Crystal-like atoms

Besides the internal and external vibrations of the molecules, there are, as already mentioned, also stochastic or at higher temperatures nearly free rotations of entire molecules in some molecular crystals (e.g. the benzene molecules in a benzene crystal or the -CH3 groups in methyl-substituted aromatics). And finally, molecules in molecular crystals, like atoms in atomic crystals, can diffuse. 

For a purpose of clarity, we have chosen to restrict the representation to crystal-like atoms. We define for each atom i the parameter A ... 

Fig. 6.18 Crystal-like atoms during annealing in the 2D-periodised case...

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

Fig. 5. The one that has non-zero values only near q=0.0 corresponds to twelve Cu atoms on the nn-shell, ci=100%. It is known that an atom on a site surrounded by like atoms behaves somewhat like an atom in a pure crystal, and would have little net charge. The conditional probability centered near q=0.2 corresponds to ci=0%, with all the neighboring atoms Zn. Such an atom behaves like a Cu impurity in a Zn crystal. The probabilities Pcu(ci,q) for ci=25%, 50%, and 75% have their centers between these limits, llte conditional probabilities have a structure themselves. Extrapolating, it should be possible to write Pcu(ci>q) a sum of the conditional probabilities Pcu(ci,C2,q) where C2 is the concentration of Cu atoms on the second nn-shell. That probability could, in turn, be written as the sum of probabilities PCu(ci,C2,C3,q), where eg is the concentration of Cu atoms on the third nn-shell.

In Chapter 5 we identified metals by their high electrical conductivity. Now we can explain why they conduct electric current so well. It is because there are some electrons present in the crystal lattice that are extremely mobile. These conduction electrons move throughout the metallic crystal without specific attachment to particular atoms. The alkali elements form metals because of the ease of freeing one electron per atom to provide a reservoir of conduction electrons. The ease of freeing these conduction electrons derives from the stability of the residual, inert gas-like atoms. 

Fig. 3 a Scheme of a bundle (Model A [8,9]). Chain repeating units are evidenced as black dots, crystalline packed stems are shown as thickened straight portions of the chain, dashed lines stand for crystal-like attractions, b A bundle comprising 4 stems, 3 loops (see Appendix). Dashed lines stand for energy attraction between crystal-like stems with a chain atoms n, 7 2, 3 are numbers of chain atoms in the loops... 

Let the atoms in the chain be numbered 0, 1,. . . , iV, and let the foreign atom be denoted by X (Fig. 1). Associated with each atom we introduce an atomic orbital < (r, m). These orbitals are divided into two sets. One set (m = X) contains only one member, which is the orbital on the foreign atom the other set (m = 0, 1,. . . , A) consists of the orbitals on the crystal atoms. Thus, we have the problem of the interaction of a hydrogen-like atom with a crystal whose normal electronic structure consists of just one band of states. 

Itinerant electrons occupy band states, which are molecular orbitals for an entire crystal they therefore belong equally to all like atoms on energetically equivalent sites and are described by band theory. 

There is an important difference between an ionic crystal like MgO and a molecular substance such as liquid or solid H20. In the molecular substance there is a clear distinction between molecular and intermolecular modes because the atoms are bound into molecules much more tightly than the molecules are bound to one another. In the ionic crystal there is no such... 

A supersolid is actually a superfluid with the crystal-like structure of a traditional solid. Inside a supersolid, the atoms are moving and flowing as superfluids, but outside, the substance maintains its shape. Supersolids had been predicted to exist in theory, but were only created in a laboratory in 2004. 

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