Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (part III: Point defect chemistry)

Journal Pre-proof Electric transport properties of rare earth doped Ybx Ca1−x MnO3 ceramics (part III: Point defect chemistry) Meimanat Rahmani, Christian Pithan, Rainer Waser

PII:

S0955-2219(19)30879-9

DOI:

https://doi.org/10.1016/j.jeurceramsoc.2019.12.035

Reference:

JECS 12948

To appear in:

Journal of the European Ceramic Society

Received Date:

27 January 2019

Revised Date:

14 December 2019

Accepted Date:

17 December 2019

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Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (part III: Point defect chemistry) Meimanat Rahmani1,2*, Christian Pithan2, Rainer Waser1,2 1 2

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

ABSTRACT

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A defect chemical model based on charge neutrality and laws of mass action is proposed to clarify the details of the chemistry of point defects for donor-doped YbxCa1-xMnO3. DC-conductivity measurements were carried out in a wide range of partial pressure of oxygen p(O2) ≈ 10-1 down to 10-19 MPa at 750⁰ C for the first time without disintegrating the ceramic sample through reduction. A comparison of the experimental observations and the theoretical defect chemical models clearly shows the possibilities for controlling charge carriers in dependence of partial pressure of oxygen p(O2) and dopant concentration. The origin of a plateau state, of a drastic decrease in conductivity in the intermediate and reduction p(O2) regimes are figured out, respectively. In addition, the kind and concentration of the electronic and ionic majority charge carriers are determined and formulated according to the proposed defect chemical model. Furthermore, phase transitions were studied in a wide range of p(O2) at elevated temperatures Keywords:

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Donor doped calcium manganite ceramic,DC- conductivity measurement, Thermogravimetric analysis,Defect chemistry model, Phase transition

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*Corresponding author: Meimanat Rahmani, Institut für elektronische Materialien, Peter Grünberg Institut (PGI 7), Forschungszentrum Jülich GmbH, 52425 Jülich, Germany, Fax: +49 2461 61-2550 Email address: [email protected]

1. Introduction

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Electronic oxides with a perovskite type or related crystallographic structure exhibit a large variety of interesting functional properties making them indispensable for the use in many electronic devices [1]. _________ Typical applications of these materials are solid state electrolytes e.g. for fuel cells [2], membranes for gas separation [3], catalysts [4] and sensors [5]. On the other hand, two

innovative potential applications for rare earth manganites are non-volatile memories based on resistive switching [6-8] and waste heat recovery techniques by thermoelectric generators [9-11]. The resistive switching mechanism and thermoelectric properties strongly depend on the concentration and nature of electrical charge carriers. The defect chemistry is quite well understood for titanate-based perovskites [12-19] and also several models explaining the mechanism of resistive switching have been proposed in the literature [20-22]. Still, however, the

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defect chemical mechanisms in CaMnO3 derived ceramics are far less well studied and

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described. Therefore, in the present work comprehensive studies were performed for the first time to clarify the electric transport properties of rare earth doped YbxCa1-xMnO3 in a wide range

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of p(O2). These properties strongly depend on the chemistry of point defects which are described

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by a defect chemical model proposed in the present study based on charge neutrality and the laws of mass action. The theoretical model described is supported by experimental DC-conductivity

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measurements, dilatometry analysis, SEM, EDX, XRD-measurements, Raman spectroscopy, iodometric titration and thermogravimetric (TGA) experiments. The details of the mentioned

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measurements can be found in previous papers of this series, Part I [23] and Part II [24]. The results reveal ionic as well as electronic charge transport conductivity contributions in

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dependence of the oxygen partial pressure p(O2).

2. Experimental procedure 2.1. Preparation and Characterization

Ytterbium doped CaMnO3 based compositions with a dopant level ranging from 0 to 10 at. % were prepared by the solid state reaction method [23]. Accordingly the Mn3+/Mn4+ ratio as well 2

as the proportion of A-site cations (Yb3+, Ca2+) relative to the overall Mn-content (degree of stoichiometry) were varied. The details can be found in a previous paper of this series (Part I) [23].

