Crystal vacancy .

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Intrinsic defects (or native or simply defects ) are imperfections in tire crystal itself, such as a vacancy (a missing host atom), a self-interstitial (an extra host atom in an otherwise perfect crystalline environment), an anti-site defect (in an AB compound, tliis means an atom of type A at a B site or vice versa) or any combination of such defects. Extrinsic defects (or impurities) are atoms different from host atoms, trapped in tire crystal. Some impurities are intentionally introduced because tliey provide charge carriers, reduce tlieir lifetime, prevent tire propagation of dislocations or are otlierwise needed or useful, but most impurities and defects are not desired and must be eliminated or at least controlled. 

The presence of defects and impurities is unavoidable. They are created during tire growtli or penetrate into tlie material during tlie processing. For example, in a crystal grown from tire melt, impurities come from tire cmcible and tire ambient, and are present in tire source material. Depending on factors such as tire pressure, tire pull rate and temperature gradients, tire crystal may be rich in vacancies or self-interstitials (and tlieir precipitates). 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

Fig. 1.6 Poinl defects (a) vacancies (Schotlky defects) (6) interstitials (Frenkel defects) (c) ideal crystal.

Crystal structure of solids. The a-crystal form of TiCla is an excellent catalyst and has been investigated extensively. In this particular crystal form of TiCla, the titanium ions are located in an octahedral environment of chloride ions. It is believed that the stereoactive titanium ions in this crystal are located at the edges of the crystal, where chloride ion vacancies in the coordination sphere allow coordination with the monomer molecules. 

Figure 7.14a illustrates the insertion of a propylene monomer into an edge vacancy in a crystal adjacent to an alkylated titanium atom. In Fig. 7.14b a cross-sectional view of the same site shows how the preferential orientation of the coordinated monomer is dictated by constraints imposed by the protuberances on the crystal surface. 

Soluble Salt Flotation. KCl separation from NaCl and media containing other soluble salts such as MgCl (eg, The Dead Sea works in Israel and Jordan) or insoluble materials such as clays is accompHshed by the flotation of crystals using amines as coUectors. The mechanism of adsorption of amines on soluble salts such as KCl has been shown to be due to the matching of coUector ion size and lattice vacancies (in KCl flotation) as well as surface charges carried by the soflds floated (22). Although cation-type coUectors (eg, amines) are commonly used, the utUity of sulfonates and carboxylates has also been demonstrated in laboratory experiments. 

Theoretical studies of diffusion aim to predict the distribution profile of an exposed substrate given the known process parameters of concentration, temperature, crystal orientation, dopant properties, etc. On an atomic level, diffusion of a dopant in a siUcon crystal is caused by the movement of the introduced element that is allowed by the available vacancies or defects in the crystal. Both host atoms and impurity atoms can enter vacancies. Movement of a host atom from one lattice site to a vacancy is called self-diffusion. The same movement by a dopant is called impurity diffusion. If an atom does not form a covalent bond with siUcon, the atom can occupy in interstitial site and then subsequently displace a lattice-site atom. This latter movement is beheved to be the dominant mechanism for diffusion of the common dopant atoms, P, B, As, and Sb (26). 

When a sibcon crystal is doped with atoms of elements having a valence of less than four, eg, boron or gallium (valence = 3), only three of the four covalent bonds of the adjacent sibcon atoms are occupied. The vacancy at an unoccupied covalent bond constitutes a hole. Dopants that contribute holes, which in turn act like positive charge carriers, are acceptor dopants and the resulting crystal is -type (positive) sibcon (Fig. Id). 

Both anatase and mtile are broad band gap semiconductors iu which a fiUed valence band, derived from the O 2p orbitals, is separated from an empty conduction band, derived from the Ti >d orbitals, by a band gap of ca 3 eV. Consequendy the electrical conductivity depends critically on the presence of impurities and defects such as oxygen vacancies (7). For very pure thin films, prepared by vacuum evaporation of titanium metal and then oxidation, conductivities of 10 S/cm have been reported. For both siugle-crystal and ceramic samples, the electrical conductivity depends on both the state of reduction of the and on dopant levels. At 300 K, a maximum conductivity of 1 S/cm has been reported at an oxygen deficiency of... 

