectric behaviour of the material. The total polarizability of the crystal owing to the space charge, dipole, ionic and electronic polarizability contributions is obtained experimentally, and it matches well with the theoretically obtained value from Penn analysis. Further, Plasmon energy and Fermi energy of the material are also calculated using Penn analysis.
Keywords: B. crystal growth; D. dielectric properties; D. ferroelectricity; D. optical properties
1
*Correspondence to: S.Kalyanaraman, Email: [email protected] Telephone: +91 94438 69658 Fax:+91 4634 283560 1. Introduction In earlier decades, crystals of the type A2B4 (where A = monovalent cation, NH4+ and its alkyl derivatives; B= bivalent transition metal cation) revealed an interesting field for studies owing to the occurrence of paraelectric-incommensurate-commensurate-ferroelectric phase transitions [1-6]. Later, a slight modification on these type of materials was carried out by adding the halogen group atoms such as A2BX4 (where X = halogen) that attracted a lot of attention due to the possibility of many successive phase transitions including incommensurate-commensurate phase ones together with their unusual physical properties [7-9]. These compounds represent the largest known group of insulating crystals with structurally incommensurate phases [10, 11]. Among these materials, zincates family materials especially Tetramethylammonium Tetracholorozincate ([N(CH3)4]2ZnCl4) and BisTetraethylammoniun Tetracholorozincate ([N(C2H5)4]2ZnCl4) have been widely studied for their structural phase transitions by various researchers using a variety of techniques in the past three decades [12-18]. Some focus on the spectroscopic features and thermal investigations of this type of materials is also found [9, 19, 20] in this series. Very few works concentrate on the polarizability and optical band gap energy of the zincates family materials of the type A2BX4 [21]. Apart from this type of materials similar studies on the optical properties of sodium acid phthalate ferroelectric material had been carried out [22]. The optical properties of these organic inorganic hybrid metal halide (A2BX4) ferroelectric materials find wide range of applications in laser devices. However, an extensive analysis of the optical constants such as band gap energy, extinction coefficient, refractive index and
2
dielectric permittivity along with the polarizbility of these ferroelectric materials is hardly found till date. In the present work, we analyse and report the optical constants of Ethylenediaminium Tetrachlorozincate ((C2H10N2)2+[ZnCl4]2-) crystal which is one of the members
of
zincates
(A2ZnCl4)
family.
Furthermore,
vibrational
spectroscopic
characterization and dielectric properties of the material are also addressed. From the obtained dielectric constant values, the polarizability of the material is calculated using Clausius–Mossotti equation. Theoretically, Penn analysis has also been made to support the obtained polarizability value in Clausius–Mossotti equation. In addition, Plasmon energy and Fermi energy are also determined through Penn analysis. 2. Experimental details All the materials used in the present study were of pure grade procured from Sigma Aldrich. The crystals under study were crystallized by slow evaporation method as given in the literature [23]. Crystals suitable for single crystal X – ray diffraction were selected and the lattice parameters were determined using Enraf –Nonius CAD – 4 diffractometer with CuKα radiation. FT – IR spectrum of the crystals were recorded in the wavenumber ranging from 4000 – 400 cm-1 (Thermo Nicolet, Avatar 370). Raman spectra of powder samples were measured using a micro Raman spectrometer (Renishaw, UK, model inVia) with 514 nm laser excitation from 1 cm-1 to 4000 cm-1. The UV – Vis reflectance and transmittance spectra were recorded using Cary– 300 instrument in the range 200-1100 nm (in terms of frequencies in the range of 1.4×1015-2.7×1014 Hz) with the resolution 1 nm. The dielectric measurements were carried out using N4L Numetric Q PSM 1735 instrument in the frequency range 1kHz-10MHz at room temperature. A polished grown crystal coated with silver paste was used to measure the capacitance. The crystal area which was used for this measurement was 0.21 mm2 (0.7 mm×0.3 mm). The Radiant Technology method (Tester
3
Name: PMF0713-334) was used for hysteresis loop study. The pelletized crystal of thickness 1.25 mm and area 1.32 cm2 was used for this measurement at room temperature. 3. Results and Discussion 3.1. Confirmation of the material 3.1.1.Single crystal XRD study The grown crystal ((C2H10N2)2+[ZnCl4]2-) is subjected to single crystal XRD study to obtain the lattice parameters and volume of the unit cell. The obtained parameters are a = 6.206 (3)Å, b = 12.882(1)Å and c= 19.108(2)Å and V= 1527(2)Å3 which agree reasonably with the literature values [23] and reveal the orthorhombic structure with the symmetry P212121 (
) of the material.