All materials prepared have been thoroughly characterized regarding to their microstructure, using SEM (Scanning Electron Microscopy, HITACHI SU8000, Japan) in combination with

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EDX (Energy-Dispersive X-ray Spectroscopy). In order to study the phase purity and crystallography Raman spectroscopy (T64000 Horiba Jobin Yvon) and XRD (X-ray diffraction,

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Huber Imaging Plate Guinier Camera G670, Germany; CuK-radiation, λ= 1.540590 Å and STOE

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STADI P diffractometer, Röntgenlabor, Reinheim, Germany) were carried out. Measurements were evaluated with Rietveld refinements of the corresponding diffraction patterns using a

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software package (CEA-CNRS, France). Iodometric titration [24] served as a valuable method for determining the valence states of the Mn-cations and of oxygen deficiency.

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These fundamental characterizations are discussed in our previous papers [23, 24]. For DCconductivity measurements, the four-probe technique was applied to rectangular shaped samples

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with dimensions of 4 x 0.7 x 10 mm3. Both DC- and TGA- measurements were investigated at a temperature of 750°C and in a wide range of p(O2) from 10-1 down to 10-19 MPa. The mentioned characterizations reveal important issues explaining the role of the dominating

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charge carriers and electrical transport mechanism.

2.2. Thermogravimetric analysis (TGA)

The phase stability in dependence of the partial pressure of oxygen p(O2) has been evaluated by thermogravimetric analysis (TGA) for grinded as sintered stoichiometric CaMnO3 ceramics. As illustrated in Fig. 1 the oxygen content of the compound increases with increasing p(O2). The 3

data imply an uncertainty of ±5 x 10-5. The reason of this enhancement is certainly related to the

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TGA 3.01 Undoped CaMnO3 3.00 2.99 2.98 2.97 2.96 2.95 2.94 -20-18-16-14-12-10 -8 -6 -4 -2 0 log p(O2) / MPa

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uptake of oxygen as discussed in the following sections.

Fig. 1: Thermogravimetric measurement for stoichiometric CaMnO3 demonstrating an increase in oxygen vacancy

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concentration with decreasing p(O2) from 10-1 to 10-18 Mpa .The uncertainty in data is ±5 x 10-5.

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For comparison, values of oxygen deficiency reported by previous investigations are listed in table 1.

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3. Principle of defect chemical models

Point defects of either electronic or ionic origin dominating the electrical conductivity of crystalline solids, can be described in detail by comparing experimental results from DC-

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measurements with theoretical thermodynamical models. The main equilibrium reactions and their mass action expressions required to construct Kröger-Vink representations [29], that visualize the p(O2) dependence of lattice point defect concentrations, are listed in table 2. The details can be found in previous reports [30, 31].

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Some thermodynamic parameters required for modeling and reported by previous studies [25-28] are listed in table 3. They include: the Enthalpy of oxidation ΔH ox0 and the Enthalpy of the disproportionation reaction ΔH D0 (Eq.4) at 750⁰C for different donor-doped CaMnO3.

4. Results and discussion

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4.1. Defect chemistry for undoped calcium manganite

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The corresponding defect diagrams for the pure undoped compound CaMnO3 and the influence

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of partial pressure of oxygen p(O2) on conductivity are shown in Fig. 2 and 3.

Fig. 2: Defect diagram calculated on the basis of equilibrium concentrations revealing dominating defects for

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undoped CaMnO3.

As shown in Fig. 2, the proposed defect chemistry model for pure CaMnO3 contains three regions: the oxidation region, the near-stoichiometric region and the reduction region. The theoretical details can be found in our previous investigation [30].

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4.1.1. The oxidizing regime: p(O2)>10-6 MPa

As Fig. 3a demonstrates, the conductivity decreases by increasing p(O2) in the region of p(O2) > 10-6 MPa with a slope of approximately only -0.014 which is by far lower than the calculated slope of -3/16. In order to understand the exact reason for this discrepancy further investigations are required. In fact, if p(O2) is sufficiently high, the oxidation reaction is the

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major source of defects. In the case of active Schottky disorder, this reaction can increase the

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number of holes while the oxygen vacancy concentration decreases, as formulated in Eq. 7.

