Large Oxygen Deficiency Research Articles

Oxygen nonstoichiometry and electrical transport properties of Pr1-xCaxMnO3 ceramics

The defect chemistry of solid solutions formed by the two orthorhombic perovskite-type compounds CaMnO3 and PrMnO3 is strongly determined by mixed valence states emerging from the presence of trivalent or tetravalent Mn-cations, Mn3+ and Mn4+. Both, thermogravimetric analysis as well as measurements of DC-conductivity at elevated temperatures in dependence of the partial pressure of oxygen quantitatively reveal the extent of oxygen vacancy formation in highly densified ceramic pellets originally consolidated by sintering in pure oxygen O2. Iodometry additionally serves to analyse the average valence state of Mn-cations and thus of the deficiency in oxygen after targeted thermal treatments under specific redox conditions. The determination of electrical transport properties including also the careful inspection of the Seebeck-effect for such specimens demonstrates that the mobility of electrons is drastically reduced when the number of oxygen vacancies increases. For the specific composition Pr0.7Ca0.3MnO3, an oxide potentially relevant for resistively switching memory device applications, this is the case when the deficiency in oxygen exceeds a concentration of 1000 ppm. Detailed crystallographic studies based on refined neutron-diffraction experiments for reduced ceramic material suggest, that the reduction in electron transfer rates between tri- and tetravalent cations of manganese originates from an anisotropy effect: In the case of comparatively large oxygen deficiency, vacancies preferentially form on lattice sites in the equatorial plane of MnO6-octahedra rather than on their apices.

Disordered Gd6UO12-δ with the cation antisite defects prepared by a combined mechanochemical−thermal method

• The rhombohedral Gd 6 UO 12-δ single phase is synthesized for the first time via mechanochemical − thermal route. • The as-prepared uranate exhibits a remarkable degree of cation antisite disorder and a relatively high concentration of oxygen vacancies . • The XRD simulations reveal a decrease of the intensity of superlattice reflections with increasing degree of cation antisite defects in Gd 6 UO 12-δ . • The nonequilibrium cation distribution in Gd 6 UO 12-δ does not influence the symmetrical geometry of polyhedra around the 3 a sites, whereas the octahedra around the 18 f sites are found to be distorted. • The six-fold coordination of cations at 18 f sites is a consequence of a relatively large oxygen deficiency in the as-prepared material. The synthesis of the rhombohedral Gd 6 UO 12-δ is reported via mechanochemical processing of stoichiometric Gd 2 O 3 /UO 2 mixtures and their subsequent annealing. Rietveld refinement of XRD data reveals that the as-prepared material exhibits a remarkable degree of cation antisite disorder and oxygen deficiency. The simulations of intensities of the selected XRD superlattice reflections are performed for limiting states of Gd 6 UO 12-δ with its most extreme degrees of the cation antisite disorder. On the basis of the estimated bond lengths it can be stated that distorted geometry of structural units in the material is a consequence of its relatively large oxygen deficiency. The cations in Gd 6 UO 12-δ prepared by mechanochemical − thermal route are distributed over the 3 a and 18 f sites of octahedral coordination with the symmetrical and distorted geometry, respectively.

Effect of Crystal Defect on Gas Sensing Properties of Co3O4 Nanoparticles.

Crystal growth-controlled Co3O4 nanoparticles were prepared to examine gas sensing properties. A cube-like, an irregular shaped, and three kinds of raspberry-type structures were observed by morphology analysis. The raspberry-type structures have an expanded lattice volume with a large oxygen deficiency area, and the cube-like structure has a contracted lattice volume as compared to the irregular shaped structure. The raspberry-type structures exhibited a higher sensor signal response than the others. A relationship between sensor properties and crystal defect was investigated, and it was revealed that the gas selectivity to a high dipole moment value of a reducing gas molecule increased with increasing oxygen deficiency area of the Co3O4 nanoparticle. It was considered that the oxygen deficiency area acted as an important reaction site, which can be attributed to the selective reaction of the Co3O4 nanoparticle with gas molecules.

