Jack C. Straton

Removal of multiple-tip artifacts from scanning tunneling microscope images by crystallographic averaging

Crystallographic image processing (CIP) techniques may be utilized in scanning probe microscopy (SPM) to glean information that has been obscured by signals from multiple probe tips. This may be of particular importance for scanning tunneling microscopy (STM) and requires images from samples that are periodic in two dimensions (2D). The image-forming current for double-tips in STM is derived with a slight modification of the independent-orbital approximation (IOA) to allow for two or more tips. Our analysis clarifies why crystallographic averaging works well in removing the effects of a blunt STM tip (that consists of multiple mini-tips) from recorded 2D periodic images and also outlines the limitations of this image-processing technique for certain spatial separations of STM double-tips. Simulations of multiple mini-tip effects in STM images (that ignore electron interference effects) may be understood as modeling multiple mini-tip (or tip shape) effects in images that were recorded with other types of SPMs as long as the lateral sample feature sizes to be imaged are much larger than the effective scanning probe tip sizes.

Crystallographic STM image processing of 2D periodic and highly symmetric molecule arrays

Crystallographic Image Processing (CIP) is applied to experimental Scanning Tunneling Microscopy (STM) images of regular (2D periodic) arrays of organic molecules on noble metal substrates. The crystallographically averaged (surface) lattices, structural motifs, and plane symmetry groups of the arrays are determined. An assessment of the samples with the goal of utilizing highly symmetric molecular arrays as calibration samples for STM is made. A brief introduction to the CIP procedures is given in an appendix.

Quantifying and enforcing two-dimensional symmetries in scanning probe microscopy images of periodic objects

The defining features of a scanning probe microscope (SPM) are a very fine “probe” that is scanned in two dimensions (2D), in very fine steps, very close to the surface of a sample, and a “probesample interactions signal” that is recorded at each scanning increment. This signal may then be digitized and displayed as a function of the magnified scanning steps. A 2D-image of the probe-sample interactions may, thus, be obtained.

Analytic Solution for a Quartic Electron Mirror

A converging electron mirror can be used to compensate for spherical and chromatic aberrations in an electron microscope. This paper presents an analytical solution to a diode (two-electrode) electrostatic mirror including the next term beyond the known hyperbolic shape. The latter is a solution of the Laplace equation to second order in the variables perpendicular to and along the mirrors radius (z(2)-r(2)/2) to which we add a quartic term (kλz(4)). The analytical solution is found in terms of Jacobi cosine-amplitude functions. We find that a mirror less concave than the hyperbolic profile is more sensitive to changes in mirror voltages and the contrary holds for the mirror more concave than the hyperbolic profile.

On the production of the positive antihydrogen ion

We provide an estimate of the cross section for the radiative attachment of a second positron into the state of the ion using Ohmura and Ohmuras (1960 Phys. Rev. 118 154) effective range theory and the principle of detailed balance. The ion can potentially be created using interactions of positrons with trapped antihydrogen, and our analysis includes a discussion in which estimates of production rates are given. Motivations to produce include its potential use as an intermediary to cool antihydrogen to ultra-cold (sub-mK) temperatures for a variety of studies, including spectroscopy and probing the gravitational interaction of the anti-atom.

{{{\rm \bar{H}}}^{+}}

A formalism is developed for evaluating probabilities and cross sections for multiple‐electron transitions in scattering of molecules and clusters by charged collision partners. First, the molecule is divided into subclusters each made up of identical centers (atoms). Within each subcluster coherent scattering from identical centers may lead to observable phase terms and a geometrical structure factor. Then, using a mean field approximation to describe the interactions between centers we obtain AI∼∑k∏keiδkIAIk. Second, the independent electron approximation for each center may be obtained by neglecting the correlation between electrons in each center. The probability amplitude for each center is then a product of single electron transition probability amplitudes, aIki, i.e. AIk≊∏iaiki. Finally, the independent subcluster approximation is introduced by neglecting the interactions between different subclusters in the molecule or cluster. The total probability amplitude then reduces to a simple product of am...

via radiative attachment

Diffraction of a primary electron beam that is precessing, i.e. Precession Electron Diffraction (PED), in a Transmission Electron Microscope (TEM) [1-8], has over the last twenty-odd years become “an invaluable tool, not only for the determination of unknown crystal structures but also in aiding the analysis of local microstructure” [8]. Seven years after its first demonstration [9], the “scanning version of PED” [4-6] rivals in popularity electron backscattering in a scanning electron microscope.

Independent center, independent electron approximation for dynamics of molecules and clusters

Crystallographic Image Processing (CIP) originated with the electron crystallography community. Nobel Laureate Sir Aaron Klug (OM, FRS) and coworkers pioneered the technique for the analysis of long-range ordered biological materials in parallel illumination Transmission Electron Microscopes (TEMs). Corrections for the effects of the TEM’s phase contrast transfer function and for less than optimal imaging conditions are part of this kind of CIP. There are also “electron microscope independent” 2D crystallography foundations to this kind of image processing.

Utility of Precession Electron Diffraction Patterns with Varying Degrees of Non-parallel Illumination from the Same Nominal Sample Area

This book chapter reviews progress in crystallographic image processing (CIP) for scanning probe microscopy (SPM) that has occurred since our description of the technique was first put into open access in this book series in the year 2010. The signal to noise ratio in all kinds of experimental images of more or less regular 2D periodic arrays is significantly enhanced by CIP and the technique is independent of the type of recording device. In the SPM imaging context, CIP can be understood as an a posteriori sharpening of the effective experimental scanning probe tip by computational means. It is now possible to remove multiple scanning probe mini-tip effects in images from 2D periodic arrays of physical objects that either self-assembled or were created artificially. Accepted within the scientific community is by now also the fact that SPM tips can change their shape and fine structure during the operation of a microscope and, thereby, obfuscate the recorded images in systematic ways. CIP restores much of the smeared out information in such images. The adaptation of a geometric Akaike Information Criterion from the robotics and computer vision community to the unambiguous detection of 2D translation symmetries enabled much of our recent progress. In the main body of this book chapter, we discuss this adaptation and briefly illustrate its utility on an example.

Progress in Crystallographic Image Processing for Scanning Probe Microscopy

The crystallographic processing of 2D periodic Scanning Probe Microscopy (SPM) images is compared to the common practice of Crystallographic Image Processing (CIP) in transmission electron microscopy (TEM). This provides motivation for the development of a dedicated computer program for CIP in SPM. The current state of our program is briefly described, and the point spread function (PSF) of an atomic force microscope (AFM) is extracted from experimental images through CIP. The use of a geometric Akaike information criterion (AIC) to supplement standard CIP procedures is discussed in some detail.