The scattering of thermal He atoms at ordered and disordered surfaces

The use of thermal energy atom scattering (TEAS) as a surface investigation tool is reviewed. Specific properties of thermal He scattering, which are particularly advantageous in surface analysis, are discussed; the main causes which hampered so far the broad application of this technique to the investigation of ordered surfaces are analysed. The recent development of TEAS based on the exploitation of the large cross section for He diffuse scattering of adsorbates and vacancies is reviewed. This development extends the capabilities of TEAS to a straightforward investigation of various aspects of disordered surfaces so far hardly accessible to other methods. Examples concerning the lateral distribution of adsorbates and defects, the mutual attraction and repulsion, 2D-phase transitions, mobility and surface diffusion are given.     

Small angle neutron scattering study of disordered and crystalline iron nanoparticle assemblies

Monodisperse surfactant-coated iron nanoparticles are used to form both disordered nanoparticle assemblies and ordered face-centered cubic nanoparticle crystals. The structural order is probed by small angle X-ray scattering, and the magnetic scattering is studied using small angle neutron scattering. The magnetic scattering corresponding to different length scales is interpreted in terms of collective correlations among the particles within the assemblies.     

Path degeneracy and EXAFS analysis of disordered materials

Analysis of EXAFS data measured on a material with a disordered local configuration environment around the absorbing atom can be challenging owing to the proliferation of photoelectron scattering paths that must be considered in the analysis. In the case where the absorbing atom exists in multiple inequivalent sites, the problem is compounded by having to consider each site separately. A method is proposed for automating the calculation of theory for inequivalent sites, then averaging the contributions from sufficiently similar scattering paths. With this approach, the complexity of implementing a successful fitting model on a highly disordered sample is reduced. As an example, an analysis of Ti K‐edge data on zirconolite, CaZrTi₂O₇, which has three inequivalent Ti sites, is presented.     

Elastic diffuse and inelastic electron scattering from surfaces with disordered overlayers

The elastic diffuse scattering of electrons can be used for structure analysis of disordered species on surfaces. Effective data acquisition is achieved with instruments which do not resolve between elastic diffuse scattering and inelastic scattering due to phonons. With a newly designed high resolution spectrometer it is shown that the inelastic intensity is of the same magnitude or larger than the elastic diffuse scattering. It is also shown however, that the total inelastic intensity changes little when a lattice gas of adsorbates is present on the surface, whereas the elastic diffuse intensity increases linearly with coverage. Thus instruments with low energy resolution may be used for the analysis of local structure of disordered adsorbates provided one measures the difference between the total diffuse scattering of the adsorbate covered and the clean surface.     

Disordered clean surfaces and adsorbates investigated with atom-surface scattering

In this paper two different physical situations are considered which can be treated with the same method: a fluid adsorbate (disordered in the x, y plane) and a clean surface with random steps (disordered in the z direction). The hard corrugated wall model is used in the eikonal approximation; the differences between the two cases arise only from the different statistical properties of the two physical situations. The differential scattering probability is evaluated. For the fluid adsorbate the latter splits into a coherent (purely specular) contribution and an incoherent one (which is, in fact, weakly inelastic and related to classical diffusion on the surface). For stepped “rough” surfaces only incoherent scattering is present and the differential scattering probability for hexagonal lattices is given.     

Scaling properties of the growing monolayer on the disordered substrate

We present results of theoretical and numerical studies the pattern formation processes in adsorptive system with the disordered substrate, representing high-entropy alloy. The lateral diffusivity of adatoms on the substrate is represented as a quenched spatial disorder. By taking into account a transference of adsorbate between first two layers we construct the reaction-diffusion model, describing evolution of adsorbate concentration on the disordered substrate. It will be shown, that at elevated values of the pressure inside a chamber the quenched spatial disorder will induce pattern formation in the system. We will show that the strength of the spatial disorder can control dynamics of nanostructured film growth, type of surface structures and scaling properties of the growing layer. This study provides an insight into details of self-organization of adatoms on the high-entropy alloys in adsorptive systems.     

Structural transformation of vapor grown carbon nanofibers studied by HRTEM

Vapor grown carbon nanofibers have been extensively manufactured and investigated in recent years. In this study commercially available vapor grown carbon nanofibers subjected to different processing and post processing conditions were studied employing high resolution TEM images. The analysis showed that the fibers consist primarily of conical nanofibers, but can contain a significant amount of bamboo nanofibers. Most conical nanofibers were found to consist of an ordered inner layer and a disordered outer layer, with the cone angle distribution of the inner layers indicating that these cannot have a stacked cone structure but are compatible with a cone-helix structure. Fibers that have been heat treated to temperatures above 1,500 °C undergo a structural transformation with the ordered inner layers changing from a cone-helix structure to a highly ordered multiwall stacked cone structure. The bamboo nanofibers were found to have a tapered multiwall nanotube structure for the wall and a multishell fullerene structure for the cap of each segment, surrounded by a disordered outer layer. When these fibers are heat treated the disordered outer layers transform to an ordered multiwall nanotube structure and merge with the wall of each segment. The end caps of each segment transform from a smooth multiwall fullerene structure to one consisting of disjointed graphene planes. A reaction-diffusion mechanism is proposed to explain the growth and structure of the bamboo nanofibers.     