Nano-particles (NPs) of WO3-type compounds by polyol route with enhanced electrochromic properties

Tungsten trioxide, synthetized as nanoparticles (NPs), then shaped as thin or thick films, has attracted considerable attention as a typical electrochromic material. Herein, the synthesis of WO3 nanoparticles by the polyol process followed or not by heat-treatments under air or argon, has allowed us to compare the electrochromic activity of powders with different morphologies and oxygen-deficiencies. Only the finest particles associated with pseudo-cubic structure due to a large oxygen-deficiency - on the contrary to the larger particles with standard monoclinic structure and W/O stoichiometric ratio - lead to films showing intense electrochromic color change from a whitish (bleached state) to a dark blue (colored state). Additionally, the as-prepared films exhibit quite fast electrochromic performance and satisfying cycling stability. The sub-stoichiometric nanoparticles prepared from polyol synthesis are of great potential for electrochromic applications.

Comparative Study of Electrical Conduction and Oxygen Diffusion in the Rhombohedral and Bixbyite Ln6MoO12 (Ln = Er, Tm, Yb) Polymorphs.

Electrical conduction and oxygen diffusion mobility in the bixbyite ( Ia3̅) and rhombohedral ( R3̅) polymorphs of the Ln6MoO12-Δ (Ln = Er, Tm, Yb; Δ = δ, δ1, δ2; δ1 > δ2) heavy lanthanide molybdates, belonging to new, previously unexplored classes of potential mixed (ionic-electronic) conductors, have been studied in the range of 200-900 °C. The oxygen self-diffusion coefficient in bixbyite ( Ia3̅) Yb6MoO12-δ phase estimated by the temperature-programmed heteroexchange with C18O2 was shown to be much higher than that for rhombohedral ( R3̅) RI (with large oxygen deficiency) and ( R3̅) RII (with small oxygen deficiency) Ln6MoO12-Δ (Ln = Tm, Yb; Δ = δ1; δ1 > δ2) oxides. According to the activation energy for total conduction in ambient air, 0.99, 0.93, and 1.01 eV in Er6MoO12-δ, Tm6MoO12-δ, and Yb6MoO12-δ bixbyites, respectively, oxygen ion conductivity prevails in the range ∼200-500 °C. Oxygen mobility data for the rhombohedral Ln6MoO12-Δ (Ln = Er, Tm, Yb; Δ = δ1, δ2) phases RI and RII indicate that the oxygen in these phases exhibits mobility at much higher temperatures, such as those above 600-700 °C. Accordingly, below 600-700 °C they have predominantly electronic conductivity. As shown by total conductivity study of Ln6MoO12-δ (Ln = Er, Tm, Yb) bixbyites ( Ia3̅) and rhombohedral phases Ln6MoO12-Δ (Ln = Er, Tm, Yb; Δ = δ1, δ2) ( R3̅) in dry and wet air, the proton conductivity contribution exists only in Ln6MoO12-δ (Ln = Er, Tm, Yb) bixbyites up to 450-600 °C and decreases with a decreasing of the lanthanide ionic radius. The obtained data on the mobility of oxygen and the presence of proton contribution in bixbyites in the 300-600 °C temperature range make it possible to confirm unequivocally that Ln6MoO12-δ (Ln = Er, Tm, Yb) bixbyites are mixed electron-proton conductors at these temperatures.

Uncovering the Effect of Lattice Strain and Oxygen Deficiency on Electrocatalytic Activity of Perovskite Cobaltite Thin Films.

Developing cost effective electrocatalysts with high oxygen evolution reaction (OER) activity is essential for large‐scale application of many electrochemical energy systems. Although the impacts of either lattice strain or oxygen defects on the OER performance of oxide catalysts have been extensively investigated, the effects of both factors are normally treated separately. In this work, the coupled effects of both strain and oxygen deficiency on the electrocatalytic activity of La0.7Sr0.3CoO3−δ (LSC) thin films grown on single crystal substrates (LaAlO3 (LAO) and SrTiO3 (STO)) are investigated. Electrochemical tests show that the OER activities of LSC films are higher under compression than under tension, and are diminished as oxygen vacancies are introduced by vacuum annealing. Both experimental and computational results indicate that the LSC films under tension (e.g., LSC/STO) have larger oxygen deficiency than the films under compression (e.g., LSC/LAO), which attribute to smaller oxygen vacancy formation energy. Such strain‐induced excessive oxygen vacancies in the LSC/STO increases the eg state occupancy and enlarges the energy gap between the O 2p and Co 3d band, resulting in lower OER activity. Understanding the critical role of strain–defect coupling is important for achieving the rational design of highly active and durable catalysts for energy devices.