3.1.2.Vibrational studies The recorded FTIR and Raman spectra are displayed in Figs. 1 and 2 respectively. and the vibrational assignments are listed in Table 1. The
asymmetric CH3 stretching
vibration peak is found to have a weak intensity as observed at 3028 cm-1 in FTIR and a medium peak in Raman at 3038 cm-1. The peaks that appeared at 2577 and 2499 cm-1 in IR spectrum are assigned to C-H stretching of CH3. The peaks found at 963 and 894 cm-1 in FTIR and at 964 and 901 cm-1 in Raman are assigned to CH3 rocking vibrations. The assignments for N-H and C-H asymmetric stretching vibrations are given to the peaks observed at 2197 cm-1 in FTIR and at 2228 cm-1 in Raman, while the peak at 1927 cm-1 in IR is assigned to N-H and C-H symmetric stretching vibrations. Considering the CH2 group vibrations, the deformation of CH2 is observed at 1485 and 1440 cm-1 in FTIR and at 1497 and 1442 cm-1 in Raman. The peaks at 1375 and 1321
cm-1 in IR are assigned to CH2
wagging vibration and it is at 1338 cm-1 in Raman. The CH2 twisting vibration mode is found at 1213 cm-1 in FTIR. The observed peaks at 1171, 1124 and 809 cm-1 in FTIR correspond to CH2 rocking vibrations and in Raman it is at 1123 and 813cm-1. C-C stretching is identified at
4
1030 cm-1 in IR and at 1036 cm-1 in Raman. Further, the peak that appeared at 469 cm-1 is assigned to skeletal vibration and the peaks at 623 and 543 cm-1 are assigned to ethylene twisting vibrations. The low frequency Raman absorption peaks occurring at 281, 218, 146, 106 and 83 cm-1 are due to internal vibrations of ZnCl42- ion [20, 24]. 3.2. Optical studies The spectral distribution of Transmission T (λ) in the wavelength range 200 – 1100 nm is displayed in Fig.3. It could be noted that the transmittance is not uniform in the whole wavelength range. High transmittance is observed in the visible region (400-700 nm). From the recorded transmittance values the absorption coefficient (α) is calculated using the following relation ⁄
(1)
where, is the thickness of the crystal. The variation of absorption coefficient as a function of incident wavelength is portrayed in Fig.4. It has been observed that the absorption coefficient values monotonically decrease with the increase of wavelength. There is no absorption found in the visible region and it predicts the insulating behaviour of the material. The maximum absorption peak found at the IR region (974 nm) could be attributed to the atomic vibrations of the crystals and therefore it cannot correspond to any transitions. Since this absorption is analogue to the infrared absorption due to vibrations in polar molecules it is called as phonon absorption [25]. The absorption coefficient values are in the order of 102 m-1 and it indicates the indirect allowed transition of the material [26]. The optical band gap energy is determined from the absorption coefficient values using Tauc relation [27] (
)
(2)
where, hυ is the photon energy, α is the absorption coefficient, Eg is the band gap and A is a constant. The value of n = ½ for direct allowed transition and 2 for indirect allowed transition. For indirect allowed transition the eqn.(2) is slightly modified as [28] 5
( where
)
(3)
is the lattice phonon energy.
In our case, the material exhibits an indirect allowed transition and hence n is equal to 2. Intercept on (
corresponds to zero absorption coefficient in Tauc plot which gives the optical band gap energy value. The observed bandgap
energy value of Ethyelenediaminium Tetracholorozincate is 3.92 eV (Fig.5) and it suggests the insulating behaviour of the material. Hence, it is likely that this material esponds to dielectric behaviour. In addition, there is only one straight line that is observed in the Tauc plot which indicates the lattice phonon energy
for our material.
Since the absorption coefficient values are nearly zero in the range 300-900 nm, the extinction coefficient ( ) which correlates to the absorption coefficient as
⁄
should
be zero for insulating materials. Fig.6. could be the evidence for this prediction. The values of refractive index (n) have been calculated using the theory of reflectivity of light. According to this theory, the reflectance (R) can be expressed by Fresnel’s coefficients [29, 30] (4) For insulating materials this equation is simplified as (5) The calculated value of refractive index with the variation of wavelength is displayed in Fig.7. The Refractive index monotonically increases with the increase of wavelength. It is interesting to observe the values of refractive index as these lie in the range of refractive indices of the known ferroelectric materials [31-35]. The value of refractive index at 470 nm is 3.4 whereas it is 3.10 at the same wavelength for the ferroelectric material PbTiO3 [36] at room temperature. Hence it predicts the possibility of ferroelectric behaviour of the studied material. 6
Further, the real and imaginary dielectric functions (
also play a vital role in the
optical properties. They have been calculated as follows (6) (7) Since k =0, the imaginary dielectric function tends to zero whereas the real dielectric function can be
. When compared with refractive index values (Fig.7), it is noticeable that the
real dielectric constant value (Fig.8) is the square of the refractive index to satisfy the relation
. It is observed that the values of dielectric constant lie in the range 4-16 and
there is a steady decrease in dielectric constant values with the increasing values of frequencies. The polarizability due to the contribution of applied external electric field (electronic polarizability) in the optical region (high frequency region) is calculated using the calculated real dielectric constant values by Clausius-Mosotti equation [37] as follows [
][ ]
(8)
where M is the molecular weight (269.29) and ρ is the density (1.862 Mg m-3)of the crystal. The calculated polarizabilities are in the range 3×10-23- 4.8×10-23 cm3. The increase of polarizability with increasing frequencies is observed in Fig. 9. 3.3. Dielectric studies Dielectric properties of the materials are based on the interaction of an external field with the electric dipole moment of the sample. The frequency dependent dielectric loss of the material is portrayed in Fig.10. The lesser value of dielectric loss implies the reasonably good quality of the crystal. Since the crystal area is lesser than the electrode area, from the measured capacitance values of the crystal and air, the dielectric constant values of the crystals are calculated by using the following equation
7
[
(
)]
(9) where Ccrys is the capacitance of the crystal. Cair is the capacitance of the air of the same dimension as the crystal, Acrys and Aair represent the area of the crystal and area of the electrode respectively [38]. The variation of dielectric constant against frequency in the audio frequency region (1000-10000 Hz) is shown in Fig.11. The dielectric constant values drastically decrease with the increasing of frequency in this region. The dielectric constant is very high at lower frequency regions contrary to the optical frequency region (high frequency) because of the contribution of all polarizability components namely dipolar, space charge, ionic and electronic. The higher value of dielectric constant (in the order of 103) than the usual dielectric material confirms that the studied material is ferroelectric in nature [39]. From the calculated dielectric constant values, the polarizabilty of the material due to the contribution of all polarizability components is calculated by Clausis-Mosotti equation. The average polarizability is found to be 5.706×10-23 cm3. On comparison with electronic polarizability values, it is concluded that electric field contributes a major part in the determination of total polarizability value. 3.4. Ferroelectric hysteresis loop study The electric field response of polarization is displayed in Fig.12. for fixed voltages of 10, 50 and 90V.The hysteresis loop obtained shows the ferroelectric nature of the material. It is observed that the remanant polarization (Pr) gets increased with the increase of applied voltage. Moreover, there is a resistive leakage along grain boundaries which is identified in the hysteresis loop at the mentioned voltages. It suggests the material is ferroelectric ceramic like the already known inorganic Perovskite structure materials BaTiO3 and PbTiO3. Further it indicates the best suitability of the material as a capacitor since it is ferroelectric ceramic.
