Corresponding author: Evgeniya V. Zabelina ( zabev@mail.ru ) © 2019 Ilya M. Anfimov, Oleg A. Buzanov, Anna P. Kozlova, Nina S. Kozlova, Evgeniya V. Zabelina.
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Citation:
Anfimov IM, Buzanov OA, Kozlova AP, Kozlova NS, Zabelina EV (2019) Impedance spectroscopy study of lanthanumgallium tantalate single crystals grown under different conditions. Modern Electronic Materials 5(2): 4149. https://doi.org/10.3897/j.moem.5.2.47082

The effect of the growth atmosphere and the type of deposited current conductive coatings on the impedance/admittance of La_{3}Ta_{0.5}Ga_{5.5}O_{14} lanthanumgallium tantalate has been revealed. The lanthanumgallium tantalate single crystals have been grown in argon and argon with admixture of oxygen gas atmospheres. Current conductive coatings of iridium, gold with a titanium sublayer, and silver with a chromium sublayer have been deposited onto the single crystals. The tests have been carried out taking into account the polarity of the specimens. The temperature and frequency dependences of the admittance of lanthanumgallium tantalate have been measured in an alternating electric field at frequencies in the 5 Hz to 500 kHz range and temperatures from 20 to 450 °C. The specimens with gold current conductive coating have the lowest admittance. Analysis of the temperature and frequency functions of the dielectric permeability has shown the absence of any frequency dependence in the entire test range.
Equivalent electric circuits have been constructed. Graphicanalytic and numeric analysis of the equivalent electric circuits of the electrode/langatate/electrode cells has shown that the admittance of the metal/langatate/metal cells is controlled by the electrochemical processes at the electrode/electrolyte/electrode interface. The absolute values of the impedance components depend on the langatate growth conditions and the type of the electrodes. Our measurements suggest that the material of the current conductive coating has a greater effect on the absolute values of the measured parameters than the growth atmosphere.
langatate, admittance, growth atmosphere, dielectric permeability, impedance spectroscopy
La_{3}Ga_{5.5}Ta_{0.5}O_{14} (LGT) lanthanumgallium tantalite pertains to the calciumgallium germanate group crystals of the langasite family which are used in mobile communication system devices, pressure sensors and piezoelectric sensors of control and monitoring systems based on direct piezoelectric effect. Lanthanumgallium tantalate finds applications in piezoelectric devices. LGT single crystals have high piezoelectric moduli [
Lanthanumgallium tantalate single crystals are grown using the Czochralski method [
Lanthanumgallium tantalate single crystals grown in different atmospheres differ in color: those grown in an argon atmosphere are almost colorless while those grown in an argon with admixture of oxygen atmosphere have a bright orange color. This is caused by the presence of point defects and their complexes in form of color centers which can be revealed using optical methods, e.g. optical spectroscopy [
The application of langatate crystals for the fabrication of hightemperature pressure sensors requires synthesizing these crystals with an electrical conductivity of ~ 10^{9} Ohm^{1} ∙ cm^{1} at ~400 °C [
The polar cut of the La_{3}Ga_{5.5}Ta_{0.5}O_{14} crystals, even with symmetrical (similar) electrodes, is an electrochemical cell. The anisotropy of the opposite sides of the crystal polar cuts causes an anisotropy of the nearelectrode processes resulting in an acceleration of the overall chemical reactions subject to the possibility of electron passage via an external circuit, i.e., in case of a short circuit. The gradients of the electrochemical potentials and the temperature field in this electrochemical cell produce an EMF and hence short circuit currents. The phenomena of EMF and short circuit currents were first observed and studied in detail in αLiIO_{3} crystals [
These phenomena have an important practical aspect since the short circuit currents caused by the nearelectrode processes may make a substantial contribution to the overall electrical response yielded from the working surface of the piezoelectric sensor. It was reported [
The deposition of current conductive metallic coatings leads to surface degradation due to the electrochemical processes [
Therefore studying the electrophysical parameters of the langatate crystals as a function of temperature for different growth conditions, further investigation into the mechanism of interaction between the current conductive coating and the langatate crystal surface and choice of current conductive coating materials are of great practical importance.
