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Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (part II: The role of grain boundaries and oxygen vacancies)
Journal of the European Ceramic Society 39 (2019) 4800–4805
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Original Article
Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (part II: The role of grain boundaries and oxygen vacancies)
T
⁎
Meimanat Rahmania,b, , Christian Pithanb, Rainer Wasera,b a b
Institut für Werkstoffe der Elektrotechnik II (IWE II), RWTH Aachen University, 52056 Aachen, Germany Institut für elektronische Materialien, Peter Grünberg Institut (PGI 7), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Calcium manganite ceramics Impedance Permittivity Grain boundaries Oxygen vacancies
A comprehensive overview is provided about the role of bulk conductivity contributions in compounds of the composition YbxCa1-xMnO3 (0–10 at. % Yb-dopant concentration). For this purpose, in-situ impedance spectroscopy was successfully employed at different temperatures (−100 up to 300 °C) and frequencies (1 Hz–1 MHz). These experiments reveal the main role of grain boundaries as well as electronic and ionic contributions in conductivity. The contribution of different resistance components in electric transport properties were proposed on the base of a double-Schottky-barrier model. Migration of oxygen vacancies and their participation in conductivity were studied and the results are confirmed by observing oxygen released using a ZrO2 oxygen sensor during dilatometry measurements in a wide range of temperatures.
1. Introduction Mixed valence alkaline earth manganites RExA1-xMnO3 with very rich and complex crystal physics and chemistry have attracted a great deal of attention recently (RE: Rare earth element; A: Alkaline metal). The incorporation of dopants introduces significant changes in the electrical and magnetic properties of these materials [1–3]. Two innovative potential applications for rare earth manganites are non-volatile memories based on resistive switching and waste heat recovery techniques by thermoelectric generators. The resistive switching mechanism and thermoelectric properties strongly depend on the concentration and nature of the charge carriers. Meanwhile several models explaining the mechanism of resistive switching have been proposed in the literature [4–7], still however the defect chemical mechanisms involved in these processes have not been understood clearly yet. This lack of information in the literature is certainly also due to complexity of this material system, since manganese cations may possess several valence states in the quaternary oxide. It is known that the valence states of Mn cations and oxygen non-stoichiometry have an important role on the resistivity of manganites [8]. Therefore the oxidation state of Mn cation has been titrated by the so called iodometric method. According to the electroneutrality principle, the relationship between the number of oxygen vacancies generated and the oxidation state of Mn cation were defined in theory. In order to understand the role of bulk conductivity contributions
⁎
and the effect of internal interfaces (grain boundaries) on the electronic structure of polycrystalline ceramics these studies were conducted by impedance spectroscopy accompanied by modeling the compounds in terms of an electrical equivalent circuit in a wide range of temperatures and frequencies. 2. Experimental procedure YbxCa1-xMnO3 (0–10 at. % Yb-dopant concentration, i.e. x = 0.001 up to 0.1) crack-free ceramic pellets with a diameter of 10–12 mm were prepared by solid state reaction. The details are described in another paper [9]. 2.1. Iodometric titration Iodometric titration experiments were performed in order to determine the average Mn valency and the corresponding oxygen content of the compounds. According to the principle of electroneutrality, the relationship between the number of oxygen vacancies generated and the oxidation state of B-site metal cations can be described theoretically. Titration is based on a complete chemical reaction between the analyte and a reagent (titrant) of known concentration which is added to the sample. Since in direct titration for CaMnO3 the end-point is very difficult to observe, back titration was used in the present study. 20 mg CaMnO3 with an excess of Potassium iodide (KI) was mixed with
Corresponding author at: Institut für elektronische Materialien, Peter Grünberg Institut (PGI 7), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany. E-mail address: [email protected] (M. Rahmani).
https://doi.org/10.1016/j.jeurceramsoc.2019.07.017 Received 19 January 2019; Received in revised form 8 July 2019; Accepted 14 July 2019 Available online 16 July 2019 0955-2219/ © 2019 Elsevier Ltd. All rights reserved.
Journal of the European Ceramic Society 39 (2019) 4800–4805
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In the present study, the impedance spectra show more than one semicircle for all the investigated samples (e.g. Fig. 5 Section 3.3). Several equivalent circuit models for each sample have been applied and it is found that the experimental impedance measurements for the investigated compounds fit well with more than one RC element in series. Consequently, it is assumed that most of the current preferentially flows through the semiconducting grains and the grain boundaries parallel to the electrode planes. Therefore, the resistance values for grain boundaries running parallel to the path of electric current can be neglected. Generally, in impedance analysis, the use of low work function electrodes is preferable, since the transfer of electrons out of the metal into the ceramic is enhanced. Therefore, electrode materials with a work function as shallow as possible are needed in order to minimize the contact resistance to the ceramic layers. In the ideal case, this contact should be ohmic. For impedance measurements, the selection of the electrode material is crucial with respect to the investigated temperature and the type of conductivity. Often applied electrodes consist of platinum, palladium, gold, indium-gallium (In-Ga) or silver. At high temperatures (T > 600 °C) platinum and gold electrodes can be used, but at temperatures below 600 °C they are relatively blocking to oxygen [13]. If the measurement temperature is lower than this, silver and InGa (T < 300 °C [14]) electrodes are preferable, as they generally have a relatively lower work function. In the present investigation, in order to form ohmic contacts and to minimize the contact resistances to the CaMnO3 ceramic layer (work function: 4.8–5.3 eV [15,16]) an In-Ga alloy with a lower work function of 4.1–4.2 eV [11] was selected as an electrode material. Liquid In-Ga electrodes which are brushed on both sides of the polished ceramics surfaces are quick and easy to apply. Thus, the contact resistance and capacitance can be neglected. Under this assumption of an only small resistive contribution of the external interfaces, the generalized equivalent circuit given in Fig. 1 can be further simplified as two RC elements; one for the grains and one for the grain boundaries perpendicular to the path of electric flow. The parallel R and C connections yield in impedanceZ*for each RC element, which generally can be expressed as Eq. (1). According to the Eq. (2), the impedanceZ*can be separated into a real Z′and imaginary Z″part, containing the imaginary unit represented by j = −1 and the angular frequency ω = 2πf.
