Retrieval of the atomic displacements in the crystal from the coherent X‐ray diffraction pattern

The retrieval of spatially resolved atomic displacements is investigated via the phases of the direct(real)‐space image reconstructed from the strained crystal's coherent X‐ray diffraction pattern. It is demonstrated that limiting the spatial variation of the first‐ and second‐order spatial displacement derivatives improves convergence of the iterative phase‐retrieval algorithm for displacements reconstructions to the true solution. This approach is exploited to retrieve the displacement in a periodic array of silicon lines isolated by silicon dioxide filled trenches.     

Approximating the number of monomer-dimer coverings of a lattice

We study the problem of counting the number of coverings of ad-dimensional rectangular lattice by a specified number of monomers and dimers. This problem arises in several models in statistical physics, and has been widely studied. A classical technique due to Fisher, Kasteleyn, and Temperley solves the problem exactly in two dimensions when the number of monomers is zero (the dimer covering problem), but is not applicable in higher dimensions or in the presence of monomers. This paper presents the first provably polynomial-time approximation algorithms for computing the number of coverings with any specified number of monomers ind-dimensional rectangular lattices with periodic boundaries, for any fixed dimensiond, and in two-dimensional lattices with fixed boundaries. The algorithms are based on Monte Carlo simulation of a suitable Markov chain, and, in constrast to most Monte Carlo algorithms in statistical physics, have rigorously derived performance guarantees that do not rely on any assumptions. The method generalizes to counting coverings of any finite vertex-transitive graph, a class which includes most natural finite lattices with periodic boundary conditions.     

Electronic and optical properties of CdS/CdZnS nanocrystals

Cd1-x ZnxS nanocrystals are prepared by a co-precipitation method with different atomic fractions of Zn.The texture,structural transformation and optical properties with increasing x value in Cd1-x ZnxS are studied with scanning electron microscopy,electron diffraction patterning,and absorption spectra respectively.Quantum confinement in a strained CdS/Cd1-xZnxS related nanodot with various Zn content values is investigated theoretically.Binding energies on exciton bound CdS/CdxZn1-xS quantum dot are computed,with consideration of the internal electric field induced by the spontaneous and piezoelectric polarizations,and thereby the interband emission energy is calculated as a function of the dot radius.The optical band gap from the UV absorption spectrum is compared with the interband emission energy computed theoretically.Our results show that the average diameter of composite nanoparticles ranges from 3 nm to 6 nm.The X-ray diffraction pattern shows that all the peaks shift towards the higher diffracting angles with an increase in Zn content.The lattice constant gradually decreases as the Zn content increases.The strong absorption edge shifts towards the lower wavelength region and hence the band gap of the films increases as the Zn content increases.The values of the absorption edge are found to shift towards the shorter wave length region and hence the direct band gap energy varies from 2.5 eV for the CdS film and 3.5 eV for the ZnS film.Our numerical results are in good agreement with the experimental results.     

Asymptotic properties of multistate random walks. I. Theory

A calculation is presented of the long-time behavior of various random walk properties (moments, probability of return to the origin, expected number of distinct sites visited) formultistate random walks on periodic lattices. In particular, we consider inhomogeneous periodic lattices, consisting of a periodically repeated unit cell which contains a finite number of internal states (sites). The results are identical to those for perfect lattices except for a renormalization of coefficients. For walks without drift, it is found that all the asymptotic random walk properties are determined by the diffusion coefficients for the multistate random walk. The diffusion coefficients can be obtained by a simple matrix algorithm presented here. Both discrete and continuous time random walks are considered. The results are not restricted to nearest-neighbor random walks but apply as long as the single-step probability distributions associated with each of the internal states have finite means and variances.     

