Brouwer Diagrams Research Articles

Quantitative Defect Chemistry Analysis and Electronic Conductivity Prediction of La0.8Sr0.2MnO3±δ Perovskite

The defect chemistry of La0.8Sr0.2MnO3±δ (LSM-20) is analyzed using the La-Sr-Mn-O quaternary thermodynamic database with the compound energy formalism model by applying the CALPHAD approach. The quantitative Brouwer diagrams for LSM-20 at 1000, 1100, and 1200°C are developed. The detailed analysis of the Mn3+ charge disproportionation behavior and the electronic conductivity in the temperature range of 1000–1200°C is carried out. The calculations on the electronic conductivity of LSM-20 show agreement with the experimental data in the literatures. In addition, the 3-D electronic conductivity contours are predicted in a wide range of oxygen partial pressure, temperature, and A-site deficiency.

Equilibrium and transient conductivity for gadolinium-doped ceria under large perturbations: I. Experiments

This is the first of a two-part paper that is concerned with measuring and interpreting equilibrium and transient conductivity for 10at.% gadolinium-doped ceria (Ce0.9Gd0.1O1.95-δ, GDC10). AC impedance spectroscopy is used to measure conductivity of slender extruded GDC10 rods at temperatures between 700 and 900°C. From the obtained Brouwer diagrams, the activation energies of the oxide ions and cerium small polarons are estimated to be 0.77 and 2.45eV respectively. Conductivity relaxation measurements from strongly reducing conditions (4% H2, 3% H2O, 93% Ar) to strongly oxidizing conditions (97% O2, 3% H2O) and vice versa reveal great asymmetries in relaxation times. Virtually instantaneous relaxations are observed in the first case, while the oxidizing-to-reducing relaxations take as long as 0.5h. This paper reports conductivity relaxations with over 20 orders of magnitude in the gas-phase oxygen partial pressure. Models and experiments are used to show that the observed asymmetries cannot be explained by electrode defects or two-dimensional end effects. The companion paper develops a Nernst–Planck–Poisson model to assist the quantitative interpretation of the measurements reported in the present paper.

Charge states of point defects in uranium oxide calculated with a local hybrid functional for correlated electrons

The formation energies and charge states of point defects in uranium dioxide are calculated from first principles, using the local hybrid functional for correlated electrons, which offers a nice alternative to LDA$+$U calculations. The possible occurrence of multiple minima in such calculations is carefully taken into account. Point defects in UO${}_{2}$ are generally found to be charged with a \ensuremath{-}4 charge for uranium vacancies, \ensuremath{-}2 for oxygen interstitials, and a charge ranging from 0 to $+$2 for oxygen vacancies depending on the position of the Fermi level. The calculated formation energies of noninteracting oxygen Frenkel pairs and Schottky defects made of the association of charged defects are in very good agreement with experimental values. A Brouwer diagram based on a point-defect model for stoichiometry variations in UO${}_{2+x}$ is built. It fails to predict the dominant concentration of oxygen interstitials in the overstoichiometric oxide but predicts that oxygen vacancies are in a $+$1 charge state in the hypostoichiometric oxide. This charge state, which differs from the one assumed in the traditional (fully ionic) picture of UO${}_{2}$, is confirmed by the obtained variation of the deviation from stoichiometry with oxygen pressure, which is consistent with experiments.

High-Temperature Protonic Conduction in LaFeO3 – SrFeO3 − δ – SrZrO3 Solid Solutions

The electrical conductivity of a pseudoternary system, consisting of , , was evaluated both in oxygen and hydrogen containing environments by a two-probe ac technique. Correlations of oxygen partial pressure, water vapor pressure, and composition dependences of the electrical conductivities with possible defect concentrations are examined by a semiquantitatively derived Brouwer diagram. In oxygen for below 0.25, major carriers were identified to be oxide ions and electron holes, while for they were a mixture of oxide ions, electron holes, and protons. In a hydrogen containing environment, the oxides with compositions for and 0.5 were unstable. Thus, the electrical conductivity was analyzed in detail for . It was found that the oxide conducts protons significantly at temperatures below , which was evidenced by the isotope effect of hydrogen and deuteron on the electrical conductivity. The electrical conductivity of the oxide increased with decreasing oxygen partial pressure due to the variation of oxygen nonstoichiometry, accompanied by partial reduction of Fe ions in the oxide. The transport number of proton increased as the oxygen partial pressure decreased. The gas partial pressure and the composition dependences of the electrical conductivity and the transport number of proton could be well explained by the conceptual Brouwer diagram proposed in this work.

Silicon‐Doped LiFePO4 Single Crystals: Growth, Conductivity Behavior, and Diffusivity

AbstractSingle crystals of silicon doped LiFePO4 with a silicon content of 1% are grown successfully by the floating zone technique and characterized by single‐crystal and powder X‐ray diffraction, secondary ion mass spectroscopy, and chemical analysis. Electron paramagnetic resonance demonstrates the presence of only Fe2+; no traces of Fe3+ are found. Impedance spectroscopy as well as step‐function polarization/depolarization (DC) measurements are carried out using the cells Ti/LiFe(Si)PO4/Ti and LiAl/LiI/LiFe(Si)PO4/LiI/LiAl. The electronic and ionic conductivities as well as the Li‐diffusivity of the sample in the major crystallographic directions ([h00], [0k0], and [00l]) are determined. Within experimental error the transport properties along the b‐ and c‐axes are found to be the same but differ significantly from the a‐axis, which exhibits lower values. Compared to undoped LiFePO4, Si‐doping leads to an increase of the ionic conductivity while the electronic conductivity decreases, which is in agreement with a donor effect. The activation energies of conductivities and diffusivities are interpreted in terms of defect chemistry and relevant Brouwer diagrams are given.