Systematic approximations in disordered systems

We discuss two systematic approximation schemes for disordered systems (random lattices) by extending the single site CPA. In the first scheme all self energy diagrams up to those includingν scattering centers are summed up. Thisν-center approximation has been discussed before and is here derived using a straightforward projection operator formalism. The second scheme is a “true” cluster-CPA in which the scattering from an arbitrarily large cluster of neighbouring atoms (ν-cluster) embedded in a random crystal is treated just in the same way as in the single site CPA. In contrast to other cluster formulations our theory preserves translational invariance and determines the self energy in a natural way. The two schemes are compared with each other concerning their practical applicability.     

Strain relief and disorder in commensurate water layers formed on Pd(111)

Water adsorbs and desorbs intact on Pd(111), forming a hydrogen-bonded wetting layer whose structure we examine by low energy electron diffraction (LEED) and He atom scattering (HAS). LEED shows that water forms commensurate (√3 × √3)R30° clusters that aggregate into a partially ordered, approximately (7 × 7) superstructure as the layer completes. HAS indicates that the water layer remains disordered on a local (approximately 10 ?) scale. Based on workfunction measurements and density functional theory simulations we propose that water forms small, flat domains of a commensurate (√3 × √3)R30° water network, separated by disordered domain boundaries containing largely H-down water. This arrangement allows the water layer to adapt its density and relieve the lateral strain associated with adsorbing water in the optimum flat atop adsorption site. We discuss different possibilities for the structure of these domain walls and compare this strain relief mechanism to the highly ordered, large unit cell structures formed on surfaces such as Pt(111).     

Elastic scattering of atoms from surfaces covered with adsorbates: Exact solution for the Einstein-model

The problem of atom scattering from surfaces covered with adsorbates is considered within the Einstein model for the adsorbate phonons. In this case the problem can be solved exactly by the use of a numerical method developed earlier by the present authors. In particular we investigate the temperature dependence of the elastic scattering. It turns out that the deviations from conventional Debye-Waller-factor theory occurring in neutron scattering and Mößbauer effect for single oscillators also show up in atom surface scattering: At higher momentum transfers the elastic scattering probability does not decrease monotonously with temperature but exhibits a maximum at non-zero temperature.     

Polarized neutron diffuse scattering experiments on disordered Cr-rich Cr-Fe alloys

The results of polarized neutron elastic diffuse scattering measurements on disordered Cr-Fe alloys with 1.5 2.4, and 12 and 14.2 at % of Fe are reported and discussed. The measurements have been done using neutron wavelength of 4.25 A in the scattering vector range 0.2Å^?1 < K < 2Å^?1 and in function of temperature. The data show clustering effects in the alloys with iron concentration starting from 2.4 at%. At the iron concentration of 14.2 at% the clusters contain about 110 atoms and extend up to about 6.3 Å from a central atom. Above a characteristic temperature the iron-rich clusters behave as superparamagnetic entities and below this temperature they are magnetically frozen.At 4.6K the average iron moment within these clusters is found to be 2.0(2)μ_B in the alloys with 12 and 14.2 at % of Fe.     

A self-consistent model calculation of the electronic structure of ordered,disordered and hydrogenated Pd3Fe

We study, within the Bethe lattice approximation, the electronic structure of the ordered, disordered and hydrogenated intermetallic Pd₃Fe. We employ a simple one-orbital per site model hamiltonian, which includes a Hubbard-like Coulomb interaction term. This is treated in the Hartree-Fock approximation. We present results for the number of electrons, magnetic moments, and density of states at the Fermi level. Good agreement with available experimental data is obtained.     

XANES: Determination of bond angles and multi-atom correlations in order and disordered systems

In contrast to conventional single-scattering probes, X-ray absorption near edge structure (XANES) is sensitive, through multiple scattering of the excited electron, not only to pairwise atomic correlations but also to higher order correlations, including bond angles. We present a flexible theory, based on a full multiple scattering cluster calculation, which can be used to extract such information in ordered, disordered and other complex systems now being studied using synchrotron radiation.     

Electronic excitations on clean and adsorbate covered Pd(111) by angle resolved electron energy loss spectroscopy

Electronic excitations on clean and adsorbate covered Pd(111) have been investigated by angle resolved electron energy loss spectroscopy. Primary energies in the range of 50–1000 eV were chosen for strong specular reflection to emphasize elastic diffraction-before-loss processes. The clean Pd spectra are compared with optical data, and good correspondence is found for the optical limit (q ? 0). The loss features are interpreted in terms of plasmon resonances and interband transitions within the framework of a recent band structure calculation. Virtually no dispersion is observed for the intrinsic Pd losses, but vertical interband transitions decay fast in the dispersive (q ≠ 0) spectra. Two adsorbate systems are investigated in this study: CO in a disordered adsorbate layer and bromine in a well-ordered $\text{(}\text{3×}\text{3 )R30°}$ structure. Adsorbate derived loss features are generally prominent in the nonspecular (q ≠ 0) spectra. While no dispersion is seen for the intramolecular 13.5 eV excitation of adsorbed CO, dispersion up to 1 eV is found for the Br 4p derived loss feature of the ordered overlayer. This is discussed in terms of a two-dimensional adsorbate band structure of bromine.     

