Mixed ionic-electronic conductivity and thermochemical expansion of Ca and Mo co-substituted pyrochlore-type Gd₂Ti₂O₇

Abstract

Phase relationships, transport properties and thermomechanical behavior of acceptor- and donor-co-substituted Gd₂Ti₂O₇ were studied for possible application in solid oxide fuel cell anodes. The range of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ solid solutions with a cubic pyrochlore-type structure was found to be limited to 0.10 < x < 0.15 and 0.05 < y < 0.10 under oxidizing conditions. No evidence of phase instability of substituted materials was detected in the course of the electrical and thermogravimetric studies down to oxygen partial pressures as low as 10⁻¹⁹ atm at 950 °C. (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics possess moderate thermal expansion coefficients compatible with solid electrolytes, (10.5–10.7) × 10⁻⁶ K⁻¹ at 25–1100 °C in air, and demonstrate remarkable dimensional stability with nearly zero chemical expansion down to p(O₂) ∼ 10⁻¹² atm at 950 °C. Though co-substitution by Mo suppresses oxygen-ionic conduction under oxidizing conditions, reducing oxygen partial pressure increases both ionic and n-type electronic transport. (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ (x = 0.07–0.10) pyrochlores are mixed conductors under SOFC anode operation conditions, but comparatively low total conductivity limits its applicability as electrode materials.

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1. Introduction

Gadolinium titanate Gd₂Ti₂O₇ belongs to the family of A₂³⁺B₂⁴⁺O₇ (or A₂³⁺B₂⁴⁺O₆O′) pyrochlore-type oxides. The pyrochlore structure may be regarded as a 2 × 2 × 2 superstructure of cation-ordered oxygen-deficient fluorite.^1,2 Larger A cations occupy 16d (1/2,1/2,1/2) sites and are eight-fold coordinated forming distorted cubes. Smaller transition metal B cations occupy 16c (0,0,0) sites and are six-fold coordinated forming distorted octahedra. O and O′ occupy 48f (X,1/8,1/8) and 8b (3/8,3/8,3/8) sites, respectively, while 8a (1/8,1/8,1/8) oxygen sites remain vacant. The position parameter X for O_48f defines the distortion from the ideal fluorite structure, ranging from the limiting value X = 0.3125 for perfect BO₆ octahedra to X = 0.375 for perfect AO₈ cubes, thus representing one of the relevant criteria for the stability of pyrochlores³ and for the impact on migration of ionic defects.⁴ All oxygen ions lie within tetrahedra of nearest neighbor cations: the 8b site has four A³⁺ neighbors, and 48f site has two A³⁺ and two B⁴⁺ neighbors. The vacant 8a site lies within a tetrahedron of four B⁴⁺ cations. The pyrochlore structure is prone to undergo significant anti-site exchange of A-site and B-site cations,⁵ also with impact on ionic migration.⁴ Thus, the pyrochlore structure is still one of the most challenging model systems, with good prospects for novel developments of ionic and mixed conductors.

Classical computational simulations indicate that oxygen-ion transport in A₂B₂O₇ pyrochlores occurs predominantly via oxygen vacancy hopping mechanism between 48f sites.^6–8 However, recent contributions are raising doubts about the wide validity of these assumptions, with deeper insight on migration mechanisms of interstitial oxygen and oxygen vacancies, and their subtle dependence on structural changes.^4,5 Still, experimental studies demonstrated that the conductivity of undoped Gd₂Ti₂O₇ is low (∼10⁻⁵ S cm⁻¹ at 900 °C), with prevailing n-type semiconducting behavior in air.^9,10 It has a low level of intrinsic anion disorder (i.e. low concentration of oxygen vacancies) and therefore rather negligible oxygen-ionic conductivity (<10⁻⁷ S cm⁻¹ at 600 °C).^11,12 On the contrary, pyrochlore-type Gd₂Zr₂O₇ demonstrates substantial structural disorder even at relatively low temperatures which induces ionic conductivity as high as 0.01 S cm⁻¹ at 900 °C.^11–13 As a result, substitution by Zr cations into titanium sublattice of Gd₂Ti₂O₇ favors intrinsic Frenkel-type disorder (vacancies in 48f sites and interstitial oxygen in 8a sites) enhancing ionic conductivity by 2.5–4.5 orders of magnitude when the concentration of zirconium cations is ≥30% of B sites.^11–13 Another approach to increase the concentration of mobile oxygen vacancies is acceptor-type substitutions in either gadolinium or titanium sublattice.^{10,11,14–17} Substitution of gadolinium by calcium was found to be most favorable increasing oxygen-ionic conductivity in (Gd_1−xCa_x)₂Ti₂O_7−δ (x = 0.05–0.10) up to 0.02–0.03 S cm⁻¹ at 900 °C;^10,11,14,15 this also suppresses the electronic transport number. Calcium has however limited solid solubility in gadolinium sublattice, ∼7 at%,^10,14 and precipitation of CaTiO₃ phase impurity at higher substitutional levels leads to decline of conductivity.

