High oxide ion conductivity in Fe and Mg doped LaGaO3 as the electrolyte of solid oxide fuel cells

La(Sr)Ga(Fe,Mg)O₃ exhibited the high oxide ion conductivity and the electrical power generating property of SOFC single cell using La_0.7Sr_0.3Ga_0.7Fe_0.2Mg_0.1O_3-δ (LSGFM) electrolyte was investigated in this study. The transport number of oxide ion is almost 0.8 in LSGFM and so open circuit potential (OCV) is as low as 0.8 V. OCV was strongly affected by anode materials and the highest OCV was achieved on Ni–Fe bimetallic anode. The extremely high power density was achieved by using LSGFM for electrolyte of SOFC. The maximum power densities of the cells can be elevated by coating with oxide ion conductor film at anode side. The maximum power density increased in the following order for coating film: LSGM > SDC > YSZ. The maximum power density of 197 and 100 mW/cm² can be achieved at 873 and 773 K, respectively, when LSGM film deposited on the anode side of LSGFM. Therefore, LSGFM can be used as electrolyte of SOFC operating at intermediate temperature.     

Characterization of LSGM films obtained by electrophoretic deposition (EPD)

The application of the electrophoretic deposition (EPD) technique to the preparation of high quality electrolyte films for intermediate temperature solid oxide fuel cells (IT-SOFCs) was investigated. Films of La_0.83Sr_0.17Ga_0.83Mg_0.17O_2.83 (LSGM) were deposited on Pt and La_0.8Sr_0.2MnO₃ (LSM) substrates from suspensions in acetone/ethanol (3:1 by volume) mixture solvent and sintered at 1300 °C. Pt supported LSGM films, 10–20 μm thick, exhibited good adhesion to the Pt substrate, well-distributed microporosity and some surface roughness. LSM supported films exhibited cracking after sintering at 1300 °C for 3 h. Up to 900 °C the bulk conductivity of the Pt supported LSGM film showed the same behaviour of LSGM pellet (E_a = 0.93 eV and 0.99 eV, respectively). The LSGM film exhibited lower bulk electrical conductivity than the latter (4.1 × 10^− 3 and 4.4 × 10^− 2 Ω^− 1 cm^− 1, respectively, at 700 °C). This difference should be ascribed to the slight Ga depletion in the LSGM film. An important issue remains the selection of adequate electrode for LSGM electrolyte films.     

Electric property of mixed conductor BaIn1−xCoxO3−δ

We synthesized BaIn_1−xCo_xO_3−δ (x = 0–0.8) with a defective perovskite structure by partly replacing In with Co in Ba₂In₂O₅. Based on XRD measurements, the synthesized compound was found to have cubic perovskite and orthorhombic brownmillerite structures depending on the amount of Co. BaIn_1−xCo_xO_3−δ (x = 0.2 and 0.3) showed high total electrical conductivities without undergoing the structural transformation that the original Ba₂In₂O₅ undergoes. Some of the samples showed both electronic and oxide ionic conductivities. At the same time, the oxide ionic conductivity was comparable with that of Ba₂In₂O₅. For example, the sample with x = 0.1 had a total electrical conductivity of 4.7 × 10^− 1 S cm^− 1 and an oxide ion transport number of 0.52 at 850 °C.     

Extraordinary fast oxide ion conductivity in La1.61GeO5−δ thin film consisting of nano-size grain

Thin films of La_1.61GeO_5−δ, a new oxide ionic conductor, were fabricated on dense polycrystalline Al₂O₃ substrates by a pulsed laser deposition (PLD) method and the effect of the film thickness on the oxide ionic conductivity was investigated on the nanoscale. The deposition parameters were optimized to obtain La_1.61GeO_5−δ thin films with stoichiometric composition. Annealing was found necessary to get crystalline La_1.61GeO_5−δ thin films. It was also found that the annealed La_1.61GeO_5−δ film exhibited extraordinarily high oxide ionic conductivity. Due to the nano-size effects, the oxide ion conductivity of La_1.61GeO_5−δ thin films increased with the decreasing thickness as compared to that in bulk La_1.61GeO_5−δ. In particular, the improvement in conductivity of the film at low temperature was significant .The electrical conductivity of the La_1.61GeO_5−δ film with a thickness of 373 nm is as high as 0.05 S cm^− 1 (log(σ/S cm^− 1) = − 1.3) at 573 K.     

