One-dimensional Crystal Structure Research Articles

New linear and layered amine-templated lanthanum sulfates

Two new amine-templated lanthanum sulfates have been synthesized hydrothermally and structurally characterized by single-crystal X-ray diffraction. La(C 4H 16N 3)(SO 4) 3·H 2O crystallizes with triclinic symmetry, space group P-1 [ a=8.2800(1) Å, b=9.5755(2) Å, c=10.4439(2) Å, α=105.689(1)°, β=102.844(1)°, γ=104.372(1)°, V=734.12(2) Å 3, Z=2]. It displays a one-dimensional crystal structure, based on lanthanum atoms connected by the sulfate groups arranged in an helical manner. La 2(H 2O) 4(C 6H 14N 2) 2(SO 4) 5·5H 2O crystallizes with orthorhombic symmetry, space group Pna2 1 [ a=13.5972(1) Å, b=10.1920(1) Å, c=25.6079(3) Å, V=3548.81(6) Å 3, Z=4]. Its layered open structure is attained by the presence of organic cations, water molecules and isolated sulfate tetrahedra between the inorganic lanthanum sulfate sheets. The decomposition of the two phases proceed through dehydration stages and lead to lanthanum oxide sulfates.

Omnidirectional elastic band gap in finite lamellar structures.

This paper presents a comprehensive theoretical analysis of the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures. We discuss the conditions for a one-dimensional layered structure, made of elastic materials, to exhibit total reflection of acoustic incident waves in a given frequency range, for all incident angles and all polarizations. The property of omnidirectional reflection can be fulfilled with a simple finite superlattice if the substrate from which the incident waves are launched is made of a material with high acoustic velocities (this is very similar to the case of omnidirectional optical mirror where the incident light is generated in vacuum). However, if the substrate is made of a material with low acoustic velocities, we propose two solutions to obtain an omnidirectional band gap, namely, the cladding of a superlattice with a layer of high acoustic velocities, which acts like a barrier for the propagation of phonons, or the association in tandem of two different superlattices in such a way that the superposition of their band structures exhibits an absolute acoustic band gap. We discuss the appropriate choices of the material and geometrical properties to realize such structures. The behavior of the transmission coefficients are discussed in relation with the dispersion curves of the finite structure embedded between two substrates. Both transmission coefficients and densities of states (from which we derive the dispersion curves) are calculated in the framework of a Green's function method.

Omnidirectional phononic reflection and selective transmission in one-dimensional acoustic layered structures

We report the theoretical evidence for the occurrence of omnidirectional reflection in one-dimensional phononic crystal structures, namely, a layered periodic structure that may exhibit total reflection of waves for all incident angles and polarizations in a given frequency range “the omnidirectional band gap”. By introducing a defect layer in the finite-size layered structure, selective waves falling within this omnidirectional band gap may be transmitted through the structure. Such acoustic materials could be used for designing high-quality acoustic mirrors and filters in many frequency ranges of interest.

Solving Crystal Structures without Fourier Mapping. I. Centrosymmetric Case

A recursive algebraic procedure for solving one-dimensional monoatomic crystal structures is presented. (If applied to projections, also a three-dimensional atom arrangement may be reconstructed.) Moduli of the geometrical parts of the corresponding structure factors serve as experimental input. The atom coordinates are found from the roots of a polynomial. For space group P1¯ with m atoms in the asymmetric unit, the first m + 1 reflections are needed for finding their signs by means of a determinant technique. Using Monte Carlo calculations, the influence of the standard uncertainties of the data on the uncertainties of the derived coordinates is simulated. In a similar way, hints for discriminating between sign variations are obtained. The resolution in direct space is better than that of a one-dimensional Fourier summation over the same number of reflections. Error-free data provide a unique solution (if homometries are excluded). For data affected by experimental uncertainties, all possible solutions (compatible with the data) are found. Their number is always finite, and it may be further reduced by employing reflection orders higher than m + 1. Some applications of the method are discussed.

Magnetic-field-induced strong diamagnetic transition in the quasi-one-dimensional halogen-bridged platinum complex

dc magnetization measurements on the quasi-one-dimensional halogen-bridged platinum complex [Pt(en${)}_{2}$][Pt(en${)}_{2}$${\mathrm{I}}_{2}$](${\mathrm{ClO}}_{4}$${)}_{4}$ (where en is ethylenediamine) reveal a magnetic-field-induced strong diamagnetic transition at fields above 20 kOe. The diamagnetic signals are as large as 3.5--72% of complete diamagnetism and show large fluctuations. A sharp diamagnetic-paramagnetic transition occurred around 180 K. There is no anisotropy visible in the diamagnetic behavior, in contrast to the one-dimensional electronic and crystal structure of this material.

Energy transfer in Li 6Gd(BO 3) 3

The synthesis and structure of the new one-dimensional material Li 6Gd(BO 3) 3 are described. The Gd 3+ fluorescence is studied from 300 to 1.5 K after selective pulsed excitation into the 6 P 7 2 manifold. Above 40 K the fluorescence decays indicate fast diffusion of the energy among intrinsic and perturbed Gd 3+ ions, and trapping by impurities. Below 40 K the energy transfer takes place dominantly towards perturbed Gd 3+ ions and is diffusion limited. This behaviour is discussed in relation with the quasi one-dimensional crystal structure.

Calculations of one-dimensional a periodic chains in the self-consistent virtual crystal approximation with random diagonal and off-diagonal elements

It is shown that the average matrix method developed earlier is identical with a self-consistent virtual crystal approximation at the Hartree-Fock level with random diagonal and off-diagonal elements. The method proposed for the calculation of approximate band structures of one-dimensional polymers and molecular crystals with compositional disorder was programmed in the CNDO/2 (complete neglect of differential overlap) approximation. Numerical results for different iso-electronic model systems show that the method yields reliable results if the different units differ not too much in the number of atoms and basis orbitals and that the general features of clustering effects are reproduced.

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

Molecular orbital theory of the electronic structures of one-dimensional molecular crystals

A non-empirical tight-binding LCAO SCF MO treatment of one-dimensional molecular crystals based on the SCF perturbation theory is presented. The simpler version of this method at the level of the CNDO/2 approximation is also given.