8
3.5. Penn analysis Penn analysis [40, 41] focuses on the dielectric constant and its related properties of the wide band gap semiconductors. In general, the dielectric constant explicitly depends on the plasmon energy, average gap (Penn gap) and the Fermi energy. The Penn gap is determined by fitting the dielectric constant (
with the plasmon energy. An attempt is
made on the use of Penn analysis for our insulating material to find the total polarizability value with the obtained high value of dielectric constant from the dielectric studies. The valence electron Plasmon energy (
) is given by
√
(10)
where, Z is the total number of valence states(Z=38 for our material), ρ is the density and M is the molecular weight of the crystal. The Fermi energy
is calculated as follows using (11)
The polarizability α is obtained as ⌈ where
⌉
(12)
is the Penn gap and
is a constant for the material which are defined by (13)
(
)
(14)
The calculated Plasmon energy is 14.76 eV and Fermi energy is 10.676 eV. Since the constant
for the original Penn model, we have to concentrate only on the polarizability
values that correspond to
whose value is nearly equal to “1”. For our material the average
is 0.991 and the average polarizability is found to be 5.717×10-23 cm3 which agrees well with the polarizability value obtained from Clausis-Mossotti equation. 9
4. Summary and Conclusion The ferroelectric Ethylenediaminium Tetrachlorozincate ((C2H10N2)2+[ZnCl4]2-) crystal is synthesized by slow evaporation method. The functional groups such as CH3, CH2 and N-H vibrations in the material are identified both in FTIR and Raman studies and ZnCl4 vibrations are identified in Raman. Together with the vibrational analysis, single crystal XRD study confirms the formation of the material in orthorhombic structure. The absence of absorption in the visible region is identified from UV-Vis studies and the absorption coefficient values (in the order of 102 m-1) suggest the indirect bang gap nature of the material. The optical bandgap energy is found to be 3.92 eV from Tauc plot and it implies the insulating behaviour of the material. The zero value of extinction coefficient supports the insulating behaviour and it leads to the absence of imaginary dielectric function. The calculated refractive index at 470 nm is 3.4 and agrees with the refractive index of the ferroelectric material PbTiO3 at the same wavelength. The real dielectric constant is derived from the refractive index values. The electronic polarizability is calculated from the real part of the dielectric constant values using the Clausius-Mossotti equation in the optical frequency region and it is found to be in the range 3×10-23- 4.8×10-23 cm3.The ferroelectric behaviour is confirmed by the large value of dielectric constant (nearly in the order of 103) obtained through dielectric studies. The obtained hysteresis loop from Radiant Technology method strongly supports the ferroelectric ceramic behaviour of the material. The experimentally calculated polarizability value (5.706×10-23 cm3) due to the contribution of all polarizability components( space charge, dipolar, ionic and electronic) is matches well with the theoretically calculated value (5.717×10-23 cm3) through Penn analysis. The electronic polarizability contribution is identified as a major part in the determination of total polarizability.
10
Acknowledgements The authors would like to thank Dr.T.R.Ravindran, Materials Science Group, IGCAR, Kalpakkam, India for recording Raman measurement. We also acknowledge the Sophisticated Analytical Instrument Facility (SAIF), Cochin University, Cochin, India for taking measurements of FTIR and UV-Vis.
References [1] M. Quilichini, J. P. Mathieu, M. LePostollec , N. Toupry, J. Phys. (Paris) 43 (1982) 787. [2] I. Ruiz Larrea, A. Lopez-Echarri, M. J. Tello, J. Phys. C 14 (1981) 3171. [3] K. Hasebe, H. Mashiyama, S. Tanisaki, J. Phys. Soc. Jpn. 49 (1 980) 1633. [4] H. Mashiyama, S. Tanisaki, J. Phys. Soc. Jpn. 50 (1981) 1413. [5] H. Shimizu, N. Abe, N. Kokubo. N. Yasuda , S. Fujimoto, Solid State Commun. 34 (1980) 363. [6] J. Sugiyama, M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc.Jpn. 49 (1980) 1405. [7] G. Amirthaganesan, U. Binesh, M. A. Kandhaswamy, M. Dhandapani, V. Srinivasan, Cryst. Res. Technol. 41 (2006)708. [8] Tsai-Shia Jung, Hsiang-Lin Liu, Jiang-Tsu Yu, Chinese J. Phys. 39(2001)344 [9] M. El glaoui, M.L. mrad, E. Jeanneau, C. Nasr, E-Journal of Chemistry 7(4)(2010)1562-1570 [10] H. Z. Cummins, Phys. Rev. 185(1990) 211. [11] J. A. Desilva, F. E. O.Melo, J. M. Filho, F. F. Germano, J. E. Horeira, J. Phys. C: Solid Stat. Phys. 19 (1986) 3797. [12] T. P. Melia, R. Merrifield, J. Chem. Soc. A, 1166 (1970). [ 13 ] A. Bencini, C. Benelli, D. Gatteschi, Inorg. Chem. 19 (1980) 1632. [ 14] C. P. Landee , E. F. Jr. Westrum, J. Chem. Thermodynamics 11 (1979) 247.