The lanthanumgallium tantalate single crystals were grown and the specimens were prepared by Fomos Materials JSC. The single crystals were Cz grown on Kristall3M units in iridium crucibles in argon with admixture of oxygen (Ar + (2%) O_{2}) and argon (Ar) gas atmospheres. The crystals were cut into specimens in the form of flatparallel plates with the working surfaces perpendicular to a 2^{nd} order symmetry axis (polar cuts) and having the thickness d ~1.5 mm and an area of ~50 mm^{2}. The specimens were not polarized before the experiments. The following current conductive coatings were deposited onto the specimen surfaces by magnetron sputtering: iridium (Ir), gold (Au), gold with a titanium sublayer (Au(Ti)) and silver with a chromium sublayer (Ag(Cr)).
The specimens were studied in the certified test laboratory Single Crystals and Stock on their Base (National University of Science and Technology MISiS) using certified methods.
The full complex resistance (impedance) of the specimens was measured using the threeelectrode method. The temperature and frequency functions of the electrophysical parameters of the specimens in an alternating electric field were measured in the 5 Hz to 500 kHz range on a complex for measuring the electrophysical parameters of highresistivity crystals the metering unit of which was a Tesla ВМ 507 impedance meter allowing for impedance measurements from 1 Ohm to 10 MOhm and phase angle measurements from 0 to 90 arc deg. The effective bias voltage was varied automatically from 3 mV to 3 V depending on the measurement range. The frequency dependences were recorded in the 20–450 °C range.
The specimens were placed in a thermal chamber between two symmetrical (made from the same material) clamping electrodes taking into account the polarity of the specimens which was determined using a piezometer under uniaxial compression.
The specimens were heated in the thermal chamber by increasing temperature with 50 °C steps.
The impedance (Z, Ohm) and the phase angle (ϕ, arc deg) were measured in an alternating electric field. The resultant Z and ϕ were further used for calculating the total complex conductivity (the admittance, σ) and the relative dielectric permeability (ε) using the following formulas:
${\sigma}_{z}=\frac{d}{{S}_{\mathrm{el}}}\frac{1}{Z}$ (1)
$\mathrm{\epsilon}=\frac{d}{{S}_{\mathrm{el}}}\frac{1}{2\mathrm{\pi}{\epsilon}_{0}}\frac{\mathrm{sin}\phi}{fZ}$, (2)
where S_{el} is the electrode area, f is the frequency, Hz, and ε_{0} is the dielectric permeability (ε_{0} = 8.86 × 10^{12} F/m).
Room temperature impedance spectroscopy measurements showed for all the specimens that their admittance values at 5 Hz in an alternating electric field are 5 orders of magnitude higher than the electrical conductivity in a constant electric field obtained earlier [
Temperature and frequency dependences of the admittance for the specimens grown in an Ar + (2%) O_{2} atmosphere with (1) gold, (2) silver and (3) iridium electrodes.
Temperature and frequency dependences of the admittance for the specimens grown in (1, 3) Ar and (2) Ar + (2%) O_{2} atmospheres with iridium electrodes: (1) T = 20¸350 °C; (2) 20–450 °C; (3) 450 °C.
Study of the temperature and frequency dependences of the admittance for the specimens grown in an Ar + (2%) O_{2} atmosphere showed that the specific admittance of the specimens depends on the electrode material (Fig.
The temperature dependences of the specific admittance for the langatate specimens grown in different atmospheres and having gold and iridium current conductive coatings suggest that the growth atmosphere affects the variation pattern of this parameter (Fig.
Study of the temperature and frequency dependences of the relative dielectric permeability (ε_{11}/ε_{0}) for the polar cut specimens with gold, silver and iridium electrodes did not reveal any frequency dependence of the dielectric permeability in the entire experimental frequency range.
The dielectric permeability of the specimens does not depend on temperature up to 400 °C and starts to exhibit temperature dependence at above 450 °C. The relative dielectric permeability was found to depend significantly on the growth atmosphere and the electrode material. Table
Dielectric permeability ε_{11} at different langatate specimen temperatures in 5 Hz to 500 kHz frequency range.