A comparison of the present defect model, experimental DC-measurements and TGA

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experiments (Fig. 3b) reveals that with increasing p(O2) above 10-6 MPa the oxygen loss from

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compound decreases gradually because of the uptake of oxygen. Accordingly, the concentration of conducting electrons [Mn Mn ] (i.e. the amount of Mn3+ cations) decreases while the

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concentration of holes [Mn Mn ] (i.e. the amount of Mn5+ cations) increases. Therefore the possibility of electron hopping over eg states of Mn3+ (t32g e0g) and Mn4+ (t32g e1g) decreases. As a

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result, the possibility of charge carrier hopping mechanism becomes less prominent. Consequently, over all conductivity decreases.

DC-measurement

b) 0.06

Undoped CaMnO3

1.8 1.7 1.6 1.5 1.4 1.3 1.2 -18 -16 -14 -12 -10 -8 -6 -4 -2 log[p(O2)] / MPa

TGA 0.05 Undoped CaMnO3 0.04 0.03 0.02 0.01 0.00 -0.01 -20-18-16-14-12-10 -8 -6 -4 -2 0 log p(O2) / MPa



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log() / S.cm-1

a) 1.9

0

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Fig. 3: The effect of wide range of p(O2) from 10-1 down to 10-16 MP on a) conductivity observed by DC measurement which have an uncertainty of ±1 x 10-4 and b) oxygen loss measured by TGA experiments for undoped CaMnO3 at 750°C ). The data imply an uncertainty of ±5 x 10-5.

4.1.2. Intermediate region At a p(O2) approximately between 10-6 MPa and 10-11 MPa (plateau-type region) the

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conductivity shows almost constant values around 47 S∙cm-1 for pure CaMnO3 and seems to be independent of p(O2). Such a plateau-like regime for donor-doped BaTiO3-based compositions

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from 10-13 up to 10-6 MPa was already observed by Daniels, et. al [32] and Katsu [18]. Here an important question arises: why is the plateau region observed in pure undoped CaMnO3 and why

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is there electron concentration not governed by oxygen vacancies?

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XRD measurements after sintering at p(O2) lower than 10-2 MPa show two secondary phases

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occurring: CaMn 32 O4 and Ca 2 Mn 4+ O4 . In addition, TGA experiments illustrate that the weight of compounds is almost constant in the same mentioned intermediate p(O2) region. Therefore it

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is suggested that weight constancy is due to the formation of secondary phases which probably form temporary barriers to oxygen migration near grain boundaries. Therefore the release of oxygen and thus weight loss is small. Accordingly, as shown in the previous defect diagrams, the oxidation process does not have a considerable effect on the electron and hole concentrations in

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the intermediate region. Consequently, decreasing p(O2) from 10-6 down to 10-11 MPa yields in a plateau region in conductivity. Therefore the expression of charge neutrality is dominated by the intrinsic electronic defects:

[Mn Mn ]  [Mn Mn ]

(10)

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According to the calculation based on equilibrium concentrations, the concentration of cation vacancies increases with the average slope of 3/4 with increasing p(O2), whereas the amount of oxygen vacancies decreases with the slope of -1/2.

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4.1.3. The reduction region From p(O2) ≈ 10-11 down to 10-16 MPa, conductivity increases with decreasing p(O2). This is also

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in agreement with TGA measurements, which show a slight increase in oxygen vacancy

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concentration after the plateau region down to 10-16 MPa. In fact, oxygen is released in order to maintain equilibrium with the ambient pressure and thus conductivity increases. Consequently,

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in this region, the oxygen vacancy term 2[VO ] is dominant and charge neutrality can be

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estimated as:

[Mn Mn ]  2[VO ]

(11)

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The electron concentration [MnMn ] and oxygen vacancy concentration [VO ] show an additional increase with the slope of -1/6. According to the Schottky disorder reaction when oxygen vacancies increase with reducing p(O2), the concentration of cation vacancies should decrease

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with an average slope of 1/4. In this region, increasing the number of electrons will enhance conductivity slightly.

