Investigation of optical, dielectric properties and conduction mechanism of LiCo0.7Mn0.3O2

The development of a multifunctional material with variety in its properties is a powerful research project. The electrochemical properties of LiCo0.7Mn0.3O2 material have attracted our attention to search electrical characterization and the optical properties of this material. The synthesis of this compound is based on a solid state method. The x-ray powder diffraction analysis shows that the compound crystallizes in the hexagonal system with the R −3 m space group. Moreover, the homogenous distribution of grain is revealed by the EDX study, thus the grain size is about 2.5 μm calculated from the scanning electron microscopy data. The band gap energy was established and seems to be equal to 1.88 eV which confirms the semiconductor character of this compound. Impedance spectroscopy was performed in the temperature ranging from 363 K to 473 K and frequency varying between 0.1 to 106Hz. The Nyquist plots confirm the presence of grains and grain boundary contribution instead of electrode polarization. The obtained conductivity properties indicates the semiconductor behavior of our compound, also it confirms its reliability for electrochemical application. Ac conductivity has been adjusted using the Jonsher power law, which allows us to confirm that the dc conductivity is thermally activated with activation energy of 400 meV and 500 meV for 363–423 K, 423–473 K regions, respectively. Temperature dependence of the exponent s reveals that the conduction process is governed by the correlated barrier hopping model (CBH). Besides, the temperature coefficient of resistivity (TCR) affirmed that LiCo0.7Mn0.3O2 is a good candidate for bolometric applications.


Introduction
Several electrode materials have been studied for years, including those of the formula LiMO 2 with M being a transition metal (M = Mn, Co, Ni, Fe, CuK..).The LiCoO 2 and LiMnO 2 compounds are among these materials that have interesting electrochemical properties [1,2].The batteries whose electrode is made of the LiCoO 2 compound have a theoretical specific capacity equal to 274 mAh g −1 and an energy density of around 1070 Wh kg −1 , yet they deliver less than half of their capacity (140 mAh g −1 ) due to structural disorders [3][4][5].This compound presents good electrical and optical properties making it a good candidate for many applications such as optoelectronic, photovoltaic solar cells gas absorbers, gas sensors, and medical treatment.In fact, its electrical conductivity is in the order of 10 −4 Ωcm −1 and its optical gap is 2.17 eV [6] indicating that the LiCoO 2 compound is a semiconductor.The other compound is the LiMnO 2 which has been widely studied as an active cathode material with a charge capacity ∼270 mAhg -1 and preliminary results indicate good stability over repeated charge-discharge cycles.Its energy density, on the other hand, is not particularly high.Partial replacement of Mn by transition metals with larger potential couplings could lead to an increase in the energy density and discharge plateaus; on the other hand, the presence of toxic and expensive Co ions in LiCoO 2 introduces an environmental problem as well as a raise the cost of the (lithium ion battery) LIB.The research work is moving towards the partial or full replacement of Co by more abundant and environmental friendly transition metal ions such as Ni and Mn to enhance the capacity of the cathode [7].Based on these results, several materials of the formula LiCo 1-y Mn y O 2 have been developed and characterized in order to satisfy the needs in electrical and electrochemical properties [8].In this work, we are studying the structure and morphology of the LiCo 0.7 Mn 0.3 O 2 compound.Besides that, we are investigating the electrical and optical properties that make the material an excellent candidate for wide range of applications.

* Synthesis
The LiCo 0.7 Mn 0.3 O 2 compound is synthesized by the solid-solid method using the following precursors; Li 2 CO 3 (Sigma-Aldrich, 99%), Co 3 O 4 (Sigma-Aldrich, 99%) andMn 2 O 3 (Sigma-Aldrich, 99%).The calculated percentages of the precursors are ground manually, the powder obtained is initially put in an oven for 24 h at 450 °C to ensure the release of CO 2 , the powder obtained is ground then put in the form of pellets.These are heated in an oven at 650 °C for 12 h in order to increase the compactness of the compound.