degassed and purified HCl in a glass ampoule. The glass ampoule was sealed. Heating the mixture leads to the dissolution of CaMnO3 and afterwards Iodine (I2) is liberated. The solution was titrated under Ar with a Na2S2O3 solution using starch as an indicator. The titrant (Na2S2O3) is added until the end of the reaction is observed (colorless solution). The precise volume of the used Na2S2O3 was noted. Several measurements for each compound were carried out and the average of the results was used for determining the average Mn valency and the corresponding oxygen content of the sample. 2.2. Impedance measurement Before each impedance measurement both sides of a pellet to be investigated were polished in order to remove eventual resistive outer surface layers. The effect of bulk conductivity contributions is observed by in-situ impedance spectroscopy at different temperatures (-100 to 300 °C) and frequencies (1 Hz to 1 MHz). These characterizations were accompanied by modeling of the compounds in terms of an electrical equivalent circuit using the WinFit-Software, Novocontrol. 2.2.1. Brick-wall model Impedance data analysis of dielectric materials can be performed according to the so called brick-wall model [10]. In this model, resistive or capacitive contributions from impedance spectra can be simulated and thus extracted from the measured frequency loci of complex electric impedance. Grains are assumed to have a cubic shape and identical dimensions. Furthermore, grain boundary layers of a thickness δg.b are postulated to separate all grains. The total number of grains can then be assumed to have a resistance Rgrain and a capacitance Cgrain. The respective contributions of the grain boundaries can be represented by Rg.b.ǁ, Cg.b.ǁ, Rg.b.⊥ and Cg.b. ⊥, where the symbol ǁ denotes grain boundaries running parallel to the path of electric conduction. The symbol ⊥ indicates grain boundaries that extend in the direction perpendicular to this path. Additionally external influences such as the resistance of ceramic-electrode interfaces Rinterface and their capacitance Cinterface as well as inductive effects, represented by Lartifacts arising from the measuring equipment and the connections to the sample have to be taken into account. The Brick-wall model for an idealized microstructure of a polycrystalline electronic ceramic and the corresponding equivalent circuit for this model are shown in Fig. 1. Often the resistance value for grain boundaries running parallel to the path of electric current can be neglected, since Rg.b.ǁ is much larger compared to Rg.b.⊥ separating grains. According to previous reports [11,12], there are two possibilities for current flow, depending on the specific situation. If grain boundaries are highly conductive, the current preferably flows along them. Therefore, only the response from grain boundaries parallel to the path of electric conduction can be seen in the impedance spectrum. On the other hand, if grain boundaries are very resistive, current flow passes in series through the bulk and the blocking perpendicular grain boundaries. This results in two separate semicircles area in the representation of the frequency dependent impedance loci in the so called Cole-Cole plot. In this case, in other words, more than one semicircle should be observed.
1 1 R = +jωC → Z ∗ = Z∗ R 1+jωRC
|Z *| =
(1)
Z′2 + Z″2
(2)
The impedance of grains and grain boundaries (g.b⊥) can be calculated separately according to the equations above. Consequently, the total impedance ZT∗can be written as: ∗ ∗ ZT∗ = Zgrain + Zg.b. ⊥
= (Z′grain + Z′g.b.⊥) +j(Z″grain + Z″g.b.⊥)
(3)
ZT∗
is plotted in the To evaluate electrochemical impedance data, complex plane which is known as Nyquist plot or complex impedance plane plot. Each point on the Nyquist plot represents the impedance at a specific frequency. Modern computer controlled impedance analyzer systems calculate automatically the dielectric constant ε´ (relative permittivity) by the ratio of measured capacitance C and C0. The geometrical capacitance C0 is given by the vacuum permittivity ε0. Complex impedance analysis allows modeling of the compounds in terms of an electrical equivalent circuit. In the present study, circuits with two, three, and four RC-elements [R1C1+R2C2+R3C3+R4C4] were used for the evaluation of all impedance spectra by complex nonlinear least squares fitting (WinFit-Software, Novocontrol). R and C indicate resistance and capacitance respectively. Depending on the temperature the best fit has been chosen. According to previous reports
Fig. 1. a) Two identical electrodes applied to the faces of a sample (idealized brick-wall microstructure consisting of identically cubic shaped grains), b) the equivalent circuit for the brick-wall model and c) simplified equivalent circuit. 4801
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oxygen content above 3. The oxygen content observed by iodometric titration for compounds with 10 at. % of Yb addition is approximately the same as for pure CaMnO3.0075, while its Mn-valence is below 4+, i.e. (Mn4−α). It seems that a larger amount of Yb addition increases the concentration of Mn3+ cations significantly. Due to the larger ionic radius of Mn3+ (0.64 Å) compared to that of Mn4+ (0.53 Å) [21] the positions of oxygen ions in the lattice might be shifted and possibly this leads to relatively easier oxygen release. Besides, at sintering in an oxidizing regime the Schottky equilibrium suppresses some of the oxygen vacancy concentration. In other words, at p(O2) above that at the stoichiometric composition, compounds take up an excess of oxygen to maintain equilibrium [22,23]. Therefore, the value for δ equals zero approximately, while still the concentration of Mn3+ cations is relatively much larger than that of Mn5+ cations. Therefore iodomometric titration analysis shows a Mn-valence less than 4+ for 10 at. % Ybcontent. XRD-measurements [9] show that with increasing Yb-dopant concentration the volume of the crystallographic unit cell increases slightly which is due to the increase in the amount of Mn3+ cations with larger ionic radius compared to Mn4+ cations. These experiments in combination with iodometric titration analysis reveal an important issue. It can be clearly understood that, however, some of the compounds show a manganese valence state above 4+, the mixture of all three valance states of manganese Mn3+, Mn4+ and Mn5+ occur in equilibrium for YbxCa1-x Mn4 ± αO3 ± δ according to the disproportional equation, expressed as:
[17,18] the resistance of grains is relatively small compared to the resistance of grain boundaries and only can be detected at high frequencies. Therefore, contributions at low frequencies typically indicate the response of grain boundaries to the electric stimulus and the specific properties of the grain or bulk are represented at high frequencies. Therefore, components at low frequencies typically indicate grain boundary contributions to the electric response and the specific properties of the grain or bulk are represented at high frequencies. 2.3. O2-gas release measurements The resulting release of oxygen gas O2 was monitored by a ZrO2sensor at the outlet of the dilatometer instrument. During the experiment, there is a constant flow of Ar in order to ensure stationary and defined conditions. In this experiment, the compounds under investigation were heated up, kept at 1350 °C for 6 h and then cooled down. As a result, the dependence of O2-release from temperature is obtained. The amount of oxygen released can be calculated by the Nernst formula. Therefore corresponding p(O2) exhaust can be formulated as:
p (O2)[bar] = 0.2064.exp(-46.42
UN [mV] ) T [K]
(3)
where UN indicates the measured Nernst voltage or Ee.m.f. and T represents the temperature in Kelvin. More details can be found in our paper Part I [9]. 3. Results and discussions
2Mn4+ ⇄ Mn3++Mn5+
3.1. Iodometric titration
Consequently, these investigations reveal that the oxygen content and concentration of charge carriers can be adjusted by adding specific amount of dopant.