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4.2. The effect of doping on conductivity As shown in Fig. 4, it is found that at p(O2) larger than 10-16 MPa with increasing donor dopant concentration from 0 at. % up to 10 at. % of Yb the conductivity increases gradually as expected: the substitution of Yb3+ cations for Ca2+ cations increases the concentration of Mn3+ cations and thus enhances the amount of charge carriers which hop between Mn3+ and Mn4+ sites. However a

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deviation from this behaviour is observed at lower p(O2). In fact, conductivity strongly depends on the density of Mn3+-Mn4+ chains which form paths for electron migration, as discussed in

DC-measurement

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2.5 1.5 1.0 0.5

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2.0

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log() / S.cm-1

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detail in the next section.

10% Yb-doped 0.1%Yb-doped Stoic.CaMnO3

0.0

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-0.5 -20-18-16-14-12-10 -8 -6 -4 -2 0 log[p(O2)] / MPa

Fig. 4: The effect of different Yb-contents on the conductivity as a function of p(O2) for compounds YbxCa1-xMnO3

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(0 to 10 at. % Yb-dopant concentration) at 750°C observed by DC-measurement with an uncertainty of ±1 x 10-4.

4.3. The origin of the plateau region of conductivity for Yb-doped CaMnO3 In the case of Yb-doped compounds, a plateau region extends from the reduction regime to 10-5 MPa for 0.1 at. % up to 0.5 at % Yb-content, and to p(O2) > 10-3 MPa for 5 at. % and 10 at % Yb-addition. This is due to the fact that the increase of the dopant concentration enhances the 9

amount of Mn3+ cations in Yb-doped compounds. The relatively larger ionic radius of Mn3+ (0.645 Å) cations compared to Mn4+ cations (0.53 Å) in CaMnO3 leads to a lower tolerance factor t deviating from unity. Accordingly, structural distortion takes place and perhaps secondary phases are formed even at higher p(O2) compared to pure CaMnO3. Therefore the

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plateau state is extended with increasing Yb-dopant concentration.

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4.4. The origin of the drastic decrease in conductivity

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As discussed in a previous paper [23], characterization results obtained by EDX, XRD, and Raman spectroscopy are in good agreement with the findings of the present study. These

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experiments show that sintering pure CaMnO3 at p(O2) below 10-2 MPa causes phase decomposition of CaMnO3 into Ca2MnO4 and CaMn2O4. Upon further reduction, released

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oxygen causes relatively larger amounts of Mn4+ cations to be reduced to Mn3+ cations. At around 10-16 MPa probably the phase CaMnO2.5 is formed. In this structure all manganese ions

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are trivalent and oxygen deficient sites facilitate ionic transport for oxygen via oxygen vacancies [33]. Then under highly reducing condition CaMnO2.5 is further reduced to CaMnO2 with Mn2+ cations. XRD-measurements successfully confirm this suggestion through a detection of CaMnO2 as a major phase after TGA measurements in the highly reducing region of

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p(O2) ≈ 10-18 MPa. Charge localization in CaMnO2 [34, 35] leads to the drastic reduction in conductivity. The crystal structures of CaMnO3, CaMnO2.5 and CaMnO2 are shown in Fig.5.

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Fig. 5: Unit cells for the crystal structures of CaMnO3, CaMnO2.5 and CaMnO2 [36]

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4.5. The effect of oxygen vacancies on conductivity

As shown in Fig. 6, in order to clarify the effect of oxygen vacancies on conductivity some of the

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data from DC-conductivity measurements (Fig. 4) and TGA-measurements were selected.

45 30 15 0

-17 -16 -5 log p(O2) / MPa

-18

-17 -16 -5 log p(O2)/ MPa

3-

S.cm-1

10% Yb-doped

175 150 125 100 75 50 25 0

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-18

-2

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-18

3.01 3.00 2.99 2.98 2.97 2.96 2.95 2.94

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60

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S.cm-1

75

3-

0.1% Yb-doped

90

-2

3.01 3.00 2.99 2.98 2.97 2.96 2.95 2.94

0.1% Yb-doped

0.1%Yb-doped

-17 -16 -5 log p(O2) / MPa

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10% Yb-doped

10%Yb-doped -18

-17 -16 -5 log p(O2) / MPa

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Fig. 6: The effect of oxygen vacancies on conductivity; p(O2) dependence of conductivity obtained from the DCmeasurements with an uncertainty of ±1 x 10-4 and the amount of oxygen loss detected from TGA-measurements with an uncertainty of ±5 x 10-5 for Yb-additions of 0.1 at % (blue) and 10 at % (black).

