Structures isomorphes MeX2O4—Evolution structurale entre 2 K et 300 K de l'antimonite FeSb2O4: Elasticité et ordre magnétique anisotropes

Neutron diffraction has been used to study the whole structural evolution of the antimony oxide FeSb₂O₄, from 2 to 300 K. The antiferromagnetic order has been investigated: at 2 K the magnetic moment is M = 3.8 μ_B. An extrapolated Néel temperature T_N = 45 ± 6 K is observed. The function M(T) below T_N is similar to that found in the isomorphous NiSb₂O₄. Magnetostrictive effects are observed. Above 70 K, the thermal expansion tensor is anisotropic with α_a ? α_c. Using the anisotropic temperature factors B_a (Ų), B_c (Ų) at 2 and 300 K, anisotropic Debye temperatures are calculated. Then, using simple approximations, mean force constants F_a, F_c are calculated; they allow to evaluate the anisotropic compressibility coefficients χ_a ～ 0.857 × 10^?11Pa^?1, χ_c ～ 0.467 × 10^?11Pa^?1; the value of the Grüneisen constant is $\text{γ}\text{= 0.33}$.     

Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

Lattice systems with a continuous symmetry

We consider perturbations of a massless Gaussian lattice field on ? ^d ,d≧3, which preserves the continuous symmetry of the Hamiltonian, e.g., $$ - H = \sum\limits_{< x,y > } {(\phi _x - \phi _y )^2 + T(\phi _x - \phi _y )^4 ,\phi _x \in \mathbb{R}.} $$ It is known that for allT>0 the correlation functions in this model do not decay exponentially. We derive a power law upper bound for all (truncated) correlation functions. Our method is based on a combination of the log concavity inequalities of Brascamp and Lieb, reflection positivity and the Fortuin, Kasteleyn and Ginibre (F.K.G.) inequalities.     

Lattice systems with a continuous symmetry

We prove that the expansion in powers of the temperatureT of the correlation functions and the free energy of the plane rotator model on ad-dimensional lattice is asymptotic to all orders inT. The leading term in the expansion is the spin wave approximation and the higher powers are obtained by the usual perturbation series. We also prove the inverse power decay of the pair correlation at low temperatures ford=3.Supported by NSF Grant No. MCS 78-01885Supported by NSF Grant No. PHY 78-15920Supported by NSF Grant No. DMR 73-04355Supported by NSF Grant No. PHY-7825390 A01On leave from: Institut de Physique Théorique, Université de Louvain, BelgiumAlso: Department of Physics     

Oxydes de plomb. I. Structure cristalline du minium Pb3O4, à température ambiante (293 K)

The structure of Pb₃O₄ at 293 K has been refined to an R value of 0.06, using 29 neutron diffraction data obtained from a powdered sample.Oxygen atoms are displaced in the quadratic cell (space group $\text{P4}{}_2\text{mbc}\text{; a = 8.811}$ Å and c = 6.563 Å) with respect to previous results obtained by several authors. The interatomic Pb^IVO and Pb^IIO distances are compared with those found in other lead oxides. While the oxygen octahedra around Pb^IV atoms are characterized by bondings a little too long, the divalent lead coordination is characterized by bondings a little too short.     

Structure, microstructure, and size dependent catalytic properties of nanostructured ruthenium dioxide

Nanostructured powders of ruthenium dioxide RuO₂ were synthesized via a sol gel route involving acidic solutions with pH varying between 0.4 and 4.5. The RuO₂ nanopowders were characterized by X-ray diffraction, scanning and transmission electron microscopy (SEM and TEM). Rietveld refinement of mean crystal structure was performed on RuO₂ nanopowders and crystallized standard RuO₂ sample. Crystallite sizes measured from X-ray diffraction profiles and TEM analysis varied in the range of 4-10 nm, with a minimum of crystallite dimension for pH=1.5. A good agreement between crystallite sizes calculated from Williamson Hall approach of X-ray data and from direct TEM observations was obtained. The tetragonal crystal cell parameter (a) and cell volumes of nanostructured samples were characterized by values greater than the values of standard RuO₂ sample. In addition, the [Ru-O₆] oxygen octahedrons of rutile structure also depended on crystal size. Catalytic conversion of methane by these RuO₂ nanostructured catalysts was studied as a function of pH, catalytic interaction time, air methane composition, and catalysis temperature, by the way of Fourier transform infrared (FTIR) spectroscopy coupled to homemade catalytic cell. The catalytic efficiency defined as FTIR absorption band intensities I(CO₂) was maximum for sample prepared at pH=1.5, and mainly correlated to crystallite dimensions. No significant catalytic effect was observed from sintered RuO₂ samples.     

Chemical Degradation in Thermally Treated Ferrite/Superconductor Multiphase Materials: Modeling Parameters

Solid state chemical evolutions are studied in the case of superconductor/ferrite composites as a function of time and temperature. Pellets have been fabricated from ferrite NiFe₂O₄ and superconducting cuprate Bi_1.6Pb_0.4Sr₂Ca₂Cu₃O_10+X (noted as Bi-2223). Two types of experimental approaches are presented: high-temperature electrical complex impedance spectroscopy, and EDAX analyses performed from scanning electron microscopy. From the in situ electrical analyses, two steps in the solid state chemical evolutions have been evidenced for the first time. They can be associated with two types of solid state reactions: (i) direct reactions between the ferrite phase and the superconducting matrix and (ii) a self-degradation of the superconducting phase probably associated with a homogenization of elements. The electrical analyses are modeled using two types of kinetics parameters. From the EDAX analyses, the local distribution of each element is determined. The concentration profiles found for the various elements (Ni, Fe, Bi, Sr, Ca, Cu) are interpreted in terms of a virtual diffusion law involving virtual D^* coefficients. These coefficients are found to be of about 10⁻¹¹ (cm²/s) in the range 800–830°C.     

Correlation inequalities and contour estimates

We give a simple estimate on the probability of contours in classical ferromagnetic spin systems, based on Griffiths' or Ginibre's correlation inequalities. This includes quite general one- and two-component spin models. Some extension also holds for alln-component anisotropic or isotropic rotators.Supported by NSF grant No. MCS78-01885.On leave from: Institut de Physique Théorique, Université de Louvain, Belgium.Supported by NSF grant No. PHY78-15920.