11
[ 15 ] M. Iwata, Y. Ishibashi, J. Phys. Soc. Jpn. 60 (1991) 3245. [16] Mahendra Pal,Anshu Agarwal, D. P. Khandelwal, H. D. Bist, J. Raman Spectrosc. 17 (1986) 345. [17] V. I. Torgasheyv, YU.I. Yuzyukl, M. Rarkiny, I. Durnev, L. T. Latush, Phys. Stat. Sol. B 165(1991)305 [18] A. R. lim, K- W.Hyung,K- S. Hong,S-Y. Jeong, Phys. Stat. Sol. B 219 (2000)389 [19] J.M. Perez-Mato, J.L. Manes, J. Fernandez, J. Zuniga, M.J. Tello, C. Socias, M.A. Arriandiaga, Phys. Stat. Sol. A 68 (1981) 29. [20] S.Kalyanaraman, V.Krishnakumar, Hans Hagemann,K.Ganesan, J.Phy. Chem.Solids 68(2007)256 [21] R. Priya , S.Krishnan , G.Bhagavannarayana , S.JeromeDas, Physica B 406 (2011) 1345–1350 [22] S. Krishnan, C. Justin Raj, S. Dinakaran, R. Uthrakumar, R. Robert, S. Jerome Das, J.Phy. Chem.Solids 69(2008)2883 [23] William T. A. Harrison, Acta Cryst. E61 (2005) m1951. [24] K. Nakamoto, Infrared and Raman Spectra of Inorganic Co-ordination Compounds, Wiley-Interscience, New York, 1978. [25] Mark Fox, Optical properties of solids, Oxford University Press, New York, 2001. [26] Rolf E.Hummel, Electronic Properties of Materials, Springer, New York, 2010. [27] J.Tauc, Amorphous and Liquid Semiconductor, Plenum Press, New York, 1979. [28] J.Bardeen, F.J. Blatt, L. H. Hall, in Proc. Internat. Conf. Photoconductivity, Atlantic City ,Wiley, New York, 1956 [29] D.P. Gosain, T.Shimizu, M.Suzuki, J. Mater. Sci. 26 (1991) 3271. [30] D.J. Gravesteijn, Appl. Opt.27(1988) 736. [31] F.A. Miranda, F.W. Vankeuls, R.R. Romanofsky, C.H. Mueller, S. Alterovitz, G.
12
Subramanyam, Integr. Ferroelectr. 42 (2002)131. [32] H,Y.Tian, W.G. Luo, X.H.Pu, P.S. Qiu, X.Y. He, A.L. Ding, Solid State Commun.117 (2001) 315-319. [33] F.M. Pontes, E.R. Leite, D.S.L. Pontes, E. Longo, E.M.S. Santos, S. Mergulhao, P.S. Pizani, Jr. F. Lanciotti, T.M. Boschi, J.A.Varela, J. A. J. Appl. Phys.91(9) (2002) 5972. [34] A.Deineka, L. Jastrabik, G. Suchaneck, G.Gerlach, Ferroelectrics 273 (2002) 155. [35] F.E. Fernandez, Y. Gonzalez, H. Liu, A. Martinez, V. Rodriguez, W. Jia, Integr. Ferroelectr. 42 (2002) 219. [36] Y.Z. Gu, D.H.Gu, F.X.Gan, Nonlinear Optics, 28(4) (2001) 283. [37] N.M. Ravindra, V.K. Srivastava, Infrared Phys. 20 (1980) 67. [38]M. Meena, C.K. Mahadevan, Crys. Res. Tech. 43(2008)166. [39] C. Kittel, Introduction to Solid State Physics,Wiley, India,2006. [40] N.M. Ravindra, R.P. Bhardwaj, K. Sunil Kumar, V.K. Srivastava, Infrared Phys. 21 (1981) 369. [41] D.R.Penn, Phys. Rev. 128 (1962) 2093
Figures
13
Fig. 1. FTIR spectrum
14
Fig.2. Raman spectrum
15
Fig. 3. Recorded Transmittance spectrum
16
Fig.4. Calculated Absorption coefficient plot
60
(αhυ)^1/2(eV/m)^1/2
50 40 30 20 10 0 1.8 2 2.22.42.62.8 3 3.23.43.63.8 4 4.24.44.64.8 5 5.25.45.65.8 6 6.2
Energy hν (eV)
Fig.5. Tauc plot (Band gap energy determination) 17
Fig. 6. Calculated extinction coefficient plot
18
Fig.7. Calculated Refractive index plot
19
Fig.8. Variation of calculated Real Dielectric constants with optical frequencies
20
Fig. 9.Electronic polarizability in optical region
21
Fig.10. Variation of dielectric loss with respect to frequency
22
Fig. 11. Dielectric constant variations in the lower frequencies
23
0.04
Polarization(μC/cm2)
0.03
Pr 90V
0.02
50V
0.01
10V
0 -0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.01 -0.02 Electric field (kV/cm) -0.03 -0.04
Fig. 12. Ferroelectric Hysteresis loop
24
0.8
Table 1. Selected vibrational assignments Wavenumber FT-IR (cm-1)
Raman(cm-1)
Assignments
3028
3038
asym.strect. of CH3
2577
------
C-H sym.stret. of CH3
2499
------
C-H sym.stret. of CH3
2197
2228
C-H and N-H asym.stret.
1927
------
C-H and N-H sym.stret.
1485
1497
def. of CH2
1440
1442
def. of CH2
1375
------
wagg. of CH2
1321
1338
wagg.of CH2
1213
------
twist.of CH2
1171
------
rock. of CH2
1124
1123
rock. of CH2
1030
1036
C-C stret.
963
964
894
901
809
813
623
------
ethylene twisting
543
------
ethylene twisting
469
------
skeletal vibration
rock. of CH3
281 218 146
internal vibrations of ZnCl42-
106 83
25
P.M.
