Atomic distribution

Although gas chromatography can give the concentration of each component in a petroleum gas or gasoline sample, the same cannot be said for heavier cuts and one has to be satisfied with analyses by chemical family, by carbon atom distribution, or by representing the sample as a whole by an average molecule. 

Characterization of a Petroleum Fraction by Carbon Atom Distribution... 

Figure A2.3.8 Atom-atom distribution functions aiid for liquid water at 25 °C detemrined...

The description of the atomic distribution in noncrystalline materials employs a distribution function, (r), which corresponds to the probability of finding another atom at a distance r from the origin atom taken as the point r = 0. In a system having an average number density p = N/V, the probability of finding another atom at a distance r from an origin atom corresponds to Pq ( ). Whereas the information given by (r), which is called the pair distribution function, is only one-dimensional, it is quantitative information on the noncrystalline systems and as such is one of the most important pieces of information in the study of noncrystalline materials. The interatomic distances cannot be smaller than the atomic core diameters, so = 0. 

In the procedure of X-ray refinement, the positions of the atoms and their fluctuations appear as parameters in the structure factor. These parameters are varied to match the experimentally determined strucmre factor. The term pertaining to the fluctuations is the Debye-Waller factor in which the atomic fluctuations are represented by the atomic distribution tensor ... 

In this paper, the electronic structure of disordered Cu-Zn alloys are studied by calculations on models with Cu and Zn atoms distributed randomly on the sites of fee and bcc lattices. Concentrations of 10%, 25%, 50%, 75%, and 90% are used. The lattice spacings are the same for all the bcc models, 5.5 Bohr radii, and for all the fee models, 6.9 Bohr radii. With these lattice constants, the atomic volumes of the atoms are essentially the same in the two different crystal structures. Most of the bcc models contain 432 atoms and the fee models contain 500 atoms. These clusters are periodically reproduced to fill all space. Some of these calculations have been described previously. The test that is used to demonstrate that these clusters are large enough to be self-averaging is to repeat selected calculations with models that have the same concentration but a completely different arrangement of Cu and Zn atoms. We found differences that are quite small, and will be specified below in the discussions of specific properties. 

For local deviations from random atomic distribution electrical resistivity is affected just by the diffuse scattering of conduction electrons LRO in addition will contribute to resistivity by superlattice Bragg scattering, thus changing the effective number of conduction electrons. When measuring resistivity at a low and constant temperature no phonon scattering need be considered ar a rather simple formula results ... 

Compounds isotypic with the k phases arc found among intcrmetallics, borides, carbides and oxides and also with silicides, germanides, arsenides, sulfides and sclcnides no nitrides, however, are found. The mode of filling the various voids in the metal host lattice of the k phases follows the schemein Ref. 4 and is presented in Table 1 for all those compounds for which the atom distribution is well known from x-ray or neutron diffraction. Accordingly, B atoms in tc-borides, Zr, Mo, W, Re)4B and Hfy(Mo, W, Re, Os)4B , occupy the trigonal prismatic interstices within the parent metal framework of a Mn, Aln,-type structure (see Table 1 see also ref. 48). Extended solid solutions are found for (Hf, Al)[Pg.140]

A second simplihcation results from introducing the Born-Oppenheimer separation of electronic and nuclear motions for convenience, the latter is most often considered to be classical. Each excited electronic state of the molecule can then be considered as a distinct molecular species, and the laser-excited system can be viewed as a mixture of them. The local structure of such a system is generally described in terms of atom-atom distribution functions t) [22, 24, 25]. These functions are proportional to the probability of Ending the nuclei p and v at the distance r at time t. Building this information into Eq. (4) and considering the isotropy of a liquid system simplifies the theory considerably. 

Filming of atomic motions in liquids was thus accomplished. More specifically, the above experiment provides atom-atom distribution functions gpv(F, t) as they change during a chemical reaction. It also permits one to monitor temporal variations in the mean density of laser-heated solutions. Finally, it shows that motions of reactive and solvent molecules are strongly correlated the solvent is not an inert medium hosting the reaction [58]. 

There are many different atomic orbitals, and each has a characteristic energy and shape. How the electrons of an atom distribute themselves among the atomic orbitals is the subject of the next two sections. 

