Packing, most dense

Clean, polycrystalline metals expose mostly their most densely packed surface, because, to create this surface, the minimum number of bonds have to be broken (see Fig. 5.3). 

The energy needed to surmount the surface dipole layer is the surface contribution to the work function. It depends very much on the structure of the surface For fee metals the (111) surface is the most densely packed surface, and has the largest work function because the dipole barrier is high. A more open surface such as fee (110) has a smaller work function. Also, when a surface contains many defects, the... 

For the metal in the interface, the surface potential of the electrolyte phase is nearly the same for all crystal orientations.29 Therefore, referring to Eq. (2), the potential of zero charge varies with the surface potential or the work funtion and is larger for the most densely packed faces. Correspondingly, atomic irregularities... 

Pack explosive densely into the bottom one fourth of the container. A tin can of about 1 gallon capacity is about ideal for most targets. The container should not be smaller than 1 quart but large diameter cardboard tubes or ordinary pails are satisfactory. 

Figure A.l Construction of the most densely packed surfaces of fee and bcc metals, and the outer atomic layer of the low-index surfaces. The hep (001) surface has the same structure as...

The problem of the variation in the surface energies of various crystal facets can be attacked from several points of view. Bravais first noted that those planes of a crystal which were most densely packed and were also separated most distantly from the neighbouring parallel plane were those which appeared most frequently in crystals he noted also that a closely packed surface was usually associated with a wide interplanar distance and vice versa. Later Willard Gibbs indicated that the most stable planes on a growing crystal were those possessing the least interfacial surface energy. 

Beside dislocation density, dislocation orientation is the primary factor in determining the critical shear stress required for plastic deformation. Dislocations do not move with the same degree of ease in all crystallographic directions or in all crystallographic planes. There is usually a preferred direction for slip dislocation movement. The combination of slip direction and slip plane is called the slip system, and it depends on the crystal structure of the metal. The slip plane is usually that plane having the most dense atomic packing (cf. Section 1.1.1.2). In face-centered cubic structures, this plane is the (111) plane, and the slip direction is the [110] direction. Each slip plane may contain more than one possible slip direction, so several slip systems may exist for a particular crystal structure. Eor FCC, there are a total of 12 possible slip systems four different (111) planes and three independent [110] directions for each plane. The... 

Low Miller index surfaces of metallic single crystals are the most commonly used substrates in LEED investigations. The reasons for their widespread use are that they have the lowest surface free energy and therefore are the most stable, have the highest rotational symmetry and are the most densely packed. Also, in the case of transition metals and semiconductors they are chemically less reactive than the higher Miller index crystal faces. 

The top layer of a (111) surface actually has sixfold symmetry, but the rotational symmetry of the top layers together is threefold. Since the near surface region can influence where gases adsorb on the surface and the LEED intensities exhibit threefold rotational symmetry at normal incidence, the (111) surface will be considered to have threefold rotational symmetry. Although most of the adsorption studies have been carried out on fee and bcc crystals, there have been several studies reported on hep crystals. For hep metals the basal or (0001) plane is the surface most frequently studied by LEED investigations and it is the most densely packed plane having threefold rotational symmetry. 

Only very few investigations have been performed with surfaces not belonging to the most densely packed planes. On Pd(210) the formation of 1 x 1- and 1 x 2-overlayer structures were observed for which the proposed structure models are reproduced in Fig. 9 (52, 60). For the 1 x 1 structure a C—O stretch frequency of 1878 cm"1 was observed which is, interestingly,... 

Table II lists a series of values for the adsorption energy of CO on the three most densely packed planes of the platinum metals at low coverages i.e., at surface concentrations that are believed to be small enough to rule out noticeable effects on these energies owing to mutual interactions between the adsorbates or the occupation of different adsorption sites. These values are therefore believed to represent the strength of the proper metal-CO bond with the adsorbate in its energetically most favorable position on the surface. These data were obtained in two different ways ...

Carefully prepared Au catalysts have a relatively narrow particle size distribution, giving mean diameters in the range 2-10 nm with a standard deviation of about 30%. A major reason why Au particles remain as NPs even after calcination 573 K is the epitaxial contact of Au NPs with the metal oxide supports. Gold particles always expose its most densely packed plane, the (111) plane, in contact with a-Fe2O3(110), Co304(lll), anatase Ti02(112), and rutile TiO2(110). 

Analysis of the TM-AFM data demonstrates that there is a good correlation (<20% difference) between the experimentally determined and calculated parameters for four of the five nanostructures (Table 4.1). The best correlation was found for assemblies [l3 (DEB)6]n (< 10%), which is the result of a most densely packed structure. It is remarkable that in the case of assembly [la3 6a3]n, the only one that is formed from the polar solvent DMSO, exhibits a significant distance between nanorods (n = 1.5). The value suggests that the nature of the solvent plays an important role. 

It may be noted that the three faces give rise to different heats of adsorption. The 110 face, which is the least densely packed with copper atoms, gives the smallest value the most densely packed 111 face gives the highest heat of adsorption. Polycrystalline copper, at low... 

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