A statistical model approximation for perovskite solid-solutions: a Raman study of lead-zirconate-titanate single crystal

Lead titanate (PbTiO3) is a classical example of a ferroelectric perovskite oxide illustrating a displacive phase transition accompanied by a softening of a symmetry-breaking mode. The underlying assumption justifying the soft-mode theory is that the crystal is macroscopically sufficiently uniform so that a meaningful free energy function can be formed. In contrast to PbTiO3, experimental studies show that the phase transition behaviour of lead-zirconate-titanate solid solution (PZT) is far more subtle. Most of the studies on the PZT system have been dedicated to ceramic or powder samples, in which case an unambiguous soft-mode study is not possible, as modes with different symmetries appear together. Our Raman scattering study on titanium-rich PZT single crystal shows that the phase transitions in PZT cannot be described by a simple soft-mode theory. In strong contrast to PbTiO3, splitting of transverse E-symmetry modes reveals that there are different locally-ordered regions. The role of crystal defects, random distribution of Ti and Zr at the B-cation site and Pb ions shifted away from their ideal positions, dictates the phase transition mechanism. A statistical model explaining the observed peak splitting and phase transformation to a complex state with spatially varying local order in the vicinity of the morphotropic phase boundary is given.Comment: Article contains four black-and-white figures, one colour figure and one Table. Symmetry analysis and details of the model are given in Appendices I and II, respectivel

Structures of K0.05Na0.95NbO3 (50–300 K) and K0.30Na0.70NbO3 (100–200 K)

Rietveld refinement using neutron powder diffraction data is reported for the potential lead-free piezoelectric material KxNa1 - xNbO3 (x = 0.05, x = 0.3) at low temperatures. The structures were determined to be of rhombohedral symmetry, space group R3c, with the tilt system a-a-a- for both compositions. It was found that some of the structural parameters differ significantly in the two structures, and particularly the NbO6 octahedral strains as a function of temperature. The 300 K profile for K0.05Na0.95NbO3 shows the coexistence of rhombohedral and monoclinic phases, which indicates that the phase boundary is close to room temperature; the phase boundary for K0.30Na0.70NbO3 is found to be at approximately 180 K

Parallel developmental genetic features underlie stickleback gill raker evolution.

BackgroundConvergent evolution, the repeated evolution of similar phenotypes in independent lineages, provides natural replicates to study mechanisms of evolution. Cases of convergent evolution might have the same underlying developmental and genetic bases, implying that some evolutionary trajectories might be predictable. In a classic example of convergent evolution, most freshwater populations of threespine stickleback fish have independently evolved a reduction of gill raker number to adapt to novel diets. Gill rakers are a segmentally reiterated set of dermal bones important for fish feeding. A previous large quantitative trait locus (QTL) mapping study using a marine × freshwater F2 cross identified QTL on chromosomes 4 and 20 with large effects on evolved gill raker reduction.ResultsBy examining skeletal morphology in adult and developing sticklebacks, we find heritable marine/freshwater differences in gill raker number and spacing that are specified early in development. Using the expression of the Ectodysplasin receptor (Edar) gene as a marker of raker primordia, we find that the differences are present before the budding of gill rakers occurs, suggesting an early change to a lateral inhibition process controlling raker primordia spacing. Through linkage mapping in F2 fish from crosses with three independently derived freshwater populations, we find in all three crosses QTL overlapping both previously identified QTL on chromosomes 4 and 20 that control raker number. These two QTL affect the early spacing of gill raker buds.ConclusionsCollectively, these data demonstrate that parallel developmental genetic features underlie the convergent evolution of gill raker reduction in freshwater sticklebacks, suggesting that even highly polygenic adaptive traits can have a predictable developmental genetic basis

Constitutive modeling of the anisotropic behavior of Mullins softened filled rubbers

Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histo-ries. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model leans on the strain amplification factor concept applied over material directions according to the Mul-lins softening evolution. In order to provide a model versatile that applies for a wide range of materials, the proposed framework does not require to postulate the mathematical forms of the elementary directional strain energy density and of the Mullins softening evo-lution rule. A computational procedure is defined to build both functions incrementally from experimental data obtained during cyclic uniaxial tensile tests. Successful compari-sons between the model and the experiments demonstrate the model abilities. Moreover, the model is shown to accurately predict the non-proportional uniaxial stress-stretch responses for uniaxially and biaxially pre-stretched samples. Finally, the model is effi-ciently tested on several materials and proves to provide a quantitative estimate of the anisotropy induced by the Mullins softening for a wide range of filled rubbers

Lobbying of Firms by Voters

A firm may induce voters or elected politicians to support a policy it favors by suggesting that it is more likely to invest in a district whose voters or representatives support the policy. In equilibrium, no one vote may be decisive, and the policy may gain strong support though the majority of districts suffer from adoption of the program. When votes reveal information about the district, the firm's implicit promise or threat can be credible