I.Yu. Sokolov

Galaxy dynamics predictions in the nonsymmetric gravitational theory

Abstract In the weak field approximation, the nonsymmetric gravitational theory (NGT) has, in addition to the Newtonian gravitational potential, a Yukawa-like potential produced by the exchange of a spin 1+ boson between fermions. If the range r0 = μ−1 is 25 kpc, then this additional potential due to the interaction with matter in the halos of galaxies can explain the flat rotation curves of galaxies and the Tully-Fisher law (L ∼ υ4) without the dark matter hypothesis. Possible fits to clusters of galaxies and gravitational lensing observations are discussed. The results are based on a linear approximation to a new perturbatively consistent version of the NGT field equations, which does not violate the weak equivalence principle.

Improved atomic force microscopy resolution using an electric double layer

High resolution (“atomic”) images of clinochlore and muscovite have been obtained in aqueous solution by inducing an electric double layer between the atomic force microscope tip and the sample surface. The electric double layer is created by the addition of a surfactant to water and greatly improves image resolution. A theoretical model is proposed to explain the improved resolution.

Theoretical and experimental evidence for ''true'' atomic resolution under non-vacuum conditions

Imaging of atomic scale features (Angstrom resolution) such as individual atoms using an atomic force microscope (AFM) remains highly controversial. Arguments that such resolution is not achievable revolve around two points: (1) that atomic scale defects are not observed and (2) often the experimental images are not reproduced theoretically. Here we show that the AFM is capable of imaging atomic features by presenting images of atomic scale defects at ∼1 A resolution. Dislocation defects and monatomic growth steps on the {001} surface of the mineral anhydrite (CaSO4) are observed in unfiltered AFM images. Furthermore, the atomic features observed in the experimental AFM images are reproduced by numerical simulation; conclusively addressing the two points above. The combination of experimental images and theoretical simulations enables the comprehensive interpretation of the images. The images of the {001} surface indicate that the AFM observes both the calcium and oxygen atoms at the cleavage plane. In ad...

The contrast mechanism for true atomic resolution by AFM in non-contact mode: quasi-non-contact mode?

Abstract Recent studies in which single point-like defects have been detected by AFM in non-contact mode, i.e., true atomic resolution, have been investigated using numerical simulations. The use of realistic interatomic interaction parameters allows us to do numerical simulations that are in very good agreement with experimental data. As a result, we are able to “separate” the different forces acting between the AFM tip and the sample surface. Calculations indicate that the force responsible for image contrast in the experimental studies is the repulsive contact force, and not the attractive contact force. This result remains the same for any reasonable set of interatomic interaction parameters.

Model dependence of AFM simulations in non-contact mode

Abstract Pairwise summation of a Lennard–Jones type potential is, because of its simplicity, an attractive method for theoretical simulation of scan images in atomic force microscopy (AFM). However, a serious problem for such simulations is the uncertainty in the AFM tip–sample interaction. While the interatomic repulsion is more or less universal, the attractive component of the interaction can include van der Waals, ionic, dipole, chemical, electrical and other kinds of forces. In the present paper, the pairwise summation method for the simulation of AFM scans is analyzed against the uncertainties in the attractive component of the interaction potential. It is shown that the simulation method produces, qualitatively, similar images of an atomic surface for a broad range of possible contributions to the attractive force interaction. This indicates that the numerical method, while relatively insensitive to the explicit attractive force contributing to the tip–sample interaction, is suitable for theoretical simulations of atomic resolution in the AFM.

Atomic resolution imaging using the electric double layer technique: friction vs. height contrast mechanisms

Atomic resolution images of the mineral astrophyllite have been obtained using the electric double layer technique [Sokolov, I.Yu., Henderson, G.S., Wicks, F.J., Applied Physics Letters 70 (1997) 17] and when immersed in water. Both friction and height images were recorded simultaneously. We find that when scanning in water, the primary contribution to the image contrast comes from the friction force, in agreement with previously published studies. However, when scanning in the presence of an electric double layer (EDL), the image contrast is primarily the result of vertical force. These results remain valid over a large range of load forces.

Imitation of non-contact mode while scanning in the presence of an electric double layer?

Abstract Non-contact atomic force microscopy (NCAFM) minimizes the physical interaction between the AFM tip and the surface of interest. Several recent studies have reported observation of single atom defects using this technique. The repulsive force is presumably the primary interatomic force (cf. our paper on pseudo-non-contact mode in this issue) responsible for the reported atomic resolution in these studies. The combination of these factors, minimal tip–sample deformation and repulsive force interaction, are responsible for the observation of the single atom defects. In the present study, we show that similar resolution can be achieved utilizing the same two factors but which employs scanning in a surfactant. The method decreases the tip–sample interaction by eliminating the attractive forces between the tip and sample. The surfactant solution induces an electrical double-layer (EDL) on the surface of the tip and sample. This EDL creates additional repulsion that is distributed over a large area, and hence does not contribute noticeably to the image contrast during scanning. However, it does compensate for the high pressures normally experienced by the tip in the absence of surfactant. In addition, the presence of the EDL enhances tip stability during the image scan. This method has been tested on surfaces of such minerals as mica, chlorite, and anhydrite.

The height dependence of image contrast when imaging by non-contact AFM

Abstract Using the pair-wise summation of the Lennard–Jones potential, we have analyzed the height dependence of the image contrast in atomic force microscopy at atomic resolution when scanning in non-contact mode. When we study the images obtained as the surfaces of constant force gradient (fast feedback on frequency shift), we find that images remain qualitatively similar for the range of tip–sample distances analyzed. However, for a slow feedback mode, which is more commonly used because of mechanical instabilities that exist in the fast feedback regime, we have found a spectrum of artefacts that are dependent on the tip–sample distance.

A Force Limitation for Successful Observation of Atomic Defects: Defect Trappong of the Atomic Force Microscopy Tip

Theoretical simulations of atomic force microscopy (AFM) scans while operating in contact mode indicate that there is a natural limit to the maximum nondestructive scan force near atomic defects. This limit is much smaller than the force calculated for nondestructive scans on a defect free surface. The limit is a function of the nature of the sample lattice and imaging medium, and results from a specific force dependence between the AFM tip and sample near the defect, which essentially “traps” the AFM tip apex at constant height in the vicinity of the defect. The AFM feedback system is unable to respond to the trapping, and consequently, the monoatomic apex of the tip collides with the sample surface as the scan continues. The collision effectively produces either a multitip or removes the defect. Further, we find that for a lattice constant less than 0.29–0.3 nm, point-like atomic vacancies cannot be observed, regardless of the scan force used and the medium in which scans are performed.