On the other hand, studies of the Gd₂Ti₂O₇–Gd₂Mo₂O₇ system demonstrated that electronic conductivity of gadolinium titanate under reducing conditions can be substantially improved substituting titanium by molybdenum.^18–20 Pyrochlore-type Gd₂Mo₂O₇ is known to exhibit high metallic-like conductivity, ∼150 S cm⁻¹ at room temperature.^21,22 Gd₂Ti₂O₇ and Gd₂Mo₂O₇ form a continuous series of solid solutions, and electrical conductivity of Gd₂(Ti_1−yMo_y)₂O_7−δ increases monotonically with molybdenum content from ∼0.24 S cm⁻¹ for y = 0.1 to ∼70 S cm⁻¹ for y = 0.7 at 1000 °C.^18,19 High electronic conductivity under reducing conditions attracted attention to Gd₂(Ti,Mo)₂O_7−δ solid solutions as potential anode materials for solid oxide fuel cells.^20,23–25 These ceramics were confirmed to exhibit good chemical compatibility with 8 mol% yttria-stabilized zirconia (8YSZ) solid electrolyte: no detectable reactivity was observed after calcination of Gd₂(Ti,Mo)₂O_7−δ + 8YSZ mixtures at 1000 °C for 1000 h.²⁰ Furthermore, Gd₂(Ti_0.7Mo_0.3)₂O₇ anodes were reported to show remarkable tolerance to sulfur while maintaining very high fuel cell performance, with anode polarization of only 0.2 ohm per cm² at 950 °C in a 10% H₂S–90% H₂ fuel gas mixture.^24,25

A critical drawback of Gd₂(Ti_1−yMo_y)₂O_7−δ solid solutions is a very limited p(O₂) range where the stable pyrochlore phase exists^18,19,24,25 and that narrows with increasing Mo concentration to only 2 orders of magnitude in p(O₂) for y = 0.7 at 600–1000 °C.^18,19 Thus, the present works was focused on moderate co-substitutions by calcium and molybdenum in gadolinium and titanium sublattices of Gd₂Ti₂O₇, respectively, aiming to induce mixed ionic-electronic conductivity under SOFC anode operation conditions while preserving phase stability over a wide range of oxygen partial pressure. Though the emphasis was on the properties important for practical application as anode materials, including phase and dimensional stability and mixed ionic-electronic transport, one also believes that improved understanding of these properties and the underlying defect chemistry will contribute to identify other prospective applications such as catalysis.

2. Experimental

Powders of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ (x = 0.07–0.20, y = 0–0.10) were prepared by solid state reaction route using Gd₂O₃ (99.9%, Sigma-Aldrich), CaCO₃ (99.95%, Sigma-Aldrich), TiO₂ (99.8%, Sigma-Aldrich) and (NH₄)₆Mo₇O₂₄·4H₂O (≥99.0%, Sigma-Aldrich) as starting reagents. Prior to the weighing, gadolinium and titanium oxides were calcined at 1000 °C for 2 h in air to remove adsorbates. Weighed and mixed components were calcined in air stepwise at 650 °C/2 h, 850 °C/5 h, 1100 °C/10 h and 1200 °C/10 h, with intermediate regrinding. After ball-milling with ethanol, the powders were compacted uniaxially at ∼40 MPa into disk-shaped samples and sintered at 1650 °C in air for 10 h. Sintering was done using Pt foil on alumina plates as supports; the samples were covered with powders of identical cation composition to act as a buffer against high-temperature losses.

Sintered ceramic samples were polished and cut into rectangular bars for dilatometric and electrical measurements. The density of ceramics was calculated from the mass and geometric dimensions of the samples. Powdered samples for X-ray diffraction (XRD) and thermal analysis were prepared by grinding the sintered ceramics in a mortar.

XRD patterns were recorded at room temperature using PANalytical X'Pert PRO diffractometer (Cu Kα radiation). Unit cell parameters were calculated using Fullprof software. Thermogravimetric analysis (TGA, Setaram SetSys 16/18 instrument, sensitivity 0.4 μg, initial sample weight ∼ 0.75 g) was carried out in flowing air, argon or 10% H₂–N₂ mixture between room temperature and 1000 °C at a constant heating–cooling rate of 2 °C min⁻¹ or isothermally as a function of time. The controlled-atmosphere dilatometric measurements (vertical Linseis L75V/1250 instrument) were performed under flowing air, argon and CO–CO₂ mixtures between room temperature and 1100 °C with a constant heating/cooling rate of 3 °C min⁻¹ or isothermally vs. time.

Total electrical conductivity (σ) was determined by impedance spectroscopy (Agilent 4284A precision LCR meter) using disk- and bar-shaped samples with applied porous Pt electrodes. The measurements were performed as function of temperature in flowing air or 10% H₂–N₂ mixture or isothermally as a function of oxygen partial pressure imposed by H₂–H₂O–N₂ and N₂–O₂ gas mixtures. The average oxygen-ion transference numbers () under O₂/air, air/argon and air/(10% H₂–N₂) oxygen partial pressure gradients were determined at 700–950 °C by the modified electromotive force (EMF) technique taking electrode polarization into account.^26,27

Oxygen partial pressure in a gas atmosphere in the course of experiments was monitored using 8YSZ solid-electrolyte sensors. Representative p(O₂) values were ∼5 × 10⁻⁵ atm in Ar and ∼10⁻²⁰ atm in 10% H₂–N₂ atmosphere, at 900 °C.

