The nature of crystals

The lines in the figure divide the crystal into identical unit cells. The array of points at the corners or vertices of unit cells is called the lattice. The unit cell is the smallest and simplest volume element that is completely representative of the whole crystal. If we know the exact contents of the unit cell, we can imagine the whole crystal as an efficiently packed array of many unit cells stacked beside and on top of each other, more or less like identical boxes in a warehouse. 

From crystallography, we obtain an image of the electron clouds that surround the molecules in the average unit cell in the crystal. We hope this image will allow us to locate all atoms in the unit cell. The location of an atom is usually given by a set of three-dimensional Cartesian coordinates, x, y, and z. One of the vertices (a lattice point or any other convenient point) is used as the origin of the unit cell s coordinate system and is assigned the coordinates x = 0, y = 0, and z = 0, usually written (0,0,0). See Fig. 2.4. 

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The very gradual recognition that matter consists of atoms stretched over more than two millennia, and that recognition was linked for several centuries with the struggles of successive generations of scientists to understand the nature of crystals. This is why I am here combining sketches of the history of atoms and of the history of crystals, two huge subjects. 

Finally attention is drawn to a germinal paper on the application of group theory to problems concerning the nature of crystals which was published in 1929 by another Nobel Prize winner, the German physicist Hans Albrecht Bethe (1906-). 

Milk fat is liquid above 40°C and completely solid below -40°C. Between these extremes it is a mixture of crystals and oil, with the latter a continuous phase. The nature of crystallization is complex because of the large number of TGs present. The properties of milk fat are the average of the properties of the TGs, and not necessarily those of the esterified fatty acids. 

The next steps toward a deeper understanding of the catalytic processes were possible through researches which elucidated the nature of crystal structures and the geometrical positions of electrons, ions, or atom groups and their energetic conditions and that also determined the factors which influence the mobility of these particles within the lattice or at phase boundaries. 

It is known that in a solid state polymerization occurs along the certain axis of the monomer crystal and extended chain crystals are formed [146]. In the polymerization from liquid phase, on the other hand, lamellar crystals are formed. This indicates that back-biting reaction proceeds not at random but in a specific manner, forced by the nature of crystals. The model of growth of lamellar crystals of polyoxymethylene is known [147]. According to this model, the subsequent layers are formed on the surface of the crystal by growth of folded chain as shown schematically below ... 

The series of litigations continued over other issues, inciuding the nature of crystal modifications (Zenith v. Bristol-Myers Squibb 1992). Zenith prepared and formulated a hemihydrate of cefadroxil, for which it submitted an ANDA to the FDA. Bristol-Myers (now Bristol-Myers Squibb) contended that the FDA should require a much more extensive new drug application (NDA) for the hemihydrate, rather than approve it within the framework of the FDA monograph for the monohydrate. BM also alleged that the Zenith product converted to the monohydrate, thereby infringing the 657 patent. Bristol-Myers theory of infringement was that the Zenith product converts to... 

The starting point for the application of molecular mechanics to ionic solids is similar to the starting point for lattice energy calculations. Indeed the method can be used to calculate lattice energies, but it is also used to study the effect of defects, the nature of crystal surfaces and properties of crystals. 

My attitude was, why shouldn t I use the understanding that I have developed of the nature of crystals in inorganic substances to proceed to predict their structures ... 

We then move on to the world of solids and learn about the nature of crystals and ways of packing spheres to form different unit cells. (11.4)... 

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