Close packing in crystals

Stable structures with empty spaces are possible only for crystals where some interatomic forces are stronger and directional, that is non-isotropic. One example are zeolites, where covalent bonding forces hold together the molecular scaffold and more than compensate for the very weak attraction across the void zones [15]. Another obvious example is water ice, with its strong hydrogen bonding network that creates 

Compound class Average Cpack and rms deviation Number of crystals Average Qelf.occ 

Another confirmation of the close packing principle can be found in the rather common occurrence [17] of the formation of clathrates, hydrates, and solvates whenever the shape of the crystallizing molecule is too complex to allow efficient self-recognition with total space occupation, highly mobile solvent molecules slip in between and are incorporated in the crystal structure as space fillers. Incidentally, no numerical indicator of the ability or even the tendency of a given molecule to form solvate crystals has ever been found, a confirmation of the difficulties encountered in the definition of numerical descriptors of molecular shape. 

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For ionic crystals there is strong attraction between cations and anions, and strong repulsion between ions having the same charge. These interactions determine structures because ions must be shielded from those with the same charge. The relative sizes of the ions are important in determining the CN. Removal of electron(s) decreases the size of a cation relative to the atom and addition of electron(s) increases the size of an anion relative to the atom. Commonly, for an MX compound the anion is larger than the cation and the anions are close packed in crystals with cations in octahedral or tetrahedral sites. 

There are more noncovalent interactions which cannot all be introduced here. Forces between multipoles have been expertly reviewed recently [12]. Also, weak interactions exist between nitrogen and halogen atoms [13], and dihydrogen bridges [14] can be formed between metal hydrides and hydrogen bond donors. Finally, close packing in crystals is an important force in crystallization and crystal engineering. The present introductory chapter will not discuss these, but rather focus on the most important ones mentioned above. 

At temperatures only slightly below the liquefaction temperatures, the liquids freeze. The solids are all simple crystals in which the atoms are close-packed in a regular lattice arrangement. The narrow temperature range over which any one of these liquids can exist suggests that the forces holding the crystal together are very much like the forces in the liquid. 

Introduction of bulky lateral substituents on monomer units to increase interchain distance and prevent close packing in polymer crystal. The use of unsymmetrically substituted monomers, resulting in a random distribution of head-to-head and head-to-tail structures in polymer chains, further helps in disrupting regularity. Some examples of substituent effects are given in Table 2.16. 

The first first direct experimental evidence for a roughening transition was reported in 1979. Several groups have studied the thermal behavior of the basal plane of a hexagonal close-packed He crystal. In a beautiful experiment Balibar and Casting obtained for this surface a roughening temperature of Tk 1.2K. 

Most metals active in cyclization belong to Group VIIIB and have either face-centered-cubic (fee) or hexagonal close packed (hep) crystal structure. 

Soft, lustrous metal silver-like appearance close-packed hexagonal crystal system density 8.78 g/cm paramagnetic magnetic moment 11.2 Bohr magnetons melts at 1,472°C vaporizes at 2,694°C electrical resistivity 195 microhm-cm at 25°C Young s modulus 6.71xl0n dynes/cm2 Poisson s ratio 0.255 thermal neutron cross section 64 barns insoluble in water soluble in acids (with reactions). 

Silvery-white metal close-packed cubic crystals lattice constant 3.8394A at 20°C density 22.42 g/cm (highest among metals) melts at 2410°C vaporizes at 4,130°C hardness 6-6.5 Mohs electrical resistivity 4.71 j,ohm-cm Young s modulus 3.75 x 10 tons/in magnetic susceptibility 0.133 x 10 cm3/g thermal neutron absorption cross section 440 barns. 

The metal substrates used in the LEED experiments have either face centered cubic (fee), body centered cubic (bcc) or hexagonal closed packed (hep) crystal structures. For the cubic metals the (111), (100) and (110) planes are the low Miller index surfaces and they have threefold, fourfold and twofold rotational symmetry, respectively. 

This structure is met in the crystals of selenium and tellurium, in which the atoms occur in chains twisted into spirals. This spiral formation is caused by the fact that valency bonds make angles of 105° with one another, and these can lead to chains of various shapes, but if a spiral is formed the atoms are closely packed in the chain so that the energy of the van der Waals forces, which are always acting, can assume a low value. 

A summary of physical and chemical constants for beryllium is compiled in Table 1 (3—7). One of the more important characteristics of beryllium is its pronounced anisotropy resulting from the close-packed hexagonal crystal structure. This factor must be considered for any property that is known or suspected to be structure sensitive. As an example, the thermal expansion coefficient at 273 K of single-crystal beryllium was measured (8) as 10.6 x 10-6 parallel to the -axis and 7.7 x 10-6 parallel to the t-axis. The actual expansion of polycrystalline metal then becomes a function of the degree of preferred orientation present and the direction of measurement in wrought beryllium. 

The (100) split-dumbbell defect in Fig. 8.5d, while having the lowest energy of all interstitial defects, still has a large formation energy (Ef = 2.2 eV) because of the large amount of distortion and ion-core repulsion required for its insertion into the close-packed Cu crystal. However, once the interstitial defect is present, it persists until it migrates to an interface or dislocation or annihilates with a vacancy. The... 

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