3. Results and discussion

3.1. Phase relationships and crystal structure

XRD patterns of as-prepared ceramic materials are given in Fig. 1. (Gd_0.93Ca_0.07)₂Ti₂O_7−δ and (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ (x = 0.07–0.10) were found to be phase-pure with cubic pyrochlore-type structure (space group Fd3̄m) isostructural to the parent Gd₂Ti₂O₇. Increasing molybdenum concentration in x = 0.07–0.10 compositions to 10% of titanium sites results in a minor precipitation of tetragonal CaMoO₄ phase, possibly because the prevailing oxidation state of molybdenum cations is 6+ and the pyrochlore structure has limited ability to tolerate oxygen hyperstoichiometry. On the other hand, increasing calcium content in (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ above x = 0.10 was found to promote the segregation of orthorhombic CaTiO₃ phase impurity, which is a stable perovskite phase. Thus, one may conclude that the (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ solid solution field at ambient p(O₂) is limited to 0.10 < x < 0.15 and 0.05 < y < 0.10.

Fig. 1 XRD patterns of as-prepared (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics. hkl indexes are given for Fd3̄m space group. Reflections of CaMoO₄ and CaTiO₃ impurities are indexed according to JCPDS PDF # 85-1267 and # 88-0790, respectively.

Substitutions have rather minor influence on the lattice parameters of single-phase solid solutions (Table 1). Lattice constants increases slightly with calcium content due to moderate differences between ionic radii of calcium and gadolinium cations ( vs. ).²⁸ Note that one neglects anti-site exchange due to major differences in ionic radii of A-site cations (Ca²⁺ and Gd³⁺) and B-site cations in their expected valence states (Ti⁴⁺ and Mo⁶⁺). Molybdenum has tendency to higher 6+ oxidation state under oxidizing conditions, with an ionic radius very similar to that of Ti⁴⁺ ( and)²⁸ However, this depends on redox conditions, and possibly also on the Mo : Ca ratio. In fact, the average valence of molybdenum cations in some pyrochlores is close to Mo⁵⁺, namely, in oxynitride pyrochlores (e.g. ref. 29). Thus, one may expect a fraction of lower valence cations (Mo⁴⁺ or Mo⁵⁺), mainly when y > 0.5x. All prepared ceramics were dense and gas-tight; the relative densities of single-phase materials were 93–96% of theoretical (Table 1).

Table 1 Properties of pyrochlore-type (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics

Composition	State	Lattice parameters		Density, g cm^−3	Relative density, %	7 − δ^a
		a, Å	X (O)
a Estimated assuming all Mo cations in oxidized phases to be in 6+ oxidation state.b After 36 h at 950 °C and p(O2) ∼ 10^−19 atm.
x = 0.07, y = 0	Oxidized	10.1929(4)	0.3189(6)	6.07	96	6.93
x = 0.07, y = 0.05	Oxidized	10.1931(2)	0.3140(7)	5.94	93	7.03
	Reduced^b	10.1933(5)	0.3166(9)	—	—	6.94
x = 0.10, y = 0.05	Oxidized	10.1937(5)	0.3277(7)	6.02	95	7.00
	Reduced^b	10.1941(5)	0.3150(8)	—	—	6.87

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3.2. Reducibility of pyrochlore phase

Thermogravimetric analysis demonstrated that powdered (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ samples start to lose oxygen from the crystal lattice on heating above ∼300 °C in reducing 10% H₂–N₂ atmosphere (Fig. 2). The reduction in the studied temperature range was found to occur in two steps. The lower-temperature process had maximum rate at ∼640 °C under applied experimental conditions, while the second process starts to accelerate at T > 870 °C.

Fig. 2 Relative changes of oxygen nonstoichiometry in (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ on cooling in air and on heating in reducing atmosphere, and derivative thermogravimetric curve on heating in reducing atmosphere.

Isothermal studies at 950 °C confirmed that reduction is a two-step process (Fig. 3). While the oxygen content in the samples remains unchanged (within experimental uncertainty) in air and in inert atmosphere, switching to reducing atmosphere results in nearly instant release of oxygen. This is followed by further slow oxygen losses from the samples.

Fig. 3 Relative changes of oxygen nonstoichiometry in (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ on isothermal reduction at 950 °C, as estimated from the thermogravimetric data.

Oxygen losses Δδ from the lattice of (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ in the first fast step were roughly estimated to be ∼0.051 oxygen atoms per formula unit for x = 0.07 and 0.060–0.067 atoms per formula unit for x = 0.10. Note that a decrease of oxidation state of molybdenum by 1 in the given compositions corresponds to change of oxygen content of 0.05 oxygen atoms per formula unit. Thus, one may assume that the first reduction step corresponds to comparatively fast Mo⁶⁺ → Mo⁵⁺ change, whereas the second comparatively slow step can be assigned to slower Mo⁵⁺ → Mo⁴⁺ transformation; this may raise doubts about previous indications that the intermediate oxidation state Mo⁵⁺ is highly unstable.³⁰ One may even assume also onset of partial Ti⁴⁺ → Ti³⁺ or even Mo⁴⁺ → Mo³⁺ reduction, on exceeding the oxygen storage ability of previous Mo⁶⁺ → Mo⁵⁺ → Mo⁴⁺ changes. Although 3+ is a rather unusual state for molybdenum in oxide compounds, the presence of Mo³⁺ in reduced molybdenum oxide has been previously suggested in the literature based on the XPS results.³¹ The oxygen nonstoichiometry range of MoO_2±δ^32,33 also indicates the presence of a fraction of Mo cations in an oxidation state lower than 4+.

