Discrete Atoms Research Articles

Dynamics of a frustrated rare gas monolayer adsorbed on a corrugated substrate: resonance and hybridization of the dispersion curves of Ar on MgO(100)

The coupled dynamics of a partially commensurate monolayer with several adsorption sites on a vibrating corrugated substrate has been determined using Green function formalism. The approach is well-adapted to physisorption mechanisms. To evaluate the static properties, both the layer and the substrate are described in terms of discrete atoms whereas the substrate dynamics is considered to be that of an elastic continuum coupled to the discrete monolayer. Numerical evaluation has been performed for the 3 × 2 Ar layer on the square substrate MgO(100). Resonances and avoided crossings of the dispersion curves of the total system are studied in that case. It is shown that hybridization processes between surface acoustic branches of the substrate and the twelve dispersion curves of the monolayer are highly selective depending on the nature (quasi-acoustical, transverse or perpendicular quasi-optical) of the branches.

Crystal structure of a novel mixed valence MoV–MoVIheteropolymolybdate cluster: [H3O+]6[Mo57V6O183(NO)6(H2O)18]6–·89H2O

Reaction of sodium molybdate (Na2MoO4·2H2O) and ammonium metavanadate (NH4VO3) with hydroxylamine hydrochloride results in the formation of the title compound, which consists of three 19-molybdate subunits being connected by six VO6 octahedra, and six bridging water molecules; both the manner of linking of the VO6 octahedra to the 19-molybdate subunit and the formation of a polymetallate cluster containing 57 discrete Mo atoms, are hitherto unknown features.

Do Eve's alleles live on?

Consider a random sample of genes at a locus, drawn from a population evolving according to the infinitely many, neutral, alleles model. The sample will have a most recent common ancestor gene, which we shall call 'Eve'. The probability distribution, for the number of genes of oldest allelic type in a sample, is known and has a neat form. Rather less is known about the distribution for the number of genes in the sample which are of the same allelic type as Eve possessed. If the latter number is positive, then these genes are automatically of the oldest type in the sample. But Eve may have no non-mutant descendants in the sample; then, the oldest allele will be a mutant arising in a line of descent after Eve. The paper studies the number of non-mutant descendants from Eve, its distribution and moments. It seems that there may be few neat results. In large samples, the proportion of genes of Eve's type has an approximate beta-like density, together with a discrete probability atom at zero, if the mutation rate parameter is low. Extinction of the allele of even the population's common ancestor is possible, but not certain, and bounds are obtained for its probability. Some comments are made about the applications and implications of the results for human mitochondrial DNA.

Metal-ceramic cohesion and the image interaction

A detailed understanding at the microscopic level of the strength of bonding at metal-ceramic interfaces, including its dependence on the crystallographic structure and chemical nature of the components, requires a model of the interatomic forces. Interatomic force models and computer simulation are widely used in the study of metal-metal and ceramic-ceramic boundaries but have not yet been applied to metal-ceramic. Recently however improvements in the microscopic modelling of metallic and ceramic cohesion together with the development of more powerful computers have opened possible ways of simulating the metal-ceramic interface which we are currently investigating. A particularly important component of the adhesive interaction across a metal-ceramic interface is believed to be the electrostatic image interaction which has no place in simple models of adhesion based on chemical bonding. This paradoxical situation is resolved. The image interaction is really a classical concept in the continuum electrostatics of point charges near a conducting surface, and makes no reference to discrete atoms. Nevertheless its equivalent attractive force close to a real metal surface can be calculated quantum mechanically for simple geometries. Fortunately, the results of these quantum mechanical calculations can be simulated by a classical interatomic force model, suggesting a way forward for atomistic simulation.

The concept of a single-domain particle

An attempt to calculate exchange and magnetostatic energies for several discrete atoms, which can only be done for larger interatomic distances, is discussed. All estimations of the single-domain particle size are based on certain approximations which apply to a continuous material, but break down in the limit of discrete atoms. It is shown that when these approximations are eliminated, a very small magnetic particle can never be completely saturated, even though such a state can be a very good approximation to the physical reality. The previous micromagnetic calculations are only approximately valid, which resolves the Brown paradox. >

Monte Carlo calculations of adsorbate placement and thermodynamics in a micropore: Xe in NaA

The canonical ensemble Monte Carlo technique is used to calculate thermodynamic properties and density distributions of Xe atoms trapped in the alpha cage of zeolite NaA, which is modelled as discrete atoms (or ions) positioned on a truncated cuboctahedron. The addition of Xe atoms to the cage causes a decrease in the calculated potential energy up to a preferred loading. Beyond this, though, further loading becomes energetically unfavourable. The angle averaged density distribution of Xe in the cage exhibits a maximum between the centre of the cage and the wall; both the position and the intensity of this maximum depend strongly on the loading. Detailed examination reveals that localized density maxima exist at discrete points within the cage and that these points move as Xe loading changes. Both the preferred Xe loading and the shape of the Xe density distribution depend strongly on the Si/Al ratio, since this parameter determines the number of charge balancing cations present. For high Si/Al ratios, th...

