3.5. Electrical properties
Based on the obtained
${Z}^{\prime}$ and
${Z}^{\u2033}$ values, the electrical conductivity σ, can be computed for each temperature
T, with the following equation:
where
d and
A represent the length and the transversal sectional area of the sample, respectively, and
$\left|{Z}^{*}\right|=\sqrt{{{Z}^{\prime}}^{2}+{{Z}^{\u2033}}^{2}}$ is the complex impedance module of the sample. It is known that [
21] in the low frequency range, (
$f\le 1\hspace{0.17em}kHz$) the value σ determined by the relation (1) represents the DC-component of the electrical conductivity,
${\sigma}_{DC}(T)$, independent on frequency but dependent on the temperature. Using the values obtained for the static conductivity, σ
_{DC}, at all the measurement temperatures
T and at the frequency f=1 kHz, we plotted the temperature dependence of static conductivity,
σ_{DC}(T), shown in
Figure 5, for all samples.
As can be seen in
Figure 5, the static conductivity, σ
_{DC}(T) increases with the temperature for all samples, indicating that the conduction process is thermally activated in the measurement temperature range (28–120) °C, at low frequency. The electrical conductivity of LMO:Ga and LMO:Y, respectively, is higher than that of LMO sample, which shows that the presence of rare earth ions of Ga
^{3+} or Y
^{3+} type in the LaMnO
_{3} perovskite sample leads to an increase in the electrical conductivity of these samples, comparative with pristine sample (LMO). On the other hand, the substituted Ga
^{3+} ions in the LaMnO
_{3} perovskite crystal lattice behave as an acceptor dopant replacing the Mn
^{3+} ions in the octahedral B-site [
22], which leads to the compensation of the charge imbalance by their oxidation. As a result, gallium doping slightly reduces the octahedral distortion and weakens the Jahn-Teller effect by highlighting electronic correlations [
23,
24], which will determine a higher increase in the electrical conductivity [
25] of the LMO system doped with Ga ions, as can be observed in
Figure 5. The Yttrium ions replace the lanthanum ions in the tetrahedral A-site of LMO perovskite crystal lattice [
26] as a result the Yttrium substitution decreases the average ionic size at La-site, which has an effect the distortion of the MnO
_{6} octahedra. Thus, the Mn
^{3+}–O–Mn
^{4+} bond angle deviates from the ideal 180°, which leads to a reduction of the hopping probability of the electron between Mn
^{3+}/Mn
^{4+} ions [
27], which will determine a smaller increase in the electrical conductivity of the LMO system doped with Y ions, as was obtained experimentally (see
Figure 5).
Also, the increase with temperature of the σ
_{DC}, is due to the increase of drift mobility of the charge carriers from the sample, in accordance with Mott’s model VRH (
variable-range-hopping) [
28]. Such a behavior with temperature of the conductivity σ
_{DC}(T), has also been observed for other perovskite materials, such as NaTaO
_{3} undoped [
29] or doped with metallic ions (Ag, Fe, Cu) [
11,
30,
31], which shows the fact as the most suitable electrical conduction mechanism in these materials is the VRH mechanism. Consequently, the σ
_{DC}(T) conductivity based on the VRH model is given by the equation:
where σ
_{0} is the pre-exponential factor and,
In Eq. (3)
k is the Boltzmann constant and
E_{A,cond} is the thermal activation energy of electrical conduction [
28]. Using Eq. (2) and the σ
_{DC}(T) conductivity values from
Figure 5, we plotted the experimental dependence,
lnσ_{DC} (T^{-1/4}), which is shown in
Figure 6.
By fitting with a straight line of the experimental dependence,
ln σ_{DC} (T^{−1∕4}) from
Figure 6, we have determined the slope B corresponding to each sample. Knowing the slope B, the thermal activation energy of electrical conduction,
E_{A,cond}, on the investigated temperature range, was determined with Eq. (3). The temperature dependence of the
E_{A,condn} (T), is shown in
Figure 7.
