One-dimensional Disorder Research Articles

One-dimensional surface states (chain states) on a metal surface: H on Ni(110).

H adsorption on Ni(110) at sample temperatures ${\mathit{T}}_{\mathit{S}}$>200 K is known to result in a one-dimensionally disordered surface exhibiting a missing/added row reconstruction with irregular row-to-row spacing but long range periodicity along the rows. Inverse photoemission shows an unoccupied surface state with wave vector perpendicular to the rows being completely quenched due to the one-dimensional disorder. In contrast, an unoccupied surface state propagating along the rows is not attenuated at all. This indicates that the latter is a one-dimensional chain state, localized to individual atom rows.

X-ray diffraction study of one-dimensionally disordered structure formation in Co-based alloys

Formation of one-dimensionally disordered (ODD) structures with non-random distribution of growth stacking faults (SF's) in Co-based alloys has been investigated by X-ray diffraction. It has been found that the usual process of growth of coarse crystals with fairly perfect h.c.p. lattice in pure Co is substituted for the accumulation of numerous thin non-randomly distributed lamellae with a h.c.p. structure in doped Co. This results in the growth SF's formation as isolated cubic type planes, clamped by neighbouring lamellae. The character of the SF's distribution in the final ODD structure is determined by ordering of the lamellae in the initial stages of the transformation.

The use of synchrotron radiation X-ray diffraction topography to determine the spatial distribution of polytypes and one dimensional disorder in SiC

Abstract Novel experimental techniques are described for studying the spatial distribution of polytypes in multipolytypic SiC crystals. These methods provide information on adjoining long-period polytypes and the intervening boundaries and their relationship to one-dimensional disorder. With the improved resolution of second-generation synchrotrons it is now possible to unravel complex multipolytype edge profiles. These are revealing previously unseen features, such as high defect density bands and fine one-dimensionally disordered layers at polytype boundaries.

Crystal structure, morphology and chemical reactivity of Tl xV 5S 8

Single crystal X-ray work reveals that with decreasing Tl content the anisotropic displacement parameter (ADP) U 22 increases indicating modified interatomic interactions of the Tl atoms, an enhanced mobility or static disorder. Furthermore, it is demonstrated that with decreasing temperature the one-dimensional disorder of the Tl atoms increases. Time dependent topotactic removal of Tl using molecular iodine in donor solvents proceeds in two steps: a relatively fast step is followed by a slow diffusion controlled reaction. About 20% of the Tl is removed within the first 60 min. After about 13 d the composition Tl 0.3V 5S 8 was reached. Further reaction results in the formation of a mixture of Tl 0.3V 5S 8 and V 5S 8. The reaction product between I 2 and Tl was identified as TlI 3 which demonstrates that Tl in Tl x V 5S 8 is in a formal oxidation state clearly below +1. The host material V 5S 8 is not attacked by I 2 as could be demonstrated by SEM. These observations imply that the vanadium sulfide is not directly involved in the redox reaction. With decreasing Tl abundance the internal mechanical stress due to anisotropic changes of the lattice parameters is increased resulting in an increased brittleness of the crystals. X-ray powder diffractometry was found to be a useful analytical tool to quantitatively determine the Tl content without destroying the sample.

Towards a unified view of polytypism in silicon carbide

Abstract In this study, a detailed survey has been made of 200 silicon carbide crystals grown by the modified Lely technique. All 200 crystals were examined using, at minimum, the combination of X-ray oscillation photography and one synchrotron topograph. This has now produced a reliable and unique database on polytypism, one-dimensional disorder, defect content, and in particular their spatial relationships. Over half (114) the crystals were multi-polytypic, some 37 displaying complex polytype combinations of which 16 included a long-period phase. For some 32 crystals, where shape and size permitted, synchrotron edge-reflection topographs could be obtained leading to depth profile models of the polytype content; 9 of these have shown up a very interesting class of configuration, the idealised form being termed a ‘sandwich’ in which a longer-period polytype layer inside the crystal is surrounded each side by shorter-period polytypes: the reverse configuration, or long-period polytype layers existing on th...