Iodometric titration reveals that increasing the Yb-dopant concentration from 0 at. % to 0.5 at. % reduces the average Mn-valency and oxygen content (Fig. 2). Probably, substitution of Yb3+ for Ca2+ (i.e. donor doping) is compensated by increasing of cation vacancies the 4+ [V Mn concentration). In other "" ] concentration (i.e. decreasing Mn words, donor doping allows the injection of electrons in the Mn4+ sublattice. Possibly this increases the concentration of Mn3+ cations. However, by adding more amount of Yb above 0.5 at. % up to 5 at. % the cation vacancy concentration reaches a critical point where the Schottky equilibrium is activated [19]:
3.2. Complex impedance Obtaining higher value for Z' at lower frequencies and low Z' value at higher frequencies indicates the presence and disappearance of space charge polarization, respectively (Fig. 3a). This is because charge carriers contributing to the polarizability are not able to align with rapidly changing external electric fields at higher frequencies. It is also observed that the curve of Z,ʹ the real part of impedance, at low frequencies shows a negative temperature coefficient of resistance type behavior. At high frequencies, the value of Zʹ merges by increasing temperatures. This behavior may be due to thermally activated charge carrier hopping conduction mechanism of electrons at elevated temperatures. As shown in Fig. 3b, at first the Zʺ values increase, reaching a peak Zʺmax and then decrease with frequency as well as with temperature. If the hopping frequency of localized electrons becomes equal to the frequency of the applied electric field a maximum peak appears [24]. At higher frequencies dipoles are not able to align fully with the electric field variations. Therefore space charge polarization and orientation polarizability disappear at higher frequencies and thus relaxation
where KS is the mass-action constant. The details about Schottky disorder reaction are described in another paper [20]. Accordingly, the compounds must reduce the oxygen vacancy concentration [V•• O ] in order to maintain equilibrium. Therefore, perhaps the compounds uptake oxygen and thus Mn5+ cations are formed. As a result iodometric titration shows Mn-valency above 4+ (Mn4+α) and
Fig. 2. a) Average Mn-valance (error bar is shown in red, which is approximately the same for all the other investigated samples) and b) corresponding oxygen content for YbxCa1xMnO3 (0 to 10 at. % Yb-doped) calculated from iodometric titration method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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Fig. 3. Frequency dependence of a) real and b) imaginary part of impedance for pure CaMnO3 at different temperatures.
Fig. 4. Schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramic: a) donor-doped grains and an acceptor state grain boundary (gb), i.e., formation of cation vacancies (during the sintering process) acting as an acceptor-doped region trapping electrons; and b) situation with an applied external electric field where some of the charge carriers do not have a sufficient energy and are trapped and accumulated in gb; A space charge layer is formed and resistance “R3″ appears. c) With increasing temperature, some of the charge carriers which possess enough energy are able to overcome the barrier, easily flow to the next grain and participate in the conduction mechanism. Accordingly, resistance “R2″ is formed. d) at T > 100 °C oxygen vacancy concentration increases. Oxygen ions hop from lattice site to lattice site under the influence of an electric field until they reach grain boundaries. Electrons formed by oxygen vacancies give rise to the resistance “R4″.The resistance contribution of the grain interior is termed as “R1″. Therefore, all the pictures (a)-(d) possess R1.
frequency of the applied electric field a maximum peak appears in the spectrum [18]. At higher frequencies, dipoles are not able to align fully with the electric field variations anymore. Therefore space charge polarization and orientation polarizability disappear at higher frequencies and thus relaxation occurs. Impedance of capacitors and inductors in a circuit depend on the frequency of the electric signal. The impedance of an inductor is directly proportional to frequency, while the impedance of a capacitor is inversely proportional to frequency. Therefore at low frequency a capacitor acts as open circuit and at high frequencies it acts as short circuit. In both these cases, there is a only relatively small current flowing which results in a small value of Z". Fig. 3b. illustrates that increasing temperature from -100 to 300 °C shifts the relaxation peak of Zʺ from around 104 Hz to higher frequencies at about 105 Hz, respectively. In fact, increasing temperature enhances the rate of hopping of electrons and ions which causes more diffusion through the compounds. Some of the charge carriers are trapped because they do not possess enough energy to overcome the barrier. These charge carriers have enough energy to align with fast changing fields at higher frequencies and thus restore the space charge polarization.
occurs. As mentioned above, higher values for the real part of impedance Z' at lower frequencies indicate the presence of space charge polarization. This type of polarization usually takes place in dielectric materials with a spatial inhomogeneous distribution of charge carrier densities. This mechanism is particular relevant for ceramics with electrically relative well conducting grains and rather insulating grain boundaries separating them and is generally referred to Maxwell-Wagner polarization. By imposing an electric field charge carriers migrate over a certain distance through the material until they are blocked at a potential barrier, such as an electrically charged grain- or phase- boundary [25] The migrating charges then become trapped within the environment of the respective interface, resulting in a space charge polarization. Such accumulation of charges locally distorts the external field and increases the overall capacitance as well as real permittivity of a dielectric material [26,27]. The imaginary part of impedance Z" represents the capacitance of an element within an electric circuit and corresponds to the energy stored. As shown in Fig. 3b, the imaginary Z" part first increases with increasing frequency reaching a maximum value Zʺmax and then decreases again. The maximum value Z"max shifts to higher frequencies with increasing temperature. The imaginary part Z" quasi represents the energy fraction of the external stimulating electric filed absorbed by separating charge carriers at a specific frequency. It characterizes the dielectric loss. When the excitation frequency of the external electric filed coincides with the resonance frequency of oscillation of specific charge carriers, losses are at their maximum. In another words, if the hopping frequency of localized electrons becomes equal to the
3.3. Electrical equivalent circuit model It is found that complex impedance for all investigated components at temperatures above 100 °C can be well modeled with four parallel RC elements, i.e. R1C1+ R2C2+ R3C3+ R4C4. A novel schematic illustration based on the double-Schottky-barrier model for polycrystalline 4803
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ceramics describes the resistance component R1 to R4 (Fig. 4). According to this model cation vacancies which have been formed during the sintering process along the grain boundaries act as acceptors and trapping areas of electrons. (i) By applying an electric field the majority charge carriers (here: electrons) migrate from the grain interior to grain boundaries. This causes a relatively high conductivity in the bulk. In the present study, the resistance contribution of the grain interior is termed as “R1″. (ii) With increasing temperature some of the charge carriers which possess sufficient energy are able to overcome the barrier, easily flow to the next grain participating in the mechanism of conduction. Accordingly, resistance “R2″ appears. (iii) Some of the charge carriers which do not have adequate energy are trapped and accumulated in grain boundaries. Therefore a space charge layer is formed which prevents excess amount of negatively charge carriers after equilibration of Fermi level. This type of charge carriers forms the resistance contribution “R3″. (iv) At T > 100 °C the concentration of the oxygen vacancies increases. Oxygen ions may hop from lattice site to lattice site under the influence of an electric field, until they reach the grain boundaries. The electrons which are left from oxygen vacancies form the resistance contribution R4. As shown in Fig. 5, the negative imaginary partZ″is plotted against the real part Z′within the frequency range from 1 Hz to 1 MHz at 150 °C for 10 at.% Yb-doped CaMnO3. The theoretical curve calculated on the basis of the respective equivalent circuit is represented as a solid red line. Four series of parallel RC circuit elements are in excellent agreement with the experimental data.