Defect Chemistry of LiFePO4

Based on experimental results, in particular, obtained on single crystals, the nature of the decisive point defects and charge carriers in is discussed, and the dependencies of their concentrations on the control parameters Li activity, doping content, and temperature are worked out. In the native regime characterized by Li deficiency δ, lithium vacancies being decisive for ion conduction are compensated by holes as decisive electronic carriers. Very close to the concentration of order (where δ is strictly zero) frozen-in native defects or non-intentional impurities dominate. We typically found lithium vacancies compensated by iron atoms on Li sites . Intentionally introduced donors such as or , have the same donor effect. The Brouwer diagrams displaying the logarithm of the defect concentration vs log lithium activity or vs log donor/acceptor content are derived. As to the temperature dependence of conductivities, trapping of holes by lithium vacancies is crucial and dominates the effective activation barrier at frozen lithium content. In particular, for the Al-doped samples, ionic association also proves important. Defect reaction and migration enthalpies are derived for electronic and ionic transport. Trapping of holes by lithium vacancies and association of lithium vacancies with impurities also turn out to be key for understanding the temperature dependence of the chemical diffusion coefficient of lithium.

Structure, Raman spectra and defect chemistry modelling of conductive pyrochlore oxides

Mixed ionic–electronic conducting pyrochlore structure oxides, with Pr and Gd on the A site and Zr, Mn, Ce, Sn, In, Mo, and Ti on the B site, were characterised by X-ray powder diffraction and Raman spectroscopy. Mn and In have a solubility around x=0.1–0.2 in Pr 2Zr 2− x Mn x O 7 and Pr 2Sn 2− x In x O 7, respectively. In the series Pr 2M 2− x M′ x O 7, where M=Sn, Zr and M′=In, Ce, we observe dopant–O 6 symmetrical stretch vibrations in addition to the host lattice modes. A defect model of a B site doped pyrochlore is developed with Pr 3+ on the A site; Zr B x (Zr 4+), Ce B′ (Ce 3+), Ce B x (Ce 4+) on the B site; O O x and V O ·· on the O site, interstitial oxygens O i″, and delocalised electrons and electron holes. Four mass action law expressions govern such a model. The defect model can rationalise why homo-valent doping, i.e. substitution of Zr(4+) by Ce(4+), can lead to an increase in ionic conductivity. The calculated Brouwer diagram for Pr 2Zr 1.6Ce 0.4O 7± δ is shown. This composition has a transition from mixed ionic p-type to presumably pure ionic conduction around pO 2=10 −7.5 atm. At pO 2<10 −15 atm the material gradually changes into the n-type regime. Typical magnitudes are finally given for the four equilibrium constants, leading to cases of pure p-type, p- to n-type and pure electrolytic behaviour of doped pyrochlores.

Point defects and electrical properties of Sn-doped In-based transparent conducting oxides

In-based transparent conducting oxides (TCOs) share the prevailing defect structure of indium–tin oxide (ITO), i.e. electrons, isolated Sn In ⋅ donors, and neutral associates, believed to be (2Sn In ⋅O i ″) x . The present work reviews the state of the literature, presents calculated Brouwer diagrams vs. oxygen partial pressure and vs. dopant concentration, and reports intermediate temperature electrical property data (thermopower, conductivity) vs. pO 2 and Sn concentration for three systems — polycrystalline bulk ITO, nanocrystalline ITO, and the recently reported ternary cation TCO, Ga 3− x In 5+ x Sn 2O 16. The influence of non-reduceable tin–oxygen complexes at high doping levels is identified for ITO. Ramifications for In-based TCO properties are discussed.

Defect Reactions and the Controlling Mechanism in the Sintering of Magnesium Aluminate Spinel

Pressureless sintering studies have been conducted for excess Al2O3, stoichiometric, and excess MgO compositions of MgAl2O4 at 1500‐1625°C. Initial powders of various compositions are prepared by solid‐state reaction of MgO and Al2O3. A Brouwer defect equilibrium diagram is constructed that assumes intrinsic defects of the Schottky type. The densification rate derived from sintering kinetics is compared with the compositions investigated when the concentration is converted to the activity of the two oxide components in MgAl2O4. The grain‐size exponent of p similar/congruent 3 suggests that densification takes place by a lattice‐diffusion mechanism in the solid state. Determined activation enthalpies of 489‐505 kJmol‐1 are close to those obtained from oxygen self‐diffusion derived in previous sintering studies. It is, therefore, proposed that oxygen lattice diffusion through vacancies is the rate‐controlling mechanism for the sintering of nonstoichiometric MgAl2O4 compositions. The discrepancy between densification‐rate ratios in experimental results and oxygen vacancy concentration in the Brouwer diagram is accounted for by the defect associates formed in the nonstoichiometric compositions.

Isochronal annealing of quenched CdS phosphors

Isochronal annealing of CdS:Cu:Cl powders with different copper and chlorine content quenched from various temperatures (150 to 1050 °C), are performed at temperatures of 100 to 400 °C, for 0.5 to 10 min. Using the method of intersection of isochronal curves the activation energies of increase and decrease of the photoluminescence emission bands are found. On the basis of Brouwer diagrams, computed for the system under study, the schemes of quasichemical defect forming reactions in connection with luminescence centres formation are determined. The activation energies attributed to these reactions are established. [Russian Text Ignored].