* Equipment
The purity of the compounds is checked using x-ray powder diffraction at the ambient temperature.This measurement was done using Panalytical X'Pert Prompd operating with copper anticathode radiation CuKα (λ = 1.5060Å) at room temperature in an angular range 10° 2θ 80°.Also, visible UV spectroscopy is used for the determination of the optical properties for the studied material, this study was carried out using 'UV-3101PC' in the wavelength range ranging (200-800 nm).The electrical measurement is carried out on pellets (8 mm in diameter and 1 mm thickness) covered with a layer of silver in a temperature ranging from 363 to 473 K with a frequency varying from 0.1 to 10 6 Hz.A Lincam type impedance meter with silver electrode was used during these analyzes with an AC alternating voltage of 100 mV.

X-ray and SEM studies
The final obtained result for the X-R refinement is shown in figure 1.The pseudo-voigt peak profile function was used.Additionally, the background was approximated by linear interpolation between a set of background points with refined height x-ray diffraction.The obtained phase was fully indexed in the R −3 m space group of the hexagonal system .The x-ray study proves the existence of a trace of Co 3 O 4 indexed by a small peak shown in the XRD diffractogram.The crystalline structure of our compound is similar to that of the LiCoO2 sample [6].The unit cell parameters and the fit criteria are reported in table 1.
The morphological study of the LiC 0.7 Mn 0.3 O 2 compound was carried out using the scanning electron microscope (SEM) to calculate the size and distribution of the grains and gain information about the porosity of the compound.Figure 2 presents the SEM images of the synthesized compound at 10 μm resolution scale.As shown, the material is dense, the grain distribution is homogeneous, and the structure of the compound is compact.The processing of these images by the image J software allowed us to determine the grain size which is about 2.5 μm.

Optical characterization
UV-Visible spectroscopy provides qualitative access to information concerning the absorbance of the compound, and its entropy.These parameters are very useful in the evaluation of the efficiency of light, and by means of the optical absorption method.This study was used to evaluate the gap energy, being a significant parameter in terms of describing materials in the solid state (for disordered materials, it is related to either a direct or an indirect transition through a band prohibited optical).Thus, the calculation of the absorption coefficient (α) allows to study the optically induced transition and to better understand the band structure of our material.The absorbance spectrum is given by figure 3, we notice the presence of two large peaks.The first peak that is observed at 225 nm with low intensity could be attributed to the charge transfer mechanism O 2-→ Co 2+ that occurs either in the same bands or in the forbidden band.The second is observed at 368 nm with high intensity due to the charge transfer O 2+− → CO 3+ [9].
The determination of the gap energy (Eg) is done based on the Kubelka-Munk equation [10,11]: Where R is the reflectance and 'e' is the thickness of the compound (e = 1 mm), the term ( ) F R e is proportional to the absorption coefficient (α).In order to calculate theEg, the Kubelka-Munk modified equation was used by multiplying F(R) by (hν) and using the coefficient (n) associated with an electronic transition as shown below: n With: n = 2 for an indirect allowed transition (drawn from α(hν) 1/2 in terms of E), n = 1/2 for an allowed direct transition (plot of α (hν) 2 depending on E).
The energy band gaps Eg can be determined from the intercepts of these plots on the energy axis, since Eg=hν when (αhν) 0.5 = 0 (figure 4 indirect allowed transition).For our compound the band gap energy is 1.88 eV, which is lower than the value obtained for LiCoO 2 (2.17 eV) [6].We notice that the insertion of Mn in LiCoO 2 compound leads to the retreatment of the forbidden band, which can be explained by the s-p-d exchange interaction between the dopant Mn 2+ and the host CoO.The doping of Mn 2+ in the CoO lattice created impurity levels.Therefore, the d orbital of Mn overlaps with the 2p orbital of oxygen and the 4 s orbital of Co.This causes an exchange interaction between these orbital, raising the valence band maximum and lowering the conduction band minimum, respectively.This demonstrates that the band gap can be tuned by changing the dopant concentration.Tuning the band gap is an important characteristic that allows CoO to be used in photovoltaic and thermoelectric.The band gap is also influenced by structural deformation that may result in  piezoelectric polarization in the system, creating local electric fields which produce band-bending effects [12][13][14][15][16].
The disorder in LiC 0.7 Mn 0.3 O 2 compound is described by the Urbagh energy, according to Urbagh's law [17], the absorbance is given by the following expression: Where α 0 is a constant, E u represents the Urbach energy (eV) and (hν) is the photon energy (eV).The Urbagh energy corresponds to the transition between the extended states in the valence band and the localized ones in the conduction band.It is an empirical parameter that denotes the degree of defects of a material [18].The Urbagh's energy for our compound is about 3.36 eV which confirm that our compound is a disordered one.This value is extracted from the slope of the curve giving the variation of Ln (α) as a function of (hν) as shown in figure 5. We notice that the disorder in this compound is greater than that of other auxides such as monophosphates (such α-NaCoPO 4 : E U = 0.451 eV, β-NaCoPO 4 : E U = 0.41 eV and γ-NaCoPO 4 : E U = 0.64 eV [19]) and orthosilicates (such Na 2 CoSiO 4 : E U = 1.54 eV [20], Na 2 Co 1-x Fe x SiO 4 : E U = 1.34 and 1.72 eV [21]).This high value Eu at room temperature was due to the degree of defect present in this material.We noticed that there was an inverse variation between the optical band gap and the disorder parameter.In fact, the band gap was characterized by the energetic difference between the tails of the bands; however, the Urbach energy was defined by the width of the tail of the valence or conduction bands.Therefore, an increase in the disorder was accompanied by a decrease in the forbidden energy band.