Fig. 6. A comparison of real dielectric permittivity ε′(ω) as a function of temperature (-100 to 300 °C) for different Yb-dopant concentrations (0–10 at. % Ybconent).
and 10 at. % respectively. Therefore a comparison of the impedance measurements and results of iodometric titration experiments reveals that the first maximum dielectric relaxation probably depends on the amount of Mn3+ cations and thus on the contribution of polarons to conductivity. A second peak appears at temperatures above 100 °C, which is possibly due to the release of oxygen. Fig. 7 clearly shows a release of O2-gas above 100 °C which is monitored by ZrO2 oxygen sensor. The same trend is also observed for all other investigated compounds YbxCa1-xMnO3-z (0 up to 10 at. % Yb-conent). Accordingly, the second peak is probably due to thermally activated oxygen vacancies. Increasing the amount of oxygen vacancy enhances electron concentration in grain boundaries. Therefore space charge polarization increases. However, at temperatures above 150 °C the rate of hopping increases and charges can overcome the potential barrier of space charge layers. Fig. 8 shows the temperature dependence (0 to 300 °C) of the resistive components calculated based on the equivalent circuit model for the compounds with an Yb-dopant concentration of 10 at. %. The green curve shows the total resistance and the others indicate different resistance components (R1, R2, R3 and R4). As mentioned in section 3.3, a schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramics is suggested in order to explain the origin of these resistive components. According to this model, for example at 150⁰C, the black square indicates R1 which represents the resistance contribution of grains, R2 is due to the contribution of charges which have enough energy to overcome the barriers (grain boundaries), R3 refers to formation of space charge layer and polarization. R4 is suggested to be due to the contribution of oxygen vacancies. To confirm this suggestion experimentally, ZrO2 oxygen sensor has been used to monitor eventual release of oxygen from the compound (Sec. 2.3). In compounds with 10 at. % Yb-addition the concentration of Mn3+
3.4. Dielectric permittivity The dimensionless dielectric permittivity parameter represents a real number indicating the factor by which the dielectric response of a certain material is larger than the value of vacuum permittivity (8.85 × 10−12 As/Vm). A surprisingly very large dielectric permittivity εʹ ≈ 106 at 103 Hz is obtained for all compounds YbxCa1-xMnO3 (0–10 at. % Yb-addition). The large dielectric value is probably due to the Maxwell-Wagner polarization because of existing grains and separating grain boundaries in the ceramic compounds. In fact, the polarization forms internal barrier capacitors at the grain boundaries. Fig. 6 demonstrates the real dielectric permittivity ε′(ω) as a function of a wide range of temperatures for different Yb-concentrations. Idometric titration (Fig. 2) shows that pure CaMnO3 and the compound with 5 at. % Yb-content possess the average manganese valence above 4+ (Mn4+α). According to the impedance measurements (Fig. 6), the first relaxation peak is not observed for the above-mentioned compounds. While the other compounds which possess larger amounts of Mn3+ show this peak clearly. i.e. compounds with an Yb-content of 0.1, 0.5
Fig. 5. Complex impedance diagram obtained experimentally for 10 at. % Ybdoped (symbols). Theoretical curve (solid red line) calculated on the basis of the respective equivalent circuit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 7. Release of O2-gas, monitored by a ZrO2 oxygen sensor using dilatometer in pure Argon for 10 at. % Yb-concentration. 4804
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[2]
[3]
[4]
[5] [6] [7]
Fig. 8. The resistive components (R1-R4) as a function of temperature based on the modeling the compounds with 10 at. % Yb-dopant concentration in terms of an electrical equivalent circuit. The green curves indicate total resistance (RT). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
[8]
[9]
[10]
cations exceeds a certain amount at which the number of Mn3+-Mn4+ states decrease. Therefore charge localization occurs which enhances the resistivity. As shown in Fig. 8, a peak in resistance at 150 °C is observed which occurs at the same temperature where the second dielectric relaxation is formed. In addition, the forth RC elements is added above 100 °C. This confirms the suggestion of diffusion of more oxygen ions from the grain interior to grain boundaries with increasing temperature above 100 °C.
[11]
[12]
[13]
4. Conclusions
[14]
Bulk conductivity measurements revealed the main role of grain boundaries as well as electronic and ionic contributions in the conductivity for YbxCa1-xMnO3 ceramics (0–10 at. % Yb-concentration) in a wide range of temperatures and frequencies. A novel schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramics is proposed which clearly describes the contribution of different resistance components in electric transport. An additional resistive component is observed in electrical equivalent circuit models at temperatures above 100 °C which probably is related to an ionic contribution due to oxygen vacancies. This is confirmed by measuring the ambient gas composition with regard to the oxygen content using a ZrO2 oxygen sensor during dilatometery measurements. A surprisingly large dielectric permittivity value εʹ around 106 at a frequency of about 103 Hz was observed. Determining the average Mn valency and corresponding oxygen content of the compounds using iodometric titration reveals that a first dielectric relaxation below 100 °C probably depends on the amount of Mn3+ cations and thus on the contribution of polarons to conductivity. The second relaxation peak is observed above 100 °C which is probably due to the thermally activated creation of oxygen vacancies. According to the present experiments the formation of oxygen vacancies and corresponding change in density of Mn3+-Mn4+ pair sites seem to play an important role in charge migration and resistance properties of the complex systems YbxCa1-xMnO3.
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22] [23] [24]
[25] [26]
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Sawa, Relationship between resistive switching characteristics and band diagramsof Ti/Pr1−xCaxMnO3 junctions, J. phys. rev. B. 80 (2009) 235113–235118, https://doi.org/10.1103/PhysRevB.80.235113. H.S. Lee, H.H. Park, M.J. Rozenberg, Manganite-based memristive heterojunction with tunable non-linear I–V characteristics, J. Royal Society of Chemistry Nanoscale 7 (2015) 6444–6450, https://doi.org/10.1039/C5NR00861A. S. Lanfredi, C. Darie, F.S. Bellucci, C.V. Colin, M.A.L. Nobre, Phase transitions and interface phenomena the cryogenic temperature domain of a niobate nanostructured ceramic, J. The Royal Soc. of Chem. Dalton Trans. 43 (2014) 10983–10998, https://doi.org/10.1039/c4dt00623b. M.A.L. Nobre, S. Lanfredi, Dielectric spectroscopy on Bi3Zn2Sb3O14 ceramic: an approach based on the complex impedance, J. Phys. Chem. Solids 64 (2003) 2457–2464, https://doi.org/10.1016/j.jpcs.2003.08.007. R. Waser, T. Baiatu, K.H. Härdtl, Dc electrical degradation of perovskite-type titanates: I, ceramics, J. Am. Ceram. Soc. 73 (1990) 1645–1673, https://doi.org/10. 1111/j.1151-2916.1990.tb09809.x. M. Rahmani, Optimization of powder and ceramic processing, electrical haracterization and defect chemistry in the system YbxCa1-xMnO3, RWTH Aachen University, Forschungszentrum Juelic, 54 (2018), XIV, 164 pp, ISBN: 978-3-95806-323-5. B. Sarbas, W. Töpper, Manganese: Natural Occurrence. Minerals (native Metal, Solid Solution, Silicide, and Carbide. Sulfides and Related Compounds. Halogenides and Oxyhalogenides. Oxides of Type MO), Springer-Verlag, Berlin Heidelberg, 2013 181 pages. D.M. Smyth, The Defect Chemistry of Metal Oxides, Oxford University Press, New York, USA, 2000 294 pages. J. Nowotny, M. Rekas, Defect chemistry of (La,Sr)MnO3, J. Am. Ceram. Soc. 81 (1998) 67–80, https://doi.org/10.1111/j.1151-2916.1998.tb02297.x. K. Bharathi, G. Markandeyulu, C.V. Ramana, Microstructure, AC impedance and DC electrical conductivity characteristics of NiFe2-xGdxO4 (x = 0, 0.05 and 0.075), J. AIP Adv. 2 (2012) 012139, https://doi.org/10.1063/1.3687219. A.J. Moulson, J.M. Herbert, 2nd ed., Electroceramics: Materils, Properties, Applications vol. 52, John Wiley & Sons, 2003 576 pages. Freude: Molecular physics, Nature science 4 (2012) 276–285 Chapter 3 http:// home.unileipzig.de/energy/freume.html. R.C. Buchanan, Ceramic material for electronics: processing, properties, and application, M. Dekker, New York, 1991532 pages.