Atmosphere  Electrode material  Dielectric permeability  
20–400 °C  450 °C  
Ar  Ir  34 ± 2  43 ± 3 
Ar + (2 %)O_{2}  Ir  43 ± 3  49 ± 3 
Ar + (2 %)O_{2}  Au  35 ± 2  39 ± 3 
Thus the electrode material has a significant effect on the dielectric permeability of the specimens. Our experimental ε_{11} are slightly higher compared with literary data. For example, ε_{11} = 26.22 [
Study of the electrophysical properties of langatates showed that the crystals interacted most strongly with gold contacts. Xray phase analysis of the polar cut surfaces showed that the degradation of the gold coating was the most intense on the surface corresponding to the negative piezoelectric charge. This effect was less pronounced for the specimens with iridium and silver electrodes.
The most illustrative method of analyzing impedance and admittance measurement results is the construction of a hodograph, i.e., a line in a complex plane described by the free end of the impedance vector with a change in frequency. The shape of the hodograph allows judgment about the equivalent circuit of the process in question and hence about the process itself.
Analysis of the impedance hodographs (Z" = f (Z')) presented in Fig.
Impedance hodographs for the test langatate electrochemical cells grown in different atmospheres and having different current conducting coatings: (a) Ar + (2%) O_{2}, Au ((1) T = 20 °C; (2) 50; (3) 100; (4) 150; (5) 200; (6) 250; (7) 300; (8) 350; (9) 400; (10) 450); (b) Ar + O_{2}, Ir ((1) T = 20 °C; (2) 100; (3) 150; (4) 200; (5) 250; (6) 300; (7) 350; (8) 400; (9) 450); (c) Ar, Au(Ti) ((1) T = 20 °C; (2) 50; (3) 100; (4) 150; (5) 200; (6) 230; (7) 400; (8) 450); (d) Ar, Ir ((1) T = 20 °C; (2) 50; (3) 100; (4) 150; (5) 200; (6) 250; (7) 300; (8) 350; (9) 400).
More complex equivalent circuits are required in order to describe the systems in which the electrodes are at least partially nonblocking. A frequencycontrolled diffusion layer forms in the nearelectrode space when the system is exposed to alternating current. The oxidationreduction reactions on the electrode surfaces are caused by the diffusion supply and removal of ions to (from) the solid electrolyte bulk (the langatate crystal). Warburg diffusion impedance emerges in this case
$\left({Z}_{\mathrm{W}}=(1j){W}_{\mathrm{F}}/\sqrt{\mathrm{\omega}}\right)$,
which includes serialconnected resistance
(${R}_{\mathrm{W}}={W}_{\mathrm{F}}/\sqrt{\mathrm{\omega}}$,
where W_{F} is the Warburg constant and ω is the frequency) and capacity
$\left({C}_{\mathrm{W}}=1/\left({W}_{\mathrm{F}}\sqrt{\mathrm{\omega}}\right)\right)$,
which are frequency dependent [
The ErshlerRandels equivalent circuit allows for the presence of electrochemical oxidationreduction reactions between active ions without specific adsorption of reaction products and charging of the double layer with indifferent ions [
The ErshlerRandels equivalent circuit is described by the following equation [
${Z}_{\mathrm{c}}={R}_{\mathrm{e}}+{Z}_{\mathrm{el}}={R}_{\mathrm{e}}+{\left(j\omega {C}_{\mathrm{d}}+\frac{1}{{R}_{\mathrm{F}}+{Z}_{\mathrm{W}}}\right)}^{1}$, (3)
where Z_{c} is the impedance of the electrode/electrolyte/electrode system (cell), R_{e} is the active electrolyte resistance, Z_{el} is the impedance of the electrochemical reactions, j is the complex unit, C_{d} is the capacity of the double layer and R_{F} is the charge transfer resistance which describes the kinetics of the electrochemical reaction the rate of which is completely controlled by the time of electron attachment or detachment by the electrochemically active particles.
The ErshlerRandels equivalent circuit is not the only possible method of describing the processes taking place in solid electrolyte electrochemical cells. This circuit does not take into account the specific adsorption of the electrochemical reaction products. The problem of impedance with allowance for the adsorption processes was first solved by the authors of an earlier work [
${Z}_{c}={R}_{\mathrm{e}}+{\left(j\omega {C}_{\mathrm{d}}+\frac{1}{{R}^{\text{'}}+{Z}_{\mathrm{w}}+1/\left(j\omega {C}^{\text{'}}\right)}\right)}^{1}$, (4)
where R' is the resistance characterizing the proper time of the elementary adsorption/desorption cycle, C' is the additional capacity of the double layer associated with the adsorption of the surfactant particles and C_{d} is part of the double layer capacity caused by indifferent ions.
