Structural, optical and dielectric studies of lithium sulphate monohydrate single crystals

X-ray intensity data of 1348 reflections (of which 453 were unique) were collected on Bruker AXS Kappa APEX II CCD area-detector diffractometer equipped with graphite monochromator using MoKα radiation (λ = 0.71073 Å). The crystal used for data collection was of dimensions 0.50 mm × 0.30 mm × 0.20 mm. The cell dimensions were determined by least-squares fit of angular settings of 1619 reflections in the θ range of 2.61° to 28.32°. The intensities were measured by ω scan mode for θ ranges from 2.61° to 28.32°; 451 reflections were treated as observed (I > 2σ (I)). The data were corrected for Lorentz, polarization and absorption factors. The structure was resolved by direct methods using SHELXS-97 [28]. All non-hydrogen atoms of the molecule were located in the best E-map. After adding two hydrogen atoms geometrically, full-matrix least-squares refinement was carried out using SHELXL-97 [29]. The final refinement cycles converged to R = 0.0174 and wR (F²) = 0.0472 for the observed data. Residual electron densities ranged from −0.308 eÅ⁻³ < Δρ < 0.161 eÅ⁻³. Atomic scattering factors were taken from the literature [66] (Table 4.2.6.8 and Table 6.1.1.4). The crystallographic data are summarized in Table 1. The geometry of the molecule was calculated using theWinGX [30], PARST [31] and PLATON [32] software. Bond lengths [Å], bond angles [°], and torsion angles for atoms of LSMH asymmetric molecule are presented in Table 2. The O–H... O interactions present in the crystal structure are shown in Table 3. An ORTEP view of the title compound with atomic labeling is shown in Fig. 1.

The intermolecular H-bonding interactions of O–H… O type forming a layer are responsible for holding the molecules together, which results in the formation of three dimensional structure shown in Fig. 2. The structure is characterized by tetrahedra of oxygen surrounding the sulpher and lithium atoms. The Li1 tetrahydron is composed of three oxygen atoms from three different SO4 groups and one oxygen from the water molecule, while the Li₂ tetrahydron is composed of four oxygen atoms from four different SO₄ groups. The crystal structure is in agreement with the structure reported in the literature [33].

From single crystal X-ray diffraction analysis the calculated lattice parameters are: a = 5.4512 Å, b = 4.8726 Å, c = 8.1724 Å, β = 107.291°, showing that the grown crystal belongs to monoclinic system with the space group P2₁, which agrees with that of reported values [33].

The valence electron plasma energy, ħω_p is calculated using the relation: ℏ<!-- ? -->ω<!-- ? -->p = 28.8 Zρ<!-- ? -->M $$\hslash {\omega _p}{\text{ = 28}}{\text{.8 }}\left[ {\frac{{Z\rho }}{M}} \right]$$ (3)

where Z = (2 × Z_Li) + (2 × Z_H) + (1 × Z_S) + (5 × Z_O) is the total number of valence electrons, ρ is the density and M is the molecular weight of LSMH.

Penn gap E_p and the Fermi energy E_F[34] is, respectively, given by the equations: Ep=ℏ<!-- ? -->ω<!-- ? -->pε<!-- e -->∞<!-- 8 -->−<!-- - -->11/2 $${E_p} \,=\, {\text{ }}\frac{{\hslash{\,\omega\, _p}}}{{{{\left( {{\varepsilon _\infty } \,-\, 1} \right)}^{1/2}}}} $$ (4)

EF = 0.2948ℏ<!-- ? -->ω<!-- ? -->p4/3 $${E_F}{\text{ = 0}}{\text{.2948}}{\left( {\hslash\,{\omega _p}} \right)^{4/3}}$$ (5)

where align_∞ is the value of dielectric constant at high frequency (1 MHz in the present case).

