Macroscopic crystals

Growth units larger than mesoparticles certainly must be able to develop translational correlation, that is, to grow into macroscopic crystals with periodic symmetry. At this point the surface of the aggregate becomes ordered very much as the inner part is. 

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Semiconductor materials are rather unique and exceptional substances (see Semiconductors). The entire semiconductor crystal is one giant covalent molecule. In benzene molecules, the electron wave functions that describe probabiUty density ate spread over the six ting-carbon atoms in a large dye molecule, an electron might be delocalized over a series of rings, but in semiconductors, the electron wave-functions are delocalized, in principle, over an entire macroscopic crystal. Because of the size of these wave functions, no single atom can have much effect on the electron energies, ie, the electronic excitations in semiconductors are delocalized. 

One of the intensively discussed topics was the question about the shape of atoms - a question with also high educational relevance, if we think of some students preconceptions. We can focus on two main positions One group of chemists observed that crystals always broke to parts with similar shapes to those of the original crystal. Therefore, their theory was that the smallest particles of atoms must have also the same shape as the macroscopic crystal. If we follow Domenico Guglielmini (1655-1710), the particles of sodium chloride would be cubic, those of calcspar would be triclinic. Hexagonal-prismatic and trigonal-prismatic crystals... 

The primary nucleation process is divided into two periods in CNT one is the so called induction period and the other is the steady (or stationary) nucleation period (Fig. 2) [16,17]. It has been proposed by CNT that small (nanometer scale) nuclei will be formed spontaneously by thermal fluctuation after quenching into the supercooled melt, some of the nuclei could grow into a critical nucleus , and some of the critical nuclei will finally survive into macroscopic crystals. The induction period is defined as the period where the nucleation rate (I) increases with time f, whereas the steady period is that where I nearly saturates to a constant rate (fst). It should be noted that I is a function of N and t,I = I(N, t). In Fig. 2, N and N mean the size of a nucleus and that of the critical nucleus, respectively. The size N is defined... 

CNT assumes that I starts increasing after an induction period, increases with increasing time and finally saturates into a steady rate, Jst. This is assumed from well-known observations of macroscopic crystals by means of the opti-... 

The typical side products in decavanadate preparations are the metavanadate and/or hexavanadate, as well as unreacted V205. These impurities are generally less soluble than the decavanadate salt and can be removed by filtration. X-Ray powder diffraction is felt to be the best criterion of phase purity unless macroscopic crystals are obtained. 

An interesting question, expressed by Boudart (1985), is the following As particle size grows from that of a small cluster to infinite value for a single macroscopic crystal, how does the value of turnover frequency change for a given reaction on a given metal ... 

An ionic compound typically contains a multitude of ions grouped together in a highly ordered three-dimensional array. In sodium chloride, for example, each sodium ion is surrounded by six chloride ions and each chloride ion is surrounded by six sodium ions (Figure 6.11). Overall there is one sodium ion for each chloride ion, but there are no identifiable sodium-chloride pairs. Such an orderly array of ions is known as an ionic crystal. On the atomic level, the crystalline structure of sodium chloride is cubic, which is why macroscopic crystals of table salt are also cubic. Smash a large cubic sodium chloride crystal with a hammer, and what do you get Smaller cubic sodium chloride crystals Similarly, the crystalline structures of other ionic compounds, such as calcium fluoride and aluminum oxide, are a consequence of how the ions pack together. 

PHENOCRYST. A textural term proposed by Iddings in 1892 for macroscopic crystals which are relatively much larger than the crystalline matrix of the igneous rock in which they occur. Rocks which have phenocrysts are called porphyntic, The term phenocryst is derived from the Greek, meaning show, and crystal. 

The origin of a crystal is still mysterious. Crystals are formed in the gas, solid, and solution phases, but the majority of crystals are formed in solution. It is generally believable that molecules and ions first gather to form nuclei in supersaturated solution and then grow to macroscopic crystals by collecting around the nuclei. However, no one has ever seen the nucleus of a crystal in solution. 

Warman, J. M. de Haas, M. P. van Hovell tot Westerflier, S. W. F. M. Binsma, J. J. M. Kolar, Z. I. Electronic processes in semiconductor materials studied by nanosecond time-resolved microwave conductivity. I. Cadmium sulfide macroscopic crystal, J. Phys. Chem. 1989, 93, 5895. 

We come back to the scheme (Section IV.C.3.b) of a small cell in a real crystal, assumed to account for the couplings in the configuration at short distances, as immersed in an effective medium representing the mean macroscopic crystal which modifies the response of the cell. 

The bulk properties of macroscopic crystals cannot be affected drastically by the difference which exists between the structure of the interior and that of a surface film which is approximately 10,000 atoms deep. However, even for macroscopic crystals, rate phenomena such as modification changes which are initiated within the surface are likely to be influenced by the environment, which would include molecules which are conventionally described as physically adsorbed. Apparently it is not generally understood that even the presence of a noble gas can affect the chemical reactivity of solids. Brunauer (3) explained that in principle physical adsorption of molecules should affect the solid in the same manner as chemisorption. As action and reaction are equal, chemisorption may have a stronger effect on both the solid and the adsorbed molecule. 

As far as macroscopic crystals are concerned, the equilibrium properties will not be noticeably affected by a change in the environment, but the interaction of adsorbed molecules with the surface may trigger a phase change which is initiated in the surface. Hence, even for macroscopic crystals, the environment may influence rate phenomena such as solid-state reactions. 

Equation (8.2.7) assumed an orthogonal macroscopic crystal of orthorhombic symmetry for a triclinic parallelepiped, the projections of k would be along a, b, c axes, with ft, nyz, nz, integers. For simplicity, hereinafter we assume a large cubic crystal, of molar dimensions, so that A = B = C = L and with volume V = L3. 

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