Close-Packed Crystal Structures

The surfaces are labeled according to the lattice plane that is exposed. The (111), (100) and (110) surfaces are perpendicular to the < 111 >, <100> and <1I0> directions in the crystal. The close-packed surface of the hep lattice, the (001) plane, [or strictly speaking the (0001) plane, because four coordinates are used for hexagonal lattices], has the same structure as the fee (111) plane [11]. 

A few metals crystallize with close-packed structures with non-... 

Further, it is observed experimentally that electron-pair bonds are frequently associated with anisotropic, i.e. directed, atomic orbitals. This gives rise to open structures. However, the electrostatic (Madelung) energy associated with ionic crystals favors close packing Therefore largely ionic crystals favor more close-packed, two-sublattice structures such as rock salt versus zinc blende. In the case of two-sublattice structures induced by d electrons, electron-pair bonds are generally prohibited by the metallic or ionic outer s and p electrons that favor close packing. Nevertheless, it will be found in Chapter III, Section II that, if transition element cations are small relative to the anion interstice and simultaneously have Rti RCf electron-pair bonds may be formed below a critical temperature. 

In real three-dimensional materials, it is clear that the various molecular constituents are all of importance in determining the equilibrium crystal structures. They obey complex steric rules according to which a structural close packing can be optimized at every temperature. All these constituents should then be taken into account correctly in the description of structural phase transitions. In the case of TCNQ salts, this means that the entire molecular system formed by the conducting TCNQ chains plus the cations has in fact to be considered. 

We have mentioned in the previous chapter the two crystalline forms of carbon diamond and graphite. The latter structure is unique among the elements, but a number of other elements of Group IV crystallize with the diamond structure ilicon, germanium, and tin (grey modification). In the B subgroup only lead has a typical metallic structure (cubic close-packed), whereas all the elements of the A subgroup crystallize with close-packed structures. In elementary silicon Si-Si = 2-35 A. 

We have said that the elements Al, In, Tl, and Pb, which crystallize with close-packed or approximately close-packed structures, are abnormal in certain respects. In the case of Al there is evidence that the atoms are not completely ionized in the pure metal and that the atomic diameter of the fully ionized Al is nearer 2-70 than 2 86 A, the closest distance of approach of atoms in aluminium itself. The melting point of the metal is only 8°C higher than that of Mg, in contrast to the rise in melting point with increase in valence in the first row and A subgroup elements ... 

The electronic configuration of the ions is essentially an inert gas configuration, the charge distribution of each ion being spherically symmetric. Consequently, ionic solids crystallize in close-packed structures. Apparently, the anions and cations do not behave like hard (nonoverlapping) spheres. Experimentally, the observed interatomic distance in solid ionic compositions is less than the sum of the ionic radii. 

It is well known that if a solute differs in its atomic size by more than 15% from the host, then limited or no solubility is likely (Hume-Rothery, 1955). Perovskite-type materials crystallize with close-packed structures, whose main feature is a presence of frameworks of tilted and distorted octahedra. Even minor substitutions on the A-site would lead to strained octahedral frameworks, and further increase may result in its destruction. Therefore, in perovskites, the conventional 15% limit initially established for metals should be reduced to the level of 10% or even less. This agrees well with the observed value Ar 0.11 A. The analysis of the critical contents via the perovskite cell deformation reveals radius limitations at 1.213, 1.212,1.210,1.208, and 1.209 A corresponding to x = 0.06, 0.06, 0.04, 0.03, and 0.02 for Er, Ho, Y, Dy, and Tb-containing Lai j Rj Ga03, respectively. Observed radii corresponding to limitations in solubility for different Lai cR cGa03 (R = Tb-Er and Y) are very close to each other. 

As described in the previous section, most metals crystallize in close-packed structures. 

Colloidal crystal A close-packed structure formed from colloidal particles analogous to an atomic crystal. 

This structure is called close packed because the number of atoms per unit volume is quite large compared with other simple crystal structures. 

As with other related rare-earth metals, gadolinium is silvery white, has a metallic luster, and is malleable and ductile. At room temperature, gadolinium crystallizes in the hexagonal, close-packed alpha form. Upon heating to 1235oG, alpha gadolinium transforms into the beta form, which has a body-centered cubic structure. 

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