Helical diffraction. II. The inclusion of a subunit of finite size

In paper I of helical diffraction [Worthington & Elliott (1989). Acta Cryst. A45, 645-654] an expression for the autocorrelation function (a.c.f.) for a helix was obtained. The Fourier transform of this a.c.f. gave a new expression for the diffracted intensity. In paper II the theory is extended to real helices containing subunits of finite size. There are two main approaches to consider. The first approach centers on the calculation of the a.c.f. of the helical array of subunits. In the special case when the subunit contains an assembly of discrete atoms, the expression for the intensity is shown to be equivalent to the classical formula of Franklin & Klug [Acta Cryst. (1955), 8, 777-780]. The second approach bypasses the a.c.f. calculation and expresses the intensity in terms of the Fourier transform of the subunit. The second approach may prove useful in molecular modeling studies of biological helical structures.

The fractal nature of a fracture surface

A kinetic model is presented which simulates the propagation of cracks in solids composed of discrete atoms. The resulting fracture surface is found to be a fractal, the dimension of which depends on the elastic constants of the material.

A hybrid model for vibrational energy transfer at the gas–solid interface: Discrete surface atoms plus a continuous elastic bulk

We introduce a discrete-continuum hybrid treatment of solid vibrations in order to describe the collisional excitation of adsorbate and defect modes by atom impacts. The inhomogeneous surface is represented by: (a) one or more atom clusters corresponding to the defect sites and their immediate neighbors, which are harmonically coupled to (b) an elastic continuous bulk. The model thus aims at reproducing the long-wavelength spectrum of the lattice as well as the high-frequency localized modes contributed by adsorbates and surface defects. The hybrid model is tested against lattice results in one-dimensional simulations that allow for analytic solution of the surface motion (which would be unfeasible for three-dimensional imperfect lattices); hybrid and lattice results are thus compared in detail under identical conditions. The model is also evaluated under the worst possible conditions for the continuum approximation, since collinear collisions correspond to three-dimensional situations in which the transferred momentum and, therefore, short-wavelength excitations are maximal. Comprehensive tests are presented for He atoms scattering from CO chemisorbed on Pt and on Ni substrates, and from N2 adsorbed on W. The scattering dynamics is treated by time-correlation functions of the transition operator previously developed for polyatomic targets [J. Chem. Phys. 84, 3162 (1987); 85, 2300 (1987); 86, 750 (1987)]. All the energetically open states are thus incorporated, as well as the thermal average over initial states, without need of basis-set expansions. Distributions of transferred energy are presented as would be observed in a one-dimensional scattering ‘‘experiment’’ using impact energies between 0.1 and 1 eV and with the solid at nonzero temperature. The collisional spectra obtained from the hybrid models are found to be in excellent agreement with those of the corresponding inhomogeneous lattices throughout wide ranges of impact velocity, surface initial temperature (including 0 K) and transferred energy. The results indicate that discrete-continuum treatments provide a powerful tool for analyzing the transfer of energy at the gas–adsorbate–solid interface.

The Direct Methods of X-ray Crystallography

The electron density function rho(r) in a crystal determines its difaction pattern, that is, both the magnitudes and phases of its x-ray diffraction maxima, and conversely. If, however, as is always the case, only magnitudes are available from the diffraction experiment, then the density function rho(r) cannot be recovered. If one invokes prior structural knowledge, usually that the crystal is composed of discrete atoms of known atomic numbers, then the observed magnitudes are, in general, sufficient to determine the positions of the atoms, that is, the crystal structure.

The Monophonematic Status of Diphthongs Revisited

Abstract This paper presents a challenge to the well-established monophonematic view of German and English diphthongs. Empirical evidence is provided by speech error patterns showing that misordered diphthongs occasionally split apart during the error process. Since both splitting up and remaining intact can be observed with diphthongs, a linear analysis, which predicts an all-or-none behaviour, proves to be inadequate. An explanation for the relative cohesiveness of these phonemes can be found in a multilevel representation within which diphthongs are two discrete atoms on the segmental level which are molecularized in the suprasegmental structure.

Selective (photo)electrochemical etching of semiconductor surfaces

The performance and output stability of various photoelectrochemical solar cells can be improved considerably by a short photoelectrochemical etching of the semiconductor surface. This paper describes the experimental work which is involved in the research of that phenomenon. A unique morphological pattern is observed on the surface of photoetched semiconductors. This pattern consists of a dense network of submicron pits. We argue that this pattern is a result of discrete dopant atoms (or vacancies), which either influence the space charge layer field in their vicinity, leading to non-homogeneous hole flow to the surface, or, what is more likely still, the dopant atoms at or near the surface are preferentially attacked by the holes. In this case, each pit represents the position of a former dopant atom or vacancy. This hypothesis is in accord with the observed pit density at the surface.

