Moderate-temperature solid-oxide fuel cells (SOFCs) are widely considered in the process of SOFC commercialization. Lower operating temperatures require a higher ionic conductivity of the electrolyte. They also require higher reactivity of the electrodes. Recently, increasing attention has been paid to moderate-temperature SOFCs with ceria as electrolyte and La 1Ϫx Sr x CoO 3 as cathode. [1][2][3] Both materials are known to have very high oxygen ionic conductivities. Another merit of this combination is that they do not react during the sintering process of cell manufacture.The conductivity in air of rare-earth-doped ceria has been well studied in the literature, as reviewed by Inaba and Tagawa. 4 Gd-or Sm-stabilized ceria has been extensively studied for such utilizations as electrolyte, anode material, and interlayer between a La 1Ϫx Sr x CoO 3 cathode and an yttria-stabilized-zirconia (YSZ) electrolyte. A characteristic of doped ceria of much importance is its n-type electronic conductivity in a reducing atmosphere. Electronic conductivity is a disadvantage for an electrolyte, but an advantage for anode materials. Ionic conductivity, however, is important for both utilizations. Thus, research on the p O2 dependence of both the ionic conductivity, i , and the electronic conductivity, e , of doped ceria is important for its applications.Because of the difficulty in dividing experimentally the total conductivity into its ionic and electronic contributions, some assumptions have been made in the literature. First, i was treated as constant for simplicity when electronic conductivity, e , was the main concern, 5-7 since the change of i in a reducing atmosphere is expected to be much smaller than that of e . Another approach assumed that the formation of additional oxygen vacancies under reducing conditions would decrease the ionic conductivity and the change could be estimated by an empirical law obtained from results of YSZ solid solutions. 8 Later, when the ionic conductivity became the main concern, it became clear that the ionic radius of doped aliovalent ion affects the conductivity heavily. Another assumption was then proposed 9 that the ionic conductivity of ceria in changing atmospheres could be approximately simulated by measuring the conductivity of La-doped ceria in air. This is because the ionic radius of La 3ϩ is very similar to that of Ce 3ϩ , so that the effect of Ce 3ϩ should be similar to that of the same amount of La 3ϩ . The ionic conductivity obtained in this way has a maximum value with increasing amounts of Ce 3ϩ (reducing p O2 ). That work, however, discussed only a high temperature (1273 K), and did not give information on the model of i and its activation energy.In the present work, we try another assumption to discuss the ionic and electronic conductivity of Gd-doped ceria (Ce 0.9 Gd 0.1 O 1.95Ϫx noted as CGO10) and (Ce 0.8 Gd 0.2 O 1.9Ϫx noted as CGO20) at moderate temperature and in the area of small oxygen nonstoichiometry. We assume that the mobilities of oxygen vacancies and electron...

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Phase transitions are characterized in several (NH4)3MF6 hexafluorometallates(III) using X‐ray diffraction and microcalorimetric techniques. For small trivalent cations (M = Al, V, Cr, Fe, Ga) an Fm3m cubic ⇄ triclinic transition occurs below room temperature. For larger trivalent species, two phase transitions are detected, the low temperature phases (at T = 290 K) being monoclinic (P21/n) and tetragonal (P4/mnc) for Sc and In, respectively. Heat capacity measurements are carried out for (NH4)3CrF6 and (NH4)3GaF6 in a miniaturized adiabatic calorimeter from 12 to 310 K. The entropy variation associated with the phase transition is ΔtrsS(269.6 K) = = 19.4 J K−1 mol−1 and ΔtrsS(246.1 K) = 21.3 J K−1 mol−1, respectively. The change in entropy is compared with those of other (NH4)3MF6 compounds and interpreted in terms of an orientational order‐disorder transition.

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The variable phase approach to potential scattering with regular spherically symmetric potentials satisfying (1), and studied by Calogero in his book 5 , is revisited, and we show directly that it gives the absolute definition of the phase-shifts, i.e. the one which defines δ ℓ (k) as a continuous function of k for all k ≥ 0, up to infinity, where δ ℓ (∞) = 0 is automatically satisfied. This removes the usual ambiguity ±nπ, n integer, attached to the definition of the phase-shifts through the partial wave scattering amplitudes obtained from the Lippmann-Schwinger integral equation, or via the phase of the Jost functions.It is then shown rigorously, and also on several examples, that this definition of the phase-shifts is very general, and applies as well to all potentials which have a strong repulsive singularity at the origin, for instance those which behave like gr −m , g > 0, m ≥ 2, etc. We also give an example of application to the low-energy behaviour of the S-wave scattering amplitude in two dimensions, which leads to an interesting result.