Phase diagram and oxygen-vacancy ordering in the CeO2-Gd2O3 system: a theoretical study

Recipes for superior ionic conductivities in thin-film ceria-based electrolytes

We employed Molecular Dynamics (MD) and Metropolis Monte Carlo (MMC) simulations to determine the oxide-ion mobility u_O in Ce_1-yGd_yO_2-y/2 (y = 0.02, 0.1, 0.2) for the range of temperatures 1400 ≤ T/K ≤ 2000 and field strengths 0.6 ≤ E/MV cm^-1 ≤ 15.0. Direct, unambiguous determination of u_O(E) from MD simulations is shown to require examination of the ions' mean displacement as a function of time. MD simulations were performed for random distributions of Gd cations and equilibrium distributions obtained by MMC calculations. All u_O(E,T,y) data obtained can be described by an (empirically augmented) analytical model with four zero-field parameters, a result that allows data to be extrapolated down to the temperatures of electrolyte operation. Specifically, the oxide-ion conductivity is predicted, for example at T = 700 K, (i) to be up to 10¹ higher for a random distribution of Gd than for an equilibrium distribution; and (ii) to be a factor of 10^0.8 higher for a 6 nm thin film than for a μm-thick sample under a potential difference of 1 V. By virtue of non-equilibrium deposition and nm-thick samples, thin films thus provide two new recipes for attaining even higher oxide-ion conductivities in ceria-based electrolytes.

Trivalent Dopant Size Influences Electrostrictive Strain in Ceria Solid Solutions

The technologically important frequency range for the application of electrostrictors and piezoelectrics is tens of Hz to tens of kHz. Sm³⁺- and Gd³⁺-doped ceria ceramics, excellent intermediate-temperature ion conductors, have been shown to exhibit very large electrostriction below 1 Hz. Why this is so is still not understood. While optimal design of ceria-based devices requires an in-depth understanding of their mechanical and electromechanical properties, systematic investigation of the influence of dopant size on frequency response is lacking. In this report, the mechanical and electromechanical properties of dense ceria ceramics doped with trivalent lanthanides (RE_0.1Ce_0.9O_1.95, RE = Lu, Yb, Er, Gd, Sm, and Nd) were investigated. Young's, shear, and bulk moduli were obtained from ultrasound pulse echo measurements. Nanoindentation measurements revealed room-temperature creep in all samples as well as the dependence of Young's modulus on the unloading rate. Both are evidence for viscoelastic behavior, in this case anelasticity. For all samples, within the frequency range f = 0.15-150 Hz and electric field E ≤ 0.7 MV/m, the longitudinal electrostriction strain coefficient (|M₃₃|) was 10² to 10⁴-fold larger than expected for classical (Newnham) electrostrictors. However, electrostrictive strain in Er-, Gd-, Sm-, and Nd-doped ceramics exhibited marked frequency relaxation, with the Debye-type characteristic relaxation time τ ≤ 1 s, while for the smallest dopants-Lu and Yb-little change in electrostrictive strain was detected over the complete frequency range studied. We find that only the small, less-studied dopants continue to produce useable electrostrictive strain at the higher frequencies. We suggest that this striking difference in frequency response may be explained by postulating that introduction of a dopant induces two types of polarizable elastic dipoles and that the dopant size determines which of the two will be dominant.

Evaluation of the Defect Cluster Content in Singly and Doubly Doped Ceria through In Situ High-Pressure X-ray Diffraction

Defect aggregates in doped ceria play a crucial role in blocking the movement of oxygen vacancies and hence in reducing ionic conductivity. Nevertheless, evaluation of their amount and the correlation between domain size and transport properties is still an open issue. Data derived from a high-pressure X-ray diffraction investigation performed on the Ce_1–x(Nd_0.74Tm_0.26)_xO_2–x/2 system are employed to develop a novel approach aimed at evaluating the defect aggregate content; the results are critically discussed in comparison to the ones previously obtained from Sm- and Lu-doped ceria. Defect clusters are present even at the lowest considered x value, and their content increases with increasing x and decreasing rare earth ion (RE³⁺) size; their amount, distribution, and spatial correlation can be interpreted as a complex interplay between the defects’ binding energy, nucleation rate, and growth rate. The synoptic analysis of data derived from all of the considered systems also suggests that the detection limit of the defects by X-ray diffraction is correlated to the defect size rather than to their amount, and that the vacancies’ flow through the lattice is hindered by defects irrespective of their size and association degree.