Porous nanostructured GdFeO3 perovskite oxides and their gas response performance to NOx

Gas sensing characteristics of rare-earth-based orthoferrite (GdFeO3) mesoporous nanostructures were prepared by a facile one-step hydrothermal process. The structural analyses of the obtained materials showed sphere, leaf and flower-like nanostructured architectures. Further, the chemiresistive gas-response properties of the GdFeO3 nanostructure were investigated with various combustible gases, such as nitric oxide (NO), nitrogen dioxide (NO2), carbon monoxide (CO), ammonia (NH3), hydrogen sulfide (H2S), formaldehyde (HCHO), ethanol (C2H5OH) and gasoline, at different operating temperatures. The sphere-like GdFeO3 nanostructure shows a significantly high resistance variation to NO compared with the other architectures, exhibits a high response (91%) when exposed to 100 ppm NO, and detects a level as low as 2 ppm (7%) at an optimum operating temperature of 140 °C. The GdFeO3 nanostructure shows an excellent stability and repeatability after successive repeated cycles with a fast response and recovery time when exposed to 100 ppm NO gas. The superior response and excellent selectivity of the perovskite GdFeO3 nanostructure are due to its higher catalytic activity, large surface area, oxygen deficiency, mesoporosity, and peculiar morphology. The response mechanism of NO on the GdFeO3 nanostructured surface is also discussed in detail.

Circulation, eddies, oxygen, and nutrient changes in the eastern tropical South Pacific Ocean

Abstract. A large subsurface oxygen deficiency zone is located in the eastern tropical South Pacific Ocean (ETSP). The large-scale circulation in the eastern equatorial Pacific and off the coast of Peru in November/December 2012 shows the influence of the equatorial current system, the eastern boundary currents, and the northern reaches of the subtropical gyre. In November 2012 the equatorial undercurrent (EUC) is centered at 250 m depth, deeper than in earlier observations. In December 2012, the equatorial water is transported southeastward near the shelf in the Peru–Chile undercurrent (PCUC) with a mean transport of 1.4 Sv. In the oxygen minimum zone (OMZ), the flow is overlaid with strong eddy activity on the poleward side of the OMZ. Floats with parking depth at 400 m show fast westward flow in the mid-depth equatorial channel and sluggish flow in the OMZ. Floats with oxygen sensors clearly show the passage of eddies with oxygen anomalies. The long-term float observations in the upper ocean lead to a net community production estimate at about 18° S of up to 16.7 mmol C m−3 yr−1 extrapolated to an annual rate and 7.7 mmol C m−3 yr−1 for the time period below the mixed layer. Oxygen differences between repeated ship sections are influenced by the Interdecadal Pacific Oscillation (IPO), by the phase of El Niño, by seasonal changes, and by eddies, and hence have to be interpreted with care. At and south of the Equator the decrease in oxygen in the upper ocean since 1976 is related to an increase in nitrate, phosphate, and in part silicate.

Insight into the structure and functional application of the Sr0.95Ce0.05CoO3-δ cathode for solid oxide fuel cells.

A new perovskite cathode, Sr0.95Ce0.05CoO3-δ, performs well for oxygen-reduction reactions in solid oxide fuel cells (SOFCs). We gain insight into the crystal structure of Sr1-xCexCoO3-δ (x = 0.05, 0.1) and temperature-dependent structural evolution of Sr0.95Ce0.05CoO3-δ by X-ray diffraction, neutron powder diffraction, and scanning transmission electron microscopy experiments. Sr0.9Ce0.1CoO3-δ shows a perfectly cubic structure (a = a0), with a large oxygen deficiency in a single oxygen site; however, Sr0.95Ce0.05CoO3-δ exhibits a tetragonal perovskite superstructure with a double c axis, defined in the P4/mmm space group, that contains two crystallographically different cobalt positions, with distinct oxygen environments. The structural evolution of Sr0.95Ce0.05CoO3-δ at high temperatures was further studied by in situ temperature-dependent NPD experiments. At 1100 K, the oxygen atoms in Sr0.95Ce0.05CoO3-δ show large and highly anisotropic displacement factors, suggesting a significant ionic mobility. The test cell with a La0.8Sr0.2Ga0.83Mg0.17O3-δ-electrolyte-supported (∼300 μm thickness) configuration yields peak power densities of 0.25 and 0.48 W cm(-2) at temperatures of 1023 and 1073 K, respectively, with pure H2 as the fuel and ambient air as the oxidant. The electrochemical impedance spectra evolution with time of the symmetric cathode fuel cell measured at 1073 K shows that the Sr0.95Ce0.05CoO3-δ cathode possesses superior ORR catalytic activity and long-term stability. Mixed ionic-electronic conduction properties of Sr0.95Ce0.05CoO3-δ account for its good performance as an oxygen-reduction catalyst.