Confinement of vibration by one-dimensional disorder, II: A numerical experiment on different ensemble averages

When producing theoretical estimates of the effect of irregularity on the vibrational behaviour of a structure, as has been described previously [1–3], one aims to predict the behaviour of a typical irregular structure within the set considered. It might be thought that this would correspond to the ensemble-averaged behaviour over the whole set, but this need not be the case. In fact there are several different possible ways of taking “the” ensemble average, which can produce remarkably different results. Some of these do indeed correspond to the typical member of the ensemble, but some of them certainly do not, since rare configurations giving very large contributions to the average distort the answer. This problem is investigated here via a numerical experiment on a very simple system: the object is to complement the discussion in a companion paper [4], which gives theoretical analysis. The aims here are threefold: to know which average is the most appropriate in a given context; to understand why the other averages are different; and to identify the anomalous configurations making them different so that these can be avoided in designing real structures. A by-product is a better understanding of the averaging procedures used in the past—it has not always been recognized that these various averages can give radically different answers, and one can find instances where what was used was perhaps the easiest approach rather than the most appropriate one. In addition, the numerical experiment described here gives a good illustration of the basic phenomenon of Anderson localization in an acoustic context.

Confinement of vibration by one-dimensional disorder, I: Theory of ensemble averaging

The use of ensemble averaging procedures in studying the dynamics of structurally irregular mechanical systems is discussed. It is found that taking a linear average over the ensemble does not always yield the behaviour of a “typical” member of that ensemble. Under certain circumstances there are occasional members with properties so exceptional as to weight the average appreciably, and the linear ensemble average can then be seriously misleading. The effect is illustrated by the response and transmission properties of two simple mechanical models, a system of coupled oscillators with varying natural frequencies, and a vibrating string or bending beam with irregularly spaced mass and spring constraints. The distinction between the ensemble average and the typical value is important in understanding the phenomenon of Anderson localization described previously [1–3] by using these two models. This paper provides some analytic results, while an accompanying paper [4] provides complementary results from a numerical study of the coupled-oscillator model.

Split solitons in the incommensurate and streaked phases of W(001)/H surfaces

Anomalous features in the infrared absorption spectrum of W(001)/H surfaces at hydrogen coverages θ ⪸ 0.37 are explained in terms of a split-soliton form of amplitude modulation of the incommensurate order parameter, the M5 surface phonon mode. At higher coverages, θ ⪸ 0.5, the wandering and overlap of split-soliton-type domain walls predominates, leading to the observed one-dimensional disorder on the surface.

One-dimensional disorder in spinach ribulose bisphosphate carboxylase crystals

X-ray diffraction photographs of the crystalline ternary complex of spinach ribulose 1,5-bisphosphate carboxylase/oxygenase (rubisco) with activators Mg2+ and CO2 diffract to high angle while showing diffraction features symptomatic of disorder. Oscillation photographs about the c* axis taken with a conventional source and collimation show streaks of intensity along c*. These intensity streaks can be resolved into satellite reflections, with underlying diffuse scattering, by employing synchrotron radiation with slits limiting the horizontal beam convergence from the monochromator and fine collimation. The disorder is discussed in terms of stacking faults between layers of molecules. The space group of a regular stack of layers, repeating every layer, would be C2. The observed space group C2221, repeating every alternate layer, is due to the statistical 'back-to- back' arrangement of cells of C2 symmetry. Three models are used to predict various features of the diffraction by these crystals. The first model, with every layer randomly shifted by either a/39 or -a/39 with respect to the previous layer, predicts constant intensity streaks for the maximally affected reflections. A rectangular modulation of odd layers within a framework of even layers predicts satellite reflections for these reflections. A random distribution of these layers predicts broadening of the affected reflections. The observation of superlattice reflections and broadening is best accounted for by considering an approximate superlattice which produces the satellite reflections with both deviations in period and by additional shifts of ± a/39 leading to the diffuse features.

Neutron diffraction study of potassium-graphite intercalation compounds at high pressure: Staging transitions and one-dimensional disorder.