Study of impedance spectroscopy
Complex impedance spectroscopy (CIS) is a primary and powerful technique for studying the electrical behavior of a material.It provides information on ion movement, electrical conductivity and relaxation time.When applying the time-reversed electric field, the frequency-dependent complex impedance is a non-destructive method that shows the volume (grain), grain boundary, and electrode contributions.Overall, the charge carrier becomes active and causes space charges to form, charge to move, and orientation of the dipole as soon as an alternating field is forced.Thus, the contribution of electrodes, grain boundaries and grains to charge transport in the material can be differentiated through the complex impedance study.The frequency dependence of the complex impedance is illustrated by the following equation: Quantitative analysis of the curves in figure 6 indicates that the real part of impedance (i.e.resistance) decreases with increasing frequency and temperature, which provides an indication from the increase in conduction with temperature and frequency (i.e. a negative temperature coefficient of resistance behavior like that of the semiconductor).The coincidence of the impedance (Z′) at higher frequencies at all temperatures indicates a possible release of space charges.Figure 7 shows the variation of the imaginary part of the impedance (Z′) with the frequency at different temperatures.We notice the presence of an asymmetric peak whose maximum moves towards high frequencies by increasing the temperature suggests the presence of temperature-dependent relaxation processes in the compound [22].To better differentiate the existing contributions in the material, we draw Nyquist diagrams.The analysis of these diagrams clearly shows that the curves showing the variation of (Z′) as a function of (Z′) are centered below the axis of the real of impedance, therefore the conduction of this material does not obey the Debye model, but it follows the Cole-Cole model.The radius of the semicircles decrease with increasing temperature indicating that the temperature coefficient of resistivity is negative [23,24].This proves that the compound LiCo 0.7 Mn 0.3 O 2 possess semi-conductive properties and also that the conduction process is thermally activated.
Characteristically, two semicircular arcs were observed.The high frequency semicircle is considered to be due to the bulk (grain) effect, while the other one observed at low frequency represents the response of grain boundary (blocking core).Thus, in the ultra-low frequency range, the electrode effect appears in the form of an open semi-circular arc.In order to distinguish the contribution of the grains and the grain boundaries, the  Maxwell-Wagner equivalent circuit model comprising of a parallel combination of a number of capacitors (C) and resistors (R) is used.As shown in figure 8, the response of the grains is modeled by a parallel combination of a resistance and a fractal capacitance, while that of the grain boundaries is presented by the parallel association of a resistance, capacitance and fractal capacity.The electrode polarization is modeled by a fractal capacitor mounted in series with the two preceding cells.The obtained values of grain and grain boundary resistances as a function of temperature are shown in figure 9.It is clear that the strength of the grains and grain boundaries decreases with increasing temperature which affirms the previously mentioned NTCR behavior .In addition we could predict the growth of the conductivity as a function of temperature.

