Crystal Stmctures

As an indication of the types of infonnation gleaned from all-electron methods, we focus on one recent approach, the FLAPW method. It has been used to detennine the band stmcture and optical properties over a wide energy range for a variety of crystal stmctures and chemical compositions ranging from elementary metals [ ] to complex oxides [M], layered dichalcogenides [, and nanoporous semiconductors The k p fonnulation has also enabled calculation of the complex band stmcture of the A1 (100) surface... 

Order and dense packing are relative in tire context of tliese systems and depend on tire point of view. Usually tire tenn order is used in connection witli translational symmetry in molecular stmctures, i.e. in a two-dimensional monolayer witli a crystal stmcture. Dense packing in organic layers is connected witli tire density of crystalline polyetliylene. 

Figure C2.17.1. Transmission electron micrograph of a Ti02 (anatase) nanocrystal. The mottled and unstmctured background is an amorjihous carbon support film. The nanocrystal is centred in die middle of die image. This microscopy allows for die direct imaging of die crystal stmcture, as well as the overall nanocrystal shape. This titania nanocrystal was syndiesized using die nonhydrolytic niediod outlined in [79].

Figure C2.17.6. Transmission electron micrograph and its Fourier transfonn for a TiC nanocrystal. High-resolution images of nanocrystals can be used to identify crystal stmctures. In tliis case, tire image of a nanocrystal of titanium carbide (right) was Fourier transfonned to produce tire pattern on tire left. From an analysis of tire spot geometry and spacing, one can detennine that tire nanocrystal is oriented witli its 11001 zone axis parallel to tire viewing direction [217].

Figure C2.17.7. Selected area electron diffraction pattern from TiC nanocrystals. Electron diffraction from fields of nanocrystals is used to detennine tire crystal stmcture of an ensemble of nanocrystals [119]. In tliis case, tliis infonnation was used to evaluate the phase of titanium carbide nanocrystals [217].

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

The ability to control pressure in the laboratory environment is a powerful tool for investigating phase changes in materials. At high pressure, many solids will transfonn to denser crystal stmctures. The study of nanocrystals under high pressure, then, allows one to investigate the size dependence of the solid-solid phase transition pressures. Results from studies of both CdSe [219, 220, 221 and 222] and silicon nanocrystals [223] indicate that solid-solid phase transition pressures are elevated in smaller nanocrystals. 

More recently, studies of the hysteresis of these phase transitions have illuminated the importance of kinetic factors in solid-solid phase transitions [224]. The change between crystal stmctures does not occur at the same point when pressure is increasing, as when it is decreasing the difference between this up-stroke and down-stroke pressure... 

Crystal stmctures of complexes of copper(II) with aromatic amine ligands and -amino acids " " and dipeptides" have been published. The stmctures of mixed ligand-copper complexes of L-tryptophan in combination with 1,10-phenanthroline and 2,2 -bipyridine and L-tyrosine in combination with 2,2 -bipyridine are shown in Figure 3.2. Note the subtle difference between the orientation of the indole ring in the two 1,10-phenanthroline complexes. The distance between the two... 

EXAFS spectra of platinum metal, having a face-centred cubic crystal stmcture, have been obtained at 300 K and 673 K. Explain what qualitative differences you might expect. How many nearest-neighbour atoms are there in this stmcture Illustrate your answer with a diagram. 

Fig. 26. Clathrate receptor chemistry (a) a chiroselective crystalline host compound (clathrand) (b) a typical guest molecule to be included in the specified configuration and (c) the crystal stmcture of the respective clathrate (A and B denote host and C the guest species) (169).

Single-Stack Acceptor. Simple charge-transfer salts formed from the planar acceptor TCNQ have a stacked arrangement with the TCNQ units facing each other (intermolecular distances of ca 0.3 nm (- 3). Complex salts of TCNQ such as TEA(TCNQ)2 consist of stacks of parallel TCNQ molecules, with cation sites between the stacks (17). The interatomic distance between TCNQ units is not always uniform in these salts, and formation of TCNQ dimers (as in TEA(TCNQ)2) and trimers (as in Cs2(TCNQ)Q can lead to complex crystal stmctures for the chainlike salts. 

In Parylene C, the single crystalline form observed is very similar to the d form of Parylene N. Its detailed crystal stmcture has been deterrnined (a = 596 pm, b = 1269 pm, c (chain axis) = 666 pm, /5 = 135.2°) (47). X-ray studies on the crystal stmcture of Parylene D have not been reported. 

Crystal Structure and Ionic Radii. Crystal stmcture data have provided the basis for the ionic radii (coordination number = CN = 6), which are summarized in Table 9 (13,14,17). For both and ions there is an actinide contraction, analogous to the lanthanide contraction, with increasing positive charge on the nucleus. 

Eig. 5. The Widmanstatten pattern ia this poHshed and etched section of the Gibbeon iron meteorite is composed of iatergrown crystals of kamacite and taenite, NiFe phases that differ ia crystal stmcture and Ni content. Ni concentration gradients at crystal boundaries ia this 3-cm-wide sample can be used to estimate the initial cooling rates and corresponding size of the asteroid from which the meteorite was derived. 

The crystal stmcture of glycerides may be unambiguously determined by x-ray diffraction of powdered samples. However, the dynamic crystallization may also be readily studied by differential scanning calorimetry (dsc). Crystallization, remelting, and recrystallization to a more stable form may be observed when Hquid fat is solidified at a carefully controlled rate ia the iastmment. Enthalpy values and melting poiats for the various crystal forms are shown ia Table 3 (52). 

Ferrites can be classified according to crystal stmcture, ie, cubic vs hexagonal, or magnetic behavior, ie, soft vs hard ferrites. A systematic classification as well as some appHcations ate given in Table 1 (see also Magnetic materials, bulk Magnetic materials, thin film). 

Fig. 4. Effect of isovalent substitutions on crystal stmcture transition temperatures of ceramic BaTiO where ( ) represents Pb (—), Ca and ( ) substitution for Ba and (—) and ( ) substitution for. Transition temperatures for pure BaTiO are 135, 15, and...

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