A novel approach to the treatment of high-pressure X-ray diffraction data is applied to several rare earth-doped ceria systems with the aim of providing an evaluation of the amount of defect aggregates and of the composition of the CeO₂-based solid solution. By this method, it is possible to effectively correlate the structural properties and ionic conductivity of the studied material.

Entropic stabilization plays a key role in the non-uniform distribution of oxygen ions and vacancy defects in gadolinium-doped ceria

Gadolinium-doped ceria (GDC) is an important fast oxygen ion conductor. O2--ion hopping in different cation environments of GDC is probed using molecular dynamics (MD). We find that at equilibrium, the O2--ions and vacancy defects arrange themselves around the relatively immobile cations in a way such that pairs of O2--ions and vacancy defect (O2--vac pair) are in greater numbers in some cation environments than others. The difference in O2--vac pair numbers is shown to originate from entropic effects in the cation environments. As a consequence of the entropic effect, the O2--vac pair distribution is practically independent of temperature between 974 and 1874 K. Even the O2- ion hopping rate and barrier are influenced by the entropic effect. This observation is in stark contrast with the standard belief that energetic interactions dominate in solid oxide materials, and entropic factors can be ignored. By analyzing the cation environment effect using k-means clustering, nine environment clusters are identified that are associated with unique values of the activation barrier and entropy. Comparisons to yttria stabilized zirconia (YSZ), yet another popular fast oxygen ion conductor, are made.

Metastable oxygen vacancy ordering state and improved memristive behavior in TiO2 crystals

Oxygen vacancy is one of the pivotal factors for tuning/creating various oxide properties. Understanding the behavior of oxygen vacancies is of paramount importance. In this study, we identify a metastable oxygen vacancy ordering state other than the well-known Magnéli phases in TiO₂ crystals from both experimental and theoretical studies. The oxygen vacancy ordering is found to be a zigzag chain along the [0 0 1] direction in the (1 1 0) plane occurring in a wide temperature range of 200-500 °C. This metastable ordering state leads to a first-order phase transition accompanied by significant enhancement of dielectric permittivity and a memristive effect featuring a low driving electric field. Our results can improve oxide properties by engineering oxygen vacancies.

A review of defect structure and chemistry in ceria and its solid solutions

Ceria and its solid solutions play a vital role in several industrial processes and devices. These include solar energy-to-fuel conversion, solid oxide fuel and electrolyzer cells, memristors, chemical looping combustion, automotive 3-way catalysts, catalytic surface coatings, supercapacitors and recently, electrostrictive devices. An attractive feature of ceria is the possibility of tuning defect-chemistry to increase the effectiveness of the materials in application areas. Years of study have revealed many features of the long-range, macroscopic characteristics of ceria and its derivatives. In this review we focus on an area of ceria defect chemistry which has received comparatively little attention - defect-induced local distortions and short-range associates. These features are non-periodic in nature and hence not readily detected by conventional X-ray powder diffraction. We compile the relevant literature data obtained by thermodynamic analysis, Raman spectroscopy, and X-ray absorption fine structure (XAFS) spectroscopy. Each of these techniques provides insight into material behavior without reliance on long-range periodic symmetry. From thermodynamic analyses, association of defects is inferred. From XAFS, an element-specific probe, local structure around selected atomic species is obtained, whereas from Raman spectroscopy, local symmetry breaking and vibrational changes in bonding patterns is detected. We note that, for undoped ceria and its solid solutions, the relationship between short range order and cation-oxygen-vacancy coordination remains a subject of active debate. Beyond collating the sometimes contradictory data in the literature, we strengthen this review by reporting new spectroscopy results and analysis. We contribute to this debate by introducing additional data and analysis, with the expectation that increasing our fundamental understanding of this relationship will lead to an ability to predict and tailor the defect-chemistry of ceria-based materials for practical applications.