Anomalous conductivity and microstructure in gadolinium doped ceria prepared from nano-sized powder

The temperature and the oxygen partial pressure dependences of the electron and hole conductivities were measured by the dc polarization method using a Hebb–Wagner's ion blocking cell for Gd_0.2Ce_0.8O_1.9 polycrystalline bodies with grain size of 0.5 μm prepared by sintering of nano-sized powder. A significant enrichment of gadolinium was observed in the vicinity of the grain boundary by TEM/EDS analyses. The electron conductivity were comparable with those of conventional Gd_0.2Ce_0.8O_1.9 polycrystalline body with grain size of 2 μm, and it followed p(O₂)^− 1/4 dependence at temperatures T = 973–1273 K. However, the observed hole conductivity was higher than that of conventional Gd_0.2Ce_0.8O_1.9, and it did not follow p(O₂)^1/4 dependence. This anomalous p(O₂) dependence disappeared after the sample was treated at T = 1773 K for 38 h and grain size was enlarged to 2–10 μm.     

Studies on the percolation limit of Ce0.9Gd0.1O1.95 in La0.6Sr0.4Co0.2Fe0.8O3−δ–Ce0.9Gd0.1O1.95 nanocomposites for solid oxide fuel cells application

A large difference in thermal expansion coefficient of electrode and electrolyte leads to imperfect electrode/electrolyte interface and hence significant polarization losses in solid oxide fuel cells. To overcome the difficulties associated with electrode and electrode/electrolyte interface, there is need to fabricate the composite cathode. Thus the present paper deals with study of La_0.6Sr_0.4Co_0.2Fe_0.8O_3−δ(LSCF)–Ce_0.9Gd_0.1O_1.95(GDC) nanocomposite with different fractions of GDC obtained by physical mixing of combustion synthesized nanopowders. No secondary phases were observed upon sintering at 1100 °C for 2 h affirming the chemical compatibility between LSCF and GDC. The composites with relatively high GDC% have higher density as a consequence of rapid grain growth and less conductivity. The nanocomposite with 50% of GDC showed electric conductivity of 30 Scm⁻¹ at 500 °C and low area specific resistance of 106 Ω cm² with 10 μs relaxation time at 200 °C.     

A-deficit LSCF for intermediate temperature solid oxide fuel cells

A-deficit La_0.54Sr_0.44Co_0.2Fe_0.8O_3 ? δ cathode material for intermediate temperature solid oxide fuel cells (IT-SOFCs) was synthesized by a citrate complexation (Pechini) route. Using La_0.54Sr_0.44Co_0.2Fe_0.8O_3 ? δ as cathode material, a superior cell performance with the maximum power density of 309, 470 and 855 mW cm^? 2 at 600, 650 and 700 °C was achieved, in contrast with the maximum power density of 266, 354 and 589 mW cm^? 2 using conventional La_0.6Sr_0.4Co_0.2Fe_0.8O_3 ? δ as cathode material at the same temperatures. The reason of this improvement was analyzed on the basis of defect chemistry. Thermal shrinkage experiment testified that the oxygen vacancies in La_0.54Sr_0.44Co_0.2Fe_0.8O_3 ? δ are more mobile than in La_0.6Sr_0.4Co_0.2Fe_0.8O_3 ? δ. Furthermore, theoretical calculation in terms of their composition and the shift of peak position in XRD pattern showed that the concentration of oxygen vacancies of La_0.54Sr_0.44Co_0.2Fe_0.8O_3 ? δ is higher than that of La_0.6Sr_0.4Co_0.2Fe_0.8O_3 ? δ. Therefore, the oxygen ion conductivity via vacancies transfer mechanism is enhanced, which induces the polarization resistance of La_0.54Sr_0.44Co_0.2Fe_0.8O_3 ? δ being decreased with a result of cell performance improved.     

