The Structures of Simple Solids

If we apply Pythagoras theorem to this case, we obtain 

Finally, we can square the result in (1) and equate this to (3) to obtain the relationship between r and a in a body-centred unit cell as  

From here the volume of the cell is Thus the fraction of space occupied by identical spheres in this 

From these results and Example 3.3, it becomes clear that closed-packed cubic lattice has the best space economy (best packing, least empty space), followed by the body-centred lattice, whereas the simple cubic packing has the lowest space economy with the highest fraction of unoccupied space. 

165 X 10 g. The volume of the unit cell is a where a is the length of the edge of the unit cell. The density equals mass divided by volume or  

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The dominant features which control the stoichiometry of transition-metal complexes relate to the relative sizes of the metal ions and the ligands, rather than the niceties of electronic configuration. You will recall that the structures of simple ionic solids may be predicted with reasonable accuracy on the basis of radius-ratio rules in which the relative ionic sizes of the cations and anions in the lattice determine the structure adopted. Similar effects are important in determining coordination numbers in transition-metal compounds. In short, it is possible to pack more small ligands than large ligands about a metal ion of a given size. 

The geometries of a number of molecules, including NF2 and NF, have been rationalized using a hard-atom model similar to that used in describing the structures of simple ionic compounds in the solid state. The calculated F—N—F angles/ (observed angles in parentheses) are NF2 104.8 (102.5) and NF3... 

As illustrated in the previous section, the metal-rich rare earth metal halides and their interstitial derivatives provide a vast collection of compounds that transcends the structural chemistry of both molecules and extended solids. On the one hand, these substances can be considered as connected or condensed clusters of the MgXi2-or MgXg-type, which may contain interstitial species. On the other hand, many of them can be derived from the structures of simple salts, e.g. NaCl or La20jS. 

Brow, R.K. (2000) Review The structure of simple phosphate glasses, J. Non-Cryst. Solids 263 and 264,... 

The structures of simple ionic solids can be classified as a few basic types. The NaCl structure is a representative example of one type. Odier compounds tiiat possess this same structure include LiF, KCl, AgCl, and CaO. Three otiier common types of crystal structures are shown in Figure 11.42 T. 

Simple interatomic potentials for describing the structure of ionic solids consist of two-body terms only and have the form (1) with Ysr = Yb-... 

To deal with complex mineralogical structures such as the silicates, Pauling introduced in 1928 several rules which are still widely used. The first of these, and the most important, stresses the formation about each cation of a coordinated anion polyhedron. Allowable anion configurations are determined from radius-ratio considerations, such as those discussed above for simple ionic solids. Although these are not really precise enough to account in exact detail for all the structures of simple ionic crystals, they still provide an excellent guide for understanding the structure of minerals such... 

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 ... 

In the last chapter we examined data for the yield strengths exhibited by materials. But what would we expect From our understanding of the structure of solids and the stiffness of the bonds between the atoms, can we estimate what the yield strength should be A simple calculation (given in the next section) overestimates it grossly. This is because real crystals contain defects, dislocations, which move easily. When they move, the crystal deforms the stress needed to move them is the yield strength. Dislocations are the carriers of deformation, much as electrons are the carriers of charge. 

Below a temperature of Toi 260 K, the Ceo molecules completely lose two of their three degrees of rotational freedom, and the residual degree of freedom is a ratcheting rotational motion for each of the four molecules within the unit cell about a different (111) axis [43, 45, 46, 47]. The structure of solid Ceo below Tqi becomes simple cubic (space group Tji or PaS) with a lattice constant ao = 14.17A and four Ceo molecules per unit cell, as the four oriented molecules within the fee structure become inequivalent [see Fig. 2(a)] [43, 45]. Supporting evidence for the phase transition at Tqi 260 K is... 

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