Interior atom

If the interaction between atoms that are not nearest neighbors is neglected, then the ratios B/A are each equal to the ratio of the number of nearest neighbors to a surface atom (across the dividing plane) to the number of nearest neighbors for an interior atom. The calculation then reduces to that given by Eq. Ill-15. 

The calculation of the surface energy of metals has been along two rather different lines. The first has been that of Skapski, outlined in Section III-IB. In its simplest form, the procedure involves simply prorating the surface energy to the energy of vaporization on the basis of the ratio of the number of nearest neighbors for a surface atom to that for an interior atom. The effect is to bypass the theoretical question of the exact calculation of the cohesional forces of a metal and, of course, to ignore the matter of surface distortion. 

Metals A and B form an alloy or solid solution. To take a hypothetical case, suppose that the structure is simple cubic, so that each interior atom has six nearest neighbors and each surface atom has five. A particular alloy has a bulk mole fraction XA = 0.50, the side of the unit cell is 4.0 A, and the energies of vaporization Ea and Eb are 30 and 35 kcal/mol for the respective pure metals. The A—A bond energy is aa and the B—B bond energy is bb assume that ab = j( aa + bb)- Calculate the surface energy as a function of surface composition. What should the surface composition be at 0 K In what direction should it change on heaf)pg, and why ... 

Since solids do not exist as truly infinite systems, there are issues related to their temiination (i.e. surfaces). However, in most cases, the existence of a surface does not strongly affect the properties of the crystal as a whole. The number of atoms in the interior of a cluster scale as the cube of the size of the specimen while the number of surface atoms scale as the square of the size of the specimen. For a sample of macroscopic size, the number of interior atoms vastly exceeds the number of atoms at the surface. On the other hand, there are interesting properties of the surface of condensed matter systems that have no analogue in atomic or molecular systems. For example, electronic states can exist that trap electrons at the interface between a solid and the vacuum [1]. 

The simplest approach to understanding the reduced melting point in nanocrystals relies on a simple thennodynamic model which considers the volume and surface as separate components. Wliether solid or melted, a nanocrystal surface contains atoms which are not bound to interior atoms. This raises the net free energy of the system because of the positive surface free energy, but the energetic cost of the surface is higher for a solid cluster than for a liquid cluster. Thus the free-energy difference between the two phases of a nanocrystal becomes smaller as the cluster size... 

Consider the surface of a solid. In the interior, we see a certain s mmetry which depends upon the structure of the solid. As we approach the surface from the interior, the symmetry begins to change. At the very surface, the surface atoms see only half the symmetry that the interior atoms do (and half of the bonding as weU). Reactions between solids take place at the surface. Thus, the surface of a solid represents a defect in itself since it is not like the interior of the solid. 

Pitera, J.W. van Gunsteren, W.F., The importance of solute-solvent van der Waals interactions with interior atoms of biopolymers, J. Am. Chem. Soc. 2001,123, 3163-3164. 

A surface atom has, by definition, a smaller number of nearest neighbors than an atom in the interior of the crystal. An interior atom in the metals with which we are concerned here, and which are all fee, has twelve nearest neighbors. On every metal crystal there will be found various types of surface atoms that differ in the number j and in the arrangement of their... 

Atoms common to two or more rings are designated by adding roman letters a , b , c , etc., to the number of the position immediately preceding. Interior atoms follow the highest number, taking a clockwise sequence wherever there is a choice. 

Figure 11. Unit orthogonal base vectors a , a2, and a3 for local Cartesian coordinate system associated with chain interior atom / . Atoms / — 1,/ ,/ + 1 lie in ah a2 plane and a2 bisects bond angle 8. Also shown are bond vectors W1 and r 1.

Note that for acyclic compounds larger than a single atom, deletion of an interior atom will always increase the number of blocks. 

Furthermore, multiple ionization, which has been postulated as being able to bring about displacements of interior atoms (30), might be extremely effective in leading to surface migrations and thermal patches, in which case surface properties could be more sensitive to electromagnetic radiation than to particle radiation. it was hoped that the present studies would shed some light on what actually happens. 

In addition to being coordinatively highly unsaturated, small clusters also are dominated by their surface properties. For example, a 19 atom cluster may have at most one or two interior atoms. Even a 100 atom cluster has only about 28 interior (bulklike ) atoms. Thus the surface sensitive properties become increasingly important as the size becomes smaller. Clusters do not possess the long range periodicity one would have with a bulk crystal. Thus we expect that each small cluster will be a unique entity, and that its ground state structure (or structures if different isomorphic structures are nearly isoenergetic) will depend sensitively on size and likely will not be simply a subunit of the bulk lattice. 

FIGURE 7-6 The Structure of Diamond, (a) Subdivision of the unit cell, with atoms in alternating smaller cubes, (b) The tetrahedral coordination of carbon is shown for the four interior atoms. 

The atomic volume a( l) is defined as a measure of the region of space enclosed by the intersection of its interatomic surfaces and an envelope of the charge density of some chosen value. An atomic surface is the union of some number of interatomic surfaces, there being one such surface for each bonded neighbour and, if the atom is not an interior atom, some portions which may be infinitely distant from the attractor. It is these latter, open portions of the atomic surface which are replaced with an envelope of the charge density, a surface on which p(r) has a constant value. An envelope of the charge density can be used to define the van der Waals shape or size of a molecule in... 

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