An oxygen permeable membrane La0.8Sr0.2(Ga0.8Mg0.2)1 − xCrxO3 − δ for a reduced atmosphere

Mixed electron hole and oxide ion conducting perovskite-type oxides, La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ (0 ≤ x ≤ 1.0)_, were prepared by solid state reaction. The phase stability and the oxygen permeation properties of the oxides were examined as a function of the content of Cr. La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ has a perovskite related tetragonal phase with x = 0.1 to 0.8. The total electrical conductivity of La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ increases with increasing x. The oxygen permeation flux across the La_0.8Sr_0.2(Ga_0.8Mg_0.2)_1 ? xCr_xO_3 ? δ membranes at higher temperatures increases with x up to x = 04. The maximum oxygen permeation flux of 1.6 × 10^? 7 mol^? 1 cm^? 2 at 1100 °C in a oxygen activity gradient of air/10^? 2 Pa is observed in La_0.8Sr_0.2(Ga_0.8Mg_0.2)_0.6Cr_0.4O_3 ? δ. This perovskite-type oxide is stable under an oxygen partial pressure of 7 × 10^? 10 Pa at 1000 °C.     

Performance of La-doped strontium titanate (LST) anode on LaGaO3-based SOFC

Ni-containing anode is currently used with many electrolytes of solid oxide fuel cells (SOFCs). However, Ni is easily oxidized and deteriorates the LaGaO₃-based electrolyte. A La-doped SrTiO₃ (LST, La_0.2Sr_0.8TiO₃) is a candidate as an anode material to solve the Ni poisoning problem in LaGaO₃-based SOFC. In this study, a single-phase LST and an LST-Gd_0.2Ce_0.8O_2 ? δ (GDC) composite were tested as the possible anodes on La_0.9Sr_0.1Ga_0.8Mg_0.2O_3 ? δ (LSGM) electrolyte. In order to further improve the anodic performance, Ni was impregnated into the LST-GDC composite anode. The performance was examined from 600 °C to 800 °C by measuring impedance of the electrolyte-supported, symmetric (anode/electrolyte/anode) cells. A polarization resistance (R_p) of LST-GDC anode was much reduced from that of LST anode. When Ni was impregnated into LST-GDC composite, the R_p value was further reduced to ~ 10% of the single-phase LST anode, and it was 1 Ωcm² at 800 °C in 97% H₂ + 3% H₂O atmosphere. A single cell with Ni-impregnated LST-GDC as an anode, Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3 ? δ (BSCF) as a cathode and LSGM as an electrolyte exhibited the maximum power density of 275 mW/cm² at 800 °C, increased from ~ 60 mW/cm² for the cell using the LST-GDC as an anode. Thus, LST-GDC composite is promising as a component of anode.     

Surface modification of Ni and Co metal nanowires through MeV high energy ion irradiation

Nickel (Ni) and cobalt (Co) metal nanowires were fabricated by using an electrochemical deposition method based on an anodic alumina oxide (Al₂O₃) nanoporous template. The electrolyte consisted of NiSO₄ · 6H₂O and H₃BO₃ in distilled water for the fabrication of Ni nanowires, and of CoSO₄ · 7H₂O with H₃BO₃ in distilled water for the fabrication of the Co ones. From SEM and TEM images, the diameter and length of both the Ni and Co nanowires were measured to be ∼ 200 nm and 5–10 μm, respectively. We observed the oxidation layers in nanometer scale on the surface of the Ni and Co nanowires through HR–TEM images. The 3 MeV Cl²⁺ ions were irradiated onto the Ni and Co nanowires with a dose of 1 × 10¹⁵ ions/cm². The surface morphologies of the pristine and the 3 MeV Cl²⁺ ion-irradiated Ni and Co nanowires were compared by means of SEM, AFM, and HR–TEM experiments. The atomic concentrations of the pristine and the 3 MeV Cl²⁺ ion-irradiated Ni and Co nanowires were investigated through XPS experiments. From the results of the HR–TEM and XPS experiments, we observed that the oxidation layers on the surface of the Ni and Co nanowires were reduced through 3 MeV Cl²⁺ ion irradiation.     