The electronic polarizability, α can be obtained using the relation [35]: α=ℏωp2SOℏωp2SO+3Ep2×MP×0.396×10−24cm−3 $$\alpha {\text{ = }}\left[ {\frac{{{{\left( \hslash {\omega _p} \right)}^2}S_O}}{{{{\left( {\hslash {\omega _p}} \right)}^2}S_{O} \rm + \rm {3}\it E_p^\rm 2}}} \right]{\text{ }} \times \frac{{M}}{{{P}}}{\text{ }} \times {\text{ 0}}{\text{.396 }} \times {\text{1}}{{\text{0}}^{ - {\text{24}}}}{\text{c}}{{\text{m}}^{ - {\text{3}}}}$$ (6)

where S₀ is a constant for a particular material which is given by: S0 = 1−<!-- - -->Ep4EF+13Ep4EF2 $$S_0{\text{ = 1}} - \left[ {\frac{{{E_p}}}{{4{E_F}}}} \right]{\text{ }} + {\text{ }}\frac{1}{3}{\left[ {\frac{{{E_p}}}{{4{E_F}}}} \right]^2} $$ (7)

The value of α obtained from the previous equation agrees with the value obtained by using Clausius-Mossotti equation: α<!-- a --> = 3M4π<!-- p -->Naρ<!-- ? -->×<!-- ? -->ε<!-- e -->∞<!-- 8 -->−<!-- - -->1ε<!-- e -->∞<!-- 8 -->+2 $$\alpha {\text{ = }}\frac{{3M}}{{4\pi { N_a}\rho }} \times \frac{{{\varepsilon _\infty } - 1}}{{{\varepsilon _\infty } + 2}}$$ (8)

The calculated parameters for the grown crystal are shown in the Table 4 and the values obtained are of the same order as reported for such type of material [36].

The optical transmission spectrum of LSMH single crystal is shown in Fig. 4. It is observed from the spectrum that the crystal shows good transmission in the entire visible region and it has been reported that such kind of material finds its application in second harmonic generation devices [39–42].The variation of optical absorption coefficient with the photon energy provides information about the band structure and the type of electronic transitions [43].

The optical absorption coefficient (α) was calculated from the transmittance using the following equation: α<!-- a --> = 2.303log1Td $$\alpha {\text{ = }}\frac{{2.303\log \left( {\frac{1}{T}} \right)}}{d} $$ (9)

where T is the transmittance and d is the thickness of the crystal. The crystal under study has an optical absorption coefficient (α) obeying the following equation (Tauc’s relation) for high photoenergies (hν): α<!-- a --> = A(hν−<!-- - -->Eg)hν $$\alpha {\text{ = }}\frac{{A\sqrt {(h\nu - {E_g})} }}{{h\nu}}$$ (10)

where A is a constant and E_g is optical band gap of the crystal. Fig. 5 shows the variation of (αhν)² versus photon energy E(eV), where the energy gap E_g is evaluated by the extrapolation of the linear part [44]. The band gap is found to be 4.49 eV. As a consequence of the wide band gap, the grown crystal has large transmittance in the visible region [45].

Fig. 5 shows the variation of absorption coefficient (α) with wavelength of LSMH crystal. From the spectrum, a low absorption in the UV and visible region reveals that it is a material possessing NLO properties. The UV cutoff wavelength was found to be 290 nm for the grown crystal. The large band gap and transparency shown by the crystals make them a possible choice for optoelectronic application [39, 46]. The transmittance (T) is given by the relation [47]: T = (1−<!-- - -->R)2exp⁡<!-- ? -->(−<!-- - -->αd)1−<!-- - -->R2exp⁡<!-- ? -->(−<!-- - -->2αd) $$T{\text{ = }}\frac{{{{(1 - R)}^2}\exp ( - \alpha d)}}{{1 - {R^2}\exp ( - 2\alpha d)}}$$ (11)

