Crystallization patterns

The extent to which small particles of Pd and Pt show evidence of oxidation after exposure to air Is also highly variable. It Is difficult to confirm the evidence of X-ray diffraction and EXAFS (25) that most particles In the 15-20A size range consist entirely of oxide. We have found that such particles usually give single crystal patterns attributable to the metals. There Is, however, considerable evidence that, in the case of Pt on alumina, the Pt crystals have a well-defined epitaxial relationship with the crystallites (20-50A diameter) of the nominally "amorphous" alumina substrate. 

Statistical information from single crystal patterns... 

In many foods, it is essential to control either sugar or ice crystal patterns and in others there is a problem of controlling both. In Table I are listed the foods in which we encounter crystalline structure problems and the type of crystals with which we are concerned. 

Von Brand, T. Nylen, M. V. Martin, G. N., Churchwell, K. Composition and crystallization patterns of calcareous corpuscels of cestodes grown in different classes of hosts. J. Parasit. 53, 683 (1967)... 

The pattern points associated with a particular lattice are referred to as the basis so that the description of a crystal pattern requires the specification of the space lattice by ai a2 a3 and the specification of the basis by giving the location of the pattern points in one unit cell by K, i= 1,2,. .., (Figure 16.1(b), (c)). The choice of the fundamental translations is a matter of convenience. For example, in a face-centred cubic fee) lattice we could choose orthogonal fundamental translation vectors along OX, OY, OZ, in which case the unit cell contains (Vg)8 + (l/2)6 = 4 lattice points (Figure 16.2(a)). Alternatively, we might choose a primitive unit cell with the fundamental translations... 

A crystal pattern may possess rotational symmetry as well as translational symmetry, although the existence of translational symmetry imposes restrictions on the order of the axes. The fundamental translations (a in eq. (1) are the basis vectors of a linear vector... 

The space group G of a crystal is the set of all symmetry operators that leave the appearance of the crystal pattern unchanged from what it was before the operation. The most general kind of space-group operator (called a Seitz operator) consists of a point operator R (that is, a proper or improper rotation that leaves at least one point invariant) followed by a translation v. For historical reasons the Seitz operator is usually written R v. However, we shall write it as (R ) to simplify the notation for sets of space-group operators. When a space-group operator acts on a position vector r, the vector is transformed into... 

In each of the equations (l)-(4) the crystal pattern appears the same after carrying out the operation signified. It follows from eq. (2) that the pattern, and therefore the subset of lattice translations... 

Exercise 16.2-1 If (R 0) e G, then R leaves the appearance of the crystal pattern indistinguishable from what it was before this operation. Therefore to maintain the crystal pattern any subsequent translation must be t. Similarly, since S P(G) it does not leave the pattern self-coincident and a subsequent translation w must therefore t, in order to restore self-coincidence. 

The direct lattice and reciprocal lattice unit cells are marked on the crystal pattern of a planar hexagonal net in Figure 16.10, using eqs. (13), (14), and (18). The scales chosen for... 

More directly, solid state physics contributed to the emergence of materials science, because of one of its foci. Spencer Weart identified three pillars on which solid state physics was erected First, X-ray diffraction techniques provided precise atomic picture of solids second, quantum mechanics provided the theoretical foundations for the description of solids and the third, more subtle pillar was the attempt to discriminate between properties depending on the idealized crystal pattern and properties dependent on accidents of either the inner arrangement or the surface of the solid. [13] This focus on structure-sensitive-properties can be seen as the main investigative pathway, to resume Frederic L. Holmes s concept, which lead to materials science. 

All wheat starches give the same A-type crystal pattern, but their degree of crystallinity is inversely proportional to amylose content. In addition, the intensity of one reflection of an amylose-lipid complex at 2 20-23° (d 4.4A) increases proportionally to the amylose level.265,271,281,284,289 The lipid content of waxy wheat starch is much lower (0.02-0.17%) than that in non-waxy wheat starch (0.6-0.7%).286,291 However, the crude fat content of waxy wheat flour is elevated by 20-40% (3-glucan and pentosan are increased by 30%.291,292 The degree of crystallinity of waxy wheat starch is reported to be 18-21% versus 13-16% for the wild type.284,289 Increases of 35% for waxy wheat starch, 23-28% for double nulls, 20-23% for single nulls and 22% for the wild type have also been reported.271... 

Crystal Blooms. A preliminary examination of crystal blooms of selected insecticides on various species of conifer bark (32) soon demonstrated a wide variation and high unpredictability in crystallization patterns. Because of this variation and the difficulty of bioassay with irregular bark surfaces, fiberboard panels were chosen as the test surface. Fiberboard is not a substitute for bark and does not simulate bark except in a general way and so was used mainly for convenience in studying the potential toxicity of crystal blooms and the broad aspects of crystallization patterns. 

Fig. 2. SEM micrograph of a rapidly electron-beam-annealed amorphous Si film that was thermally evaporated on a silica substrate. The 20-keV, 1-//A electron beam was focused to 2 /im and raster scanned at a rate of 2.5 cm sec-1, (a) Shows a periodic crescent-shaped explosive crystallization pattern, (b) Two different types of explosive crystallization features appear at slightly higher scan speed.

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