Effective utilization of spray pyrolyzed CeO2 as optically passive counter electrode for enhancing optical modulation of WO3

Nanocrystalline cerium oxide (CeO₂) thin films were deposited onto the fluorine doped tin oxide coated glass substrates using methanolic solution of cerium nitrate hexahydrate precursor by a simple spray pyrolysis technique. Thermal analysis of the precursor salt showed the onset of crystallization of CeO₂ at 300 °C. Therefore, cerium dioxide thin films were prepared at different deposition temperatures from 300 to 450 °C. Films were transparent (T ~ 80%), polycrystalline with cubic fluorite crystal structure and having band gap energy (Eg) in the range of 3.04–3.6 eV. The different morphological features of the film obtained at various deposition temperatures had pronounced effect on the ion storage capacity (ISC) and electrochemical stability. The larger film thickness coupled with adequate degree of porosity of CeO₂ films prepared at 400 °C showed higher ion storage capacity of 20.6 mC cm^? 2 in 0.5 M LiClO₄ + PC electrolyte. Such films were also electrochemically more stable than the other studied samples. The Ce⁴⁺/Ce³⁺ intervalancy charge transfer mechanism during the bleaching–lithiation of CeO₂ film was directly evidenced from X-ray photoelectron spectroscopy. The optically passive behavior of the CeO₂ film (prepared at 400 °C) is affirmed by its negligible transmission modulation upon Li⁺ ion insertion/extraction, irrespective of the extent of Li⁺ ion intercalation. The coloration efficiency of spray deposited tungsten oxide (WO₃) thin film is found to enhance from 47 to 53 cm² C^? 1 when CeO₂ is coupled with WO₃ as a counter electrode in electrochromic device. Hence, CeO₂ can be a good candidate for optically passive counter electrode as an ion storage layer.     

Redox behaviour,chemical compatibility and electrochemical performance of Sr2MgMoO6 − δ as SOFC anode

The double perovskite Sr₂MgMoO_6 − δ (SMM) has been proposed as a potential anode material for direct hydrocarbon oxidation in solid oxide fuel cells (SOFCs). The oxygen nonstoichiometry and electrical conductivity dependence of Sr₂MgMoO_6 − δ have been determined as a function of the oxygen partial pressure by coulometric titration and impedance spectroscopy techniques. The chemical compatibility of Sr₂MgMoO_6 − δ with most of the typical electrolytes commonly used in SOFCs i.e. La_0.8Sr_0.2Ga_0.8Mg_0.2O_3 − δ (LSGM), Ce_0.8Gd_0.2O_2 − δ (CGO) and Zr_0.84Y_0.16O_2 − δ (YSZ), was investigated. Reactivity between SMM and all these electrolytes has been found above 1000 °C, although the reaction is most severe with ZrO₂-based electrolytes. Area-specific polarisation resistance of the SMM/LSGM/SMM symmetrical cells indicates that the polarisation resistance increases with the firing temperature of the electrodes due to chemical interaction between LSGM and SMM layers. A CGO buffer layer between the anode and electrolyte was also used to prevent an excessive interdiffusion of ionic species between these components, resulting in better performance. Power densities of 330 and 270 mW cm^− 2 were reached at 800 °C for SMM/CGO/LSGM/LSCF and SMM/LSGM/LSCF electrolyte-supported cells, respectively; with 600-μm-thick LSGM electrolyte, using humidified H₂ as fuel and air as oxidant. XPS and XRPD studies on SMM powders annealed in air and diluted CH₄ atmospheres showed that the surface of SMM powders is mainly formed by SrMoO₄ and metal carbonates.     

Conductivity and oxygen permeability of a novel oxide Pr2Ni0.8 − x Cu0.2FexO4 and its application to partial oxidation of CH4

Iron-doped Pr₂Ni_0.8Cu_0.2O₄ was studied as a new mixed electronic and oxide-ionic conductor for use as an oxygen-permeating membrane. An X-ray diffraction analysis suggested that a single phase K₂NiF₄-type structure was obtained in the composition range from x = 0 to 0.05 in Pr₂Ni_0.8 − xCu_0.2Fe_xO₄. It is considered that the doped Fe is partially substituted at the Ni position in Pr₂NiO₄. The prepared Pr₂NiO₄-based oxide exhibited a dominant hole conduction in the P_O2 range from 1 to 10^− 21 atm. The electrical conductivity of Pr₂Ni_0.8−xCu_0.2Fe_xO₄ is as high as 10² S cm^− 1 in the temperature range of 873–1223 K and it gradually decreased with the increasing amount of Fe substituted for Ni. The oxygen permeation rate was significantly enhanced by the Fe doping and it was found that the highest oxygen permeation rate (60 μmol min^− 1 cm^− 2) from air to He was achieved for x = 0.05 in Pr₂Ni_0.8 − xCu_0.2Fe_xO₄. Since the chemical stability of the Pr₂NiO₄-based oxide is high, Pr₂Ni_0.75Cu_0.2Fe_0.05O₄ can be used as the oxygen-separating membrane for the partial oxidation of CH₄. It was observed that the oxygen permeation rate was significantly improved by changing from He to CH₄ and the observed permeation rate reached a value of 225 μmol min^− 1 cm^− 2 at 1273 K for the CH₄ partial oxidation.     