Growth and characterisation of single grain Al-Cu-Ru icosahedral quasicrystals from self-fluxes

ABSTRACT

In order to obtain high-quality single grains of the Al-Cu-Ru icosahedral quasicrystal (iQC), suitable for a structure analysis, the crystal growth conditions with the self-flux method have been studied. The melts of the master alloys with the compositions of Al_57.0+xCu_39.5-xRu_3.5 (x?=?0, 2.5, 5, 7.5, 10) and Al_62.0Cu_34.0+y Ru_4.0-y (y?=?0, 0.5, 1.5) were held at 1150°C for 2?h, then cooled down to 800, 900, or 1000°C at a rate of ?2?K/h, and subsequently retained for various durations, up to 750?h. Single grain iQCs having several millimetre-sizes, which were evaluated their quality by powder X-ray diffraction (XRD), were grown throughout this study. The peak of (664004) reflection in powder XRD of the iQCs grown at 1000°C has approximately 50% narrower width than that grown at 800°C. The inhomogeneity of the compositions intra- as well as inter-grains grown at 800°C was observed. High-quality single grains with homogeneous composition could be achieved with a long-time annealing at 900°C or regardless of the annealing time at 1000°C. By changing the Al/Cu ratio of the master alloys, the composition could also be controlled for the iQCs grown at 1000°C. Single-crystal XRD experiment with synchrotron radiation on Al_66.6Cu_16.4Ru_17.0 iQC, grown at 1000°C, resulted in the collection of 2680 independent Bragg reflections that confirms the high-quality of the sample. The phase retrieval of the diffraction data resulted successfully in obtaining the structure solution, which reveals some characteristic features of this face-centred iQC structure.     

Decagonal quasicrystals

Following the discovery of two dimensional quasicrystals in rapidly solidified Al-Mn alloys by us and L. Bendersky in 1985, a number of fascinating studies has been conducted to unravel the atomic configuration of quasicrystals with decagonal symmetry. A comprehensive mapping of the reciprocal space of decagonal quasicrystals is now available. The interpretation of the diffraction patterns brings out the comparative advantages of various indexing schemes. In addition, the nature of the variable periodicity can be addressed as a form of polytypism. The relation between decagonal quasicrystals and their crystalline homologues will be explored with emphasis on Al₆₀Mn₁₁Ni₄ and ‘Al₃Mn’. It will also be shown that decagonal quasicrystals are closely related to icosahedral quasicrystals, icosahedral twins and vacancy ordered phases.     

Zur spektralen Verteilung der Turbulenzenergie und ihrer Komponenten in turbulenten Grenzschichten

On the Spectral Distribution of Turbulent Energy and Components in Turbulent Boundary Layers KOLMOGOROV 's theory of the inertial subrange of energy spectrum is presented for turbulent boundary layers. As a consequence KOVASZNAY 's formula for the transfer of kinetic energy is confirmed. It is shown that the structure of the turbulent transfer of momentum in boundary layers is analogous to the structure of the transfer of kinetic energy in the spectrum. For the spectral distribution of the turbulent shear stress in the subrange a k^?3 law (k wave number) – apparently in agreement with measurements – is derived from dimensional arguments. It follows that the exchange of energy among the components of turbulent energy in the subrange is some orders of magnitude smaller than the latter.     

Exchange‐Biased Fe3−xO4‐CoO Granular Composites of Different Morphologies Prepared by Seed‐Mediated Growth in Polyol: From Core–Shell to Multicore Embedded Structures

Magnetically contrasted granular hetero‐nanostructures are prepared by seed‐mediated growth in polyol, properly combining two oxide phases with different magnetic order, ferrimagnetic (F) partially oxidized magnetite Fe_3−xO₄ and antiferromagnetic (AF) cobalt oxide. Spinel Fe_3−xO₄ nanoparticles are first synthesized and then used as seeds for rock salt CoO nanocrystals growth. Three different hetero‐nanostructure designs are realized, acting on the content ratio between the seeds and the deposit's precursors during the synthesis. For all of them, the spinel and the rock salt phases are confirmed by X‐ray diffraction and high‐resolution transmission electron microscopy. Both phases are obtained in high‐crystalline quality with a net epitaxial relationship between the two crystallographic lattices. Mössbauer spectrometry confirms the cobalt cation diffusion into the spinel seeds, giving favorable chemical interfacing with the rock salt deposit, thus prevailing its heterogeneous nucleation and consequently offering the best condition for exchange‐bias (EB) onset. Magnetic measurements confirm EB features. The overall magnetic properties are found to be a complex interplay between dipolar interactions, exchange anisotropy at the F/AF interface, and magnetocrystalline anisotropy enhancement in the F phase, due to Co²⁺ diffusion into iron oxide's crystalline lattice. These results underline the powerfulness of colloidal chemistry for functional granular hetero‐nanostructured material processing.     