XRD analysis of powdered (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ samples after reduction in 10% H₂–N₂ flow (p(O₂) ∼ 10⁻¹⁹ atm) at 950 °C for 36 h did not reveal any significant changes in XRD patterns (Fig. 4), except the appearance of tiny unidentified peaks on the background level. The minor increase of lattice parameters is also comparable to experimental error (Table 1). Table 1 lists also the values of oxygen nonstoichiometry of reduced pyrochlores estimated assuming that all Mo cations in oxidized phases were hexavalent. One should also note that even after 36 h of reduction the oxygen content does not tend to a constant value, indicating very slow reduction kinetics. Though this is less sluggish than reported for perovskite-like donor-doped strontium titanates at temperatures ≤1000 °C (e.g. ref. 34 and 35), the long-term stability under applied conditions remains uncertain; the p(O₂) value in the course of reduction was below the Mo/MoO₂ boundary³⁶ and also below the stability boundary of Gd₂(Ti_0.3Mo_0.7)₂O_7−δ.^18,19

Fig. 4 XRD patterns of powdered (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics, as-prepared (oxidized) and reduced for 36 h at p(O₂) ∼ 10⁻¹⁹ atm and T = 950 °C.

3.3. Electrical properties under oxidizing conditions

The results of impedance spectroscopy studies demonstrated that grain boundary contribution to the total resistivity can be neglected at T ≥ 650 °C in the case of (Gd_0.93Ca_0.07)₂Ti₂O_7−δ and above 750 °C for (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics. At lower temperatures, grain boundary resistivity rapidly increases with cooling and becomes dominant in Mo-substituted materials below 500–600 °C. Hereafter in this work, the discussion of electrical conductivity refers to grain-bulk electrical properties, unless otherwise indicated.

Fig. 5 shows electrical conductivity of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics in air. The average oxygen-ion transference numbers under air/oxygen gradient determined by the modified EMF technique are listed in Table 2. (Gd_0.93Ca_0.07)₂Ti₂O_7−δ ceramics demonstrated comparatively high oxygen-ionic conductivity with minor (∼3%) electronic contribution to total electrical transport, in excellent agreement with previous reports.¹⁵ Decreasing temperature below ∼780 °C results in an increase in activation energy (Fig. 5 and Table 3). A change in slope of Arrhenius dependencies of electrical conductivity is characteristic of many oxygen-ion conductors, including fluorite-type stabilized zirconia and doped ceria,³⁷ pyrochlore-type Gd₂(Ti_1−yZr_y)₂O₇,¹³ and perovskite-type (La,A)(Ga,Mg)O_3−δ,³⁸ and is usually ascribed to partial ordering in the oxygen sublattice due to point defect association in the low-temperature range.

Fig. 5 Temperature dependence of electrical conductivity of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics in air.

Table 2 Average oxygen-ion transference numbers determined by modified EMF technique

Composition	T, °C	Average under oxygen partial pressure gradient
		O2/air	Air/Ar^a	Air/10% H2–N2^b
a p(O2) in Ar flow was 5 × 10^−5 atm.b p(O2) in 10% H2–N2 flow corresponded to 2 × 10^−20 atm at 900 °C.
x = 0.07, y = 0	900	0.968		0.991
	800	0.969		0.998
	700	0.970		0.998
x = 0.07, y = 0.05	950	E^obs/E^theor ≤ 0.001	E^obs/E^theor ≤ 0.001	0.406
	900			0.386
	850			0.368
	800			0.344
	750			0.331
	700			0.288
x = 0.10, y = 0.05	950	0.592	0.727	0.697
	900	0.595	0.750	0.674
	850	0.609	0.779	0.665
	800	0.627	0.808	0.685
	750	0.645	0.837	0.664
	700	0.672	0.863	0.700

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Table 3 Activation energy for total and partial ionic and electronic conductivities in air^a

Composition	Conductivity	T, °C	EA, kJ mol^−1
a Note: the activation energy was calculated using Arrhenius model σ = (A0/T)exp(−EA/(RT)); given errors are standard errors.
x = 0.07, y = 0	σtotal	250–780780–1010	99.8 ± 0.577.1 ± 1.0
	σO	700–900	87.8 ± 3.0
	σe	700–900	90.5 ± 2.4
x = 0.07, y = 0.05	σtotal ≈ σe	370–770770–1010	39.2 ± 0.273.6 ± 1.3
x = 0.10, y = 0.05	σtotal	400–780780–1010	36.6 ± 0.385.2 ± 1.6
	σO	800–950	77.4 ± 2.4
	σe	800–950	88.5 ± 0.8