Modification of B-site doping of perovskite LaxSr1 − xFe1 − y−zCoyCrzO3 − δ oxide by Mg2+ ion

Co-doping B-site of perovskite oxide La_xSr_1 ? xCo_yFe_1 ? yO_3 ? δ (LSCFO) with Cr⁶⁺ and Mg²⁺ ions has been attempted in this research for revamping chemical stability and oxygen ionic conductivity of this mixed conducting oxide. It is known that partial substitution for B-site cations of LSCFO by Cr gives rise to a significant improvement on chemical and thermal stability of the perovskite oxide. On the basis of this doped structure, introduction of an immaterial dose of Mg²⁺ ion into its B-site results in a microstructure consisting of smaller grains with higher density than its precursor. Furthermore, the resulting perovskite oxide La_0.19Sr_0.8Fe_0.69Co_0.1Cr_0.2 Mg_0.01O_3 ? δ (LSFCCMO) displays higher O^2? conductivity than the solely Cr-doped LSCFO besides the improved chemical stability against reduction in 5% CH₄/He stream at 850 °C. A detailed examination of the oxidation states of B-site transition metal ions by XPS has also been conducted as a part of structural characterizations of LSFCCMO. The assessment of relative O^2? conductivity shows that the grain boundary area plays a more important role than the bulk phase in facilitating ion transport, but with comparable boundary areas the higher densification level is favorable.     

Thickness dependence of Ic and Jc of LTG-SmBCO coated-conductor on IBAD-MgO tapes

We have reported SmBa₂Cu₃O_y (SmBCO) films on single crystalline substrates prepared by low-temperature growth (LTG) technique. The LTG-SmBCO films showed high critical current densities in magnetic fields compared with conventional SmBCO films prepared by pulsed laser deposition (PLD) method. In this study, to enhance critical current (I_c) in magnetic field, we fabricated thick LTG-SmBCO films on metal substrates with ion-beam assisted deposition (IBAD)-MgO buffer and estimated the I_c and J_c in magnetic fields.All the SmBCO films showed c-axis orientation and cube-on-cube in-plane texture. T_c of the LTG-SmBCO films were 93.1–93.4 K. J_c and I_c of a 0.5 μm-thick SmBCO film were 3.0 MA/cm² and 150 A/cm-width at 77 K in self-field, respectively. Those of a 2.0 μm-thick film were 1.6 MA/cm² and 284 A/cm-width respectively. Although I_c increased with the film thickness increasing up to 2 μm, the I_c tended to be saturated in 300 A/cm-width. From a cross sectional TEM image of the SmBCO film, we recognized a-axis oriented grains and 45° grains and Cu–O precipitates. Because these undesired grains form dead layers, I_c saturated above a certain thickness. We achieved that I_c in magnetic fields of the LTG-SmBCO films with a thickness of 2.0 μm were 88 A/cm-width at 1 T and 28 A/cm-width at 3 T.     

Synthesis of ammonia at atmospheric pressure with Ce0.8M0.2O2−δ (M = La,Y, Gd,Sm) and their proton conduction at intermediate temperature

Ionic conduction in fluorite-type structure oxide ceramics Ce_0.8M_0.2O_2−δ (M = La, Y, Gd, Sm) at temperature 400–800 °C was systematically studied under wet hydrogen/dry nitrogen atmosphere. On the sintered complex oxides as solid electrolyte, ammonia was synthesized from nitrogen and hydrogen at atmospheric pressure in the solid states proton conducting cell reactor by electrochemical methods, which directly evidenced the protonic conduction in those oxides at intermediate temperature. The rate of evolution of ammonia in Ce_0.8M_0.2O_2−δ (M = La, Y, Gd, Sm) is up to 7.2 × 10^− 9, 7.5 × 10^− 9, 7.7 × 10^− 9, 8.2 × 10^− 9 mol s^− 1 cm^− 2, respectively.     

