Atomic schematic

Figure 1.12 The three different types of cluster size dependence of catalytic conversion. Rates are considered normalized per exposed surface atom (schematic).

Fig. 1-7 Electronic transitions in an atom (schematic). Emission processes indicated by arrows.

Figure 1. The interaction potential (van der Waals potential) for a pair of rare gas atoms (schematic).

As any bright chemist or physicist might have guessed already, the bad scaling behavior does not stem from the chemistry (or physics) itself, it is a consequence of the mathematical apparatus. Consider a large one-dimensional system composed of many different atoms, schematically depicted in the following Scheme 2.9 ... 

Although these two papers contain no theoretical statements other than those just cited, their content is consistent with the idea that Kekule was deliberately building the factual groundwork for a future more general statement about how one might use the substitution-values of atoms schematically to build up proposed molecular constitutions. It is even possible that Kekule may have chosen precisely the fulminate series for his efforts because it so clearly illustrated the "tet-ratomic" (i.e., tetravalent) nature of carbon. ... 

Figure 5.21. Primary ensemble effect (a) multimolecular atom adsorption to a metal surface (b) decrease in heat of adsorption by site blocking. S indicates an adsorbed sulfur atom, (schematic denotes a site consisting of one or more surface metal atoms).

Fig. VIII-1. Schematic illustration of the scanning tunneling microscope (STM) and atomic force microscope (AFM). (From Ref. 9.)...

While field ion microscopy has provided an effective means to visualize surface atoms and adsorbates, field emission is the preferred technique for measurement of the energetic properties of the surface. The effect of an applied field on the rate of electron emission was described by Fowler and Nordheim [65] and is shown schematically in Fig. Vlll 5. In the absence of a field, a barrier corresponding to the thermionic work function, prevents electrons from escaping from the Fermi level. An applied field, reduces this barrier to 4> - F, where the potential V decreases linearly with distance according to V = xF. Quantum-mechanical tunneling is now possible through this finite barrier, and the solufion for an electron in a finite potential box gives... 

Figure Al.7.4. Schematic illustration of two Si atoms as they would be oriented on the (100) surface, (a) Bulk-tenuiuated structure showing two dangling bonds (lone electrons) per atom, (b) Synnnetric dimer, in which two electrons are shared and each atom has one remaining dangling bond, (c) Asynnnetric dimer in which two electrons pair up on one atom and the otiier has an empty orbital.

Figure Al.7.6. Schematic diagrams of the DAS model of the Si(l 11)-(7 x 7) surface structure. There are 12 adatoms per unit cell in the outennost layer, which each have one dangling bond perpendicular to the surface. The second layer, called the rest layer, also has six rest atoms per unit cell, each with a perpendicular dangling bond. The comer holes at the edges of the nnit cells also contain one atom with a dangling bond.

FigureBl.7.2. Schematic representations of alternative ionization methods to El and PI (a) fast-atom bombardment in which a beam of keV atoms desorbs solute from a matrix (b) matrix-assisted laser desorption ionization and (c) electrospray ionization.

Figure Bl.7.12. A schematic diagram of a typical selected-ion flow (SIFT) apparatus. (Smith D and Adams N G 1988 The selected ion flow tube (SIFT) studies of ion-neutral reactions Advances in Atomic and Molecular Physics vol 24, ed D Bates and B Bederson p 4. Copyright Academic Press, Inc. Reproduced with pennission.)...

Figure Bl.19.18. Schematic of an atomic force microscope showing the optical lever principle.

Figure Bl.24.2. A schematic representation of an elastic collision between a particle of massM and energy Eq and a target atom of mass M2. After the collision the projectile and target atoms have energies of and 2 respectively. The angles 0 and ( ) are positive as shown. All quantities refer to tire laboratory frame of reference.

Figure Bl.24.14. A schematic diagram of x-ray generation by energetic particle excitation, (a) A beam of energetic ions is used to eject inner-shell electrons from atoms in a sample, (b) These vacancies are filled by outer-shell electrons and the electrons make a transition in energy in moving from one level to another this energy is released in the fomi of characteristic x-rays, the energy of which identifies that particular atom. The x-rays that are emitted from the sample are measured witli an energy dispersive detector.

Figure B2.5.1 schematically illustrates a typical flow-tube set-up. In gas-phase studies, it serves mainly two purposes. On the one hand it allows highly reactive shortlived reactant species, such as radicals or atoms, to be prepared at well-defined concentrations in an inert buffer gas. On the other hand, the flow replaces the time dependence, t, of a reaction by the dependence on the distance v from the point where the reactants are mixed by the simple transfomiation with the flow velocity vy...

Figure B3.2.4. A schematic illustration of an energy-independent augmented plane wave basis fimction used in the LAPW method. The black sine fimction represents the plane wave, the localized oscillations represent the augmentation of the fimction inside the atomic spheres used for the solution of the Sclirodinger equation. The nuclei are represented by filled black circles. In the lower part of the picture, the crystal potential is sketched.

Figure C2.9.3 Schematic diagrams of the interfaces reaiized by (a) tire atomic force microscope, (b) tire surface forces apparatus and (c) tire quartz crystai microbaiance for achieving fundamentai measurements of friction in weii defined systems.

Figure C3.2.18.(a) Model a-helix, (b) hydrogen bonding contacts in tire helix, and (c) schematic representation of tire effective Hamiltonian interactions between atoms in tire protein backbone. From [23].

The PEF is a sum of many individual contributions, Tt can be divided into bonded (bonds, angles, and torsions) and non-bonded (electrostatic and van der Waals) contributions V, responsible for intramolecular and, in tlic case of more than one molecule, also intermoleculai interactions. Figure 7-8 shows schematically these types of interactions between atoms, which arc included in almost all force field implementations. 

Schematic energy surfaces for all-atom (left) and simplified (right) models. 

An important feature of aldol addition is that carbon-carbon bond formation occurs between the a carbon atom of one aldehyde and the carbonyl group of another This is because carbanion (enolate) generation can involve proton abstraction only from the a carbon atom The overall transformation can be represented schematically as shown m Figure 18 5... 

Schematic model of AgCI showing difference between bulk and surface atoms of silver. Silver and chloride ions are not shown to scale.

Schematic diagram of a hoiiow cathode iamp showing mechanism by which atomic emission is obtained.

Schematic diagram of a muitichannei atomic emission spectrometer, showing the arrangement of muitipie exit siits and detectors for the simuitaneous anaiysis of severai eiements.

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