Advanced functional oxide thin films grown by pulsed-laser deposition

Pulsed-laser deposition is now a largely used growth method to prepare functional and multifunctional oxide films for application in microelectronics, spintronics, optics, materials for energy… The functional properties of such oxide films are strongly depending on the crystalline structure, and on the chemical composition through the local environment of cationic species surrounded by oxygen. While large oxygen deficiency cannot be obtained by classical growth method or in bulk state, oxide films with a high content of oxygen vacancies may be obtained by PLD. For oxide systems presenting possible stable sub-oxides, the formation of oxygen vacancies is linked to a decrease of the cationic valence state. A complete reduction can be observed leading to particular electronic properties: the case of TiOx (1.5<x<2) will be therefore presented and discussed. When no thermodynamically stable sub-oxides can be involved, the large oxygen deficiency may lead to the formation of nanocomposite films constituted by a metallic phase embedded in a stoichiometric oxide matrix. This phase separation induced by the control of oxygen pressure during the growth is in particular evidenced on Ga2Ox (2.1<x<3) films and their related physical (electrical and optical) properties are discussed.

Electrical, optical and etching properties of Zn-Sn-O thin films deposited by combinatorial sputtering

Zn-Sn-O (ZTO) films are known to be able to form an amorphous phase, which provides a smooth surface morphology as well as etched side wall, when deposited by using the conventional sputtering technique and, therefore, to have a potential to be applied as transparent thin film transistors. In this study, ZTO thin films were prepared by using combined sputtering of ZnO and SnO2 targets, and the dependences of their electrical and optical properties on the composition and the deposition parameters were examined. The Sn content in the films was varied in the range of 35 ∼ 85 at.%. The deposition was carried out at room temperature, 150 and 300 °C, and the oxygen content in sputtering gas was varied from 0 to 1 vol.%. Sn-rich films had better electrical properties, but showed large oxygen deficiency when deposited at low oxygen partial pressures. ZTO films with Sn contents lower than 55 at.% had good optical transmission, but the electrical properties were poor due to very low carrier concentrations. A high Hall mobility of larger than 10 cm2/Vs could be obtained in the carrier density range 1017∼1020 cm−3, and the etching rate was measurable for films with Sn content up to 70 at.% when using a dilute HCl solution, indicating a good possibility of utilizing ZTO films for device applications.

Sn-substituted LiMn2O4 thin films prepared by RF magnetron sputtering

The spinel thin films of LiMn2O4 and LiSn0.0125Mn1.975O4 prepared by RF magnetron sputtering were studied with focusing on structural and electrochemical properties. The LiSn0.0125Mn1.975O4 thin films showed the superior properties, i.e., a high capacity retention of 94% at the current rate of 5 C after 90 cycles, due to the increase in Mn valence and the decrease in oxygen deficiency. The larger oxygen deficiency in undoped LiMn2O4 thin films was confirmed by the increased lattice volume and structural degeneration.

Nanocomposite oxide thin films grown by pulsed energy beam deposition

Highly non-stoichiometric indium tin oxide (ITO) thin films were grown by pulsed energy beam deposition (pulsed laser deposition-PLD and pulsed electron beam deposition-PED) under low oxygen pressure. The analysis of the structure and electrical transport properties showed that ITO films with a large oxygen deficiency (more than 20%) are nanocomposite films with metallic (In, Sn) clusters embedded in a stoichiometric and crystalline oxide matrix. The presence of the metallic clusters induces specific transport properties, i.e. a metallic conductivity via percolation with a superconducting transition at low temperature (about 6 K) and the melting and freezing of the In–Sn clusters in the room temperature to 450 K range evidenced by large changes in resistivity and a hysteresis cycle. By controlling the oxygen deficiency and temperature during the growth, the transport and optical properties of the nanocomposite oxide films could be tuned from metallic-like to insulating and from transparent to absorbing films.