Detailed (00L) neutron scattering profiles have been measured versus hydrostatic pressure (0P20 kbar) at room temperature for potassium-graphite intercalation compounds ${\mathrm{KC}}_{\mathrm{x}}$ with 8x40. The average density of filled galleries along the c axis decreases with increasing P, implying a concomitant increase in the (average) areal K density within a gallery. We observe both large P regions exhibiting continuous evolution of different stages, and narrow P regions where the average stage changes abruptly. The Hendricks-Teller model of one-dimensional disorder is used to fit entire diffraction profiles over extended q ranges. Some of the high-P staging and disorder effects are attributable to P-induced in-plane intercalate densification, the sequence of gallery occupancy and its perfection being a secondary consequence. Other features are entirely controlled by interlayer interactions: e.g., a pure stage-4 phase evolves asymptotically with increasing P at 6--7 kbar for 36x39, whereas a commensurate 2\ifmmode\times\else\texttimes\fi{}2 in-plane density would be compatible with a pure stage-4 phase only for x=32.0. We demonstrate from the fits that the fractional stage-(3/2) phase in ${\mathrm{KC}}_{8}$, reported earlier by us to occur between 15 and 19 kbar, exhibits c-axis correlations no worse than other high-P phases, indicating that this unusual structure represents a true equilibrium phase and does not result simply from random layer sequencing.

Temporal intensity variations in RHEED patterns during film growth of GaAs by MBE

Observations of the intensity oscillations for various features in RHEED patterns during MBE growth of GaAs, GaAlAs and Ge are reported and correlated with the mechanism of crystal growth. Growth is predominantly by a two-dimensional layer-by-layer mechanism, but there is evidence of roughening, probably on a scale by a few monolayer step heights and this may be enhanced by the presence of impurities and deviations from stoichiometry. For GaAs(001)-(2×4) reconstructed surfaces, a combination of dynamic and static RHEED observations provides clear evidence for the presence of one-dimensional disorder as well as surface steps. The cababilities and future potential of time varying RHEED observations during film growth will be discussed.

β-NbBr5, eine neue Modifikation von Niobpentabromid mit einer eindimensionalen Lagenfehlordnung/ β-NbBr5, a New Modification of Niobium Pentabromide Having One-Dimensional Stacking Disorder

Abstract While trying to react NbBr5 with sulfur in a closed tube, crystals of the new modification β-NbBr5 were obtained. Its X-ray diffraction patterns have sharp reflexions and diffuse streaks showing the presence of a one-dimensional disorder. From the sharp reflexions alone, a statistically averaged sub-structure results; it has the space group Ccmm and the lattice constants a0 = 644, b0 = 1867 and c0 = 615 pm. Taking into account the diffuse streaks, the true structure was deduced; its lattice constants are a = 2a0, c = Co, b indefinite due to the disorder. β-NbBr5 is isostructural to tantalum pentaiodide. It consists of layers of (NbBr5)2 molecules that are stacked with displacement faults in the direction of b. The bromine atoms have a hexagonal close-packing arrangement.

Dynamics of film growth of GaAs by MBE from Rheed observations

Detailed observations have been made of the intensity oscillations in the specularly reflected and various diffracted beams in the RHEED pattern during MBE growth of GaAs, Ga x Al1−x As and Ge. The results indicate that growth occurs predominantly in a two-dimensional layer-by-layer mode, but there is some roughening, which is enhanced by deviations from stoichiometry and the presence of impurities. In the case of the GaAs (001) −2×4 reconstructed surface a combination of dynamic and static RHEED measurements has provided firm evidence for the presence of one-dimensional disorder features as well as surface steps.

GaAs(001)−c(4×4): A chemisorbed structure

We have carried out an experimental study of the As-stable $\mathrm{GaAs}(001)\ensuremath{-}c(4\ifmmode\times\else\texttimes\fi{}4)$ reconstruction using a combination of molecular-beam epitaxy with reflection electron diffraction, angle-resolved photoemission, and surface-sensitive core-level photoemission. (The measurements were performed at Laboratoire pour l'Utilisation du Rayonnement Electromagn\'etique, Universit\'e Paris---Sud, F-91405 Orsay, France.) Apart from the surface symmetry, the electron-diffraction data show one-dimensional disorder along the [110] direction, probably corresponding to a corrugated-sheet structure in reciprocal space. Photoemission from surface states having dangling-bond character shows a onefold periodicity and an energy dispersion of 0.65 eV along [110], while along [$\overline{1}10$] the dispersion is much smaller, but there is a doubling of the periodicity. Observations of the $\mathrm{As}3d$ and $\mathrm{Ga}3d$ core levels show a surface $\mathrm{As}3d$ component at 0.62 eV higher binding energy than the bulk component, indicative of As---As bonding. The $\mathrm{Ga}3d$ surface core-level shift is very small and the line shape is similar to that from the (2 \ifmmode\times\else\texttimes\fi{} 4) surface. The experimental results can be understood on the basis of an As overlayer structure, for which we propose specific models derived from trigonally bonded chemisorbed As.