Iwasita T, Hoster H, John-Anaker A, Lin WE, Vielstich W. 2000. Methanol oxidation on PtRu electrodes. Influence of surface structure and Pt-Ru atom distribution. Langmuir 16 522-529. 

Electrochemical Properties All C Vs are presented on two different scales to show both the larger and smaller peaks in sufficient detail. At low Pt surface concentrations, the base CVs are very similar to those of the Pt island-modified Ru(OOOl) surfaces (see Fig. 14.5). With increasing Pt surface content, however, the charge in the Hupmore than one Ru atom were required for OHad and/or Hupd adsorption. Since the atom distribution in PcRui a /Ru(0001) surface alloys is very close to a random distribution [Hoster et al., 2008], the number of Ru sites is proportional to xj/u or (1 — xpt)". As is evident from the plot in Fig. 14.6, the experimental data agree very... 

Hosier H, Bergbreiter A, Erne P, Hager T, Rauscher H, Behm RJ. 2008. Atomic distribution in well-defined PtxRui x/Ru(0001) monolayer surface alloys. Phys Chem Chem Phys 10 3812. 

When the atoms differ in size or when the metals are chemically different, structures with ordered atomic distributions are considerably more likely. Since the transition from a... 

A position sensitive detector (PSD) is employed, of which there are several types used effectively around the world. One type is essentially a square array of multianodes, as shown in Figure 1.6. By measuring the time-of-flight and the coordinates of the ions upon the PSD, it is possible to map out a two-dimensional elemental distribution. The elemental maps are extended to the z-direction by ionizing atoms from the surface of the specimens. The z position is inferred from the position of the ion in the evaporation sequence, so that the atom distribution can be reconstructed in a three-dimensional real space. 

The effect can be applied, for example, to estimate a bond length or atomic spacing, to observe valence electron spin distribution around a specific atom and to derive information of the nearest neighbor atom distribution in a disordered system such as amorphous, under an expansion of the theory. 

Since the most active catalytic sites are usually steps, kinks, and surface defects, atomically resolved structural information including atomic distribution and surface structure at low pressure, possible surface restructuring, and the mobility of adsorbate molecules and of the atoms of the catalyst surface at high temperature and high pressure is crucial to understanding catalytic mechanisms on transition metal surfaces. The importance of studying the structural evolution ofboth adsorbates... 

The atomic distribution of positive charge must be taken into account when considering work functions for different crystal faces of solid metals. The chemical potential /x is a bulk property and... 

As 9 is varied, the fluorescent yield from target species a distance z above the mirror will be modulated according to equations (2.97) and (2.98) as a result of the movement inwards of the nodes and antinodes of the XSW. The phase and amplitude of this modulation are a measure of the mean position z and the width of the atom distribution. 

There are many metal alloys that contain interstitial atoms embedded in the metal structure. Traditionally, the interstitial alloys most studied are those of the transition metals with carbon and nitrogen, as the addition of these atoms to the crystal structure increases the hardness of the metal considerably. Steel remains the most important traditional interstitial alloy from a world perspective. It consists of carbon atoms distributed at random in interstitial sites within the face-centered cubic structure of iron to form the phase austenite, which exists over the composition range from pure iron to approximately 7 at % carbon. 

The analysis of x-ray diffraction data is divided into three parts. The first of these is the geometrical analysis, where one measures the exact spatial distribution of x-ray reflections and uses these to compute the size and shape of a unit cell. The second phase entails a study of the intensities of the various reflections, using this information to determine the atomic distribution within the unit cell. Finally, one looks at the x-ray diagram to deduce qualitative information about the quality of the crystal or the degree of order within the solid. This latter analysis may permit the adoption of certain assumptions that may aid in the solving of the crystalline structure. 

Examples of alternative descriptions of the unit cell In a number of cases, in order for instance, to compare a given atomic distribution and arrangement with several others, it may be useful to use different descriptions of the same structure (to refer to different, but obviously equivalent, unit cells). The transformations (of the unit cell constants and, consequently, of the coordinates of the atomic positions) are described, for the general case, for instance, in the International Tables (Hahn 2002). A few, frequently used, transformation formulae of the unit cell constants are reported here. 

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