Oxygen deficiency in oxide films grown by PLD

The incorporation of oxygen atoms in oxide films grown by pulsed laser deposition depends upon the oxygen pressure and laser power density. By carefully controlling these two parameters it is possible to control the oxygen deficiency in the samples, and thus to change their physical properties from insulating and transparent to absorbing and conducting. By using X-ray diffraction, Rutherford backscattering spectroscopy and resistivity measurements, we show that depending upon the oxide materials oxygen deficiency in the films can induce either the growth of stable sub-oxide phases or the formation of nanocomposite films by phase separation. The first case corresponds to oxides with a mixed valency cation like Ti, which leads to the formation of stable, crystalline and highly conductive TiO x sub-oxide phases. The second case is well described by the indium tin oxides (ITO) in which a large oxygen deficiency leads to metallic clusters embedded into a stoichiometric matrix, i.e. nanocomposite films. This phenomenon is due to the fact that sub-oxides of these compounds are not stable and thus the oxygen deficiency induced a phase separation.

Structural characterization of dense reduced BaTiO 3 and Ba 0.95La 0.05TiO 3 nanoceramics showing colossal dielectric values

BaTiO 3− x and Ba 0.95La 0.05TiO 3− x nanoceramics showing colossal permittivity values have been characterized. While starting powders are of cubic symmetry, X-ray and Neutron Diffraction techniques and Raman Spectroscopy measurements show that the one-step processed ceramics obtained by Spark Plasma Sintering (SPS) contain cubic and tetragonal phases. Rather large oxygen deficiency determined in such ceramics by Electron Micro Probe analysis and Electron Energy Loss Spectroscopy analyzes is explained by the presence of Ti 3+, as evidenced by X-ray Photoelectron Spectroscopy measurements. Transmission Electron Microscopy and High Resolution Transmission Electron Microscopy show that these ceramics contain 50–300 nm grains, which have single-domains, while grain boundaries are of nanometer scale. Colossal permittivity values measured in our dense nanoceramics are explained by a charge hopping mechanism and an interfacial polarization of a large number of polarons generated after sample reduction in SPS apparatus.

Pulsed laser-induced oxygen deficiency at TiO 2 surface: Anomalous structure and electrical transport properties

We have studied pulsed laser-induced oxygen deficiencies at rutile TiO 2 surfaces. The crystal surface was successfully reduced by excimer laser irradiation, and an oxygen-deficient TiO 2− δ layer with 160 nm thickness was formed by means of ArF laser irradiation at 140 mJ/cm 2 for 2000 pulses. The TiO 2− δ layer fundamentally maintained a rutile structure, though this structure was distorted by many stacking faults caused by the large oxygen deficiency. The electrical resistivity of the obtained TiO 2− δ layer exhibited unconventional metallic behavior with hysteresis. A metal–insulator transition occurred at 42 K, and the electrical resistivity exceeded 10 4 Ω cm below 42 K. This metal–insulator transition could be caused by bipolaronic ordering derived from Ti–Ti pairings that formed along the stacking faults. The constant magnetization behavior observed below 42 K is consistent with the bipolaronic scenario that has been observed previously for Ti 4O 7. These peculiar electrical properties are strongly linked to the oxygen-deficient crystal structure, which contains many stacking faults formed by instantaneous heating during excimer laser irradiation.