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It is observed that for compounds with 0.1 at.% Yb addition, conductivity increases with decreasing p(O2) down to 10-16 MPa. The TGA measurements in the mentioned p(O2) region show an increase in oxygen loss, which probably indicates that the number of oxygen vacancies is increasing. Therefore conductivity increases too, since it depends on the oxygen vacancy concentration. In the case of 10 at. % Yb-dopant concentration, no detectable oxygen loss is observed down to 10-16 MPa and conductivity also remains nearly constant. Both experimental

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evidences obtained from different methods are in agreement. However below 10-16 MPa a drastic

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decrease in conductivity is observed and the TGA measurements show a significant increase in oxygen loss. The origin of this drastic change in conductivity and oxygen loss below 10-16 MPa

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could be due to a phase transition as explained in the previous section.

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The interesting issue is that this process is reversible, i.e. with increasing p(O2) resistance R decreases fast. A resistance value of around 7 Ω is observed by keeping the sample at p(O2) =

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10-1 MPa over night. However, after that R decreases very slowly.

4.6. Defect chemical modeling for 0.1 at. % Yb-doped CaMnO3

The proposed defect chemical model for pure CaMnO3 contains three regions, while donordoped CaMnO3 reveals four regions. As demonstrated in Fig. 7, the extra region is observed for

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0.1 at % Yb-content in the range of 10-5 < p(O2) <10-4 MPa which elucidates the ionic compensation of the extrinsic donors by cation vacancies.

 ]+2[VCa  ]  constant [YbCa ]  4[VMn

(12)

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Consequently, in the mentioned region oxygen vacancies and cation vacancies are independent of p(O2). Concentrations of electron and hole can be calculated as follow:  ][VMn  ])1/6 K I ([VCa [MnMn ]  p(O2 ) 1/4 1/6 KP

(13)

1/6

p(O2 )1/4

(14)

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Kp   [Mn Mn ]     ]   [VCa ][VMn

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For p(O2) lower than 10-5 MPa, as discussed above, the amount of oxygen released is negligible

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due to the formation of secondary phases. As a result, the electron concentration is governed by the amount of donor addition and charge neutrality is approximated by [MnMn ]  [YbCa ]

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which is thus independent of p(O2). Therefore the conductivity of donor-doped CaMnO3 shows a

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conductivity plateau in that specific region. It is also found that the slight increase in conductivity after the plateau region down to 10-16 MPa is due to the slight oxygen release from the compounds in order to maintain an equilibrium state. Since each oxygen ion leaves two

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electrons, this results in an increase in charge carrier concentration which causes gradual increase in conductivity. The drastic reduction in conductivity below 10-16 MPa could be due to a phase transition into CaMnO2. As explained in section 4.5, charge localization in CaMnO2 leads to a

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drastic reduction in conductivity.

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b) 0.06

DC-measurement

TGA 0.05 0.1% Yb-doped 0.04 slope: 0.2 0.03 (Log(Conductivity) /S.cm-1) 0.02 (Log(Conductivity) /S.cm-1) (Log(Conductivity) /S.cm-1) 0.06 0.01 (Log(Conductivity) /S.cm-1) 0.00 (Log(Conductivity) /S.cm-1) -0.01 -20-18-16-14-12-10 -8 -6 -4 -2 0 log p(O2) / MPa

0.1% Yb-doped

2.0 1.5 1.0 0.5 0.0 -0.5 -20-18-16-14-12-10 -8 -6 -4 -2 0 logp(O2) / MPa

[MnMn ] -1/6 -1/6

[MnMn ] 1/6

1/4

VMn , VCa 

[MnMn ]

[MnMn ] 1/4 [MnMn ] 3/16

[MnMn ]

V  , V  3/16 VMn , VCa [MnMn ] Mn ] [Mn -1/4 -1/2 -3/16 VMn , VCa  [VO ] [VO ] -1/8 3/4 Mn

   VO 

-15

-5

[YbCa ]

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log conc.