Based on the experimental results obtained by impedance spectroscopy we determined the components of the complex resistance Z for the abovementioned equivalent circuits for all the specimens using an analytical method. The basic principle of the analytical method used is the construction of sets of equations (5)–(12) to include the experimentally measured parameters (ω, Z and ϕ) and coefficients composed of the electrochemical impedance components [
For analysis of the ErshlerRandels equivalent circuit and the equation describing this circuit we will introduce the following notations [
$\frac{1}{j\omega}={x}^{2}$ (5)
Then
$x=\frac{1j}{\sqrt{2}}{\mathrm{\omega}}^{0.5};{x}^{2}=j{\mathrm{\omega}}^{1};{x}^{3}=\frac{1+j}{\sqrt{2}}{\omega}^{1.5}$ ;
${x}^{4}={\mathrm{\omega}}^{2};{x}^{5}=\frac{1j}{\sqrt{2}}{\mathrm{\omega}}^{2.5}$;
Equation (4) can be rewritten as follows [
${Z}_{\mathrm{c}}=\frac{\sqrt{2}{a}_{3}{x}^{3}+{a}_{2}{x}^{2}+\sqrt{2}{a}_{1}x+{a}_{0}}{{b}_{2}{x}^{2}+\sqrt{2}{b}_{1}x+{b}_{0}}$, (6)
where a_{0} = R_{e}R_{F}C_{d}; a_{1} = R_{e}W_{F}C_{d}; a_{2} = R_{F} + R_{e}а_{3} = W_{F}; b_{0} = R_{F}C_{d}; b_{1} = W_{F}C_{d}; b_{2} = 1.
Alternatively, the impedance of the cell can be written in the following form [
${Z}_{\mathrm{c}}={Z}_{a}jZr$, (7)
where Z_{a} = Z sinϕ and Z_{r} = Z cosϕ.
Substituting the result into Eq. (6) and equalizing the real and imaginary components we obtain two equations with six variables [
$\begin{array}{c}{a}_{0}+{a}_{1}{\mathrm{\omega}}^{0.5}{a}_{3}{\mathrm{\omega}}^{1.5}{b}_{1}\left({Z}_{a}{Z}_{r}\right){\mathrm{\omega}}^{0.5}{b}_{0}{Z}_{a}={Z}_{r}{\mathrm{\omega}}^{1}\end{array}$ (8)
$\begin{array}{c}{a}_{1}{\mathrm{\omega}}^{0.5}+{a}_{2}{\mathrm{\omega}}^{1}+{a}_{3}{\mathrm{\omega}}^{1.5}{b}_{1}\left({Z}_{a}+{Z}_{r}\right){\mathrm{\omega}}^{0.5}{b}_{0}{Z}_{r}={Z}_{a}{\mathrm{\omega}}^{1}\end{array}$ (9)
We take three frequency values and the respective Z_{a} and Z_{r} and as a result obtain a system of six linear equations with six variables a_{0}, a_{1}, a_{2}, a_{3}, b_{0} and b_{1}. Solving the set of equations we obtain the parameters of the equivalent circuit from the following equations:
${R}_{\mathrm{e}}=\frac{{a}_{0}}{{b}_{0}};{C}_{\mathrm{d}}={\left[\left(\frac{{a}_{2}}{{b}_{0}}\right)\left(\frac{{R}_{\mathrm{e}}}{{b}_{0}}\right)\right]}^{1};R{C}_{\mathrm{d}}={\left(\mathrm{\omega}{C}_{\mathrm{d}}\right)}^{1}$;
${R}_{\mathrm{F}}={a}_{2}{R}_{\mathrm{e}};{W}_{\mathrm{F}}={a}_{3};{C}_{\mathrm{W}}={\left({W}_{\mathrm{F}}\sqrt{\omega}\right)}^{1};{R}_{\mathrm{W}}=\frac{{W}_{\mathrm{F}}}{\sqrt{\omega}}$
For the FrumkinMelikGaikazyan equivalent circuit the full impedance of the system is written as follows [
${Z}_{\mathrm{c}}=\frac{{a}_{4}{x}^{4}+\sqrt{2}{a}_{3}{x}^{3}+{a}_{2}{x}^{2}+\sqrt{2}{a}_{1}x+{a}_{0}}{{b}_{2}{x}^{2}+{b}_{1}x\sqrt{2}+{b}_{0}}$ (10)