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Original Article
Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (part II: The role of grain boundaries and oxygen vacancies)
T
⁎
Meimanat Rahmania,b, , Christian Pithanb, Rainer Wasera,b a b
Institut für Werkstoffe der Elektrotechnik II (IWE II), RWTH Aachen University, 52056 Aachen, Germany Institut für elektronische Materialien, Peter Grünberg Institut (PGI 7), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany
A R T I C LE I N FO
A B S T R A C T
Keywords: Calcium manganite ceramics Impedance Permittivity Grain boundaries Oxygen vacancies
A comprehensive overview is provided about the role of bulk conductivity contributions in compounds of the composition YbxCa1-xMnO3 (0–10 at. % Yb-dopant concentration). For this purpose, in-situ impedance spectroscopy was successfully employed at different temperatures (−100 up to 300 °C) and frequencies (1 Hz–1 MHz). These experiments reveal the main role of grain boundaries as well as electronic and ionic contributions in conductivity. The contribution of different resistance components in electric transport properties were proposed on the base of a double-Schottky-barrier model. Migration of oxygen vacancies and their participation in conductivity were studied and the results are confirmed by observing oxygen released using a ZrO2 oxygen sensor during dilatometry measurements in a wide range of temperatures.
1. Introduction Mixed valence alkaline earth manganites RExA1-xMnO3 with very rich and complex crystal physics and chemistry have attracted a great deal of attention recently (RE: Rare earth element; A: Alkaline metal). The incorporation of dopants introduces significant changes in the electrical and magnetic properties of these materials [1–3]. Two innovative potential applications for rare earth manganites are non-volatile memories based on resistive switching and waste heat recovery techniques by thermoelectric generators. The resistive switching mechanism and thermoelectric properties strongly depend on the concentration and nature of the charge carriers. Meanwhile several models explaining the mechanism of resistive switching have been proposed in the literature [4–7], still however the defect chemical mechanisms involved in these processes have not been understood clearly yet. This lack of information in the literature is certainly also due to complexity of this material system, since manganese cations may possess several valence states in the quaternary oxide. It is known that the valence states of Mn cations and oxygen non-stoichiometry have an important role on the resistivity of manganites [8]. Therefore the oxidation state of Mn cation has been titrated by the so called iodometric method. According to the electroneutrality principle, the relationship between the number of oxygen vacancies generated and the oxidation state of Mn cation were defined in theory. In order to understand the role of bulk conductivity contributions
⁎
and the effect of internal interfaces (grain boundaries) on the electronic structure of polycrystalline ceramics these studies were conducted by impedance spectroscopy accompanied by modeling the compounds in terms of an electrical equivalent circuit in a wide range of temperatures and frequencies. 2. Experimental procedure YbxCa1-xMnO3 (0–10 at. % Yb-dopant concentration, i.e. x = 0.001 up to 0.1) crack-free ceramic pellets with a diameter of 10–12 mm were prepared by solid state reaction. The details are described in another paper [9]. 2.1. Iodometric titration Iodometric titration experiments were performed in order to determine the average Mn valency and the corresponding oxygen content of the compounds. According to the principle of electroneutrality, the relationship between the number of oxygen vacancies generated and the oxidation state of B-site metal cations can be described theoretically. Titration is based on a complete chemical reaction between the analyte and a reagent (titrant) of known concentration which is added to the sample. Since in direct titration for CaMnO3 the end-point is very difficult to observe, back titration was used in the present study. 20 mg CaMnO3 with an excess of Potassium iodide (KI) was mixed with
Corresponding author at: Institut für elektronische Materialien, Peter Grünberg Institut (PGI 7), Forschungszentrum Jülich GmbH, 52425, Jülich, Germany. E-mail address: [email protected] (M. Rahmani).
https://doi.org/10.1016/j.jeurceramsoc.2019.07.017 Received 19 January 2019; Received in revised form 8 July 2019; Accepted 14 July 2019 Available online 16 July 2019 0955-2219/ © 2019 Elsevier Ltd. All rights reserved.
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In the present study, the impedance spectra show more than one semicircle for all the investigated samples (e.g. Fig. 5 Section 3.3). Several equivalent circuit models for each sample have been applied and it is found that the experimental impedance measurements for the investigated compounds fit well with more than one RC element in series. Consequently, it is assumed that most of the current preferentially flows through the semiconducting grains and the grain boundaries parallel to the electrode planes. Therefore, the resistance values for grain boundaries running parallel to the path of electric current can be neglected. Generally, in impedance analysis, the use of low work function electrodes is preferable, since the transfer of electrons out of the metal into the ceramic is enhanced. Therefore, electrode materials with a work function as shallow as possible are needed in order to minimize the contact resistance to the ceramic layers. In the ideal case, this contact should be ohmic. For impedance measurements, the selection of the electrode material is crucial with respect to the investigated temperature and the type of conductivity. Often applied electrodes consist of platinum, palladium, gold, indium-gallium (In-Ga) or silver. At high temperatures (T > 600 °C) platinum and gold electrodes can be used, but at temperatures below 600 °C they are relatively blocking to oxygen [13]. If the measurement temperature is lower than this, silver and InGa (T < 300 °C [14]) electrodes are preferable, as they generally have a relatively lower work function. In the present investigation, in order to form ohmic contacts and to minimize the contact resistances to the CaMnO3 ceramic layer (work function: 4.8–5.3 eV [15,16]) an In-Ga alloy with a lower work function of 4.1–4.2 eV [11] was selected as an electrode material. Liquid In-Ga electrodes which are brushed on both sides of the polished ceramics surfaces are quick and easy to apply. Thus, the contact resistance and capacitance can be neglected. Under this assumption of an only small resistive contribution of the external interfaces, the generalized equivalent circuit given in Fig. 1 can be further simplified as two RC elements; one for the grains and one for the grain boundaries perpendicular to the path of electric flow. The parallel R and C connections yield in impedanceZ*for each RC element, which generally can be expressed as Eq. (1). According to the Eq. (2), the impedanceZ*can be separated into a real Z′and imaginary Z″part, containing the imaginary unit represented by j = −1 and the angular frequency ω = 2πf.