Selective (photo)electrochemical etching of semiconductor surfaces

Abstract The performance and output stability of various photoelectrochemical solar cells can be improved considerably by a short photoelectrochemical etching of the semiconductor surface. This paper describes the experimental work which is involved in the research of that phenomenon. A unique morphological pattern is observed on the surface of photoetched semiconductors. This pattern consists of a dense network of submicron pits. We argue that this pattern is a result of discrete dopant atoms (or vacancies), which either influence the space charge layer field in their vicinity, leading to non-homogeneous hole flow to the surface, or, what is more likely still, the dopant atoms at or near the surface are preferentially attacked by the holes. In this case, each pit represents the position of a former dopant atom or vacancy. This hypothesis is in accord with the observed pit density at the surface.

Partons in antiquity

We point out that the idea of confined quarks or partons as constituents of the elementary particles was already present in the Greek atomic theory. We describe some similarities and differences between ancient and modern confinement, and we suggest that in both cases the idea is in large part a response to an inherent conflict between the intuitive notion of infinite divisibility and the idea of discrete fundamental atoms of matter.

Reply by Author to R. A. Oman

The reader is referred to Refs. 3-8, in which the principles of the thermal and structural scattering regimes were discovered3 and developed4 by extensive numerical experiments, and verified by laboratory experiments of at least four teams of investigators .5'8 In the structural scattering regime the surface atoms comprise an array of particles, the aggregate potential surface of which appears much more irregular to an incident particle of high kinetic energy (compared to the characteristic pairwise binding energy) than to one of low energy. In thermal scattering the thermal motion of the solid atoms dominates over this structure so that collisions are much more like gas-gas encounters. It can be shown fairly easily9 that in the structural domain thermal motion is insignificant, recoil in the lattice can be dealt with by considering each impact atom as supported by a separate foundation, and each impact atom acts as a scattering center. This implies a nearly conservative force field, with energy extraction from the incident particle possible only by recoil of the impacted atoms. In such a scenario the components of the velocity vector of a scattered particle are each directly influenced by the complete incident velocity vector. Kinslow's model would appear to require that there be no significant memory of the incident energy, thereby requiring both geometric surface roughness and microscopic roughness in the potential surface due to the presence of discrete atoms to be

Elastic interaction between linear polymeric chains and periodic potentials

AbstractThe elastic displacement of an axially stressed chain within crystalline surroundings, which was first treated by Chevychelov, is reexamined. We compare the results obtained for homogeneously distributed masses with that for discrete atoms, considering the nonuniformity of the potential of a crystal containing hydrogen bonds. In polyethylene and polyamide the maximum mechanical excitation of a chain penetrates into the crystal a distance of 15 to 20 chain atoms. The effect of the relative position of the crystal boundary on the stress‐strain field was studied and the energy of defects calculated.

Lattice statics applied to screw dislocations in cubic metals

Abstract In this paper we present an extension of the work of Maradudin (1958) designed to allow for general relaxations of the lattice rows about the cores of 〈111〉 and 〈110〉 dislocations in b.c.c. and f.c.c. metals respectively, assuming no dissociation of either core. Moderately long-range forces (up to fifth neighbours) are included, and we determine the lattice configuration within the harmonic approximation. Thus our results are directly comparable with those of linear elasticity. However, since we treat the lattice as a regular array of discrete atoms throughout, our results should be trustworthy everywhere except in the immediate region of the core.

On the continuum model for gas-surface interactions

A three-dimensional isotropic continuum model is used to look at the gas-surface interaction problem. Results for energy transfer to the continuum when acted upon by a transient force pulse approximating that expected during a collision process indicate a negligible amount is propagated into the solid as stress waves. This appears to support claims of researchers using discrete lattice atom models which ignore energy transfer to any but a surface array of atoms.

Stream Order as a Measure of Sample Source Uncertainty

The Horton stream order at the outlet of a drainage basin is a direct measure of the uncertainty (entropy) of the source supplying any discrete particle or atom detected at the outlet. If m is the order of the main stream in a basin, the uncertainty that the source lies in the drainage area of an ith order tributary is given by m ‐ i. This may be interpreted as representing the minimum number of tests or samples needed to find a single contamination source in a sequential search of a drainage basin. Similarly Scheidegger's consistent stream order may be interpreted as being the number of samples required to search a basin for a single source when the link magnitude of the outlet is known. Because natural streams usually have multiple contaminant sources and cannot be expressed as a simple branching process, a convenient estimate of the average number of samples needed to find a single source is given by (rb ‐ 1) (m ‐ i) where rb is the bifurcation ratio.

The morphology of interstitial aggregates in iron

A discrete atom model is described for body-centred cubic iron and used to investigate the nucleation and growth of interstitial aggregates. The results provide a consistent explanation of the origin and final orientation of the interstitial loops observed after low-temperature neutron irradiation in α-iron.