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Substitution of 5% of titanium by molybdenum results in suppression of ionic transport in (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ and a significant drop in electrical conductivity (Fig. 5). The ion transference numbers under oxygen/air gradient decrease to values below the experimental error of the EMF technique: the ratio between observed and theoretical EMF was ∼0.001 at 950 °C and decreased on cooling (Table 2). (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics demonstrated even lower conductivity, but higher oxygen-ion transference number (0.59–0.67) at 700–950 °C (Table 2). These differences are summarized in Fig. 6, which shows temperature dependencies of partial ionic and electronic conductivities estimated from the total conductivity in air and average transference numbers under O₂/air gradient. The determined transference numbers relate to the total (grain interior and boundaries) electrical transport; therefore, the values of partial conductivities for Mo-substituted ceramics are shown only for T ≥ 800 °C.

Fig. 6 Temperature dependence of partial oxygen-ionic (σ_O) and electronic (σ_e) conductivities of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics estimated from the data on total conductivity in air and average transference numbers under O₂/air gradient. Note that, for (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ, σ_total ≈ σ_e and σ_O ∼ 10⁻⁶ to 10⁻⁵ S cm⁻¹ at 950 °C.

Acceptor-type substitution by calcium is expected to be compensated by formation of oxygen vacancies, while donor-type substitution by Mo^5+/6+ may be compensated by incorporation of interstitial oxygen ions (e.g. into 8a sites), and co-additions of acceptor and donor may compensate each other. Thus, a general electroneutrality condition for (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ is, therefore, expressed by:

where [Ca′_Gd] = 2x, , , and , and , respectively, per formula unit. Variations of electrical conductivity and partial ionic contribution with composition reflect a transition between dominating compensation mechanisms under oxidizing conditions: from acceptor compensation via oxygen vacancy formation in (Gd_0.93Ca_0.07)₂Ti₂O_7−δ:to donor compensation via interstitial oxygen formation in hyperstoichiometric (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ (assuming predominant 6+ state of Mo cations):

Apparently, incorporation of extrinsic interstitial oxygen strongly suppresses the concentration of oxygen vacancies originating from intrinsic anti-Frenkel disorder:

if one assumes prevailing hexavalent Mo⁶⁺ and that the difference between donor and acceptor contributions play a prevailing effect which exceeds largely the contribution of anti-Frenkel disorder, , and thus:

This explains decrease in oxygen-ionic conductivity occurring via oxygen vacancy migration between 48f sites. Note that decline in ionic conductivity with niobium substitution was reported earlier for the Yb₂(Ti_1−yNb_y)₂O₇ system, although the authors claimed that Nb substituted in a 4+ oxidation state and attributed the decrease of ionic transport to trapping of oxygen anions by dopant cations.³⁹

Finally, in (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ, acceptor and donor nearly compensate each other:

while oxygen vacancy concentration is governed, most likely, by the intrinsic contribution of anti-Frenkel disorder (eqn (4)). These changes of compensation mechanism results in a transition from predominantly ionic (for exclusive acceptor additive, x = 0.07 and y = 0) to predominantly electronic (for 2y > x) and then to mixed ionic-electronic transport (for 2y = x) under oxidizing conditions.

Contrary to (Gd_0.93Ca_0.07)₂Ti₂O_7−δ, Arrhenius dependencies of total electrical conductivity of Mo-substituted ceramics show a transition from high-T regime with higher activation energy (74–85 kJ mol⁻¹) to low-T regime with lower E_A (37–39 kJ mol⁻¹) (Fig. 5 and Table 3). Similar behavior was reported for Gd₂(Ti_1−yNb_y)₂O₇ (y = 0.01–0.10) pyrochlores, although under quenched conditions and at lower temperatures, with lower activation energy attributed to electron hopping between Nb⁴⁺ and Nb⁵⁺.⁴⁰ Another comment is that the electrical conductivity data for (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics doped beyond the solid solubility limits (Fig. 7) seem to support the above conclusion that solid solution formation field extends to x ∼ 0.125 and y ∼ 0.075. This is reflected by increased conductivity for x = 0.15 (higher ionic transport induced by acceptor substitution) and for y = 0.10 (probably, due to increased electronic transport contributed by electronic hopping between Mo⁶⁺ and residual Mo⁵⁺) as compared to single-phase (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ (x = 0.07–0.10).

Fig. 7 Comparison of total (bulk + grain boundary) electrical conductivity of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics in high-temperature range in air.