Study of the permittivity and the complex modulus
The dielectric response of any material can be demonstrated using the dielectric constant as follows: e w e w = ¢ + j " Where ε(ω) is the complex dielectric constant, ε′(ω) represents the real part that refers to the energy stored outside, and ε″(ω) represents the imaginary part that reflects the energy dissipation of the applied electric field.
The imaginary and real parts of the dielectric constant are related to the complex impedance by the following  equations [25]: Were C 0 = (ε 0 A)/d (C 0 is the capacity of free space while ε 0 represents the permittivity of free space.d is the thickness of the pellet while A represents the area of the surface of the electrode).The dielectric measurement of the studied compound was performed in a frequency range from 0.1 to 10 6 Hz for temperature ranging from 363 to 473 K as shown in figures 10 and 11: Both factors are similar in their behaviors, where they reached the highest values in the low frequency region and their values decreased significantly with the steady increase of frequency values.This is expected since with increasing frequency of the applied electric field, dipoles, space charges and ions gradually fail to follow the rapidly changing field and therefore cease to contribute to the polarization effect.Additionally, we notice that the real part of the dielectric permittivity is thermally activated since it increases as the temperature goes up.This refers basically to the fact that more dipoles are polarized and follow the field orientation [26].This finding implies that the prepared sample is a powerful candidate as an active channel or dielectric gates to be used in FET devices [27].Starting from their physical meanings, ε′(ω) and ε″(ω) play a very important role in the ionic conduction process.The latter is controlled by four major types of polarization (interfacial, dipolar, electronic and ionic).In the low frequency range, the observed behavior of the dielectric constant is due to the effects of the interfacial and dipolar polarizations which explain the non-Debye behavior.At high frequencies, the ionic and electronic polarizations dominate the origin of lower values of the dielectric constant.The imaginary part of the permittivity is adjusted by the following equation [28]: With σ fc is the conductivity of free charge, ε ∞ is the limit of the dielectric permittivity at high frequencies, while the limit at low frequencies is presented by the term ε s , τ symbolizes the relaxation time, the frequency exponent is indicated by the parameter m, and β is the modified Cole-Cole parameter which has a value between 0 and 1.Using the previous equation, we obtain a good agreement between experimental and theoretical data.From this adjustment we can extract the variation of (σ f.c ) versus 1000/T (K −1 ) as shown in the figure S1: We notice the existence of two different regions according to the activation energy value (E aI = 0.41 eV and E aII = 0.59 eV).This variationat T = 413 K is possibly due to a phase transition or variation in the conduction mechanism.To better differentiate the different dielectric responses existing in the material, we use the loss factor dielectric loss factor tg (γ) represented by figure S2.In the low frequency region, tg (γ) exhibits a maximum and then decreases at high frequencies.This behavior is explained by the fact that at low frequencies, the grain boundaries are active.Therefore, the dissipation factor is higher since the exchange of electrons between Mn 3+ and Mn 4+ need more energy which corresponds to a low conductivity.However, in the region of higher frequencies, which corresponds to the conductive grains, the jumping of electrons requires less energy, leading to a low value of the loss factor.
In order to study the relaxation phenomenon, it's necessary to study the complex modulus (M * = M'+ jM') which is represented by the inverse of the complex permittivity.This physical quantity represents a simple tool for clarifying the existence of the electrical relaxation mechanism as well as the space charge distribution: by unmasking the effect of the electrodes.With the continuity of the dielectric displacement, the relaxation of the electric field will be clearly seen in the electric module.Figure 12 represents the variation of the imaginary part of the complex modulus: The peaks observed are asymmetrical and their widths slightly greater than that of the Debye.The maxima of these peaks shift towards the high frequencies by increasing the temperature which affirms the existence of a mechanism of jump.All these observations were confirmed by the analysis that is done by using Bergman's equation that is stated as follow [29]: With M′ max is the maximum of the complex modulus equal to ω max and β is the Kohlrausch parameter which varies between 0 and 1.From the adjustment of the experimental data by this equation we have obtained the variation of M′ max and β depending on the temperature as shown in figure S3.The temperature dependence of M′ max show that it increases quickly up to 413 K and stays almost constant at 0.45 for the temperature greater than 413 K .The values of β do not exceed unity, which confirms that we are in the presence of a non-Debye-type relaxation.The variation of the relaxation time as a function of temperature is a powerful way to verify the existence of a change in the properties of the material essentially that is related to a phase transition presented by a change in slope.
The curve in figure 13 clearly shows the existence of a change in slope at T = 413 K combined with a doubling in activation energy from 0.34 eV at low temperature to 0.59 eV at high temperature which is in a good agreement with the one obtained from the permittivity adjustment.This concordance suggests that the conduction will be ensured by a simple conduction mechanism.