Local magnetic field distributions in superconducting niobium at 4.2 K by neutron diffraction

Neutron diffraction experiments on flux line lattices in superconducting Nb are reported. From the integral reflectivities of the (10), (11), (20), (21) and (31) reflections the absolute values of the formfactors were obtained as a function of the flux density. Considering certain properties of the flux line lattice it is also possible to determine the phases of the formfactors. From this the local field distribution in the mixed state could be calculated by Fourier-transformation. The dependence of the resulting maximum, minimum, and saddle point fields on the flux density and on the impurity parameter is discussed and compared with theory.     

Symmetry of electrostatic interaction between pyrophosphate DNA molecules

We study chiral electrostatic interaction between artificial ideal homopolymer DNA-like molecules in which a number of phosphate groups of the sugar-phosphate backbone are exchanged for the pyrophosphate ones. We employ a model in which the DNA is considered as a one-dimensional lattice of dipoles and charges corresponding to base pairs and (pyro)phosphate groups, respectively. The interaction between molecules of the DNA is described by a pair potential U of electrostatic forces between the two sets of dipoles and charges belonging to respective lattices describing the molecules. Minima of the potential U indicate orientational ordering of the molecules and thus liquid crystalline phases of the DNA. We use numerical methods for finding the set of minima in conjunction with symmetries verified by the potential U . The symmetries form a non-commutative group of 8th order, S . Using the group S we suggest a classification of liquid crystalline phases of the DNA, which allows several cholesteric phases, that is polymorphism. Pyrophosphate forms of the DNA could clarify the role played by charges in their liquid crystalline phases, and open experimental research, important for nano-technological and bio-medical applications.     

The problem of the structural characterization of nanoobjects: Incommensurate reflections and diffraction averaging

It is shown that two outwardly conflicting diffraction effects observed in ordering compositions with nanodimensional antiphase domains are of the same nature. The first effect manifests itself in the depression of some of superstructure reflections; the second is associated with the appearance of extra reflections incommensurate with the composition’s structure. The effects are stimulated by changes in the phases of scattered waves upon transitioning through antiphase boundaries.     

Crystal structure of the high pressure phases of bismuth bi iii and bi iii′ by high energy synchrotron x-ray diffraction

Abstract

This paper reports the results of a synchrotron X-ray diffraction study on the crystal structures of Bi 111 and Bi 111′ which have been known to form under high pressure but have, for a long time, been unsolved. Powdered samples were compressed in a cubic-type multi-anvil press, MAXID, and diffraction data were collected using an Imaging Plate with monochromatized radiation of an energy of 49.7 keV. It was possible to identify at 3.8 GPa forty-eight reflections for Bi I11 in the sin θ / δ range from 1.6 nm^?1 to 5.6 nm^?1, which were indexed in terms of a tetragonal unit cell with a=0.8659 nm and c═ O·4238 nm (2=10). Analysis based on the observed intensities of the reflections led to a structure in which atoms form a distorted body-centered cubic lattice. It is of the same type as the structure of the high pressure phase of antimony Sb 11. When pressure was increased across the suggested transition pressure 4.3 GPa between Bi III and Bi III′ to 6.6 GPa, no change in the diffraction pattern was observed, indicating that there is no distinction between the two phases as long as the crystal structure is concerned. Discussion is given on the sequence of high pressure phase transitions in the Group Vb elements.     

Critical behavior of three-state Potts model on decagonal covering quasilattice

The three-state Potts model on a 2D decagonal covering quasilattice is investigated by means of the Monte Carlo simulation. The periodic boundary conditions are realized on a rhombus-like covering pattern. By use of the finite-size scaling analysis, we obtain the critical temperature and the critical exponents. The critical temperature is higher than that of the square lattice mainly due to the larger mean coordination number of the covering model. The critical exponents are close to the corresponding values of the 2D periodic lattices, which means that the Potts model on the covering structure may belong to the same universal class as that of the periodic lattices.     