The effect of space-charge formation on the grain-boundary energy of an ionic solid

Taking the model system of an oxide containing acceptor dopant cations and charge-compensating oxygen vacancies, we calculate at the continuum level the change in the excess grain-boundary energy of an ionic solid upon space-charge formation. Two different cases are considered for the space-charge layers: (i) only vacancies attain electrochemical equilibrium and (ii) both dopants and vacancies attain electrochemical equilibrium. The changes calculated for a specific set of grain boundaries indicate that, depending on dopant concentration, space-charge formation can decrease the excess free energy by up to 15% in the first case and by up to 45% in the second case. The possibility of the excess grain-boundary energy going to zero and the possible effects of an external electric field on the excess grain-boundary energy are also discussed. This article is part of a discussion meeting issue 'Energy materials for a low carbon future'.

Ionic conductivity and local structural features in Ce1-xSmxO2-x/2

Sm-Doped ceria is one of the most promising materials to be used as electrolyte in solid oxide fuel cells due to its remarkable ionic conductivity values in the intermediate temperature range. Transport properties and local structural features of Ce1-xSmxO2-x/2 (0.1 ≤ x ≤ 0.7) were studied by an impedance/μ-Raman spectroscopy coupled approach up to 1073 K. Results suggest that C-based nanosized defect clusters are responsible for the drop in ionic conductivity observed even at x = 0.2, i.e. at a Sm content lower than necessary to allow C domains to reach the percolation threshold through crystallites. Moreover, within the fluorite-type compositional region, with increasing the Sm content, defect clusters undergo a rearrangement resulting in the enlargement of C-based domains rather than in the increase of their number; at higher x, on the contrary, both the size and amount of C domains increase in parallel.

Rare Earth Doped Ceria: The Complex Connection Between Structure and Properties

The need for high efficiency energy production, conversion, storage and transport is serving as a robust guide for the development of new materials. Materials with physical-chemical properties matching specific functions in devices are produced by suitably tuning the crystallographic- defect- and micro-structure of the involved phases. In this review, we discuss the case of Rare Earth doped Ceria. Due to their high oxygen diffusion coefficient at temperatures higher than ~500°C, they are very promising materials for several applications such as electrolytes for Solid Oxide Fuel and Electrolytic Cells (SOFC and SOEC, respectively). Defects are integral part of the conduction process, hence of the final application. As the fluorite structure of ceria is capable of accommodating a high concentration of lattice defects, the characterization and comprehension of such complex and highly defective materials involve expertise spanning from computational chemistry, physical chemistry, catalysis, electrochemistry, microscopy, spectroscopy, and crystallography. Results coming from different experimental and computational techniques will be reviewed, showing that structure determination (at different scale length) plays a pivotal role bridging theoretical calculation and physical properties of these complex materials.

Rare-Earth-Doped Ceria Systems and Their Performance as Solid Electrolytes: A Puzzling Tangle of Structural Issues at the Average and Local Scale

Rare-earth (RE)-doped ceria systems, in particular when RE ≡ Nd, Sm, or Gd, are well-known to be characterized by high values of ionic conductivity in the intermediate temperature range, which, in principle, makes them ideal solid electrolytes in solid oxide fuel and electrolysis cells. Defect chemistry turns out to be a pivotal issue in this framework because ionic conductivity is driven by the ability of oxygen vacancies to move through the lattice, and any form of defect clustering tends to depress the efficiency of oxygen transport. In this viewpoint, not only are factors at the average scale assessed, such as the compositional extent of the CeO₂-like solid solution, but also the occurrence of local inhomogeneities due to vacancy-dopant association is discussed in correlation with its central role in hindering the migration of vacancies. The relationship between the stability of the hybrid phase and the RE³⁺ ionic size is presented, and the highly complementary role of Raman spectroscopy toward X-ray diffraction is described in detail. The key points of the whole discussion are finally used to identify the most relevant structure-related parameters affecting ionic conductivity in the studied material.