degassed and purified HCl in a glass ampoule. The glass ampoule was sealed. Heating the mixture leads to the dissolution of CaMnO3 and afterwards Iodine (I2) is liberated. The solution was titrated under Ar with a Na2S2O3 solution using starch as an indicator. The titrant (Na2S2O3) is added until the end of the reaction is observed (colorless solution). The precise volume of the used Na2S2O3 was noted. Several measurements for each compound were carried out and the average of the results was used for determining the average Mn valency and the corresponding oxygen content of the sample. 2.2. Impedance measurement Before each impedance measurement both sides of a pellet to be investigated were polished in order to remove eventual resistive outer surface layers. The effect of bulk conductivity contributions is observed by in-situ impedance spectroscopy at different temperatures (-100 to 300 °C) and frequencies (1 Hz to 1 MHz). These characterizations were accompanied by modeling of the compounds in terms of an electrical equivalent circuit using the WinFit-Software, Novocontrol. 2.2.1. Brick-wall model Impedance data analysis of dielectric materials can be performed according to the so called brick-wall model [10]. In this model, resistive or capacitive contributions from impedance spectra can be simulated and thus extracted from the measured frequency loci of complex electric impedance. Grains are assumed to have a cubic shape and identical dimensions. Furthermore, grain boundary layers of a thickness δg.b are postulated to separate all grains. The total number of grains can then be assumed to have a resistance Rgrain and a capacitance Cgrain. The respective contributions of the grain boundaries can be represented by Rg.b.ǁ, Cg.b.ǁ, Rg.b.⊥ and Cg.b. ⊥, where the symbol ǁ denotes grain boundaries running parallel to the path of electric conduction. The symbol ⊥ indicates grain boundaries that extend in the direction perpendicular to this path. Additionally external influences such as the resistance of ceramic-electrode interfaces Rinterface and their capacitance Cinterface as well as inductive effects, represented by Lartifacts arising from the measuring equipment and the connections to the sample have to be taken into account. The Brick-wall model for an idealized microstructure of a polycrystalline electronic ceramic and the corresponding equivalent circuit for this model are shown in Fig. 1. Often the resistance value for grain boundaries running parallel to the path of electric current can be neglected, since Rg.b.ǁ is much larger compared to Rg.b.⊥ separating grains. According to previous reports [11,12], there are two possibilities for current flow, depending on the specific situation. If grain boundaries are highly conductive, the current preferably flows along them. Therefore, only the response from grain boundaries parallel to the path of electric conduction can be seen in the impedance spectrum. On the other hand, if grain boundaries are very resistive, current flow passes in series through the bulk and the blocking perpendicular grain boundaries. This results in two separate semicircles area in the representation of the frequency dependent impedance loci in the so called Cole-Cole plot. In this case, in other words, more than one semicircle should be observed.
1 1 R = +jωC → Z ∗ = Z∗ R 1+jωRC
|Z *| =
(1)
Z′2 + Z″2
(2)
The impedance of grains and grain boundaries (g.b⊥) can be calculated separately according to the equations above. Consequently, the total impedance ZT∗can be written as: ∗ ∗ ZT∗ = Zgrain + Zg.b. ⊥
= (Z′grain + Z′g.b.⊥) +j(Z″grain + Z″g.b.⊥)
(3)
ZT∗
is plotted in the To evaluate electrochemical impedance data, complex plane which is known as Nyquist plot or complex impedance plane plot. Each point on the Nyquist plot represents the impedance at a specific frequency. Modern computer controlled impedance analyzer systems calculate automatically the dielectric constant ε´ (relative permittivity) by the ratio of measured capacitance C and C0. The geometrical capacitance C0 is given by the vacuum permittivity ε0. Complex impedance analysis allows modeling of the compounds in terms of an electrical equivalent circuit. In the present study, circuits with two, three, and four RC-elements [R1C1+R2C2+R3C3+R4C4] were used for the evaluation of all impedance spectra by complex nonlinear least squares fitting (WinFit-Software, Novocontrol). R and C indicate resistance and capacitance respectively. Depending on the temperature the best fit has been chosen. According to previous reports
Fig. 1. a) Two identical electrodes applied to the faces of a sample (idealized brick-wall microstructure consisting of identically cubic shaped grains), b) the equivalent circuit for the brick-wall model and c) simplified equivalent circuit. 4801
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oxygen content above 3. The oxygen content observed by iodometric titration for compounds with 10 at. % of Yb addition is approximately the same as for pure CaMnO3.0075, while its Mn-valence is below 4+, i.e. (Mn4−α). It seems that a larger amount of Yb addition increases the concentration of Mn3+ cations significantly. Due to the larger ionic radius of Mn3+ (0.64 Å) compared to that of Mn4+ (0.53 Å) [21] the positions of oxygen ions in the lattice might be shifted and possibly this leads to relatively easier oxygen release. Besides, at sintering in an oxidizing regime the Schottky equilibrium suppresses some of the oxygen vacancy concentration. In other words, at p(O2) above that at the stoichiometric composition, compounds take up an excess of oxygen to maintain equilibrium [22,23]. Therefore, the value for δ equals zero approximately, while still the concentration of Mn3+ cations is relatively much larger than that of Mn5+ cations. Therefore iodomometric titration analysis shows a Mn-valence less than 4+ for 10 at. % Ybcontent. XRD-measurements [9] show that with increasing Yb-dopant concentration the volume of the crystallographic unit cell increases slightly which is due to the increase in the amount of Mn3+ cations with larger ionic radius compared to Mn4+ cations. These experiments in combination with iodometric titration analysis reveal an important issue. It can be clearly understood that, however, some of the compounds show a manganese valence state above 4+, the mixture of all three valance states of manganese Mn3+, Mn4+ and Mn5+ occur in equilibrium for YbxCa1-x Mn4 ± αO3 ± δ according to the disproportional equation, expressed as:
[17,18] the resistance of grains is relatively small compared to the resistance of grain boundaries and only can be detected at high frequencies. Therefore, contributions at low frequencies typically indicate the response of grain boundaries to the electric stimulus and the specific properties of the grain or bulk are represented at high frequencies. Therefore, components at low frequencies typically indicate grain boundary contributions to the electric response and the specific properties of the grain or bulk are represented at high frequencies. 2.3. O2-gas release measurements The resulting release of oxygen gas O2 was monitored by a ZrO2sensor at the outlet of the dilatometer instrument. During the experiment, there is a constant flow of Ar in order to ensure stationary and defined conditions. In this experiment, the compounds under investigation were heated up, kept at 1350 °C for 6 h and then cooled down. As a result, the dependence of O2-release from temperature is obtained. The amount of oxygen released can be calculated by the Nernst formula. Therefore corresponding p(O2) exhaust can be formulated as:
p (O2)[bar] = 0.2064.exp(-46.42
UN [mV] ) T [K]
(3)
where UN indicates the measured Nernst voltage or Ee.m.f. and T represents the temperature in Kelvin. More details can be found in our paper Part I [9]. 3. Results and discussions
2Mn4+ ⇄ Mn3++Mn5+
3.1. Iodometric titration
Consequently, these investigations reveal that the oxygen content and concentration of charge carriers can be adjusted by adding specific amount of dopant.
