Nonlinear dynamics for proper ferroelastic transitions for which the landau condition is violated

On the basis of a lattice model the domain structure for ferroelastic transformations is examined. The model accounts for both strongly nonlinear and competing interactions which allow for, in some situations, the propagation of nonlinear excitations. The model can be mostly applied to proper ferroelastic transformations of which In-Tl, Ti-Ni, etc.… are good prototypes. The phonon dispersion of the transverse acoustic waves obtained in the linearized case is discussed and the results show first a phonon softening at nonzero wave-number and next an upwards convexity of the phonon branch near the long-wavelength limit. This can be seen as pre-transitional effects. In a fully nonlinear case we consider vanishing dilatation transformations and the continuum approximation is applied to the one-dimensional version. Then, we investigate nonlinear excitations; three main classes of solution are found: i) quasi-harmonic solutions corresponding to periodically modulated structures in space which is a precursor effect of the elastic transformation, ii) an array of solitons made of periodic arrangements of parent-elastic domains and iii) a moving strain soliton. All the significant results are numerically illustrated by means of the microscopic model. Finally, the similarity to martensitic transformations and some extensions of the model are outlined.     

X-ray diffuse scattering from incommensurable structures

X-Ray diffuse scattering from a series of examples where the reason for the existence of incommensurable features is fairly well understood, is described. They include in particular non stoichiometric compounds such as [DIPS Φ₄(l₃)0.76] and such as intercalated graphite RbC₂₄. and quasi one dimensional conductors. A particular emphasis is given on various 1 - D conductors and to the relation of the incommensurability to the characteristics of the electron conduction bands.     

Zur Bestimmung des Kohlenstoffs

Ohne Zusammenfassung     

Ground state of the quasi-1D compound BaVS3 resolved by resonant magnetic x-ray scattering

Resonant magnetic x-ray scattering near the vanadium L2,3-absorption edges has been used to investigate the low temperature magnetic structure of high quality BaVS3 single crystals. Below T(N)=31 K, the strong resonance revealed a triple-incommensurate magnetic ordering at the wave vector (0.226 0.226 ξ) in hexagonal notation, with ξ=0.033. The azimuthal-angle dependence of the scattering signal and time-dependent density functional theory simulations indicate an antiferromagnetic order within the ab plane with the spins polarized along a in the monoclinic structure.     

Cesium ordering and electron localization-delocalization phenomena in the quasi-one-dimensional diphosphate tungsten bronzes: Cs1‒xP8W8O40

We present a structural investigation of the family of quasi-one-dimensional (quasi-1D) conductors, which exhibit intriguing charge transport properties where, for x small, the conductivity exhibits a crossover from a semiconducting to a metallic like regime when the temperature decreases. In these materials the double zig-zag chains, together with the diphosphate groups, delimit channels which are partially filled with the ions. It is found, from an X-ray diffuse scattering investigation, that at room temperature the ions are locally ordered on a lattice of well-defined sites in the channel direction and not ordered between neighboring channels. These ions form 1D incommensurate concentration waves whose periodicity depends on the stoichiometry. In upon cooling, the intrachannel order increases significantly, and an interchannel order between the 1D concentration waves develops. But, probably because of kinetic effects, no tridimensional (3D) long range order of the ions is achieved at low temperature. The 3D low-temperature local order has been determined and it is found that the phase shift between the concentration waves minimizes their Coulomb repulsions. This local order is increasingly reduced as the Cs concentration diminishes. We interpret the intriguing features of the electrical conductivity in relationship with the thermal evolution of the Cs ordering effects. We suggest that in , for x small, a localization-delocalization transition of the Anderson type occurs due to the thermal variation of the Cs disorder. When x increases, the enhancement of the disorder leads to a localization of the electronic wave function in the whole temperature range measured. Finally, and probably because of the disorder, no charge density wave instability is revealed by our X-ray diffuse scattering investigation. Received: 10 October 1997 / Received in final form: 11 December 1997 / Accepted: 16 December 1997     

Structural evidence for an incommensurable modulated structure in single crystals of bis-p-toluene sulphonate of 2,4-hexadiyne-1,6-diol

X-ray scattering from monomer crystals of bis-p-toluene sulphonate (PTS) diacetylene at low temperatures reveal the existence, between 206 K and 163 K, of an incommensurable modulated structure, just above the already reported low temperature superstructure.     

On the Topology of Real Algebraic Plane Curves

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use sub-resultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gröbner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in non-generic positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on high-degree non-generic curves.