3.4. Electrical conductivity as function of oxygen partial pressure

Fig. 8 shows oxygen partial pressure dependence of electrical conductivity of Gd₂Ti₂O₇-based ceramics at 900 °C. The shape of log σ–log p(O₂) curves strongly depends on the dopant compensation mechanism. In agreement with literature reports on (Gd_1−xCa_x)₂Ti₂O_7−δ system^10,14 and also according to the ion transport number (Table 2), (Gd_0.93Ca_0.07)₂Ti₂O_7−δ ceramics show a plateau-like behavior over a wide range of oxygen partial pressure where ionic transport is dominant. The conductivity starts to increase under highly reducing conditions; expanded vertical scale also reveals a minor p-type contribution in oxidizing atmospheres. This behavior is markedly different from the σ vs. p(O₂) dependence observed for co-substituted (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ with an electronic plateau under inert and oxidizing conditions, and then a rather unusual transition to mixed conduction under reducing conditions, as revealed by the average ion transport number. The electronic plateau can be ascribed to hopping involving co-existence of Moⁿ⁺ ions of different oxidation states, such as the prevailing Mo⁴⁺/Mo⁶⁺ pair proposed earlier,⁴¹ or Mo⁵⁺/Mo⁶⁺ if one considers the evidence of 2-step changes in oxygen stoichiometry (Fig. 2 and 3). In fact, 2-electron hopping seems unusual in high-temperature mixed conductors, even if bipolaron have been considered in other materials such as conducting polymers⁴² and superconductors.⁴³

Fig. 8 Oxygen partial pressure dependence of electrical conductivity of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics at 900 °C. Dotted lines are guide for the eye.

The electrical conductivity of mixed-conducting (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics is also unusual, since its mixed conducting behavior is observed in the oxidizing region with p(O₂) ∼ 5 × 10⁻³ to 10⁻¹ atm, with a conductivity minimum characteristic of a state when σ_n = σ_p and with slightly prevailing ionic transport. The latter is confirmed by increased average > 0.5 under air/argon gradient (Table 2). In addition, one expects much higher mobility of electronic species μ_n, μ_p ≫ μ_V as reported by others,³⁰ implying even larger differences between the concentrations of ionic and electronic carriers, i.e.:

where the subscripts identify different ionic and electronic contributions to the total conductivity. Note also that one expects a prevailing ionic conductivity by vacancies, except possibly at very high temperatures, when the diffusivities of interstitial oxygen and vacancies converge to each other.⁴ Thus,and the corresponding power law dependences for the concentrations of electrons and electron holes near the conductivity minimum can be predicted on combining this nearly constant concentration of ionic defects with the equilibrium constants of reactions of reduction and band–band transfer (electronic disorder):

Actually, the activation energy of ionic conductivity (Table 3) seems to be close to the expected value for the temperature dependence of mobility, contradicting the assumption that the concentration of ionic carriers is controlled by formation of anti-Frenkel defects. Thus, it seems that ionic carriers in (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ are still determined by an extrinsic mechanism, presumably by a slight excess of acceptor additive, as a result of incomplete oxidation to hexavalent Mo⁶⁺ possibly combined with minor molybdenum oxide losses at high sintering temperatures due to the high volatility of MoO₃.³³ Note that this is specific of the hexavalent state, implying much lower losses by stabilizing lower valence states, as expected under reducing conditions. Thus, one may assume a nearly constant concentration of oxygen vacancies, determined by volatilization during sintering and the resulting effective balance between acceptor and donor species (possibly including also slight redistribution of Ca²⁺ ions into octahedral sites to maintain A : B cation ratio):

Under these circumstances:

Nevertheless, this still results in increase in p-type conductivity in the mixed-conducting (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ, onset of a minor p-type contribution in the ionic-conducting composition (Gd_0.90Ca_0.07)₂Ti₂O_7−δ, and increase of both n-type electronic and oxygen-ionic conductivities under reducing conditions in all compositions. The p(O₂) corresponding to the onset of the conductivity rise depends on donor and acceptor concentrations (and therefore on charge compensation mechanism and conductivity level in the plateau region). Note the increment of total conductivity of (Gd_1−xCa_x)₂Ti₂O_7−δ ceramics at reduced oxygen pressures was attributed previously only to increasing electronic contribution assuming p(O₂)-independent ionic conductivity.^10,14 The results of this work demonstrate that this is not correct for (Gd_0.93Ca_0.07)₂Ti₂O_7−δ, as reflected by higher average under air/10% H₂–N₂ gradients when compared to transference numbers under oxidizing conditions (Table 2). Co-substituted (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ (x = 0.07–0.10) ceramics are both mixed ionic-electronic conductors at reduced oxygen partial pressure (Table 2), but exhibit lower total electrical conductivity compared to Mo-free composition at intermediate oxygen partial pressures (Fig. 8), corresponding to fuel electrodes under significant fuel conversion or anodic overpotentials.

Under strongly reducing conditions with p(O₂) ∼ 10⁻²¹ atm at 900 °C, all materials show comparable total electrical conductivity (Fig. 8 and 9), although (Gd_0.93Ca_0.07)₂Ti₂O_7−δ is prevailing ionic conductor, and Mo-containing ceramics are mixed-conducting oxides. Semiconducting behavior indicates that concentrations of Ti³⁺ and Mo⁴⁺ are still too low to form a broad conduction band leading to metallic conductivity, and instead electronic transport occurs by electron hopping via Ti⁴⁺/Ti³⁺ and Mo⁵⁺/Mo⁴⁺ pairs. As in air, Arrhenius dependencies of electrical conductivity of Mo-substituted ceramics tend to lower activation energy on cooling.

Fig. 9 Temperature dependence of electrical conductivity of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics in 10% H₂–N₂ atmosphere (p(O₂) ∼ 3 × 10⁻²¹ atm at 900 °C).