Landau levels in disordered alloys

The electronic structure of a substitutionally disordered alloy in a uniform magnetic field has been studied on a simple model of scattering potentials (zero range potentials). The coherent potential and single-site aproximation have been employed. It turned out that in wide energy region the Dingle temperature, characterizing the decay of the amplitude of de Haas — van Alphen oscillations, is determined by the part of self-energy which does not depend on magnetic field. The field dependent part is important only for a few Landau levels at the bottom of the band. The results can be applied to simple metals and semi-metals.     

Molecular adsorption and growth of n-butane adlayers on Pt(1 1 1)

The molecular adsorption of n-butane and the growth of n-butane adlayers on Pt(1 1 1) was investigated using molecular beam techniques, temperature-programmed desorption (TPD) and low-energy electron diffraction (LEED). It is found that as the surface coverage of n-butane increases, structural changes occur in the adlayer at surface temperatures near 98 K that are accompanied by changes in the binding energy and mobility of the adsorbed species. The film growth process can be divided into four distinct coverage regimes. At low coverages (θ<0.14 ML, where 1 ML is defined as one butane molecule per Pt atom) a disordered monolayer forms in which the butane molecules prefer to lie parallel to the surface in order to minimize their binding energy. At coverages from 0.14 to 0.20 ML, ordered regions develop within the monolayer in which the butane molecules also lie parallel to the surface. The binding energy in the ordered phase is lower than that in the disordered phase due to repulsive intermolecular interactions. A more densely-packed ordered phase begins to form at 98 K after the low-coverage ordered phase saturates at 0.20 ML. The experimental results suggest that the n-butane molecules tilt away from the surface in the high-coverage ordered phase. Finally, a disordered second layer phase forms after the high coverage ordered phase saturates at 0.35 ML. The molecules in the second layer are very mobile at 98 K and rapidly diffuse to the edges of the beam spot. Interchange of molecules between the second layer and ordered monolayer is found to govern the net rate of second layer diffusion at surface temperatures less than 133 K. The adsorption probability of n-butane on Pt(1 1 1) continuously increases with increasing coverage, with no significant dependencies on the structure of the n-butane adlayer. This finding indicates that the long-range arrangements and molecular orientations of a mobile alkane adlayer have a negligible influence on the intrinsic adsorption dynamics, suggesting that the energy transfer processes that facilitate adsorption are highly localized.     

Nonlinear impedances of thermoacoustic stacks with ordered and disordered structures

Nonlinear impedances of two thermoacoustic stacks with ordered structures （plate-type and pipe-type） and one with a disordered structure （copper mesh） are studied. The linear resistances, nonlinear coefficients and effective acoustic masses of the stacks are extracted from the experimental results based on an analogical model of nonlinear impedances of porous materials. The resistance and nonlinear coefficient of the disordered stack are found to be much larger than those of the ordered stacks, which have similar volume porosities. In the ordered stacks, the resistance is only marginally influenced by the length of the stack, while in the disordered stack, the resistance increases significantly with the length. These charac- teristics of the impedances of ordered and disordered stacks are explained with the minor loss theory and the tortuosity of a stack.     

Suppression of spin-orbit scattering in strongly disordered gold nanojunctions

We discovered that spin-orbit scattering in strongly disordered gold nanojunctions is strongly suppressed relative to that in weakly disordered gold thin films. This property is unusual because in weakly disordered films spin-orbit scattering increases with disorder. Granularity and freezing of spin-orbit scattering inside the grains explains the suppression of spin-orbit scattering. We propose a generalized Elliot-Yafet relation that applies to a strongly disordered granular regime.     

Electronic structure of disordered Pd3Fe

The electronic structure of disordered Pd₃Fe is studied within an almost self-consistent KKR-CPA procedures. Our starting point are the self-consistent potentials for the ordered ferromagnetic Pd₃Fe obtained by the LMTO method. We perform the ferromagnetic calculation and examine the influence of disorder on the electronic structure of this alloy through the analysis of the Bloch spectral functions and densities of states and compare our results with experiment. We also propose a mechanism for the formation of magnetic moments in ferromagnetic alloys.     

Magnetic susceptibility in the edged topological disordered nanoscopic cylinder

The effects of edged topological disorder on magnetic susceptibility are investigated in a nanoscopic cylinder threaded by a magnetic flux. Persistent current versus even or odd number of electrons shows different signs in ordered and disordered cylinders and also in short or long ones. In addition, temperature-averaged susceptibility has only diamagnetic signs in strong regimes and it is associated with paramagnetic signs in ordered and weak disordered ones. Besides, in an edged topological disordered cylinder, the temperature-averaged susceptibility decreases by raising the temperature somewhat and then increasing initiates and finally at high temperature tends to zero as the ordered one.