A new crystalline phase has been discovered in the Bi2O3–GeO2–HNO3–H2O quartet system. The new phase was slowly precipitated at room temperature under atmospheric pressure from a strongly acidic aqueous solution (pH ~0.2) containing dissolved bismuth oxide, germanium oxide, dilute ammonia, and nitric acid. Characterization and crystal structure analyses were carried out by means of powder X-ray diffraction (PXRD), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) spectroscopy, high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), thermogravimetry (TG)–mass spectrometric analysis, and solid-state nuclear magnetic resonance (NMR) spectroscopy. The molecular formula was established as BiGeO2(OH)2(NO3). The crystal structure of this new phase was elucidated from PXRD data by a combination of direct and charge-flipping methods. The new phase was found to have the space group Pbca with lattice parameters of a = 1.145510(10) nm, b = 0.495346(5) nm, and c = 1.81676(2) nm. This new phase was observed to possess a layered structure consisting of BiO6 polyhedra, GeO5 trigonal bipyramids and nitrate ions.

•Defect concentration in MgO-doped lanthanum silicate oxyapatite•Defect concentrations are quantitatively evaluated from the material density.•Mg ions are substituted not only on La sites but also on Si site.The distribution of magnesium ions at the lanthanum and silicon sites in MgO-doped lanthanum silicate oxyapatite as well as the concentration of neutral lanthanum vacancies were determined using densities and chemical compositions of the doped samples. On the basis of the density data, it was found that magnesium ions are substituted at the silicon site as well as the lanthanum sites in the oxyapatite phase. Owing to the existence of neutral lanthanum vacancies, it was difficult to evaluate the number of the oxygen ions present, which are related to the oxygen ion conductivity of the compound, from the chemical compositions of the samples alone. Further, it was found that the fact that the total conductivity of MgO-doped lanthanum silicate oxyapatite depends on the MgO concentration as well as that of other defects could not be explained on the basis of conventional defect chemistry.

We discuss the thermodynamic meaning of the oxygen overpotential, and derive a fundamental theoretical equation for the impedance spectrum of a system comprising an oxygen ion conductor and a metallic electrode under a mixture of oxygen and inert gas, as might be found at the cathode of a solid oxide fuel cell. Our derivation combines aspects of classical irreversible thermodynamics, Wagner's theory and the concepts of the interfacial conductivity theory. The oxygen overpotential at the oxygen ion conductor/metallic electrode interface under steady state conditions is found to be related to the rate of entropy production by neutral oxygen diffusion and desorption from the interface to the gas phase. The generalized impedance equation derived in this study can be applied not only under open cell conditions but also in the steady state polarized condition, which corresponds to experimental impedance measurements under a d.c. bias voltage. When the oxygen flux, resulting from a small perturbation force, follows Fick's first law, and the relaxation process proceeds via the change in adsorbed concentration of oxygen on the electrode surface, the impedance spectrum becomes semicircular in the Nyquist diagram. The electrode resistance and the electrode capacitance estimated from equivalent electric circuit analysis reflect the chemical reaction response, or in other words, the chemical resistance and chemical capacitance.Highlights► Meaning of the oxygen overpotential was investigated by irreversible thermodynamics. ► The electrode impedance is modeled based on interfacial conductivity theory. ► Extended interfacial conductivity is proposed based on this model.

•Theoretical formulae of electrochemical impedance were derived.•Impedance relations were derived from the interfacial conductivity theory.•Five types of impedance formulae were derived depending on the conditions.•Specific parameters are related to the interfacial conductivity.Theoretical impedance relationships in a limiting process with non-steady-state surface diffusion were derived based on the interfacial conductivity concept at the interface between an oxygen ion conductor and a metallic electrode. While the non-steady-state surface diffusion of adsorbed neutral oxygen on the metallic electrode could be described by Fick's second law, approximated and equivalent equations to the Warburg impedance and Gerischer impedance were derived according to the boundary conditions and occurrence of dissipation by the chemical reaction. The diffusion related to the electrochemical impedance signal is not the diffusion of the oxygen ions. In addition, it is not necessary to assume an electrochemical potential gradient or profile of the free electrons in the metallic electrode. The relationships obtained in this paper indicate that electrochemical potential measured by an instrument is clearly defined by the electrochemical potential of free electrons at the triple phase boundary. The meaning of the equivalent electrical circuits corresponding to the impedance spectra is reconsidered from the view points of the interfacial conductivity concept.

In this study, we determined the crystallographic nature and electrical transport properties of Nd9.20(SiO4)6O1.8 and (La0.46Nd0.54)9.33(SiO4)6O2, which are defect-containing oxyapatites. The intensity data measured by synchrotron powder X-ray diffraction were analyzed by a Rietveld method. From the total conductivity data, the oxygen partial pressure region where the oxygen ionic conductivity (σO2-) predominates was determined to narrow down owing to the substitution of neodymium ions. A comparison of various solid solutions under similar temperature conditions ranging from 873 K to 1273 K showed that the σO2- values were lowest for (La0.46Nd0.54)9.33(SiO4)6O2 samples. The activation energy of the oxygen ionic conductivity increased with an increasing neodymium content.Highlights► Synthesis of lanthanum silicate and neodymium silicate solid solution. ► Structural analysis of oxyapatite solid solution by Synchrotron X-ray diffraction. ► Discovery of the mixed conduction properties of neodymium contained oxyapatite.

Low-temperature formation routes of lanthanum silicate and neodymium silicate oxyapatites were analyzed by a combination of powder X-ray diffraction and thermogravimetric/differential thermal analysis by using precursors prepared from the water-based sol–gel method. Oxyapatite phase was found to form at about 1073 K in the case of lanthanum silicate and at about 1273 K in the case of neodymium silicate — temperatures much lower than those for a conventional solid-state reaction method. In each system, the oxyapatite phase was formed after decomposition of the lanthanoid oxycarbonate or metastable lanthanoid oxide. In particular, decomposition of lanthanum oxycarbonate was found to play an important role in lanthanum silicate oxyapatite formation. In addition to proposing a crystal structure for the lanthanoid oxycarbonate, we hypothesize an in-situ chemical pulverization process due to the delamination of lanthanoid oxide by carbon dioxide dissociation.Highlights► Analyses on low-temperature formation route of lanthanoid silicate oxyapatites. ► Low-temperature synthesis by water-based sol–gel method. ► In-situ chemical pulverization process due to the delamination of lanthanoid oxide.

A novel synthesis method of lanthanum silicate apatite was developed by a sol–gel method using an aqueous solution system. The processes of apatite phase formation were investigated by X-ray diffraction (XRD) analysis and thermogravimetric/differential thermal analyses (TG–DTA) using a precursor and heat-treated samples between 873 K and 1773 K. Crystal structure refinement of the sample heat-treated at 1773 K was carried out by using XRD and high resolution neutron powder diffraction profiles. Based on the combined results of XRD and TG–DTA, lanthanum dioxide carbonate (La2O2CO3) was found to be contained in the sample heat-treated below 873 K. Lanthanum silicate apatite was formed above 1073 K, a temperature that was in good agreement with the decomposition temperature of La2O2CO3. Furthermore, it was found that the profiles of powder XRD and high resolution neutron powder diffraction could be refined by the oxy-apatite structure with the space group P63/m (No. 176).