Compositional uniformity, domain patterning and the mechanism underlying nano-chessboard arrays

We propose that systems exhibiting compositional patterning at the nanoscale, so far assumed to be due to some kind of ordered phase segregation, can be understood instead in terms of coherent, single phase ordering of minority motifs, caused by some constrained drive for uniformity. The essential features of this type of arrangements can be reproduced using a superspace construction typical of uniformity-driven orderings, which only requires the knowledge of the modulation vectors observed in the diffraction patterns. The idea is discussed in terms of a simple two dimensional lattice-gas model that simulates a binary system in which the dilution of the minority component is favored. This simple model already exhibits a hierarchy of arrangements similar to the experimentally observed nano-chessboard and nano-diamond patterns, which are described as occupational modulated structures with two independent modulation wave vectors and simple step-like occupation modulation functions.Comment: Preprint. 11 pages, 11 figure

Influencia del software de geometría dinámica en la visualización matemática

Este trabajo tiene como objetivo exponer los aspectos teóricos relativos a la influencia del software de Geometría dinámica en el desarrollo de la visualización matemática con base a los resultados de las principales investigaciones realizadas en este ámbito. Se describe el marco teórico en el que encuadramos la presente investigación, y en particular se define el término visualización y se expone su importancia en el aprendizaje de la Geometría. Asimismo, se enuncian las dificultades que se encuentran en la práctica de la visualización y se explican las distintas pruebas existentes para evaluar la visualización. En último lugar, se detallan los beneficios del uso del software de Geometría dinámica para el desarrollo de la visualización

Incommensurate instability and lattice dynamics of potassium selenate within a semiempirical rigid-ion model

The lattice dynamics of potassium selenate is analyzed using a rigid-ion model with the selenate groups reduced to rigid bodies. The interatomic forces have been adjusted only using static structural data. The number of adjustable parameters varies from two to five. Such a simple model is already sufficient to reproduce semiquantitatively the phonon dynamics of the real system. In particular, the model exhibits the lattice instability leading to the existence of an incommensurate phase. The characteristics of the resulting soft mode agree with those observed experimentally. The calculated eigenvector, in excellent agreement with the experimental one, is rather insensitive to the details of the interactions. This explains the strong similarities of the incommensurate modulations in most A2BX4 compounds. On the other hand, the form of the soft-phonon branch strongly depends on the force model. It is sufficient to fit the model to the static structure observed at 145 K instead of the one at room temperature, to provoke a conspicuous softening of the branch. The branch minimum is specially sensitive to some potassium-oxygen interactions. The relative size of the cations plays an essential role in the origin of the incommensurate instability. For comparison the results of a similar analysis for Cs2SeO4 are presented. In this case, the unstable or soft character of the lowest 2 branch disappears.Dirección General de Investigación Científica y Técnica PB87-074

Optimized local modes for lattice dynamical applications

We present a new scheme for the construction of highly localized lattice Wannier functions. The approach is based on a heuristic criterion for localization and takes the symmetry constraints into account from the start. We compare the local modes thus obtained with those generated by other schemes and find that they also provide a better description of the relevant vibrational subspace.Comment: 6 pages, ReVTeX, plus four postscript files for figure

High-temperature phase transitions in SrBi_2Ta_2O_9 film: a study by THz spectroscopy

Time-domain THz transmission experiment was performed on a $\rm SrBi_2Ta_2O_9$ film deposited on sapphire substrate. Temperatures between 300 and 923 K were investigated and complex permittivity spectra of the film were determined. The lowest frequency optic phonon near 28 cm$^{-1}$ reveals a slow monotonic decrease in frequency on heating with no significant anomaly near the phase transitions. We show that the dielectric anomaly near the ferroelectric phase transition can be explained by slowing down of a relaxational mode, observed in the THz spectra. A second harmonic generation signal observed in a single crystal confirms a loss of center of symmetry in the ferroelectric phase and a presence of polar clusters in the intermediate ferroelastic phase.Comment: subm. to J. Phys.: Condens. Matte