Iodometric titration reveals that increasing the Yb-dopant concentration from 0 at. % to 0.5 at. % reduces the average Mn-valency and oxygen content (Fig. 2). Probably, substitution of Yb3+ for Ca2+ (i.e. donor doping) is compensated by increasing of cation vacancies the 4+ [V Mn concentration). In other "" ] concentration (i.e. decreasing Mn words, donor doping allows the injection of electrons in the Mn4+ sublattice. Possibly this increases the concentration of Mn3+ cations. However, by adding more amount of Yb above 0.5 at. % up to 5 at. % the cation vacancy concentration reaches a critical point where the Schottky equilibrium is activated [19]:
3.2. Complex impedance Obtaining higher value for Z' at lower frequencies and low Z' value at higher frequencies indicates the presence and disappearance of space charge polarization, respectively (Fig. 3a). This is because charge carriers contributing to the polarizability are not able to align with rapidly changing external electric fields at higher frequencies. It is also observed that the curve of Z,ʹ the real part of impedance, at low frequencies shows a negative temperature coefficient of resistance type behavior. At high frequencies, the value of Zʹ merges by increasing temperatures. This behavior may be due to thermally activated charge carrier hopping conduction mechanism of electrons at elevated temperatures. As shown in Fig. 3b, at first the Zʺ values increase, reaching a peak Zʺmax and then decrease with frequency as well as with temperature. If the hopping frequency of localized electrons becomes equal to the frequency of the applied electric field a maximum peak appears [24]. At higher frequencies dipoles are not able to align fully with the electric field variations. Therefore space charge polarization and orientation polarizability disappear at higher frequencies and thus relaxation
where KS is the mass-action constant. The details about Schottky disorder reaction are described in another paper [20]. Accordingly, the compounds must reduce the oxygen vacancy concentration [V•• O ] in order to maintain equilibrium. Therefore, perhaps the compounds uptake oxygen and thus Mn5+ cations are formed. As a result iodometric titration shows Mn-valency above 4+ (Mn4+α) and
Fig. 2. a) Average Mn-valance (error bar is shown in red, which is approximately the same for all the other investigated samples) and b) corresponding oxygen content for YbxCa1xMnO3 (0 to 10 at. % Yb-doped) calculated from iodometric titration method. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
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Fig. 3. Frequency dependence of a) real and b) imaginary part of impedance for pure CaMnO3 at different temperatures.
Fig. 4. Schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramic: a) donor-doped grains and an acceptor state grain boundary (gb), i.e., formation of cation vacancies (during the sintering process) acting as an acceptor-doped region trapping electrons; and b) situation with an applied external electric field where some of the charge carriers do not have a sufficient energy and are trapped and accumulated in gb; A space charge layer is formed and resistance “R3″ appears. c) With increasing temperature, some of the charge carriers which possess enough energy are able to overcome the barrier, easily flow to the next grain and participate in the conduction mechanism. Accordingly, resistance “R2″ is formed. d) at T > 100 °C oxygen vacancy concentration increases. Oxygen ions hop from lattice site to lattice site under the influence of an electric field until they reach grain boundaries. Electrons formed by oxygen vacancies give rise to the resistance “R4″.The resistance contribution of the grain interior is termed as “R1″. Therefore, all the pictures (a)-(d) possess R1.
frequency of the applied electric field a maximum peak appears in the spectrum [18]. At higher frequencies, dipoles are not able to align fully with the electric field variations anymore. Therefore space charge polarization and orientation polarizability disappear at higher frequencies and thus relaxation occurs. Impedance of capacitors and inductors in a circuit depend on the frequency of the electric signal. The impedance of an inductor is directly proportional to frequency, while the impedance of a capacitor is inversely proportional to frequency. Therefore at low frequency a capacitor acts as open circuit and at high frequencies it acts as short circuit. In both these cases, there is a only relatively small current flowing which results in a small value of Z". Fig. 3b. illustrates that increasing temperature from -100 to 300 °C shifts the relaxation peak of Zʺ from around 104 Hz to higher frequencies at about 105 Hz, respectively. In fact, increasing temperature enhances the rate of hopping of electrons and ions which causes more diffusion through the compounds. Some of the charge carriers are trapped because they do not possess enough energy to overcome the barrier. These charge carriers have enough energy to align with fast changing fields at higher frequencies and thus restore the space charge polarization.
occurs. As mentioned above, higher values for the real part of impedance Z' at lower frequencies indicate the presence of space charge polarization. This type of polarization usually takes place in dielectric materials with a spatial inhomogeneous distribution of charge carrier densities. This mechanism is particular relevant for ceramics with electrically relative well conducting grains and rather insulating grain boundaries separating them and is generally referred to Maxwell-Wagner polarization. By imposing an electric field charge carriers migrate over a certain distance through the material until they are blocked at a potential barrier, such as an electrically charged grain- or phase- boundary [25] The migrating charges then become trapped within the environment of the respective interface, resulting in a space charge polarization. Such accumulation of charges locally distorts the external field and increases the overall capacitance as well as real permittivity of a dielectric material [26,27]. The imaginary part of impedance Z" represents the capacitance of an element within an electric circuit and corresponds to the energy stored. As shown in Fig. 3b, the imaginary Z" part first increases with increasing frequency reaching a maximum value Zʺmax and then decreases again. The maximum value Z"max shifts to higher frequencies with increasing temperature. The imaginary part Z" quasi represents the energy fraction of the external stimulating electric filed absorbed by separating charge carriers at a specific frequency. It characterizes the dielectric loss. When the excitation frequency of the external electric filed coincides with the resonance frequency of oscillation of specific charge carriers, losses are at their maximum. In another words, if the hopping frequency of localized electrons becomes equal to the
3.3. Electrical equivalent circuit model It is found that complex impedance for all investigated components at temperatures above 100 °C can be well modeled with four parallel RC elements, i.e. R1C1+ R2C2+ R3C3+ R4C4. A novel schematic illustration based on the double-Schottky-barrier model for polycrystalline 4803
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ceramics describes the resistance component R1 to R4 (Fig. 4). According to this model cation vacancies which have been formed during the sintering process along the grain boundaries act as acceptors and trapping areas of electrons. (i) By applying an electric field the majority charge carriers (here: electrons) migrate from the grain interior to grain boundaries. This causes a relatively high conductivity in the bulk. In the present study, the resistance contribution of the grain interior is termed as “R1″. (ii) With increasing temperature some of the charge carriers which possess sufficient energy are able to overcome the barrier, easily flow to the next grain participating in the mechanism of conduction. Accordingly, resistance “R2″ appears. (iii) Some of the charge carriers which do not have adequate energy are trapped and accumulated in grain boundaries. Therefore a space charge layer is formed which prevents excess amount of negatively charge carriers after equilibration of Fermi level. This type of charge carriers forms the resistance contribution “R3″. (iv) At T > 100 °C the concentration of the oxygen vacancies increases. Oxygen ions may hop from lattice site to lattice site under the influence of an electric field, until they reach the grain boundaries. The electrons which are left from oxygen vacancies form the resistance contribution R4. As shown in Fig. 5, the negative imaginary partZ″is plotted against the real part Z′within the frequency range from 1 Hz to 1 MHz at 150 °C for 10 at.% Yb-doped CaMnO3. The theoretical curve calculated on the basis of the respective equivalent circuit is represented as a solid red line. Four series of parallel RC circuit elements are in excellent agreement with the experimental data.