 VO   

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]+2[VCa ] [MnMn ]  4[VMn ]  2[VCa ] [MnMn ]  2[VO ] [MnMn ]  [YbCa ] [YbCa ]  4[VMn

Ca

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c)

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2.5

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log() / S.cm

-1

a)

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log p(O2) / MPa

Fig. 7: a) The conductivity as a function of p(O2) for the compound Yb0.001Ca0.999MnO3 at 750°C observed by DCconductivity measurement which have an uncertainty of ±1 x 10-4, b) oxygen loss as a function of p(O2) measured

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by TGA experiments at the same temperature. The data imply an uncertainty of ±5 x 10-5 and c) corresponding theoretical defect diagram calculated based on the equilibrium concentrations.

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5. Conclusions

The present study addresses the answers on the main questions about the details of the chemistry of point defects, ionic as well as electronic, regarding charge transport that contribute to conductivity for donor-doped YbxCa1-xMnO3 ceramics. A comparison of experimental observations and theoretical defect chemical models clearly shows the way for controlling charge 14

carriers in dependence of partial pressure of oxygen p(O2) and dopant concentrations. The results obtained from TGA and DC-conductivity measurements demonstrate the effect of oxygen vacancies on conductivity. The origin of a plateau state in conductivity is explained to be probably due to the formation of secondary phases where oxygen ions do not substantially influence the electron and hole concentrations. The origin of significant reduction in conductivity in p(O2) below 10-16 MPa is found to be due to a drastic loss of oxygen at high reduction region.

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This leads to the formation of the phase CaMnO2. Ordered oxygen vacancies in the CaMnO2

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structure cause charge localization and thus conductivity decreases drastically. According to the experimental evidence of the present study the formation of oxygen vacancies and the

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corresponding change in density of Mn3+-Mn4+ pair sites seem to play an important role in the

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phase transition behaviour, charge migration and resistance properties of the complex system YbxCa1-xMnO3. It is found that CaMnO3 occurs as an orthorhombic phase after sintering at

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1350⁰C in gas composition of 100% O2. At p(O2) below 10-2 MPa Ca2MnO4 and CaMn2O4 phases are observed. By further reduction below 10-16 MPa CaMnO2.5 (orthorhombic) and then

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CaMnO2 (cubic) phases are formed. The obtained information probably will be useful for better understanding the effect of resistive switching as well as thermoelectric properties for the investigated compounds and possibly for other similar complex oxide systems.

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[22] C. Rodenbücher, W. Speier, G. Bihlmayer, U. Breuer, R. Waser and K. Szot, Cluster-like resistive switching of SrTiO3:Nb surface layers, New J. Phys. 15 (2013) 103017 1-15. https://doi.org/10.1088/1367-2630/15/10/103017. [23] M. Rahmani, C. Pithan, R. Waser, Electric transport properties of rare earth doped YbxCa1-xMnO3 ceramics (Part I: Optimization

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[36] ICSDWeb: "Crystal Structure",Forschungszentrum Juelich GmbH (2017).

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Figure caption Fig. 1: Thermogravimetric measurement for stoichiometric CaMnO3 demonstrating an increase in oxygen vacancy concentration with decreasing p(O2) from 10-1 to 10-18 Mpa with uncertainty ±5 x 10-5.……………………………..4

Fig. 2: Defect diagram calculated on the basis of equilibrium concentrations revealing dominating defects for undoped CaMnO3.……………………………………………………………………………………….………….6

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Fig. 3: The effect of wide range of p(O2) from 10-1 down to 10-16 MP on a) conductivity observed by DC measurement which have an uncertainty of ±1 x 10 -4 and b) oxygen loss measured by TGA experiments for

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undoped CaMnO3 at 750°C ). The data imply an uncertainty of ±5 x 10 -5.………………………………………8

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Fig. 4: The effect of different Yb-contents on the conductivity as a function of p(O2) for compounds YbxCa1-xMnO3 (0 to 10 at. % Yb-dopant concentration) at 750°C observed by DC-measurement with an uncertainty of ±1 x 10-4.