Electrical conductivity
The study of electrical conductivity has a very important role in understanding the behavior of the material.The electrical conductivity σ * is defined by the following equation: The real part of this quantity: The behavior of the real part of the conductivity as a function of frequency and temperature is shown in figure 14.
The substitution of Co by Mn in the LiCoMnO 2 compound decreases the gap energy from 2.17 to 1.88 eV and therefore the electronic conductivity increases.This can be explained by the presence of Mn in the states of several valences (Mn 2+ , Mn 3+ , Mn 4+ ) [30][31][32].Figure 14 shows that the conductivity of our compound (<1.2 10 −4 Ω −1 cm −1 ) is lower than that of the cobalt-based compound (between 10 −3 and 10 −4 Ω −1 cm −1 ).Indeed, the lithium ions are freer in the LiCoO 2 compound and therefore the ionic conductivity is greater in this material than that of the LiCo 0.7 Mn 0.3 O 2 compound.We can also conclude that the ionic conductivity always remains more dominant than the electronic conductivity in these materials.The frequency dependence of the conductivity shows the existence of two parts; the first part is at low frequencies where the conductivity remains invariable, the second part which is at high frequencies where the conductivity has a character of dispersion essentially due to the jump of the charge carriers activated by the increase in frequency.This behavior is typical to that described by the universal law of Jonsher given by the following formula [31]: Where σ dc illustrates the conductivity at low frequencies and Aω s describes the phenomenon of dispersion at high frequencies.The adjustment of the experimental data by this equation allows us to plot the variation of Ln(σ dc ) as a function of (1000/T) as well as the variation of the exponent 's' as a function of temperature.The change in slope is also detected for the variation of Ln (σ dc ) (figure 15).A comparison of the activation energies shows that the values obtained for the conductivity are very close to those obtained for the complex modulus which suggests that the conduction is ensured by a simple jump pattern.To verify this hypothesis, we plot the variation of the exponent s as a function of temperature (the curve in inserted in figure 15), as shown the exponent s is less than unity and decreases with increasing temperature; this behavior is described by the CBH model [33][34][35].Comparing this result with this obtained for LiCoO 2 compound, we note that at low temperature the CBH model is obtained for both compound but at high temperature is not the case.The conduction in the LiCo 0.7 Mn 0.3 O 2 compound is ensured by the CBH model or that in LiCoO 2 compound is ensured by NSPT model.This change of mechanism for LiCoO 2 compound can be explained by the peak detected by DSC which can be related to a structural change.Elliot proposed a correlated barrier hopping (CBH) model to explain AC conduction in a semiconductor [36].As its name suggests,  conductivity is ensured by the jump of the charge carrier on the Coulomb barrier separating two defect centers.The jumping of charge carriers is thermally activated, for this model the conductivity is given by the following expression: With n being the number of polarons involved in the hopping, NN p is proportional to the square of the localized states density, ε′ is the value of the dielectric constant for a fixed frequency while R ω represents the jump distance given by the following equation [36,37]: where w M is the height of the potential barrier.The jump in this model can be ensured by a simple polaron (single polaron hopping) or double polaron (two polaron hopping simultaneously between defects).The exponent 's' for this model is expressed as follows [34,37]: In the case where W k M B has a large value , the exponent s is expressed as follow: The value of w M in relation to the already calculated activation energy is the tool for distinguishing the number of charge carriers performing the jump.Indeed, if w M = E a /2 conduction is ensured by the correlated jump of two polarons (CBHB) and if w M = E a /4 the jump is made by a single polaron (CBHS) [36].Figure S4 gives the linear fit of the (1-s) curve as a function of temperature.For low temperatures (T < 413 K) the value w M is equal to 0.091 eV which represents one fourth of the activation energy (E aI = 0.4 eV) which affirms that the conduction is ensured by the jump of a single polaron, whereas for high temperatures (T > 413 K), w M = 0.21 eV which is equal to half of the activation energy (E aII = 0.55 eV) confirming the existence of a correlated double polaron jump.These results explain well the change in slope observed previously by ln(σ dc ) and ln(τ) as a function of the inverse of temperature.The adjustment of Ln(σ ac ) as a function of (1000/T) for the two temperature ranges (figure S5) that is made by following the previous deductions shows a good agreement between the theoretical data and the experimental results which confirms our choice.From this adjustment we were able to extract the variation of the density of the localized states for selected frequencies values.The density of localized states quantifies the number of electronic states likely to be occupied.For a single polaron hopping an increase in frequency is accompanied by an increase in localized states density which is expected since an increase in frequency (figure 16)) stimulates the mobility of charge carriers [38].While it is not the case for the bipolaron hopping in which we can attribute the reduction of the localized states density as a function of the frequency to the increase in the disorder therefore the diminution of stabilities of states from which the nonlocalization of the latter [39,40].
Throughout the work we have spoken of the negative temperature resistivity coefficient behavior of the compound (NTCR).To confirm this property we calculated the coefficient of resistivity in temperature using the following equation: Where ρ = 1/σ dc and T represent the resistivity and temperature, respectively.We plotted the variation of TCR versus temperature in figure 17.It is clear that the value of this factor is negative until reaching −5 (%) K −1 , which makes our compound an excellent candidate for detecting infrared radiations and infrared bolometric applications.
The optical and electrical study shows that our material behaves like a semiconductor with conductivity between 10 −5 and 10 −4 Ω −1 cm −1 .A change in the conduction mechanism from CBHS to CBHB model was observed at 413 K accompanied by an increase in the activation energy.The synthesized compound LiCo 0.7 Mn 0.3 O 2 is less toxic and characterized by a high electronic conductivity even though it has lower electrical conductivity when compared to the mother compound (LiCoO 2 ).Therefore, our material is a good candidate for Li-ion battery applications.