Shajinshinu,
S www.elsevier.com/locate/jpcs
PII: DOI: Reference:
S0022-3697(15)30012-3 http://dx.doi.org/10.1016/j.jpcs.2015.07.007 PCS7585
To appear in: Journal of Physical and Chemistry of Solids Received date: 25 February 2015 Revised date: 22 May 2015 Accepted date: 6 July 2015 Cite this article as: S. Kalyanaraman, P.M. Shajinshinu and S .Vijayalakshmi, Refractive index, band gap energy, dielectric constant and polarizability calculations of ferroelectric Ethylenediaminium Tetrachlorozincate crystal, Journal of Physical and Chemistry of Solids, http://dx.doi.org/10.1016/j.jpcs.2015.07.007 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Refractive index, Band gap energy, Dielectric constant and Polarizability calculations of Ferroelectric Ethylenediaminium Tetrachlorozincate crystal S.Kalyanaramana,*, P.M.Shajinshinua,b,S.Vijayalakshmia a
PG& Research Department of Physics, Sri Paramakalyani College, Alwarkurichi -627 412, India b
Department of Physics, Sun College of Engineering and Technology, Nagercoil -629 902 ,
India
Abstract Single crystal of Ethylenediaminium Tetrachlorozincate has been grown by slow evaporation method. The single crystal XRD study confirms the orthorhombic structure of the crystal. The presence of functional group vibrations are ascertained through FTIR and Raman studies. In optical studies, the insulating behaviour of the material is established by Tauc plot. The refractive index and the real dielectric constant of the crystal are calculated. The electronic polarizability in the high frequency optical region is also calculated from the dielectric constant values by using the Clausius-Mossotti equation. The large value of dielectric constant is identified through dielectric studies and it points to the ferroelectric behaviour of the material. Further an experimental study confirms the ferroelectric behaviour of the material. The total polarizability of the crystal owing to the space charge, dipole, ionic and electronic polarizability contributions is obtained experimentally, and it matches well with the theoretically obtained value from Penn analysis. Further, Plasmon energy and Fermi energy of the material are also calculated using Penn analysis.
Keywords: B. crystal growth; D. dielectric properties; D. ferroelectricity; D. optical properties
1
*Correspondence to: S.Kalyanaraman, Email: [email protected] Telephone: +91 94438 69658 Fax:+91 4634 283560 1. Introduction In earlier decades, crystals of the type A2B4 (where A = monovalent cation, NH4+ and its alkyl derivatives; B= bivalent transition metal cation) revealed an interesting field for studies owing to the occurrence of paraelectric-incommensurate-commensurate-ferroelectric phase transitions [1-6]. Later, a slight modification on these type of materials was carried out by adding the halogen group atoms such as A2BX4 (where X = halogen) that attracted a lot of attention due to the possibility of many successive phase transitions including incommensurate-commensurate phase ones together with their unusual physical properties [7-9]. These compounds represent the largest known group of insulating crystals with structurally incommensurate phases [10, 11]. Among these materials, zincates family materials especially Tetramethylammonium Tetracholorozincate ([N(CH3)4]2ZnCl4) and BisTetraethylammoniun Tetracholorozincate ([N(C2H5)4]2ZnCl4) have been widely studied for their structural phase transitions by various researchers using a variety of techniques in the past three decades [12-18]. Some focus on the spectroscopic features and thermal investigations of this type of materials is also found [9, 19, 20] in this series. Very few works concentrate on the polarizability and optical band gap energy of the zincates family materials of the type A2BX4 [21]. Apart from this type of materials similar studies on the optical properties of sodium acid phthalate ferroelectric material had been carried out [22]. The optical properties of these organic inorganic hybrid metal halide (A2BX4) ferroelectric materials find wide range of applications in laser devices. However, an extensive analysis of the optical constants such as band gap energy, extinction coefficient, refractive index and
2
dielectric permittivity along with the polarizbility of these ferroelectric materials is hardly found till date. In the present work, we analyse and report the optical constants of Ethylenediaminium Tetrachlorozincate ((C2H10N2)2+[ZnCl4]2-) crystal which is one of the members
of
zincates
(A2ZnCl4)
family.
Furthermore,
vibrational
spectroscopic
characterization and dielectric properties of the material are also addressed. From the obtained dielectric constant values, the polarizability of the material is calculated using Clausius–Mossotti equation. Theoretically, Penn analysis has also been made to support the obtained polarizability value in Clausius–Mossotti equation. In addition, Plasmon energy and Fermi energy are also determined through Penn analysis. 2. Experimental details All the materials used in the present study were of pure grade procured from Sigma Aldrich. The crystals under study were crystallized by slow evaporation method as given in the literature [23]. Crystals suitable for single crystal X – ray diffraction were selected and the lattice parameters were determined using Enraf –Nonius CAD – 4 diffractometer with CuKα radiation. FT – IR spectrum of the crystals were recorded in the wavenumber ranging from 4000 – 400 cm-1 (Thermo Nicolet, Avatar 370). Raman spectra of powder samples were measured using a micro Raman spectrometer (Renishaw, UK, model inVia) with 514 nm laser excitation from 1 cm-1 to 4000 cm-1. The UV – Vis reflectance and transmittance spectra were recorded using Cary– 300 instrument in the range 200-1100 nm (in terms of frequencies in the range of 1.4×1015-2.7×1014 Hz) with the resolution 1 nm. The dielectric measurements were carried out using N4L Numetric Q PSM 1735 instrument in the frequency range 1kHz-10MHz at room temperature. A polished grown crystal coated with silver paste was used to measure the capacitance. The crystal area which was used for this measurement was 0.21 mm2 (0.7 mm×0.3 mm). The Radiant Technology method (Tester
3
Name: PMF0713-334) was used for hysteresis loop study. The pelletized crystal of thickness 1.25 mm and area 1.32 cm2 was used for this measurement at room temperature. 3. Results and Discussion 3.1. Confirmation of the material 3.1.1.Single crystal XRD study The grown crystal ((C2H10N2)2+[ZnCl4]2-) is subjected to single crystal XRD study to obtain the lattice parameters and volume of the unit cell. The obtained parameters are a = 6.206 (3)Å, b = 12.882(1)Å and c= 19.108(2)Å and V= 1527(2)Å3 which agree reasonably with the literature values [23] and reveal the orthorhombic structure with the symmetry P212121 (
) of the material.