Oxidation of ultra-thin zinc films on Rh(100) surface

The oxidation of submonolayer zinc films on Rh(100) surface by O₂ gas has been studied using low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and scanning tunneling microscopy (STM). With a zinc coverage of 0.8 ML, an atomically flat ultra-thin zinc oxide film formed at an oxygen partial pressure of 2 × 10^? 8 mbar and a temperature of 150 °C. The zinc oxide film showed a c(16 × 2) LEED pattern. The high resolution STM image of the zinc oxide film showed single dotted spots and double dotted spots arranged linearly and periodically along the [01¯1] direction. We propose an atomic arrangement model of the film accounting for the LEED pattern, the STM image, and the atomic arrangement of the bulk ZnO(0001) surface.     

Micro-solid oxide fuel cell using thick-film ceria

A fabrication method that does not use lithography or etching processes for thick-film based micro-SOFCs (Solid Oxide Fuel Cells) was described and discussed. In this study, a new type of micro-SOFC was fabricated using a free-standing thick-film electrolyte with ~ 20 μm thickness. This structure has the advantages of both electrolyte-support and electrode-support type SOFCs. Generally, the electrolyte should be thicker than e.g., ~ 150 μm since a thinner electrolyte easily cracks in a self-supporting mode during the fabrication procedure. Thus, a new mounting method was developed in order to use a thin-electrolyte film. In this study, a ~ 20 μm-thick GDC (Gd-doped ceria) electrolyte film was successfully mounted on a ~ 400 μm-thick GDC ring by sintering these two pieces together. Ni-GDC and Sm_0.5Sr_0.5CoO₃ were brush painted as an anode and a cathode, respectively. With this new configuration, it was possible to construct an electrolyte-supported SOFC using a thick-film ceria-based electrolyte and measure the power density. The open-circuit voltage (OCV) of the cell in 97%H₂ + 3%H₂O/air was ~ 0.87 V and the maximum power density was ~ 270 mW/cm² at 600 °C. The result shows that the high performance is achievable for the micro-SOFCs using a thick-film ceria-electrolyte operating at 600 °C.     

Ba0.5Sr0.5Co0.8Fe0.2O3−δ thin film microelectrodes investigated by impedance spectroscopy

The electrochemical properties of geometrically well-defined Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCF) microelectrodes have been investigated by impedance spectroscopy. The microelectrodes of 20–100 μm diameter and 100 nm thickness were prepared by pulsed laser deposition (PLD), photolithography and argon ion beam etching. The oxygen reduction reaction at these model electrodes is limited by interfacial processes, i.e. by the oxygen surface exchange and/or by the transfer of oxide ions across the electrode/electrolyte boundary, whereas the resistance associated with the transport of oxide ions through the bulk of the thin film electrode is negligible. The experiments revealed an extremely low absolute value of the electrochemical surface exchange resistance of only 0.09 (± 0.03) Ω cm² at 750 °C in air, which is more than a factor of 50 lower than the corresponding value measured for La_0.6Sr_0.4Co_0.8Fe_0.2O_3−δ (LSCF) microelectrodes of the same geometry. The dependence of this and other electrochemical quantities such as the chemical bulk capacitance or the BSCF/YSZ interfacial resistance on temperature has been studied between 500 and 750 °C.     

Electrical transport properties of doubly Gd- and Al-doped LaGa0.9Mg0.1O2.95 perovskite compounds

Oxide ion conduction properties of La_1−xGd_xGa_0.8Al_0.1Mg_0.1O_2.95 were discussed in terms of tolerance factor and free volume. The oxide ion conductivities increased with Gd content and attained the maximum at x = 0.10. Enhancement in oxide ion conduction up to x = 0.10 was attributable to the approach to an optimum tolerance factor, which is reportedly around 0.96, whereas degradation above x = 0.10 was considered to result from the reduction of free volume caused by replacement of smaller Gd for La.