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Fig. 5: Unit cells for the crystal structures of CaMnO3, CaMnO2.5 and CaMnO2 [36]………………………………12

Fig. 6: The effect of oxygen vacancies on conductivity; p(O2) dependence of conductivity obtained from the DC-

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measurements with an uncertainty of ±1 x 10-4 and the amount of oxygen loss detected from TGA-measurements with an uncertainty of ±5 x 10-5 for Yb-additions of 0.1 at % (blue) and 10 at % (black).…………………………12

Fig. 7: a) The conductivity as a function of p(O2) for the compound Yb0.001Ca0.999MnO3 at 750°C observed by DCconductivity measurement which have an uncertainty of ±1 x 10 -4, b) oxygen loss as a function of p(O2) measured

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by TGA experiments at the same temperature. The data imply an uncertainty of ±5 x 10 -5 and c) corresponding theoretical defect diagram calculated based on the equilibrium concentrations.……………………………………15

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Table 1: Oxygen deficiency at 10-2 MPa and at 10-6 MPa, at 750⁰C for different donor-doped CaMnO3 composition reported by previous studies. Ekaterina et. al. [25] CaMnO3-δ

Imponenti et. al. [26] Ca0.9Sr0.1MnO3-δ

Leonidove et. al. [27] Ca0.9Pr0.1MnO3–δ

Goldyreva et.al. [28] Ca0.6Sr0.4MnO3-δ

Goldyreva et. al. [28] Ca0.55Sr0.4La0.05MnO3-δ

3

2.98

3

2.96

2.98

2.95

2.88

2.99

2.88

2.91

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Reference Compound 3-δ at 10-2 MPa 3-δ at 10-5 MPa

Intrinsic Ionic disorder: Schottky disorder   Vca nil   +VMn +3VO    Mn3+ MnMn Mn

(Thermal excitation of charge carriers) Mn Reduction reaction: 1 ×  2MnMn  +VO + O2 2MnMn +OO×   2

Mn

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Oxidation reaction:

 Mn

3  3OOX +VMn +VCa +6[MnMn ] O2   2

 Mn5+

(2)

(3)

ΔHS ) k BT

 ]=KI [MnMn ][MnMn

(4)

 Mn

4+

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 MnMn +MnMn  2Mn   × Mn

 ][VMn  ][VO ]3 =KS =KSexp([VCa

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Intrinsic electronic defect:

(1)

Eq.

Mass-action expression

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Eq .

Equilibrium reaction

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Table 2: The equilibrium reactions and mass-action expressions in the proposed defect chemical model for YbxCa1-xMnO3

 ]2 [VO ]p(O2 )1 2 = Kn [MnMn

(5)

(7)

n-type

(6)

region ][VCa ][MnMn ]6 [VMn =Kp p(O2 )3 2

p-type

(8)

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region  ]+2[VCa ]+4[VMn ]=2[VO ]+[MnMn ]  [D ] General charge neutrality condition: [MnMn

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0 Table 3: Enthalpy of oxidation ΔH ox and the Enthalpy of the disproportionation reaction (Eq.4) ΔH D0 at 750⁰C for different donor-doped CaMnO3

Ref.

Ekaterina et. al. 2012[25]

Imponenti et. al. 2016[26]

Leonidove et. al 2016[27]

Goldyreva et. al. 2015[28]

Comp.

CaMnO3-δ

Ca0.9Sr0.1MnO3-δ

Ca0.9Pr0.1MnO3–δ

Ca0.6Sr0.4MnO3-δ

0 ΔH OX

−286±10 Orthorhombic

at 10-2 MPa ~ -220 at 10-2 MPa ~ -195

265.0 ± 2.8 Orthorhombic

-148.2 cubic

_

82.0 ± 1.3 Orthorhombic

-190±7 cubic

ΔH D0

28.8 cubic

31.7 cubic

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(KJ/mol)

78.0±4.0 Orthorhombic 33.4±1.8 cubic

-164.6 cubic

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(KJ/mol)

Goldyreva et. al. 2015[28] Ca0.6-ySr0.4LayMnO3- δ (y = 0.05)

20