3.1.2.Vibrational studies The recorded FTIR and Raman spectra are displayed in Figs. 1 and 2 respectively. and the vibrational assignments are listed in Table 1. The
asymmetric CH3 stretching
vibration peak is found to have a weak intensity as observed at 3028 cm-1 in FTIR and a medium peak in Raman at 3038 cm-1. The peaks that appeared at 2577 and 2499 cm-1 in IR spectrum are assigned to C-H stretching of CH3. The peaks found at 963 and 894 cm-1 in FTIR and at 964 and 901 cm-1 in Raman are assigned to CH3 rocking vibrations. The assignments for N-H and C-H asymmetric stretching vibrations are given to the peaks observed at 2197 cm-1 in FTIR and at 2228 cm-1 in Raman, while the peak at 1927 cm-1 in IR is assigned to N-H and C-H symmetric stretching vibrations. Considering the CH2 group vibrations, the deformation of CH2 is observed at 1485 and 1440 cm-1 in FTIR and at 1497 and 1442 cm-1 in Raman. The peaks at 1375 and 1321
cm-1 in IR are assigned to CH2
wagging vibration and it is at 1338 cm-1 in Raman. The CH2 twisting vibration mode is found at 1213 cm-1 in FTIR. The observed peaks at 1171, 1124 and 809 cm-1 in FTIR correspond to CH2 rocking vibrations and in Raman it is at 1123 and 813cm-1. C-C stretching is identified at
4
1030 cm-1 in IR and at 1036 cm-1 in Raman. Further, the peak that appeared at 469 cm-1 is assigned to skeletal vibration and the peaks at 623 and 543 cm-1 are assigned to ethylene twisting vibrations. The low frequency Raman absorption peaks occurring at 281, 218, 146, 106 and 83 cm-1 are due to internal vibrations of ZnCl42- ion [20, 24]. 3.2. Optical studies The spectral distribution of Transmission T (λ) in the wavelength range 200 – 1100 nm is displayed in Fig.3. It could be noted that the transmittance is not uniform in the whole wavelength range. High transmittance is observed in the visible region (400-700 nm). From the recorded transmittance values the absorption coefficient (α) is calculated using the following relation ⁄
(1)
where, is the thickness of the crystal. The variation of absorption coefficient as a function of incident wavelength is portrayed in Fig.4. It has been observed that the absorption coefficient values monotonically decrease with the increase of wavelength. There is no absorption found in the visible region and it predicts the insulating behaviour of the material. The maximum absorption peak found at the IR region (974 nm) could be attributed to the atomic vibrations of the crystals and therefore it cannot correspond to any transitions. Since this absorption is analogue to the infrared absorption due to vibrations in polar molecules it is called as phonon absorption [25]. The absorption coefficient values are in the order of 102 m-1 and it indicates the indirect allowed transition of the material [26]. The optical band gap energy is determined from the absorption coefficient values using Tauc relation [27] (
)
(2)
where, hυ is the photon energy, α is the absorption coefficient, Eg is the band gap and A is a constant. The value of n = ½ for direct allowed transition and 2 for indirect allowed transition. For indirect allowed transition the eqn.(2) is slightly modified as [28] 5
( where
)
(3)
is the lattice phonon energy.
In our case, the material exhibits an indirect allowed transition and hence n is equal to 2. Intercept on (
corresponds to zero absorption coefficient in Tauc plot which gives the optical band gap energy value. The observed bandgap
energy value of Ethyelenediaminium Tetracholorozincate is 3.92 eV (Fig.5) and it suggests the insulating behaviour of the material. Hence, it is likely that this material esponds to dielectric behaviour. In addition, there is only one straight line that is observed in the Tauc plot which indicates the lattice phonon energy
for our material.
Since the absorption coefficient values are nearly zero in the range 300-900 nm, the extinction coefficient ( ) which correlates to the absorption coefficient as
⁄
should
be zero for insulating materials. Fig.6. could be the evidence for this prediction. The values of refractive index (n) have been calculated using the theory of reflectivity of light. According to this theory, the reflectance (R) can be expressed by Fresnel’s coefficients [29, 30] (4) For insulating materials this equation is simplified as (5) The calculated value of refractive index with the variation of wavelength is displayed in Fig.7. The Refractive index monotonically increases with the increase of wavelength. It is interesting to observe the values of refractive index as these lie in the range of refractive indices of the known ferroelectric materials [31-35]. The value of refractive index at 470 nm is 3.4 whereas it is 3.10 at the same wavelength for the ferroelectric material PbTiO3 [36] at room temperature. Hence it predicts the possibility of ferroelectric behaviour of the studied material. 6
Further, the real and imaginary dielectric functions (
also play a vital role in the
optical properties. They have been calculated as follows (6) (7) Since k =0, the imaginary dielectric function tends to zero whereas the real dielectric function can be
. When compared with refractive index values (Fig.7), it is noticeable that the
real dielectric constant value (Fig.8) is the square of the refractive index to satisfy the relation
. It is observed that the values of dielectric constant lie in the range 4-16 and
there is a steady decrease in dielectric constant values with the increasing values of frequencies. The polarizability due to the contribution of applied external electric field (electronic polarizability) in the optical region (high frequency region) is calculated using the calculated real dielectric constant values by Clausius-Mosotti equation [37] as follows [
][ ]
(8)
where M is the molecular weight (269.29) and ρ is the density (1.862 Mg m-3)of the crystal. The calculated polarizabilities are in the range 3×10-23- 4.8×10-23 cm3. The increase of polarizability with increasing frequencies is observed in Fig. 9. 3.3. Dielectric studies Dielectric properties of the materials are based on the interaction of an external field with the electric dipole moment of the sample. The frequency dependent dielectric loss of the material is portrayed in Fig.10. The lesser value of dielectric loss implies the reasonably good quality of the crystal. Since the crystal area is lesser than the electrode area, from the measured capacitance values of the crystal and air, the dielectric constant values of the crystals are calculated by using the following equation
7
[
(
)]
(9) where Ccrys is the capacitance of the crystal. Cair is the capacitance of the air of the same dimension as the crystal, Acrys and Aair represent the area of the crystal and area of the electrode respectively [38]. The variation of dielectric constant against frequency in the audio frequency region (1000-10000 Hz) is shown in Fig.11. The dielectric constant values drastically decrease with the increasing of frequency in this region. The dielectric constant is very high at lower frequency regions contrary to the optical frequency region (high frequency) because of the contribution of all polarizability components namely dipolar, space charge, ionic and electronic. The higher value of dielectric constant (in the order of 103) than the usual dielectric material confirms that the studied material is ferroelectric in nature [39]. From the calculated dielectric constant values, the polarizabilty of the material due to the contribution of all polarizability components is calculated by Clausis-Mosotti equation. The average polarizability is found to be 5.706×10-23 cm3. On comparison with electronic polarizability values, it is concluded that electric field contributes a major part in the determination of total polarizability value. 3.4. Ferroelectric hysteresis loop study The electric field response of polarization is displayed in Fig.12. for fixed voltages of 10, 50 and 90V.The hysteresis loop obtained shows the ferroelectric nature of the material. It is observed that the remanant polarization (Pr) gets increased with the increase of applied voltage. Moreover, there is a resistive leakage along grain boundaries which is identified in the hysteresis loop at the mentioned voltages. It suggests the material is ferroelectric ceramic like the already known inorganic Perovskite structure materials BaTiO3 and PbTiO3. Further it indicates the best suitability of the material as a capacitor since it is ferroelectric ceramic.