Interaction potentials for diffraction of a He atom by a NaCl(001) surface

There exist two quite different sets of experimental results for the He-NaCl(001) interaction potential, inferred from bound-state resonance measurements of associated ⁴He-NaCl(001) bound-state energies E_n: Frankl's group has found a lowest bound-state energy E₀ ≈ −4.1 meV, whereas Benedek's group has found evidence of a deeper interaction potential well, with E₀≈ −7.2 meV. Furthermore, there are strong physical arguments for the existence of the deeper well. In the present paper, interaction potentials, based on empirical pairwise He-Na⁺ and He-Cl⁻ interactions, for diffraction of a He atom by a NaCl(001) surface are considered. Comparisons of close-coupling diffraction calculations with experimental data of Frankl's group are made, and values of the empirical parameters are inferred. On the basis of these comparisons, it is concluded that the lowest bound state proposed by Benedek's group is absent, and that the correct bound-state energies are those proposed by Frankl's group.     

Binary phase gratings for star couplers with high splitting ratio

Binary phase transmission gratings exhibiting a certain number N of central diffraction orders of equal intensity can be used to construct star couplers of the 1-to-N and N-to-N type. The calculation of the grating's groove structure is described, and first experimental results are presented.     

Solitons in PT–symmetric optical lattices with spatially periodic modulation of nonlinearity

We study the existence and stability of solitons forming in PT–symmetric optical lattices with spatially periodic modulation of the local strength of the nonlinear media. We found that the spatial modulation of the nonlinearity significantly affects the stability of solitons in PT–symmetric optical lattices. With the decrease of the strength of nonlinear refractive index modulation, the soliton's stability domain increases, whereas with the increase of the period of nonlinear refractive index modulation, the corresponding soliton's stability range narrows. In addition, we also investigate the influence of variation of the amplitude of the linear PT–symmetric lattice potential on soliton dynamics, in the presence of spatially periodic modulation of nonlinearity.     

MBE[(GaAs)l(Ga1-λAlxAs)m]n/GaAS(001)一维超晶格的X射线双晶衍射测量

本文着重介绍了MBE[(GaAs)l(Ga1-xAlxAs)m]n/GaAs(001)一维超晶格的X射线双晶衍射测量方法。根据卫星峰的出现,证明超晶格的存在。基于超晶格的台阶模型和X射线衍射的运动学理论,推导出超晶格多结构参数的计算方法。并对X射线双晶给出的其他信息做了必要的讨论。     

Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Structure analysis of multiphase systems by anomalous small-angle X-ray scattering

The theory of small-angle scattering is reviewed with special attention paid to the anomalous scattering and multiphase systems. A general equation is derived that describes the scattering of a multiphase system as a sum of scattering functions of each of the phases, as if it scattered alone in a two-phase system, and interphase interference scattering functions. These scattering functions depend only on the spatial distribution of the phase boundaries, but not on the scattering density. Contrast variation techniques are most rewarding when the scattering density of only one phase can be varied. For anomalous small-angle X-ray scattering (ASAXS), this means the most favourable is the case in which resonant atoms are contained in one phase only. The general equation involves n(p ? 1) unknown partial atomic number density differences, where p is the number of phases and n the number of the different atom types in the sample. These partial atomic number density differences can be found if a suitable structure model is applied to calculate the phase scattering functions. Then, the phase compositions and densities can be calculated by solving a system of linear equations incorporating the atom number conservation law. The partial structure factors formalism is also reviewed. Corresponding equations for a system of n types of atoms and p phases are derived. The number of independent partial structure factors is p(p ? 1)/2 and depends on the number of phases, but not on the number of the types of the atoms in the sample, as in the case of wide-angle scattering.     

Planar defects in the icosahedral phase in quasicrystal-forming AlCuFe alloys

Electron microscopy has revealed that, upon the formation of a stable icosahedral (i) AlCuFe phase, there arise a large number of planar defects. The revealed defects are nanometer-sized coherent intergrowths of the P1-pentagonal approximant. It has been found that the formation of these defects is the result of a nonequilibrium intermediate transformation. The intergrowths are located in the planes with the fivefold symmetry axis and give rise to an elastic-strain state of the i-phase. Analysis of the diffraction contrast has revealed the presence of phason and phonon atomic displacements due to the mismatch between the quasiperiodic (i-phase) and periodic (P1-phase) lattices. The formed structure exhibits a higher electrical resistance as compared to the i-phase and has been considered as a model state of the imperfect icosahedral phase with preferred phonon displacements.