X-Ray Diffraction and Transmission Electron Microscopy Study of One-Dimensional Disorder Polytypes in SiC

Silicon carbide crystallizes into several structural modifications whose c-periodicities vary from 1 nm to more than 100 nm. Its high period structures are found to consist of intergrowth of smaller period structures at the unit cell level. The X-ray diffraction studies show that SiC crystals often possess one-dimensional disorder which is characterized by continuous streaks in X-ray diffraction patterns along ho.1 reciprocal lattice rows. However, it is shown that these streaks can also arise as a result of extremely high c-periodicities of the crystals as their ho.1 spots cannot be resolved easily. This contribution reports the observation of only few representative cases of so-called one-dimensional disordered crystals as observed in their X-ray and electron diffractions with lattice imaging.

Electrical resistivity of an exactly solvable random model exhibiting a smeared phase transition

The effect of impurities on the critical behaviour of the electrical resistivity due to spin-electron scattering is investigated within the context of the random mean spherical model, an exactly solvable model with one-dimensional disorder, exhibiting a smeared phase transition due to Griffiths singularities. It is shown that the singular part of the temperature derivative of the resistivity will have the same behaviour as the specific heat at the transition point, a relationship that is not self-evident for random systems.

X-ray topography study on imperfections in synthetic mica (fluorophlogopite) crystal

The X-ray diffraction topography study of imperfections in synthetic mica (fluorophlogopite) crystal is reported. The main defects in synthetic fluorophlogopite crystal are one-dimensional disorder, sub-grain boundaries and dislocations. The orientations of the sub-grain boundaries and dislocations are normal to the growth front. Many defects in synthetic micas originate from the seed crystal. By controlling the orientation of the seed crystal, large-sized fluorophlogopite crystals with almost no central defects have been synthesized. In view of its excellent chemical and electrical properties, flat surface and strong X-ray diffraction intensity, large-sized fluorophlogopite crystal will find many important applications in various fields.

Studies on the compounds in BaFeS system. II. Disordered intergrowth structure in [formula omitted] observed by electron microscopy

Shattered crystallites of Ba 3 Fe 1+x S 5 ( 1 3 ≤ x ≤ 2 5 ) were examined by electron microscopy. Both β-Ba 9Fe 4S 15 ( x = 0.333) and Ba 15Fe 7S 25 ( x = 0.40), previously reported members of Ba 3 p Fe q S 5 p series, were identified by electron diffraction patterns, and supercell periodicities, 25.5 Å ( ⋍3a 0 ) and 42.0 Å ( ⋍5a 0 ), respectively, were resolved as lattice fringes. Some crystals with intermediate compositions showed electron diffraction patterns with diffuse superlattice reflections. Their lattice fringe patterns showed a microscopic disordered intergrowth structure consisting of three periodicities, 3 a 0, 5 a 0, and 4 a 0. The intergrowth structure is a disordered one and can be analyzed based on the one-dimensional disorder model of Fe occupation in the hexagonal rings of the Ba 3S 5 framework. It is also characteristic of the “microsyntactic” intergrowth.

Elastic diffuse neutron scattering due to D-D correlation functions seen in Ih ice

Elastic diffuse neutron scattering in the hhl plane of Ih ice at 120K is consistent with the random-walk approximation model reflecting Bernal-Fowler ice rules. Additional diffuse l-streaks were found, indicating a further one-dimensional disorder.

A X-RAY STUDY OF IMPERFECTION IN SYNTHETIC FLUOROPHLOGOPITE CRYSTAL

This paper describes the results of X-ray study of imperfection in the single crystal of large area synthetic fluorophlogopite. By using X-ray Laue method, it is showed that in synthetic mica there is a greater degree of one-dimensional disorder, and therefore there are a number of disarranged regions of stacking sequence and their boundaries. The X-ray diffraction topography method shows that most of sub-grain boundaries and dislocations originate from the seed and run normal to the growth surfaces. The density of crystal defects in the region near the crystal surface is greater than that in the center. The difference in the distribution of defects between synthetic mica and natural mica was investigated. The relationships between defects in synthetic mica plate and their performances as used to construct condenser were also studied and discussed.