Volume interaction

Molecular Interactions Volume 3 H. Ratujczak, W. J. Orville-Thomas, M. Redshaw, Eds., John Wiley Sons, New York (1982). 

Electron Probe Microanalysis, EPMA, as performed in an electron microprobe combines EDS and WDX to give quantitative compositional analysis in the reflection mode from solid surfaces together with the morphological imaging of SEM. The spatial resolution is restricted by the interaction volume below the surface, varying from about 0.2 pm to 5 pm. Flat samples are needed for the best quantitative accuracy. Compositional mapping over a 100 x 100 micron area can be done in 15 minutes for major components Z> 11), several hours for minor components, and about 10 hours for trace elements. 

The volume of analysis, i.e., the diameter and depth of the analyzed region, is limited by a combination of the elastic and inelastic scattering.The maximum depth of the interaction volume is described by the Kanaya-Okayama electron range ... 

The specimen must be homogeneous throughout the interaction volume sampled by the beam, since X rays of different energies originate from different depths. 

The spatial resolution in quantitative analysis is defined by how large a particle must be to obtain the required analytical accuracy, and this depends upon the spatial distribution of X-ray production in the analysed region. The volume under the incident electron beam which emits characteristic X-rays for analysis is known as the interaction volume. The shape of the interaction volume depends on the energy of the incident electrons and the atomic number of the specimen, it is roughly spherical, as shown in Figure 5.7, with the lateral spread of the electron beam increasing with the depth of penetration. 

With a thermionic electron source, and a foil thickness of 100 nm, the volume of specimen excited is of the order 10-5 pm3. With a FEG source in a dedicated STEM, however, with a foil of 1 nm thickness this specimen-beam interaction volume can be as small as 10 8pm3. Very small signal levels are thus to be expected in AEM, hence the importance of employing higher brightness sources and the need to modify the specimen-detector configuration to maximize the collection angle. 

Ideally the EDS should only receive the X-rays from beam-specimen interaction volume, but it is not possible to prevent radiation from the microscope stage and... 

Enhancement of x2 will lead to improvement (in terms of efficiency per interaction volume) in the following applications up-conversion in the visible or near U.V. of powerful I.R. laser radiation, frequency modulation of a laser carrier beam, optical parametric oscillation and amplification for solid state infrared tunable coherent devices. 

Fig. 8 Schematic of electron beam interaction with a sample and the electron beam interaction volumes for electron-specimen interactions.

The interference process in this collinear approach is, however, different from the interference realized by mixing the local oscillator and the CARS field on a beam splitter. Interference takes place in the sample, which, in the presence of multiple frequencies, mediates the transfer of energy between the beams that participate in the nonlinear process. The local oscillator mixes with the anti-Stokes polarization in the focal volume, and is thus coherently coupled with the pump and Stokes beams in the sample through the third-order polarization of the material. In other words, the material s polarization, and its ability to radiate, is directly controlled in this collinear interferometric scheme. Under these conditions, energy from the local oscillator may flow to the pump and Stokes fields, and vice versa. For instance, when the local oscillator field is rout of phase with the pump/Stokes-induced anti-Stokes polarization in the focal interaction volume, complete depletion of the local oscillator may occur. The energy of the local oscillator field is not redistributed in terms... 

The ability to control the phase of focal fields at different locations in the interaction volume has interesting applications when combined with interferometric mixing techniques. When a local oscillator field is focus engineered and overlapped with... 

Electron microprobes can be used in spot mode to measure the chemical compositions of individual minerals. Mineral grains with diameters down to a few microns are routinely measured. The chemical composition of the sample is determined by comparing the measured X-ray intensities with those from standards of known composition. Sample counts must be corrected for matrix effects (absorption and fluorescence). The spatial resolution of the electron microprobe is governed by the interaction volume between the electron beam and the sample (Fig. A.l). An electron probe can also be operated in scanning mode to make X-ray maps of a sample. You will often see false-color images of a sample where three elements are plotted in different colors. Such maps allow rapid identification of specific minerals. EMP analysis has become the standard tool for characterizing the minerals in meteorites and lunar samples. 

Let us first focus on Figure 10.5a. Assume that every atom in sphere 1 attracts every atom in sphere 2 with an energy given by Equation (33). If (pNA/M) is the number of atoms per cubic centimeter in the material, then there are (pNA/M)dVia atoms in a volume element of sphere 1 and (pNA/M)dV2a atoms in a volume element of sphere 2. The number of pairwise interactions between the two volume elements is (1/2) (pNA/M)2 dV dV. The factor (1/2) enters since each pair is counted twice. This number times the interaction per pair gives the increment in potential energy for the two interacting volume elements in case (a) ... 

Figure 2. (a) Interaction of small spherical molecules. The molecule at 2, on the inner edge of a square potential well of width x, is in contact with the central molecule 1. At 2 it is on the outer edge of the well. The radius 2r defines the exclusion volume around the central molecule the shell between radius 2r and (2r+x) defines its interaction volume. (6) Interaction of spherical shell-molecules. Atoms 1 and 2 on their respective shells are in contact on the inner edge of a square well of width x. Atoms 1 and 2 are beyond the outer edge of the well. If the shell-atoms are taken as uniformly smeared around the shells, the energy of interaction between the molecules should be approximately proportional to the overlap volume Va, the region in which the shells are closer than x. 

This equation acknowledges that real molecules have size. They have an exclusion volume, defined as the region around the molecule from which the centre of any other molecule is excluded. This is allowed for by the constant b, which is usually taken as equal to half the molar exclusion volume. The equation also recognizes the existence of a sphere of influence around each molecule, an interaction volume within which any other molecule will experience a force of attraction. This force is usually represented by a Lennard-Jones 6-12 potential. The derivation below follows a simpler treatment (Flowers Mendoza 1970) in which the potential is taken as a square-well function as deep as the Lennard-Jones minimum (figure 2a). Its width x is chosen to give the same volume-integral, and defines an interaction volume Vx around the molecule, which will contain the centre of any molecule in the square well. This form of molecular pair potential then appears in the Van der Waals equation as the constant a, equal to half the product of the molar interaction volume and the molar interaction energy. 

Osbourn, A.E., Wubben, J.P., Daniels, M J. Saponin detoxification by phytopathogenic fungi. In Plant-Microbe Interactions Volume 2. Stacey, G, Keen, N.T. ed., New York Chapman and Hall, 1995a, pp. 99-124. Osbourn, A. Bowyer, P., Lunness, P., Clarke, B., Daniels, M. Fungal pathogens of oat roots and tomato leaves employ closely related enzymes to detoxify different host plant saponins. Mol Plant Microb Interact 1995b 8 971-978. 

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