8
3.5. Penn analysis Penn analysis [40, 41] focuses on the dielectric constant and its related properties of the wide band gap semiconductors. In general, the dielectric constant explicitly depends on the plasmon energy, average gap (Penn gap) and the Fermi energy. The Penn gap is determined by fitting the dielectric constant (
with the plasmon energy. An attempt is
made on the use of Penn analysis for our insulating material to find the total polarizability value with the obtained high value of dielectric constant from the dielectric studies. The valence electron Plasmon energy (
) is given by
√
(10)
where, Z is the total number of valence states(Z=38 for our material), ρ is the density and M is the molecular weight of the crystal. The Fermi energy
is calculated as follows using (11)
The polarizability α is obtained as ⌈ where
⌉
(12)
is the Penn gap and
is a constant for the material which are defined by (13)
(
)
(14)
The calculated Plasmon energy is 14.76 eV and Fermi energy is 10.676 eV. Since the constant
for the original Penn model, we have to concentrate only on the polarizability
values that correspond to
whose value is nearly equal to “1”. For our material the average
is 0.991 and the average polarizability is found to be 5.717×10-23 cm3 which agrees well with the polarizability value obtained from Clausis-Mossotti equation. 9
4. Summary and Conclusion The ferroelectric Ethylenediaminium Tetrachlorozincate ((C2H10N2)2+[ZnCl4]2-) crystal is synthesized by slow evaporation method. The functional groups such as CH3, CH2 and N-H vibrations in the material are identified both in FTIR and Raman studies and ZnCl4 vibrations are identified in Raman. Together with the vibrational analysis, single crystal XRD study confirms the formation of the material in orthorhombic structure. The absence of absorption in the visible region is identified from UV-Vis studies and the absorption coefficient values (in the order of 102 m-1) suggest the indirect bang gap nature of the material. The optical bandgap energy is found to be 3.92 eV from Tauc plot and it implies the insulating behaviour of the material. The zero value of extinction coefficient supports the insulating behaviour and it leads to the absence of imaginary dielectric function. The calculated refractive index at 470 nm is 3.4 and agrees with the refractive index of the ferroelectric material PbTiO3 at the same wavelength. The real dielectric constant is derived from the refractive index values. The electronic polarizability is calculated from the real part of the dielectric constant values using the Clausius-Mossotti equation in the optical frequency region and it is found to be in the range 3×10-23- 4.8×10-23 cm3.The ferroelectric behaviour is confirmed by the large value of dielectric constant (nearly in the order of 103) obtained through dielectric studies. The obtained hysteresis loop from Radiant Technology method strongly supports the ferroelectric ceramic behaviour of the material. The experimentally calculated polarizability value (5.706×10-23 cm3) due to the contribution of all polarizability components( space charge, dipolar, ionic and electronic) is matches well with the theoretically calculated value (5.717×10-23 cm3) through Penn analysis. The electronic polarizability contribution is identified as a major part in the determination of total polarizability.
10
Acknowledgements The authors would like to thank Dr.T.R.Ravindran, Materials Science Group, IGCAR, Kalpakkam, India for recording Raman measurement. We also acknowledge the Sophisticated Analytical Instrument Facility (SAIF), Cochin University, Cochin, India for taking measurements of FTIR and UV-Vis.
References [1] M. Quilichini, J. P. Mathieu, M. LePostollec , N. Toupry, J. Phys. (Paris) 43 (1982) 787. [2] I. Ruiz Larrea, A. Lopez-Echarri, M. J. Tello, J. Phys. C 14 (1981) 3171. [3] K. Hasebe, H. Mashiyama, S. Tanisaki, J. Phys. Soc. Jpn. 49 (1 980) 1633. [4] H. Mashiyama, S. Tanisaki, J. Phys. Soc. Jpn. 50 (1981) 1413. [5] H. Shimizu, N. Abe, N. Kokubo. N. Yasuda , S. Fujimoto, Solid State Commun. 34 (1980) 363. [6] J. Sugiyama, M. Wada, A. Sawada, Y. Ishibashi, J. Phys. Soc.Jpn. 49 (1980) 1405. [7] G. Amirthaganesan, U. Binesh, M. A. Kandhaswamy, M. Dhandapani, V. Srinivasan, Cryst. Res. Technol. 41 (2006)708. [8] Tsai-Shia Jung, Hsiang-Lin Liu, Jiang-Tsu Yu, Chinese J. Phys. 39(2001)344 [9] M. El glaoui, M.L. mrad, E. Jeanneau, C. Nasr, E-Journal of Chemistry 7(4)(2010)1562-1570 [10] H. Z. Cummins, Phys. Rev. 185(1990) 211. [11] J. A. Desilva, F. E. O.Melo, J. M. Filho, F. F. Germano, J. E. Horeira, J. Phys. C: Solid Stat. Phys. 19 (1986) 3797. [12] T. P. Melia, R. Merrifield, J. Chem. Soc. A, 1166 (1970). [ 13 ] A. Bencini, C. Benelli, D. Gatteschi, Inorg. Chem. 19 (1980) 1632. [ 14] C. P. Landee , E. F. Jr. Westrum, J. Chem. Thermodynamics 11 (1979) 247.