where
${a}_{0}=\frac{{R}^{\text{'}}{R}_{e}{C}_{d}}{1+{C}_{d}{\left({C}^{\text{'}}\right)}^{1}};{a}_{1}=\frac{W{R}_{e}{C}_{d}}{1+{C}_{d}(C\text{'}{)}^{1}};{a}_{2}={R}_{e}+\frac{R\text{'}}{1+{C}_{d}{\left({C}^{\text{'}}\right)}^{1}}$;
${a}_{3}=\frac{W}{1+{C}_{\mathrm{d}}{\left({C}^{\text{'}}\right)}^{1}};{a}_{4}=\frac{{\left({C}^{\text{'}}\right)}^{1}}{1+{C}_{\mathrm{d}}{\left({C}^{\text{'}}\right)}^{1}}$;
${b}_{0}=\frac{{R}^{\text{'}}{C}_{d}}{1+{C}_{d}{\left({C}^{\text{'}}\right)}^{1}};{b}_{1}=\frac{W{C}_{d}}{1+{C}_{d}{\left({C}^{\text{'}}\right)}^{1}};{b}_{2}=1$;
Separating the terms with real and imaginary coefficients we obtain two linear equations with seven variables [
${a}_{0}+{a}_{1}{\omega}^{0.5}{a}_{3}{\omega}^{1.5}{a}_{4}{\omega}^{2}{b}_{1}\left({Z}_{a}+{Z}_{r}\right){\omega}^{0.5}{b}_{0}{Z}_{a}={Z}_{r}{\omega}^{1}$ (11)
${a}_{1}{\omega}^{0.5}+{a}_{2}{\omega}^{1}+{a}_{3}{\omega}^{1.5}{b}_{1}\left({Z}_{a}+{Z}_{r}\right){\omega}^{0.5}{b}_{0}{Z}_{r}={Z}_{a}{\omega}^{1}$. (12)
The coefficients a_{i} and b_{i} can be found by constructing a set of eight equations with seven variables. Solution of that set of equations allows determining the parameters of the equivalent circuit from the following equations [
${R}_{\mathrm{e}}=\frac{{a}_{0}}{{b}_{0}};{C}_{\mathrm{d}}={\left[\left(\frac{{a}_{0}}{{b}_{0}}\right)\left(\frac{{R}_{\mathrm{e}}}{{b}_{0}}\right)\right]}^{1}$
${R}_{Cd}={\left(\mathrm{\omega}{C}_{d}\right)}^{1};{R}^{\text{'}}={b}_{0}\left[{\left({C}^{\text{'}}\right)}^{1}+{\left({C}_{d}\right)}^{1}\right]$
${C}^{\text{'}}={a}_{4}^{1}{C}_{\mathrm{d}};{R}_{{C}^{\text{'}}}={\left(\mathrm{\omega}{C}^{\text{'}}\right)}^{1}$
${W}_{\mathrm{F}}=\frac{{R}^{\text{'}}{b}_{1}}{{b}_{0}};{C}_{\mathrm{W}}={\left({W}_{\mathrm{F}}\sqrt{\mathrm{\omega}}\right)}^{1};{R}_{\mathrm{W}}=\frac{{W}_{\mathrm{F}}}{\sqrt{\mathrm{\omega}}}$
By way of example we present the results of Z component calculation using the ErshlerRandels equivalent circuit (Table
Parameters of the ErshlerRandels equivalent circuit for the Au/langatate/Au electrochemical circuit (growth atmosphere Ar + (2 %) O_{2}).
ω  Z _{c}, 10^{5} Ohm  R _{e}, 10^{3}  С _{d}, 10^{10}  R _{Cd}, 10^{5}  R _{F}, 10^{6}  W _{F}, 10^{18}  R _{W},  С _{W},  

Hz  Experimental  Calculated  Ohm × m  F/m^{2}  Ohm × m  Ohm × m  Ohm × m × s^{–1/2}  Ohm × m  F/m^{2} 
At 20 °С  
2500  60  60  1  0.7  60  70  50  1 × 10^{8}  4 × 10^{–12} 
100 000  1  1  1  2 × 10^{7}  6 × 10^{–13}  
500 000  0.3  0.3  0.3  8 × 10^{6}  3 × 10^{–13}  
At 450 °С  
2500  20  20  2  1  40  3  0.4  8 × 10^{5}  5 × 10^{–10} 
100 000  1  1  1  1 × 10^{5}  8 × 10^{–11}  
500 000  0.2  0.2  0.2  5 × 10^{4}  4 × 10^{–11} 
Parameters of the FrumkinMelikGaikazyan equivalent circuit for the Au/langatate/Au electrochemical circuit (growth atmosphere Ar + (2 %) O_{2}).