Bismuth radical catalysis in the activation and coupling of redox-active electrophiles

Radical cross-coupling reactions represent a revolutionary tool to forge C(sp3)–C and C(sp3)–heteroatom bonds, by means of transition metals, photoredox or electrochemical approaches. This study demonstrates how a low-valent bismuth complex is able to undergo one-electron oxidative addition with redox-active alkyl radical precursors in an autonomous manner, mimicking the behavior of first-row transition metals. This reactivity paradigm for bismuth gives rise to unique radical-equilibrium complexes, which could be fully characterized in solution and solid state. The resulting Bi(III)–C(sp3) intermediates display divergent reactivity patterns depending on the α-substituents of the alkyl fragment. Mechanistic investigations on this reactivity led to the development of a bismuth-catalyzed C(sp3)–N cross-coupling reaction that operates under mild conditions and accommodates synthetically relevant N-heterocycles as coupling partners

Magnetic superspace groups and symmetry constraints in incommensurate magnetic phases

Although superspace formalism has become the standard approach for the analysis of structurally modulated crystals, it has remained during the last thirty years almost unexplored as a practical tool to deal with magnetic incommensurate structures. This situation has recently changed with the development of new computer tools for magnetic phases based on this formalism. In this context we show here that, as in the case of nonmagnetic incommensurate systems, the concept of superspace symmetry provides a simple, efficient and systematic way to characterize the symmetry and rationalize the structural and physical properties of incommensurate magnetic materials. The method introduces significant advantages over the most commonly employed method of representation analysis for the description of the magnetic structure of a crystal. But, more importantly, in contrast with that method, it consistently yields and classifies all degrees of freedom of the system. The knowledge of the superspace group of an incommensurate magnetic material allows to predict its crystal tensor properties and to rationalize its phase diagram, previous to any appeal to microscopic models or mechanisms. This is especially relevant when the properties of incommensurate multiferroics are being studied. We present first a summary of the superspace method under a very practical viewpoint particularized to magnetic modulations. Its relation with the usual representation analysis is then analyzed in detail, with the derivation of important general rules for magnetic modulations with a single propagation vector. The power and efficiency of the formalism is illustrated with various selected examples, including some multiferroic materials

Large ferroelectric polarization in the new double perovskite NaLaMnWO6_{6} induced by non-polar instabilities

Based on density functional theory calculations and group theoretical analysis, we have studied NaLaMnWO$_{6}$ compound which has been recently synthesized [Phys. Rev. B 79, 224428 (2009)] and belongs to the $AA'BB'{\rm O}_{6}$ family of double perovskites. At low temperature, the structure has monoclinic $P2_{1}$ symmetry, with layered ordering of the Na and La ions and rocksalt ordering of Mn and W ions. The Mn atoms show an antiferromagnetic (AFM) collinear spin ordering, and the compound has been reported as a potential multiferroic. By comparing the low symmetry structure with a parent phase of $P4/nmm$ symmetry, two distortion modes are found dominant. They correspond to MnO$_{6}$ and WO$_{6}$ octahedron \textit{tilt} modes, often found in many simple perovskites. While in the latter these common tilting instabilities yield non-polar phases, in NaLaMnWO$_{6}$ the additional presence of the $A$-$A^{'}$ cation ordering is sufficient to make these rigid unit modes as a source of the ferroelectricity. Through a trilinear coupling with the two unstable tilting modes, a significant polar distortion is induced, although the system has no intrinsic polar instability. The calculated electric polarization resulting from this polar distortion is as large as $\sim$ 16 ${\mu}{\rm C/cm^{2}}$. Despite its secondary character, this polarization is coupled with the dominant tilting modes and its switching is bound to produce the switching of one of two tilts, enhancing in this way a possible interaction with the magnetic ordering. The transformation of common non-polar purely steric instabilities into sources of ferroelectricity through a controlled modification of the parent structure, as done here by the cation ordering, is a phenomenon to be further explored.Comment: Physical Chemistry Chemical physics (in press