Structural, optical, and electrical properties of epitaxial titanium oxide thin films on LaAlO3 substrate

Titanium oxide thin films were prepared by pulsed-laser deposition on LaAlO3 single crystal substrate at 700 °C. Pure anatase films are obtained at high oxygen pressure (10−1 mbar), while the rutile phase is evidenced at low oxygen pressure (10−5 mbar) despite a large oxygen deficiency (O/Ti=1.75). From asymmetric x-ray diffraction measurements, the in-plane epitaxial relationships be0tween the substrate and the titanium oxide phases are highlighted. Optical constants (refractive index n and extinction coefficient k) were deduced from ellipsometric measurements. The optical band gap energies of the anatase and rutile films are found to be 3.4 and 3.3 eV, respectively. Since the nearly stoichiometric anatase films are resistive (&amp;gt;103 Ω cm), the large oxygen deficiency in rutile films leads to noticeable increase in the conductivity due to the Ti3+ species, which supply electrons in the conduction band. At low temperature (T&amp;lt;200 K) the resistivity of rutile films versus temperature may be explained by a variable range hopping mechanism based on both two or three dimensional electron transfer between the Ti3+ and Ti4+ species.

Infrared study of a [formula omitted] micrometric transistor channel

We studied the polaron conductivity in a field-effect transistor (FET) based on the doped oxide La 0.7 Sr 0.3 MnO 3 - δ , where the electric field penetration depth is enhanced due to suppression of metallic conduction by large oxygen deficiency δ , by mid-infrared microspectroscopy (wavelengths from 1.4 to 12 μ m ) on a 3 μ m wide active channel. Synchrotron radiation was used to obtain the mid-infrared response at the diffraction limit. We found that bound polarons, although clearly detected, play a minor role in the electric field-induced dc conductivity modulation, which may be then attributed to the accumulation/depletion of free carriers.

Thin films of oxygen-deficient perovskite phases by pulsed-laser ablation of strontium titanate

An oxygen-deficient phase has been formed by pulsed-laser ablation of strontium titanate under vacuum conditions $({10}^{\ensuremath{-}7}\phantom{\rule{0.3em}{0ex}}\mathrm{mbar})$. By the complementary use of Rutherford backscattering spectrometry and x-ray diffraction, the composition and structure of films were determined. A large oxygen deficiency is revealed in the films as the corresponding formula is $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{2.5}$. This understoichiometry means that ${\mathrm{Ti}}^{3+}$ are present in such films, while only ${\mathrm{Ti}}^{4+}$ is observed in stoichiometric compound $(\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3})$. The presence of ${\mathrm{Ti}}^{3+}$ species in the $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{2.5}$ films was checked by x-ray absorption spectroscopy. The $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{2.5}$ films were found to crystallize in the cubic perovskite structure with a lattice parameter of $0.40\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, considerably higher than that of the stoichiometric compound $(0.39\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$. The $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{2.5}$ films were epitaxially grown on MgO single-crystal substrates, with a ``cube-on-cube'' in-plane orientation with the substrate. In contrary to stoichiometric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ films which are perfectly insulating, the $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{2.5}$ films were found to be conductor or semiconductor at room temperature, depending on the growth temperature. Resistivities at room temperature in the ${10}^{\ensuremath{-}3}--{10}^{\ensuremath{-}2}\phantom{\rule{0.3em}{0ex}}\ensuremath{\Omega}\phantom{\rule{0.3em}{0ex}}\mathrm{cm}$ range are thus obtained.

Interface Defect Chemistry and Effective Conductivity in Polycrystalline Cerium Oxide

Polycrystalline cerium oxide exhibits increasing electronic and decreasing ionic conductivity upon reduction of the grain size. In the present study, the origin of this effect was examined. Temperature-programmed reduction (TPR) and oxygen titration measurements on nanocrystalline cerium oxide revealed a large excess oxygen deficiency associated with the surface. Using a two-phase model for the combined system of the bulk phase in equilibrium with a surface layer, this enhanced oxygen deficiency could be explained by a reduced binding energy of surface oxygen ions in agreement with results from atomistic computer simulations. The model also revealed that this segregation of oxygen vacancies is the origin of an intrinsic space charge potential. Translating this effect to polycrystalline cerium oxide and taking into account the segregation of dopants and the accumulation/depletion of charge carriers, it was possible to model the grain size dependence of electrical conductivity and thermopower of polycrystalline cerium oxide. A straightforward 1-dimensional numerical model and a change from Boltzmann to Fermi-Dirac statistics allowed to calculate the conductivity of heavily doped polycrystalline cerium oxide for grain sizes in the range of 5–10,000 nm and acceptor concentrations up to 20%. Using this approximation, the effect of grain size on mixed ionic/electronic conductivity and the electrolytic domain boundary was investigated.