Crystals leaf-shape

To find the equilibrium form of a crystal, the following Wullf construction [20] can be used, which will be explained here, for simplicity, in two dimensions. Set the centre of the crystal at the origin of a polar coordinate system r,6. The radius r is assumed proportional to the surface tension 7( ), where 6 defines the angle between the coordinate system of the crystal lattice and the normal direction of a point at the surface. The anisotropy here is given through the angular dependence. A cubic crystal, for example, shows in a two-dimensional cut a clover-leaf shape for 7( ). Now draw everywhere on this graph the normals to the radius vector r = The... 

The ground term of the cP configuration is F. That of is also F. Those of and d are " F. We shall discuss these patterns in Section 3.10. For the moment, we only note the common occurrence of F terms and ask how they split in an octahedral crystal field. As for the case of the D term above, which splits like the d orbitals because the angular parts of their electron distributions are related, an F term splits up like a set of / orbital electron densities. A set of real / orbitals is shown in Fig. 3-13. Note how they comprise three subsets. One set of three orbitals has major lobes directed along the cartesian x or y or z axes. Another set comprises three orbitals, each formed by a pair of clover-leaf shapes, concentrated about two of the three cartesian planes. The third set comprises just one member, with lobes directed equally to all eight corners of an inscribing cube. In the free ion, of course, all seven / orbitals are degenerate. In an octahedral crystal field, however, the... 

Fig. 10 Four common types of crystal habit in polyethylene and long alkanes (a) rhombic lozenge bounded by 110 facets (b) lozenge truncated by curved 100 faces (Toda s type B) (c) leaf-shaped crystal bounded solely by curved 100 faces (step propagation rate v equals h = Gno/sin(

PHYSICAL PROPERTIES yellow, leaf-shaped crystals aromatic odor chloroform-like odor soluble in alcohol, benzene, chloroform, ether, petroleum ether, mineral acids, and oils, insoluble in water MP (114-117°C, 237-243°F) DN (lOSOkg/m ) SG (1.05) VP (3.3 x 10 mmHg at 25°C). 

Lu et al. electrodeposited Tb02.x coatings onto copper substrates from a nitrate solution using the base generation method [113]. SEM images of the electrodeposited Tb02 x samples showed flower-like structures made up of numerous leaf-like nanosheets, in which the leaf-shaped nanosheets were approximately 100 nm in thickness and 1 pm in width. The crystal structure was analyzed by powder XRD. The values of the lattice constant were close to those of XbOi Ts. 

Wherever we look, we seem to see matter demonstrating order, whether it is the regularity of a leaf on a tree, our own ten fingers and toes, or the shape of crystals. It is not surprising that the study of matter has also been the search for order, both in... 

A further series of hydroxyanthraquinones were isolated by Raistrick at the same time from Helminthosporium species. These organisms are found on cereals and grasses. When Helminthosporium gramineum, the causative organisms of a leaf stripe disease of barley, was grown on a Czapek-Dox medium it imparted a deep-red colour to the medium. Under some conditions the underside of the mycelial mat was partially covered with dark-red needle-shaped crystals. The main constituent was a trihydroxyanthraquinone, helminthosporin (7.8). Its structure was... 

By pulling, a single crystal metal fiber is drawn out of the molten mass at a slow, uniform rate (e.g., 0.2 mm./sec.) while cooled and protected by a stream of inert gas (Ns, COg). A small mica leaf with a hole in the middle, floating on the surface of the molten mass, serves as a die for the fiber and determines the thickness of the wire-shaped single crystal (Czochralsky Von Gompprz Mark, Polany and Schmid [12]). 

Work on tRNA yields a of 23-2.5 nm by X-ray scattering. Many of the earliest studies predated the crystal structure determination of tRNA in 1974 [347-355] and thus attempted to elucidate its overall shape on the basis of the clover-leaf base-pairing model from sequence data. Open structures were discarded in favour of more compact schemes. Many folded structures were, however, compatible with the experimental data, while a simple triaxial body was not. The observation of two distinct i xs values led to the development in 1970 of a model with one large and two small ellipsoids whose main axes are parallel to one another and are arranged in an L-shape [353], and which anticipated the L-shape determined by crystallography (Fig. 26). Other studies on tRNA have investigated its melting... 

Silver fulminate (SF) is a white crystalline material with heat of formatiOTi 179 kJ mol [15]. It crystallizes in the form of small rosettes or star-shaped clusters. Two polymorphic forms have been reported—orthorhombic and trigonal. The crystal shape depends on reaction conditions (temperature, concentration) during sUver fulminate preparation [94]. Recrystallization from ammonia leads to needles and multiple growths of leaf-like habits [92]. Long (4—5 mm) needle-shaped crystals were prepared by Singh and investigated by X-ray analysis. It was found that the crystal is orthorhombic [95]. The crystal structure of SF was later investigated in detail by Britton and Dunitz [96, 97] and their results were confirmed by Barrick et al. [98]. Ammonium acetate solution ( 20 %) is recommended as the solvent for... 

A variety of alternative crystal shapes can be produced by forced hydrolysis of inorganic salts. For instance, copper basic sulphate crystals with a uniform leaf-like appearance (Figure 7) can be prepared by heating copper sulphate solutions in the presence of urea (8). Similarly, zinc oxide needles can be obtained by heating zinc nitrate solutions in the presence of triethanolamine (TEA), sodium hydroxide and hydrazine. Figure 8. 

Unfortunately, while the leaf-like copper basic sulphate crystals and the rod-like zinc oxide crystals had uniform particle shapes, in both cases, the particle sizes varied appreciably, as evident from Figures 7 and 8. For this reason, experimental programmes are continuing with a view to identifying the reaction conditions which give uniformly-sized crystals. 

---