Imaging real-space

Real-space three-dimensional imaging in air, vacuum, or solution with unsurpassed resolution high-resolution profilometry imaging of nonconductors (SFM). 

The prindple of a LEED experiment is shown schematically in Fig. 4.26. The primary electron beam impinges on a crystal with a unit cell described by vectors ai and Uj. The (00) beam is reflected direcdy back into the electron gun and can not be observed unless the crystal is tilted. The LEED image is congruent with the reciprocal lattice described by two vectors, and 02". The kinematic theory of scattering relates the redprocal lattice vectors to the real-space lattice through the following relations... 

Since the introduction of scanning tunnelling microscopy, a family of scanning probe microscopies (SPMs) have been developed (Table 3.1), with three main branches resulting from three different types of probe. All of the methods have in common the ability to image surfaces in real space at nanometre or better resolution, are straightforward to implement and are relatively low in cost. 

Soon after the invention of the STM as a tool for imaging surfaces in real space, it was discovered that the microscope could also be used (or misused) for surface manipulations, that is, for nano structuring of surfaces [5]. The extremely close vicinity of the STM tip and the sample surface required by the tunnel process... 

It is complete because of fiber symmetry. The 2D Fourier transform of this image is not related to the searched slice, but to a projection of the correlation function. In contrast, the sought-after slice in real space... 

Figure 8.27. Steps preceding the computation of a CDF with fiber symmetry from recorded raw data The image is projected on the fiber plane, the equivalent of the Laplacian in real space is applied, the background is determined by low-pass filtering. After background subtraction the interference function is received... 

PE, the united atom model. We considered a sufficiently long PE chain made up of 5000 united atoms under periodic conditions in each direction. The initial amorphous sample prepared at 600 K was quenched to 100 K and drawn up to 400%. The sample was then quickly heated to various crystallization temperatures, and the molecular processes of fiber formation were monitored in situ via the real-space image and its Fourier transform, the structure function S3d([Pg.79]

The late 1980s saw the introduction into electrochemistry of a major new technique, scanning tunnelling microscopy (STM), which allows real-space (atomic) imaging of the structural and electronic properties of both bare and adsorbate-covered surfaces. The technique had originally been exploited at the gas/so id interface, but it was later realised that it could be employed in liquids. As a result, it has rapidly found application in electrochemistry. 

With the above described experimental measures, we are ready to image single crystal electrodes in-situ, in real space, in real time and with atomic-scale resolution. This will be plentiful demonstrated in the following. 

I believe, it is fair to state that scanning tunneling microscopy and related techniques such as atomic force microscopy have a tremendeous potential in metal deposition studies. The inherent nature of the deposition process which is strongly influenced by the defect structure of the substrate, providing nucleation centers, requires imaging in real space for a detailed picture of the initial stages. This is possible with an STM, the atomic resolution being an extra bonus which helps to understand these processes on... 

Figure 9b, Real-space image of a new type of graphite intercalate (with FeCl2), There are two sheets of guest material accommodated in an expanded interlamellar space. Inset shows computed...

Conventional HRTEM operates at ambient temperature in high vacuum and directly images the local structure of a catalyst at the atomic level, in real space. In HRTEM, as-prepared catalyst powders can be used without additional sample preparation. The method does not normally require special treatment of thin catalyst samples. In HRTEM, very thin samples can be treated as WPOs, whereby the image intensity can be correlated with the projected electrostatic potential of the crystal, leading to the atomic structural information characterizing the sample. Furthermore, the detection of electron-stimulated XRE in the EM permits simultaneous determination of the chemical composition of the catalyst. Both the surface and sub-surface regions of catalysts can be investigated. 

Yields atomic resolution images of surface in real space surfaces... 

To be specific, let R(/ denote the position in the periodically repeated cell, which is the z th image to the right and the /th image on top of the central cell. (A potentially third dimension remains unaffected and will therefore not be mentioned in the following discussion.) The position in real space of the vector R,y = (X, Y)jj would be... 

Traditionally the performance of HRTEM is judged in terms of its ability to resolve two adjacent atom columns. Resolution is ruled by a few basic principles A position dependent image intensity g(r) is described as a convolution of the specimen function f(r) with a point spread function h(r). It is convenient to express this convolution in real space as a product in reciprocal space ... 

Figure 9. Simplified ray diagram (Abbe diagram) that shows simultaneous formation of the diffraction pattern and the corresponding real space image in a transmission electron microscope (TEM).

To discuss the influence of aberrations in the HRTEM image formation process in more detail, it is convenient to work in Fourier space, where the real-space quantities I r), T (r), V r), and T r) are related to their counterparts 7(g), T (g), Vp(g) and T(g) by a Fourier Transformation. Distances, d, in direct space correspond to spatial frequencies, g, in Fourier space. With this approach, the electron wave can be expressed as... 

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