The reflectance in terms of the optical absorption coefficient can be derived from the equation: R=1±1−exp⁡(−αd)+exp⁡(αd)1+exp⁡(−αd) $${{R = }}\frac{{1 \pm \sqrt {1 - \exp ( - \alpha d) + \exp (\alpha d)} }}{{1 + \exp ( - \alpha d)}} $$ (12)

Fig. 7 shows variation of dielectric constant (∊′) of LSMH crystal with temperature at different frequencies. It is observed that ∊′ shows almost no variation with temperature up to 105 °C and above this temperature ∊′ changes rapidly showing a peak at around 130 °C. The inset of Fig. 7 shows variation of dielectric constant with temperature at 100 kHz. The possible reason for this peak is either due to structural phase transition or due to dehydration, i.e. removal of water molecule from the LSMH crystal. From literature study we have found that LSMH is non ferroelectric [11], so the possibility of structural phase transition can be ruled out. The dielectric anomaly is thus due to dehydration of the crystal. As water is a polarized molecule, below 105 °C the water molecule is coordinated (interaction) to different atoms of the crystal which prevents the reorientation of the molecular dipole. With the increase in temperature above 105 °C this interaction breaks down, water molecule orients easily which leads to an increase in dielectric constant that attains the maximum value at 130 °C. The orientational polarization shown by the water molecule, because of its asymmetrical bonding structure results in its permanent dipole moment. Beyond 130 °C a decrease in orientational polarization due to gradual loss of water molecules and irregular motion of permanent dipole moments leads to a decrease in dielectric constant [48]. As such, it is proposed that the anomalous dielectric behavior shown by LSMH crystal is due to the presence of coordinated water molecule which is also supported by TGA data shown in Fig. 16. Thus, the absorption of water molecules by a crystal surface can affect the dielectric constant of the crystal and contribute to dielectric peak as reported in the literature [49–51]. Beyond 145 °C, the title crystal shows normal behavior and dielectric constant increases with temperature as observed in various polar materials [52].

Fig. 8 shows the variation of dielectric loss with temperature at different frequencies and also shows peak at around 130 °C. Since energy is needed for the reorientation of a molecule in order to overcome the surrounding molecules resistance, the orientation process depends on temperature. In the temperature range of 105 °C < T < 130 °C, the increase in dielectric constant occurs because more energy is dissipated for reorienting the permanent dipoles in the direction of applied field which results in an increase in dissipation loss in this temperature range. Thus, it is evident that the peak in dielectric loss is mostly independent of frequency and is a feature of polar dielectrics, where losses due to electrical conduction also occur apart from dipole losses [52].

Fig. 9 shows variation of dielectric constant (∊′) with frequency at different temperatures which represents normal behavior of dielectric materials. The mechanism behind the variation of (∊′) with frequency is polarization phenomena. At low frequency, all the four polarization mechanisms, namely space charge, orientational, electronic and ionic contribute to dielectric constant. The high value of dielectric constant at low frequency may be attributed to interfacial polarization in which the mobile charge carriers are hampered by a physical barrier which stops generation of localized polarization in the crystal. At higher frequencies, the lower value of dielectric constant is due to the gradual loss of significance of these polarizations and material response to the field is missing.

The frequency dependent dielectric loss (D) at different temperatures displayed in Fig. 10 shows normal behavior consisting in that both dielectric constant and dielectric loss show inverse frequency dependence at low frequencies. It is observed that dielectric loss is frequency independent beyond 100 kHz due to dipole rotation, because at higher frequencies the orientational polarization ceases and energy does not need to be spent to rotate the dipoles. At higher frequencies the dipoles fail to follow the field change and react to such fields feebly causing that the dielectric losses are smaller. It is suggested that LSMH crystal shows low frequency dispersion (LFD) or the quasi-DC process (QDC) behavior because of absence of any loss peak in the dielectric dispersion [53]. The lower values of dielectric loss with higher frequencies for this crystal suggest that the material possesses enhanced optical quality with lesser defects and this parameter is of vital importance for nonlinear optical materials and their application [54].

