Related Crystals

Nucleation. Crystal nucleation is the formation of an ordered soHd phase from a Hquid or amorphous phase. Nucleation sets the character of the crystallization process, and it is, therefore, the most critical component ia relating crystallizer design and operation to crystal size distributions. 

In this book, the process of plastic deformation and the related crystal defects liave been discussed repeatedly. In Section 2.1.6, the distinction between continuum... 

A further result of Sadler s 2D-simulation was a relation between the step density and growth rate on the one hand and the inclination of the surface with respect to the principal axes on the other. From this relation crystal shapes were derived which show considerable curvature. This result of an exact treatment stands in contrast to Frank s mean-field curvature expression which gives essentially flat profiles. We will return to the discussion of curved edges in Sect. 3.6.3. 

It is not possible to predict from the related crystal structure alone whether the compound will melt to a liquid crystalline phase or not, because the anisotropic molecules (calamitic and discotic ones) form in favourable anisotropic packing. As a rule long shaped rod-like molecules quite often possess a layered arrangement in the solid state regardless of whether the compound is mesogenic or not. 

X-Ray diffraction has an important limitation Clear diffraction peaks are only observed when the sample possesses sufficient long-range order. The advantage of this limitation is that the width (or rather the shape) of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow, see for example the (111) and (200) reflections of large palladium particles in Fig. 4.5. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The two XRD patterns of supported Pd catalysts in Fig. 4.5 show that the reflections of palladium are much broader than those of the reference. The Scherrer formula relates crystal size to line width ... 

The Scherrer formula relates crystal size to line width ... 

Baroni S, de Gironcoli S, Dal Corso A, Giannozzi P (2001) Phonons and related crystal properties from density-functional perturbation theory. Rev Modem Phys 73 515-562 Basile LJ, Ferraro JR, LaBonville P, Wall MD (1973) A study of force fields for tetrahedral molecules and ions. Coord Chem Rev 11 21-69... 

Model building remains a useful technique for situations where the data are not amenable to solution in any other way, and for which existing related crystal structures can be used as a starting point. This usually happens because of a combination of structural complexity and poor data quality. For recent examples of this in the structure solution of polymethylene chains see Dorset [21] and [22]. It is interesting to note that model building methods for which there is no prior information are usually unsuccessful because the data are too insensitive to the atomic coordinates. This means that the recent advances in structure solution from powder diffraction data (David et al. [23]) in which a model is translated and rotated in a unit cell and in which the torsional degrees of freedom are also sampled by rotating around bonds which are torsionally free will be difficult to apply to structure solution with electron data. 

X-ray structural methods. As examples for the three related crystal structures, molecular structures of compounds 26 and 27 are shown (Figure 10). 

Hartman and Perdok f6Q-62 > in 1955 developed a theory which related crystal morphology to its internal structure on an energy basis. They concluded that the morphology of a crystal is governed tty a chain of strong bonds (called periodic bond chains (PBC)), which run through the structure. The period of these strong bond chains is called the PBC veaor. In addition, Hartman and Perdok divided the crystal face into three types. These types are ... 

Ultimate properties of toughness (energy to rupture), tensile strength, and maximum extensibility are all affected by strain-induced crystallization. In general, the higher the temperature the lower the extent of crystallization and consequently the lower these stress/strain related properties. There is also a parallel result brought about by the presence of increased amounts of diluent since this also discourages stress-related crystallization. 

Comparison of P Static and MAS Spectra of KD2PO4 and Related Crystals... 

Mass balance at the boundary provides an equation relating crystal growth rate to other parameters ... 

Oxygen positions were calculated from known coordination polyhedra in related crystal structures. 

The topic of color centers in NaCl and related crystals will be discussed more fully in Section 10.1.2. 

J. A. Weil, Use of symmetry-related crystal sites for measuring tensor properties in magnetic resonance.. Magn. Reson., 1973, 10, 391-393, Erratum Note that tiie last 4 rows of Table I are tainted. Please see the correct version in Table V of Ref. 12. 

The width of diffraction peaks carries information on the dimensions of the reflecting planes. Diffraction lines from perfect crystals are very narrow. For crystallite sizes below 100 nm, however, line broadening occurs due to incomplete destructive interference in scattering directions where the X-rays are out of phase. The Scherrer formula relates crystal size to line width ... 

William Whewell (1794-1866) introduces a notation system relating crystal faces to coordinate axes (Miller indices). These were published in a book by Whewell s student William Hallowes Miller (1801-1880) in 1839. 

Problems in Relating Crystal Strnctnres and Solntion Composition... 

Wurtz, J. M., Egner, U., Heinrich. N., Moras, D., Mueller-Fahrnow, A. Three-Dimensional Models of Estrogen Receptor Ligand Binding Domain Complexes, Based on Related Crystal Structures and Mutational and Structure-Activity Relationships Data,/. Med. Chem. 1998, 41, 1803-1814. 

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