Fig. 6. A comparison of real dielectric permittivity ε′(ω) as a function of temperature (-100 to 300 °C) for different Yb-dopant concentrations (0–10 at. % Ybconent).
and 10 at. % respectively. Therefore a comparison of the impedance measurements and results of iodometric titration experiments reveals that the first maximum dielectric relaxation probably depends on the amount of Mn3+ cations and thus on the contribution of polarons to conductivity. A second peak appears at temperatures above 100 °C, which is possibly due to the release of oxygen. Fig. 7 clearly shows a release of O2-gas above 100 °C which is monitored by ZrO2 oxygen sensor. The same trend is also observed for all other investigated compounds YbxCa1-xMnO3-z (0 up to 10 at. % Yb-conent). Accordingly, the second peak is probably due to thermally activated oxygen vacancies. Increasing the amount of oxygen vacancy enhances electron concentration in grain boundaries. Therefore space charge polarization increases. However, at temperatures above 150 °C the rate of hopping increases and charges can overcome the potential barrier of space charge layers. Fig. 8 shows the temperature dependence (0 to 300 °C) of the resistive components calculated based on the equivalent circuit model for the compounds with an Yb-dopant concentration of 10 at. %. The green curve shows the total resistance and the others indicate different resistance components (R1, R2, R3 and R4). As mentioned in section 3.3, a schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramics is suggested in order to explain the origin of these resistive components. According to this model, for example at 150⁰C, the black square indicates R1 which represents the resistance contribution of grains, R2 is due to the contribution of charges which have enough energy to overcome the barriers (grain boundaries), R3 refers to formation of space charge layer and polarization. R4 is suggested to be due to the contribution of oxygen vacancies. To confirm this suggestion experimentally, ZrO2 oxygen sensor has been used to monitor eventual release of oxygen from the compound (Sec. 2.3). In compounds with 10 at. % Yb-addition the concentration of Mn3+
3.4. Dielectric permittivity The dimensionless dielectric permittivity parameter represents a real number indicating the factor by which the dielectric response of a certain material is larger than the value of vacuum permittivity (8.85 × 10−12 As/Vm). A surprisingly very large dielectric permittivity εʹ ≈ 106 at 103 Hz is obtained for all compounds YbxCa1-xMnO3 (0–10 at. % Yb-addition). The large dielectric value is probably due to the Maxwell-Wagner polarization because of existing grains and separating grain boundaries in the ceramic compounds. In fact, the polarization forms internal barrier capacitors at the grain boundaries. Fig. 6 demonstrates the real dielectric permittivity ε′(ω) as a function of a wide range of temperatures for different Yb-concentrations. Idometric titration (Fig. 2) shows that pure CaMnO3 and the compound with 5 at. % Yb-content possess the average manganese valence above 4+ (Mn4+α). According to the impedance measurements (Fig. 6), the first relaxation peak is not observed for the above-mentioned compounds. While the other compounds which possess larger amounts of Mn3+ show this peak clearly. i.e. compounds with an Yb-content of 0.1, 0.5
Fig. 5. Complex impedance diagram obtained experimentally for 10 at. % Ybdoped (symbols). Theoretical curve (solid red line) calculated on the basis of the respective equivalent circuit. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
Fig. 7. Release of O2-gas, monitored by a ZrO2 oxygen sensor using dilatometer in pure Argon for 10 at. % Yb-concentration. 4804
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[2]
[3]
[4]
[5] [6] [7]
Fig. 8. The resistive components (R1-R4) as a function of temperature based on the modeling the compounds with 10 at. % Yb-dopant concentration in terms of an electrical equivalent circuit. The green curves indicate total resistance (RT). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).
[8]
[9]
[10]
cations exceeds a certain amount at which the number of Mn3+-Mn4+ states decrease. Therefore charge localization occurs which enhances the resistivity. As shown in Fig. 8, a peak in resistance at 150 °C is observed which occurs at the same temperature where the second dielectric relaxation is formed. In addition, the forth RC elements is added above 100 °C. This confirms the suggestion of diffusion of more oxygen ions from the grain interior to grain boundaries with increasing temperature above 100 °C.
[11]
[12]
[13]
4. Conclusions
[14]
Bulk conductivity measurements revealed the main role of grain boundaries as well as electronic and ionic contributions in the conductivity for YbxCa1-xMnO3 ceramics (0–10 at. % Yb-concentration) in a wide range of temperatures and frequencies. A novel schematic illustration based on the double-Schottky-barrier model for polycrystalline ceramics is proposed which clearly describes the contribution of different resistance components in electric transport. An additional resistive component is observed in electrical equivalent circuit models at temperatures above 100 °C which probably is related to an ionic contribution due to oxygen vacancies. This is confirmed by measuring the ambient gas composition with regard to the oxygen content using a ZrO2 oxygen sensor during dilatometery measurements. A surprisingly large dielectric permittivity value εʹ around 106 at a frequency of about 103 Hz was observed. Determining the average Mn valency and corresponding oxygen content of the compounds using iodometric titration reveals that a first dielectric relaxation below 100 °C probably depends on the amount of Mn3+ cations and thus on the contribution of polarons to conductivity. The second relaxation peak is observed above 100 °C which is probably due to the thermally activated creation of oxygen vacancies. According to the present experiments the formation of oxygen vacancies and corresponding change in density of Mn3+-Mn4+ pair sites seem to play an important role in charge migration and resistance properties of the complex systems YbxCa1-xMnO3.
[15]
[16]
[17]
[18]
[19]
[20]
[21]
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