As can be observed from
Figure 7,
E_{A,cond} increases linearly with the temperature, in all the investigated range, from 0.177 eV to 0.218 eV for sample 1 (LMO), from 0.175 eV to 0.213 eV for LMO:Ga sample and from 0.172 eV to 0.210 eV for LMO:Y sample. As a result, the presence of rare earth ions Ga
^{3+} or Y
^{3+} type in the LMO perovskite sample leads to a decrease of the thermal activation energy of electrical conduction, corresponding to these samples (LMO:Ga and LMO:Y), compared to LMO sample, thus determining the increase in conductivity in doped materials, in relation to the electrical conductivity of the undoped sample, as to obtained experimentally (see
Figure 5). The mechanism of electrical conduction in the investigated samples can be explained by a hopping process of the charge carriers between the localized states [
28,
32] on the temperature range, through which
σ_{DC}(T), with another relationship can be expressed:
Here,
T_{0} is characteristic temperature coefficient, which represents a measure of the degree of disorder [
28], being given by the relation:
where,
λ ≅16.6, is a dimensionless constant [
28];
α ≅10
^{9} m
^{-1} represents the degree of localization and
N(E_{F}) is the density of the localized states at the Fermi level
E_{F} [
22,
33]. From Eqs. (2–5), after some calculations the following relation for the
N(E_{F}), result:
Using the values obtained for
E_{A,cond} (T) from
Figure 7 and Eq. (6), we computed
N(E_{F}) from the temperature range (28-120) °C at a low frequency (
f = 1 kHz), for all three samples, obtaining the following values: N(E
_{F})
_{S1}=1.158͘˴10
^{18} cm
^{-3}˴eV
^{-1}, N(E
_{F})
_{S2}=1.288͘˴10
^{18} cm
^{-3}˴eV
^{-1} and N(E
_{F})
_{S3}=1.231˴10
^{18} cm
^{-3}˴eV
^{-1}. The obtained result shows that the density of states at the Fermi level N(E
_{F}), does not depend on the temperature remaining constant on the whole investigated domain, as to shown recently in the papers [
34,
35], for other oxide materials (Fe-P or Cu-Mn type). Also, it is observed that the value of N(E
_{F}) for LMO is lower than the values N(E
_{F}), obtained for LMO:Ga and LMO:Y which contain rare earth ions (Ga and Y, respectively), in the investigated temperature range. This result is in agreement with the fact that the thermal activation energy of electrical conduction,
E_{A,cond} of doped materials is smaller than
E_{A,cond} of LMO sample (see
Figure 7). As a result we advance the statement that the decreasing of
E_{A,cond} leads to an increase of the density of states at Fermi level N(E
_{F}) and to explain this statement, it is necessary to determine two other Mott parameters corresponding to the VRH model: the hopping distance,
R and the hopping energy
W, with the relations [
28,
33]:
From equation (7), using the values of , we have determined the hopping distance,
R, corresponding to the samples, at each temperature within the range (28 – 120)
^{0}C. Knowing the hopping distance
R and using equation (8) we have determined the hopping energy
W, for studied samples. The temperature dependencies of the Mott parameters
R and
W, corresponding to the investigate samples, are shown in
Figure 8.
From
Figure 8, it is observed that by increasing of temperature, the hopping distance R decreases with (
Figure 8 a)) and the hopping energy W increases (
Figure 8 b)), for all the investigated samples. Also, both
R and
W for the LMO sample, are higher than for the LMO:Ga and LMO:Y, at all the temperatures. This result is in agreement with our previous statement on the increase of density of states at Fermi level N(E
_{F}) of the modified samples which contain rare earth ions (Ga and Y, respectively) due to the decrease of
R and
W, in these samples compared to
R and
W of LMO material, thus causing a decrease in the thermal activation energy of conduction
E_{A,cond} of Ga or Y doped LaMnO
_{3} relative to
E_{A,cond}, of undoped LaMnO
_{3}.
Following these promising results observed for the lanthanum manganite compounds it can be assessed that more studies are needed to determine their potential as candidates for energy conversion, metal–air battery or fuel cell electrodes owing to their unique physical and electronic properties.
Taking into account the obtained results namely that the electrical and structural properties of the synthesized Ga or Y doped LaMnO_{3} ceramics powders can be changed by design and of the temperature variation, demonstrate the potential of these materials can be used in thermo-electric devices and sensors applications.