ω  Z _{c}, 10^{5} Ohm  R _{e}, 10^{3}  С _{d}, 10^{10}  R _{Cd}, 10^{5}  R _{F}, 10^{6}  W _{F}, 10^{18}  R _{W},  С _{W},  
Hz  Experimental  Calculated  Ohm × m  F/m^{2}  Ohm × m  Ohm × m  Ohm × m × s^{–1/2}  Ohm × m  F/m^{2} 
At 20 °С  
2500  60  60  3  6  6 × 10^{6}  50  1 × 10^{8}  30  10 
100 000  1  2  2 × 10^{5}  3 × 10^{6}  5  2  
250 000  0.5  0.7  6 × 10^{4}  1 × 10^{6}  3  1  
500 000  0.3  0.3  3 × 10^{4}  6 × 10^{5}  2  1  
At 450 °С  
2500  20  50  50  3  1 × 10^{7}  0.4  9 × 10^{5}  4  90 
100 000  1  7  3 × 10^{5}  2 × 10^{4}  0.7  10  
250 000  0.5  3  1 × 10^{5}  9 × 10^{3}  0.4  9  
500 000  0.2  1  7 × 10^{4}  5 × 10^{3}  0.3  6 
The effect of the impedance components in the equivalent circuits is determined by analyzing the experimental results using three criteria:
$\text{if}{R}_{C\mathrm{d}}{R}^{*},\text{then}{Z}_{\mathrm{c}}={R}_{\mathrm{e}}+{R}^{*}$,
where R^{*} = R_{F} + R_{W} for the ErshlerRandels equivalent circuit or R^{*} = R' + R_{W} + R_{C'} for the FrumkinMelikGaikazyan equivalent circuit;
$\text{if}{R}_{C\mathrm{d}}{R}^{*},\text{then}{Z}_{\mathrm{c}}={R}_{\mathrm{e}}+{R}_{C\mathrm{d}}$;
$\text{if}{R}_{C\mathrm{d}}\approx {R}^{*},\text{then}{Z}_{\mathrm{c}}={R}_{\mathrm{e}}+\left({R}_{C\mathrm{d}}{R}^{*}/{R}_{C\mathrm{d}}+{R}^{*}\right)$.
Analysis of the impedance components showed that the impedance of the electrochemical cells considered is mainly controlled by the processes occurring in the nearelectrode regions. At room temperature the resistance of the electrolyte itself R_{e} is by 2–4 orders of magnitude lower than the resistance of the nearelectrode regions (R_{C}_{d}, R', R_{W} and R_{C'}). It is only at high frequencies (about 500 kHz) and temperatures (above 450 °C) that the resistances of the nearelectrode reactions and the electrolyte R_{e} become comparable and the properties of the electrolyte itself start to show. A similar impedance dependence is observed in the Au/langatate/Au solid electrolyte cells (growth atmosphere Ar) and the Ir/langatate/Ir solid electrolyte cells (growth atmosphere Ar + (2 %) O_{2}).
At room temperature the impedance of the Ag/langatate/Ag and Ir/langatate/Ir cells (growth atmosphere Ar + (2 %) O_{2}) depends most significantly on the resistance of the double layer. Whereas for the ErshlerRandels equivalent circuit the difference between the double layer resistance R_{Cd} and the impedance caused by the electrochemical reactions (R_{F} + R_{W}) is 1–2 orders of magnitude, for the FrumkinMelikGaikazyan equivalent circuit the difference between R_{C}_{d} and (R’ + R_{W} + R_{C’}) is 2–3 orders of magnitude. Another impedance dependence is observed for the Ir/langatate/Ir cells (growth atmosphere Ar): at room temperature Z_{c} for the FrumkinMelikGaikazyan equivalent circuit is controlled by the adsorption/desorption electrochemical processes (R', R_{W} and R_{C}_{’}), while for the ErshlerRandels equivalent circuit Z_{c} is controlled by R_{C}_{d}; with an increase in temperature (same as for the Ag/langatate/Ag cell (growth atmosphere Ar + (2 %) O_{2})) the double layer charging resistance makes the largest contribution.