3.5. Defect chemistry

A defect chemistry model is developed to support the analysis of transport properties; this analysis and method of solving are similar to those reported earlier,⁴¹ and are based on the expected reactions of anti-Frenkel disorder (eqn (4)), reduction (eqn (9)), band–band transfer (eqn (10)), and valence changes of molybdenum ions, described as follows, to emphasize correlations between concentration of ionic charge carriers and polaron hoping between molybdenum cations with different valence states:

In order to establish correlations between transport properties and defect chemistry, one estimated the mobility of oxygen vacancies from the ionic conductivity plateau of composition (Gd_0.93Ca_0.07)₂Ti₂O_7−δ: μ_V = σ_O/(e[Ca′_Gd]) ≈ 3.6 × 10⁻⁴ cm² V⁻¹ s⁻¹. Differences relative to other reported results³⁰ may be related to contents of aliovalent additives, with expected impact on defect interactions and mobility. The n-type contribution in this composition was also evaluated from the average ionic transport numbers under air/H₂ gradient; this was combined with eqn (14) and a typical value of electron mobility μ_n ≈ 0.014 cm² V⁻¹ s⁻¹ at 900 °C (ref. 44) to evaluate the order of magnitude of the equilibrium constant of the reduction reaction (eqn (9)) k_red ≈ 10⁴⁷ cm⁻⁹ atm^1/2. Indeed, this depends on the assumed value of mobility and vice versa.³⁰ Corresponding results for the p-type conductivity were also evaluated by transport number measurements under O₂/air gradients and used to estimate the mobility of holes for a typical value of equilibrium constant of band–band transfer k_e ≈ 2.9 × 10³⁰ cm⁻⁶,⁴⁵ combined with the actual value of k_red; this also yields μ_p ≈ 0.014 cm² V⁻¹ s⁻¹. One also assumed a typical value of equilibrium constant for anti-Frenkel disorder k_aF ≈ 2.8 × 10²⁷ cm⁻⁶ taken from ref. 45.

The parameters estimated for composition (Gd_0.93Ca_0.07)₂Ti₂O_7−δ were then used to predict a defect chemistry model for composition (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ, based also on the measured dependence of total conductivity and transport number; this is shown in Fig. 10. The model includes polaron hopping, assuming that this may comprise single-electron hopping between pairs and with similar mobilities, i.e.:

Fig. 10 Defect chemistry diagram of (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ composition at 900 °C (top) and corresponding fitting of transport properties (bottom). Experimental data are shown by circles. The average oxygen-ion transference number t_O,av corresponds to air/p(O₂) gradient.

The actual fitting reproduces quite well the measured transport properties and indicates that the prevailing hopping contribution involves the pair rather than , as given by corresponding equilibrium constants k₁ ≫ k₀. Note that this is needed to reach reasonable fitting for the average ion transport number. In addition, this is consistent with the changes in oxygen stoichiometry upon exposition to reducing atmosphere (Fig. 3) with an initial fast evolution within the expected range for reduction of Mo⁶⁺ to Mo⁵⁺ and then lower (and slower) contribution of subsequent reduction to Mo⁴⁺.

One also obtained good fitting for the transport properties of the mixed conducting composition (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ (Fig. 11). One expects however previous molybdenum oxide losses during sintering, as explained above. Then, the effective concentration of oxygen vacancies was estimated on combining the conductivity minimum with the ionic transport number under air/Ar gradient and mobility of vacancies; this also allowed one to re-assess the effective Mo contents. In addition, suitable fitting of the transport properties of this sample required significantly higher mobilities of electron holes and polarons and slightly lower mobility of vacancies (Table 4), to reproduce the measured dependence of conductivity on oxygen partial pressure and average values of ionic transport number. Lower equilibrium constants of reduction of Mo⁶⁺ to lower valence are also needed to attain good fitting, thus indicating lower reducibility of composition (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ compared to (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ, as expected on increasing the concentration of the acceptor-type additive.

Fig. 11 Defect chemistry diagram of nominal (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ composition at 900 °C (top) and corresponding fitting of transport properties (bottom). Experimental data are shown by circles. The average oxygen-ion transference number t_O,av corresponds to air/p(O₂) gradient.

Table 4 Relevant defect chemistry parameters

	x = 0.07, y = 0	x = 0.07, y = 0.05	x = 0.10, y = 0.05
kaF, cm^−6	2.8 × 10^27	2.8 × 10^27	2.8 × 10^27
kred, cm^−9 atm^1/2	10^47	10^47	10^47
ke, cm^−6	2.9 × 10^30	2.9 × 10^30	2.9 × 10^30
k0, atm^1/4	—	10^4	5 × 10^3
k1, atm^1/4	—	5 × 10^6	3 × 10^5
μn, cm^2 V^−1 s^−1	0.014	0.014	0.014
μp, cm^2 V^−1 s^−1	0.014	0.014	0.042
μV, cm^2 V^−1 s^−1	3.6 × 10^−4	3.6 × 10^−4	2.4 × 10^−4
μH, cm^2 V^−1 s^−1	—	3.3 × 10^−5	2 × 10^−4

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3.6. Thermal expansion and dimensional stability

Pyrochlore-type (Gd_0.93Ca_0.07)₂Ti₂O_7−δ ceramics demonstrate nearly linear dilatometric behavior in air at 25–1100 °C and moderate average thermal expansion coefficient (TEC, Table 5) close to that of 8YSZ.^46,47 Moderate substitution with molybdenum and minor variations of calcium content have rather negligible effect on TEC values, albeit slightly improving linearity of expansion at higher temperatures (Fig. 12 and Table 5).