The real and imaginary parts of susceptibility increase rapidly towards lower frequencies and LSMH crystal seem to obey the power law of the type: χ^∞ω⁽ⁿ⁻¹⁾ such that 0 < n < 1, where χ is the electric susceptibility of the material which is related to the real part of dielectric constant as χ = ∊′–1. In order to obtain the value of n we have plotted logχ versus logω as shown in Fig. 11 and from the slope, the value of n = 0.9 was obtained. The universal fractional power law is obeyed by the variety of solid materials, including low loss dielectrics, dipolar materials, hopping electronic systems, ionic conductors, semiconductors, p-n junctions, interfacial phenomena and mechanical relaxation [55].

From Fig. 12 it is observed that the increase in electrical conductivity with temperature is due to the motion of charge carriers (polarons and free ions) and AC conductivity shows temperature and frequency dependence. The inset of Fig. 12 shows the variation of AC conductivity with temperature at 1 MHz. The increase in mobility of charge carriers in polymeric and semiconductor materials results in variation of conductivity with temperature and frequency [56]. In LSMH crystal it is observed that the increase in conductivity with temperature from 105 °C to 130 °C is due to dissociation of water molecule into H⁺ and OH⁻ ions which in turn increase the concentration of charge carriers. Such type of conduction is described as protonic conduction [57]. Beyond 130 °C, because of dehydration of water molecule, the conductivity decreases due to the decrease in the concentration of H⁺ and OH⁻ ions as is also observed in the thermal analysis of the crystal (Fig. 16). Since LSMH crystal contains only one water molecule, so the increase in conductivity is not as large as reported for the loss of seven water molecules in crystals [48]. Above 145 °C, after the complete dehydration of LSMH, the increase in conductivity is due to the movement of Li+ ions. So, the conductivity variation is due to both types of ions, that is protons and lithium cations. Thus, the crystal can be used as an electrolyte in solid state batteries at high temperatures [58].

Arrhenius equation σ_ac = σ_oexp (–Ea/kT) was used to calculate the activation energy of LSMH crystal before the transition temperature (130 °C). Fig. 13 shows the plot of lnσ_ac versus 1000/T at 1 kHz before transition temperature. The activation energy obtained from the slope is 0.24 eV for the crystal.

Earlier, Jonscher showed the variation of electrical conductivity σ_ac with frequency for various solids, including polymers, glasses and crystals [59]. Generally, in conduction band AC conductivity decreases with an increase in frequency while it increases with frequency in case of hopping conduction. Also below phonon frequencies (low frequencies) the ordered solids show no frequency dependence of their conductivity.

In limited frequency region, as shown in Fig. 14, the AC conductivity of the LSMH crystal as a function of frequency seems to obey Jonscher’s universal power law [59, 60]; σ(ω) = σ_o + Aω^s, where σ_o is the DC conductivity which forms the frequency-independent plateau in the low frequency region, A is temperature dependent constant, and s is temperature dependent power law exponent with values of 0 < s < 1. When s = 0, electrical conduction is frequency independent (DC conduction) that is conduction at very low frequency, and when s > 0, the conduction is frequency dependent (AC conduction) [61].

In the present study, the value of s is calculated from the plot of ln (σ_ac) versus ln (ω) at 50°C as shown in Fig. 15. The value of s of 0.66, calculated from the slope of this graph confirms that s lies in the range of 0 < s < 1 and obeys power law.This increasing behavior of conductivity with frequency shows hopping conductivity of protons via hydrogen bonds [62]. The proton-proton interaction occurs as a result of electric field which produces directional flow of charge carriers by hopping mechanism. When proton tries to move, it has to pass through the strain field caused by the cloud of virtual thermal phonons thus forming a quasiparticle, like polaron. This quasiparticle disperses at higher frequencies of applied AC field. When the cloud of phonons disperses, protons move and contribute to conductivity [48].