Crystal faces, types

It is emphasized that the delta L law does not apply when similar crystals are given preferential treatment based on size. It fails also when surface defects or dislocations significantly alter the growth rate of a crystal face. Nevertheless, it is a reasonably accurate generahzation for a surprising number of industrial cases. When it is, it is important because it simphfies the mathematical treatment in modeling real crystallizers and is useful in predicting crystal-size distribution in many types of industrial crystallization equipment. 

In principle, there is also the possibility that concurrent reactions, with different kinetics, may proceed at more than one type of site or at different crystal faces. 

Benniston AC, Haniman A (2008) Artificial photosynthesis. Materials Today 11 26-34 Inoue T, Fujishima A, Konishi S, Honda K (1979) Photoelectrocatalytic reduction of carbon dioxide in aqueous suspensions of semiconductor powders. Nature 277 637-638 Halmann M (1978) Photoelectrochemical reduction of aqueous carbon dioxide on p-type gallium phosphide in liquid junction solar cells. Nature 275 115-116 Heminger JC, Carr R, Somorjai GA (1987) The photoassisted reaction of gaseous water and carbon dioxide adsorbed on the SrH03 (111) crystal face to form methane. Chem Phys Lett 57 100-104... 

A wide variety of solid materials are used in catalytic processes. Generally, the (surface) structure of metal and supported metal catalysts is relatively simple. For that reason, we will first focus on metal catalysts. Supported metal catalysts are produced in many forms. Often, their preparation involves impregnation or ion exchange, followed by calcination and reduction. Depending on the conditions quite different catalyst systems are produced. When crystalline sizes are not very small, typically > 5 nm, the metal crystals behave like bulk crystals with similar crystal faces. However, in catalysis smaller particles are often used. They are referred to as crystallites , aggregates , or clusters . When the dimensions are not known we will refer to them as particles . In principle, the structure of oxidic catalysts is more complex than that of metal catalysts. The surface often contains different types of active sites a combination of acid and basic sites on one catalyst is quite common. 

The electrocrystallization on an identical metal substrate is the slowest process of this type. Faster processes which are also much more frequent, are connected with ubiquitous defects in the crystal lattice, in particular with the screw dislocations (Fig. 5.25). As a result of the helical structure of the defect, a monoatomic step originates from the point where the new dislocation line intersects the surface of the crystal face. It can be seen in Fig. 5.48 that the wedge-shaped step gradually fills up during electrocrystallization after completion it slowly moves across the crystal face and winds up into a spiral. The resultant progressive spiral cannot disappear from the crystal surface and thus provides a sufficient number of growth... 

The electrocatalytic oxidation of methanol was discussed on page 364. The extensively studied oxidation of simple organic substances is markedly dependent on the type of crystal face of the electrode material, as indicated in Fig. 5.56 for the oxidation of formic acid at a platinum electrode. 

The fourth and final crystal structure type common in binary semiconductors is the rock salt structure, named after NaCl but occurring in many divalent metal oxides, sulfides, selenides, and tellurides. It consists of two atom types forming separate face-centered cubic lattices. The trend from WZ or ZB structures to the rock salt structure takes place as covalent bonds become increasingly ionic [24]. 

A calculation based on the decrease of the electron density at the surface and on the relaxation of the top lattice plane resulted22 in values such as 190 and 1234 erg/cm2 for the 100 faces of sodium and aluminum, respectively. The above relaxation, that is, the ratio of the interplanar distance in bulk to that in the external region was calculated23, assuming a Morse type interatomic potential. The above ratio appeared to be, e.g., 1.13 for the 100 face of calcium, and 1.016 for the 111 face of lead. The relaxation lowered the energy 7 by 0.5 to 7% for different metals and crystal faces. 

Figure 3.16. Some simple defects found on a low-index crystal face 1, the perfect flat face, a terrace 2, an emerging screw dislocation 3, the intersection of an edge dislocation with the terrace 4, an impurity adsorbed atom 5, a monatomic step in the surface, a ledge 6, a vacancy in the ledge 7, a kink, a step in the ledge 8 an adatom of the same type as the bulk atoms 9, a vacancy in the terrace 10, an adatom on the terrace. (From Ref. 12, with permission from Oxford University Press.)...

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 ... 

The ciystal habit of sucrose and adipic add crystals were calculated from their intern structure and from the attachment energies of the various crystal faces. As a first attempt to indude the role of the solvent on the crystal habit, the solvent accessible areas of the faces of sucrose and adipic add and were calculated for spherical solvent probes of difierent sizes. In the sucrose system the results show that this type of calculation can qualitatively account for differences in solvent (water) adsorption hence fast growing and slow growing faces. In the adipic add system results show the presence of solvent sized receptacles that might enhance solvent interadions on various fares. The quantitative use of this type of data in crystal shape calculations could prove to be a reasonable method for incorporation of solvent effeds on calculated crystal shapes. 

Mixed crystals of type II have been used in the form of thin films on electrodes as well as in the form of chemically synthesized powders immobilized on electrodes. Depending on the radii of the ions involved in the synthesis, solid solutions can also be formed as single phases. In the case of K CuCo[Fe(CN)(5] films, XRD results indicated that a single phase with a cubic face-centered symmetry was formed [31]. The situation is more complex in the case of K NiPd[Fe(CN)6] deposited as a thin film on electrodes [32]. Kulesza etal. have pointed out that there is a critical concentration of Pd + below which Pd + was taken as the countercation at interstitial position, while above that value a solid solution is formed in which both Ni " " and Pd + are nitrogen coordinated. 

In Fig. 4.1 we depict three lattice types of the cubic system and the crystal faces with the highest reticular density (the density of lattice points per unit area) in each t5q)e. 

Figure 4.1. Crystal faces with the highest rank in the order of morphological importance (with the highest reticular density) for P. F. and I lattice types of the cubic system (a) P lattice, 100) (b) F lattice. Ill) (c) I lattice. (110).

Figure 5.1. Surface microtopographs seen on three types of crystal faces (Kossel crystal), (a) F face (b) S face (c) K face.

Crystal faces with curved or wavy surfaces, not exhibiting either striations or step patterns, are rarely encountered. In most cases, these faces appear by dissolution. Rough interfaces grow by the adhesive-type growth mechanism, their normal... 

The earliest interest in surface microtopographs observable on crystal faces developed in the 1920s these observations were made using reflection-type microscopes on etch figures seen in natural mineral crystals [1], [2]. At that time. 

---