11
[ 15 ] M. Iwata, Y. Ishibashi, J. Phys. Soc. Jpn. 60 (1991) 3245. [16] Mahendra Pal,Anshu Agarwal, D. P. Khandelwal, H. D. Bist, J. Raman Spectrosc. 17 (1986) 345. [17] V. I. Torgasheyv, YU.I. Yuzyukl, M. Rarkiny, I. Durnev, L. T. Latush, Phys. Stat. Sol. B 165(1991)305 [18] A. R. lim, K- W.Hyung,K- S. Hong,S-Y. Jeong, Phys. Stat. Sol. B 219 (2000)389 [19] J.M. Perez-Mato, J.L. Manes, J. Fernandez, J. Zuniga, M.J. Tello, C. Socias, M.A. Arriandiaga, Phys. Stat. Sol. A 68 (1981) 29. [20] S.Kalyanaraman, V.Krishnakumar, Hans Hagemann,K.Ganesan, J.Phy. Chem.Solids 68(2007)256 [21] R. Priya , S.Krishnan , G.Bhagavannarayana , S.JeromeDas, Physica B 406 (2011) 1345–1350 [22] S. Krishnan, C. Justin Raj, S. Dinakaran, R. Uthrakumar, R. Robert, S. Jerome Das, J.Phy. Chem.Solids 69(2008)2883 [23] William T. A. Harrison, Acta Cryst. E61 (2005) m1951. [24] K. Nakamoto, Infrared and Raman Spectra of Inorganic Co-ordination Compounds, Wiley-Interscience, New York, 1978. [25] Mark Fox, Optical properties of solids, Oxford University Press, New York, 2001. [26] Rolf E.Hummel, Electronic Properties of Materials, Springer, New York, 2010. [27] J.Tauc, Amorphous and Liquid Semiconductor, Plenum Press, New York, 1979. [28] J.Bardeen, F.J. Blatt, L. H. Hall, in Proc. Internat. Conf. Photoconductivity, Atlantic City ,Wiley, New York, 1956 [29] D.P. Gosain, T.Shimizu, M.Suzuki, J. Mater. Sci. 26 (1991) 3271. [30] D.J. Gravesteijn, Appl. Opt.27(1988) 736. [31] F.A. Miranda, F.W. Vankeuls, R.R. Romanofsky, C.H. Mueller, S. Alterovitz, G.
12
Subramanyam, Integr. Ferroelectr. 42 (2002)131. [32] H,Y.Tian, W.G. Luo, X.H.Pu, P.S. Qiu, X.Y. He, A.L. Ding, Solid State Commun.117 (2001) 315-319. [33] F.M. Pontes, E.R. Leite, D.S.L. Pontes, E. Longo, E.M.S. Santos, S. Mergulhao, P.S. Pizani, Jr. F. Lanciotti, T.M. Boschi, J.A.Varela, J. A. J. Appl. Phys.91(9) (2002) 5972. [34] A.Deineka, L. Jastrabik, G. Suchaneck, G.Gerlach, Ferroelectrics 273 (2002) 155. [35] F.E. Fernandez, Y. Gonzalez, H. Liu, A. Martinez, V. Rodriguez, W. Jia, Integr. Ferroelectr. 42 (2002) 219. [36] Y.Z. Gu, D.H.Gu, F.X.Gan, Nonlinear Optics, 28(4) (2001) 283. [37] N.M. Ravindra, V.K. Srivastava, Infrared Phys. 20 (1980) 67. [38]M. Meena, C.K. Mahadevan, Crys. Res. Tech. 43(2008)166. [39] C. Kittel, Introduction to Solid State Physics,Wiley, India,2006. [40] N.M. Ravindra, R.P. Bhardwaj, K. Sunil Kumar, V.K. Srivastava, Infrared Phys. 21 (1981) 369. [41] D.R.Penn, Phys. Rev. 128 (1962) 2093
Figures
13
Fig. 1. FTIR spectrum
14
Fig.2. Raman spectrum
15
Fig. 3. Recorded Transmittance spectrum
16
Fig.4. Calculated Absorption coefficient plot
60
(αhυ)^1/2(eV/m)^1/2
50 40 30 20 10 0 1.8 2 2.22.42.62.8 3 3.23.43.63.8 4 4.24.44.64.8 5 5.25.45.65.8 6 6.2
Energy hν (eV)
Fig.5. Tauc plot (Band gap energy determination) 17
Fig. 6. Calculated extinction coefficient plot
18
Fig.7. Calculated Refractive index plot
19
Fig.8. Variation of calculated Real Dielectric constants with optical frequencies
20
Fig. 9.Electronic polarizability in optical region
21
Fig.10. Variation of dielectric loss with respect to frequency
22
Fig. 11. Dielectric constant variations in the lower frequencies
23
0.04
Polarization(μC/cm2)
0.03
Pr 90V
0.02
50V
0.01
10V
0 -0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
-0.01 -0.02 Electric field (kV/cm) -0.03 -0.04
Fig. 12. Ferroelectric Hysteresis loop
24
0.8
Table 1. Selected vibrational assignments Wavenumber FT-IR (cm-1)
Raman(cm-1)
Assignments
3028
3038
asym.strect. of CH3
2577
------
C-H sym.stret. of CH3
2499
------
C-H sym.stret. of CH3
2197
2228
C-H and N-H asym.stret.
1927
------
C-H and N-H sym.stret.
1485
1497
def. of CH2
1440
1442
def. of CH2
1375
------
wagg. of CH2
1321
1338
wagg.of CH2
1213
------
twist.of CH2
1171
------
rock. of CH2
1124
1123
rock. of CH2
1030
1036
C-C stret.
963
964
894
901
809
813
623
------
ethylene twisting
543
------
ethylene twisting
469
------
skeletal vibration
rock. of CH3
281 218 146
internal vibrations of ZnCl42-
106 83
25