These results suggest that the impedance of the Ir/langatate/Ir, Au/langatate/Au (growth atmosphere Ar + (2 %) O_{2}) and the Au/langatate/Au (growth atmosphere Ar) cells is largely controlled by the double layer resistance (at temperatures of about 20 °C) and the resistance caused by the electrochemical reactions at the electrode/electrolyte/electrode interface (at high temperatures). On the contrary, the impedance of the Ag/langatate/Ag cell (growth atmosphere Ar + (2 %) O_{2}) and the Ir/langatate/Ir (langatate growth atmosphere Ar) cell is controlled by the double layer resistance in the entire experimental temperature range. The highest resistance R_{W} was observed for the Ir/langatate/Ir cell and the lowest one, for the Au/langatate/Au cell. Thus, there is a clear dependence of the impedance/admittance of the metal/langatate/metal systems both on the material of the current conductive coating and on the measurement temperature and frequency.
Analysis of our calculation results does not suggest definitively that preference should be given to either of the two equivalent circuits since the contribution of the observed adsorption processes to the impedance of the cells is very small.
It is assumed that langatate contains two types of ions:
– indifferent carriers which participate in the charge transfer via the electrolyte and control its bulk resistance but do not take part in the electrochemical reactions occurring at the electrode/electrolyte boundary;
– active ions which participate in the electrochemical reactions.
In accordance with the earlier reported defect formation model for langatate crystals [
Thus, oxygen and gallium vacancies are indifferent carriers which participate in the charge transfer via the solid electrolyte and control its bulk resistance. In this case the basic electrical neutrality equation is written in the following form:
$3{V}_{\mathrm{O}}^{2+}+3{V}_{\mathrm{Ga}}^{3}\rightleftarrows 0$.
When an electric field is applied the oxygen vacancies rush toward the negatively charged electrode (cathode) resulting in an excess of oxygen ions at the positive electrode (anode), whereas gallium vacancies rush toward the anode causing an excess of gallium ions at the cathode. It seems that the oxygen and gallium ions are those active particles which participate in the nearelectrode electrochemical reactions.
Expectably, at least one form of electrochemically active matter (oxygen or gallium ions) or both of them enter into reaction and are adsorbed at the electrode in the form of electrochemical reaction products. Since the same particles participate in the Faraday process and in the double layer charging, one cannot clearly distinguish between the charging current and the Faraday current. These processes end up interrelated, and one can in fact judge about a single electrochemical process which results in the change of the electrode surface state and in the occurrence of the oxidationreduction reactions.
The model suggested here is based on the assumption that the charging of the double electric layer, i.e., the accumulation or deficiency of indifferent ions at the electrode/electrolyte interface, should be accompanied by redistribution of electrochemically active ions. If this is true, this redistribution will show itself in the impedance measurements as a relaxation process of charging the capacitance С' via the active resistance R' and the diffusion impedance Z_{W}.
The effect of the growth atmosphere and the type of deposited current conductive coatings on the impedance/admittance of lanthanumgallium tantalate was revealed. The admittance of the specimens with gold coating is 30% lower than that of the specimens with gold electrodes and 20% lower than that of the specimens with iridium electrodes. We show that the specific admittance of the test langatate crystals does not depend on temperature if the impedance is measured in an alternating electric field at temperatures below 400 °C. The langatate growth atmosphere was shown to influence the specific dielectric permeability (ε_{11}/ε_{0}) of the polar cuts of the langatate crystals. The dielectric permeability ε_{11} proved to be temperature dependent in the entire experimental frequency range.
Information on the origins of the impedance components for langatate with deposited electrodes was obtained by analyzing equivalent circuits for the electrode/langatate/electrode cells using graphicanalytic and numeric nethods.
Construction of equivalent circuits and analysis of the hodographs and calculated impedance components showed that the admittance of the metal/langatate/metal cells is controlled by the electrochemical processes at the electrode/electrolyte/electrode interface. The impedance components depend on the growth atmosphere, the electrode material and the measurement temperature and frequency.