Table 5 Average thermal expansion coefficients of (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ ceramics in air

Composition	T, °C	([small alpha, Greek, macron] × 10^6) ± 0.1, K^−1
x = 0.07, y = 0	30–150/150–800/800–1100	9.8/10.4/11.3
	30–1100	10.6
x = 0.07, y = 0.05	30–150/150–1100	9.9/10.8
	30–1100	10.7
x = 0.10, y = 0.05	30–150/150–1100	9.5/10.6
	30–1100	10.5

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Fig. 12 Dilatometric curves of (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics in air.

Fig. 13 shows dimensional changes of (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics under isothermal conditions, on stepwise decrease of oxygen partial pressure from ambient to ∼10⁻¹² atm at 950 °C. The data were collected after equilibration at each p(O₂) for ∼24 h. Literature data on some fluorite- and perovskite-type oxides are shown for comparison. Ceramic oxides containing variable-valence cations often show dimensional changes on varying oxygen partial pressure at elevated temperatures. This phenomenon is usually referred to as chemical expansion or chemical strain and originates from two simultaneous competing processes occurring on reduction: (i) formation of oxygen vacancies leading to lattice contraction due to electrostatic interactions, and (ii) simultaneous increase of cation radii causing lattice expansion due to steric effects.⁵² The latter contribution has a stronger impact, and oxygen losses at reduced p(O₂) typically result in overall expansion of crystal lattice in the case of perovskite and fluorite structures (Fig. 13). In contrast, pyrochlore-type (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics demonstrate nearly zero dimensional changes in the studied p(O₂) range despite oxygen losses on reduction. One may conclude that increasing oxygen deficiency under the studied conditions is associated mainly with reduction of molybdenum cations, while dimensional stability is provided by the pyrochlore-type titanate lattice. The results of isothermal dilatometric studies are in agreement with negligible changes of room-temperature lattice parameters after reduction under even more reducing conditions (Table 1).

Fig. 13 Relative dimensional changes of (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics on reducing oxygen partial pressure at 950 °C. Literature data on perovskite- and fluorite-type oxides are shown for comparison: (La_0.9Sr_0.1)_0.98Cr_0.6Fe_0.3Mg_0.1O_3−δ (LSCFM),⁴⁸ (La_0.75Sr_0.25)_0.95Mn_0.5Cr_0.5O_3−δ (LSMC),⁴⁹ (La_0.25Sr_0.75)_0.95Mn_0.5Ti_0.5O_3−δ (LSMT),⁴⁹ Ce_0.9Gd_0.1O_2−δ (CGO10),⁵⁰ and Ce_0.9Pr_0.1O_2−δ (CPO10).⁵¹ L₀ corresponds to the sample length at given temperature in air. Dotted lines are guide for the eye.

4. Conclusions

(i) The domain of single-phase solid solutions with cubic pyrochlore-type structure in (Gd_1−xCa_x)₂(Ti_1−yMo_y)₂O_7−δ system is limited to 0.10 < x < 0.15 and 0.05 < y < 0.10 under oxidizing conditions;

(ii) (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics demonstrate good phase stability in a wide range of oxygen partial pressures: no degradation or phase decomposition was evidenced in the course of electrical and thermogravimetric studies and by subsequent XRD;

(iii) Dopant compensation mechanism and type of dominating charge carriers under oxidizing conditions strongly depend on calcium/molybdenum ratio. Electrical conductivity decreases with Mo substitution and changes from predominantly oxygen-ionic in (Gd_0.93Ca_0.07)₂Ti₂O_7−δ to predominantly electronic in (Gd_0.93Ca_0.07)₂(Ti_0.95Mo_0.05)₂O_7−δ and to mixed ionic-electronic in (Gd_0.90Ca_0.10)₂(Ti_0.95Mo_0.05)₂O_7−δ;

(iv) Reducing oxygen partial pressure increases both ionic and n-type electronic conductivities in substituted Gd₂Ti₂O₇ ceramics. (Gd_1−xCa_x)₂(Ti_0.95Mo_0.05)₂O_7−δ ceramics exhibit mixed conductivity under SOFC anode operation conditions, which is lower compared to (Gd_0.93Ca_0.07)₂Ti₂O_7−δ and too low for electrode applications, except possibly to enhance electrocatalytic activity;

(v) Co-substituted ceramics show moderate thermal expansion coefficients similar to that of 8YSZ, and remarkable dimensional stability on variations of oxygen partial pressure at 950 °C.

Acknowledgements

This work was done within the scope of projects IF/01072/2013/CP1162/CT0001, IF/01344/2014 and project CICECO-Aveiro Institute of Materials POCI-01-0145-FEDER-007679 (FCT ref. UID/CTM/50011/2013), financed by national funds through the FCT/MEC and when appropriate co-financed by FEDER under the PT2020 Partnership Agreement.

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