Conclusion
In our work the synthesized compound crystallizes in the hexagonal system with the space group R −3 m.The morphological study shows the homogeneous distribution of grains with an average size of about 2.5 μm.A detailed analysis of the impedance data illustrates the contribution of grains and grain boundaries as well as electrode polarization.The real part of the dielectric permittivity is thermally activated since it increases as the temperature goes up.This refers basically to the fact that more dipoles are polarized and follow the field orientation.This finding implies that the prepared sample is a powerful candidate as an active channel or dielectric gates to be used in FET devices.The partial substitution of cobalt by manganese in the LiCoO 2 compound allows to increase the electronic conductivity (minimizing the optical band gap from 2.17 to 1.88 eV).The study of electrical conductivity shows the semiconductor behavior of our compound with an electrical conductivity between 10 −5 and 10 −4 (Ωcm) −1 which is lower than that of LiCoO 2 compound (the ionic conduction of our compound is lower than that of LiCoO 2 compound).The conduction mechanism in this material changes from a CBHS model for T > 413 K to a CBHB model for T > 413 K accompanied by an increase in activation energy from 0.40 to 0.55 eV.The electrical performance of this material suggests that the compound is a good candidate for Li-ion battery applications.Thus from this study we have extracted the TCR factor which is negative and reaches a value −5% (K-1) leaving our compound compatible with applications based on the detection of infrared rays.

Figure 2 .
Figure 2. SEM images for the studied compound and the corresponding particle size histogram.

Figure 6 .
Figure 6.Frequency dependence of real part of impedance.

Figure 7 .
Figure 7. Variation of imaginary part of impedance us a function of frequency.

Figure 9 .
Figure 9. Variation in the strength of the grains and grain boundaries of the LiCo 0.7 Mn 0.3 O 2 compound.

Figure 10 .
Figure 10.Frequency variation of the real part of the permittivity of LiCo 0.7 Mn 0.3 O 2 .

Figure 11 .
Figure 11.Frequency variation of the imaginary part of the permittivity of LiCo 0.7 Mn 0.3 O 2 .

Figure 12 .
Figure 12.Frequency variation of the imaginary part of complex modulus.

Figure 14 .
Figure 14.The variation of conductivity as a function of frequency.

Figure 16 .
Figure 16.Frequency variation of the localized states density.

Table 1 .
Unit cell parameters and fit criteria of LiCo 0.7 Mn 0.3 O 2 compound.