This conceptual link extends to surfaces that are not so obviously similar in stmcture to molecular species. For example, the early Ziegler catalysts for polymerization of propylene were a-TiCl. Today, supported Ti complexes are used instead (26,57). These catalysts are selective for stereospecific polymerization, giving high yields of isotactic polypropylene from propylene. The catalytic sites are beheved to be located at the edges of TiCl crystals. The surface stmctures have been inferred to incorporate anion vacancies that is, sites where CL ions are not present and where TL" ions are exposed (66). These cations exist in octahedral surroundings, The polymerization has been explained by a mechanism whereby the growing polymer chain and an adsorbed propylene bonded cis to it on the surface undergo an insertion reaction (67). In this respect, there is no essential difference between the explanation of the surface catalyzed polymerization and that catalyzed in solution. 

Dehydrogenation is considered to occur on the corners, edges, and other crystal defect sites on the catalyst where surface vacancies aid in the formation of intermediate species capable of competing for hydrogen with ethylbenzene. The role of the potassium may be viewed as a carrier for the strongly basic hydroxide ion, which is thought to help convert highly aromatic by-products to carbon dioxide. 

When ahovalent, ie, different valence, impurities are added to an ionic soHd, the crystal lattice compensates by forming defects that maintain both electrical neutraUty and the anion to cation ratio of the host lattice. For example, addition of x mol of CaO to Zr02 requires the formation of x mol of oxygen vacancies. 

Certain perovskites with Pb on the A site are particularly important and show pronounced piezoelectric characteristics (PbTiO, PZT, PLZT). Different responses are found in BaTiO and PZT to the addition of donor dopants such as La ". In PZT, lead monoxide [1317-36-8] PbO, lost by volatilization during sintering, can be replaced in the crystal by La202, where the excess positive charge of the La " is balanced by lead vacancies, leading to... 

Color from Color Centers. This mechanism is best approached from band theory, although ligand field theory can also be used. Consider a vacancy, for example a missing CF ion in a KCl crystal produced by irradiation, designated an F-center. An electron can become trapped at the vacancy and this forms a trapped energy level system inside the band gap just as in Figure 18. The electron can produce color by being excited into an absorption band such as the E transition, which is 2.2 eV in KCl and leads to a violet color. In the alkaU haUdes E, = 0.257/where E is in and dis the... 

The other major defects in solids occupy much more volume in the lattice of a crystal and are refeiTed to as line defects. There are two types of line defects, the edge and screw defects which are also known as dislocations. These play an important part, primarily, in the plastic non-Hookeian extension of metals under a tensile stress. This process causes the translation of dislocations in the direction of the plastic extension. Dislocations become mobile in solids at elevated temperamres due to the diffusive place exchange of atoms with vacancies at the core, a process described as dislocation climb. The direction of climb is such that the vacancies move along any stress gradient, such as that around an inclusion of oxide in a metal, or when a metal is placed under compression. 

The second mechanism is that of vacancy diffusion. When zinc diffuses in brass, for example, the zinc atom (comparable in size to the copper atom) cannot fit into the interstices - the zinc atom has to wait until a vacancy, or missing atom, appears next to it before it can move. This is the mechanism by which most diffusion in crystals takes place (Figs. 18.7 and 10.4). 

Polymers are a little more complicated. The drop in modulus (like the increase in creep rate) is caused by the increased ease with which molecules can slip past each other. In metals, which have a crystal structure, this reflects the increasing number of vacancies and the increased rate at which atoms jump into them. In polymers, which are amorphous, it reflects the increase in free volume which gives an increase in the rate of reptation. Then the shift factor is given, not by eqn. (23.11) but by... 

The diffusion coefficient corresponding to the measured values of /ch (D = kn/4nRn, is the reaction diameter, supposed to be equal to 2 A) equals 2.7 x 10 cm s at 4.2K and 1.9K. The self-diffusion in H2 crystals at 11-14 K is thermally activated with = 0.4 kcal/mol [Weinhaus and Meyer 1972]. At T < 11 K self-diffusion in the H2 crystal involves tunneling of a molecule from the lattice node to the vacancy, formation of the latter requiring 0.22 kcal/mol [Silvera 1980], so that the Arrhenius behavior is preserved. Were the mechanism of diffusion of the H atom the same, the diffusion coefficient at 1.9 K would be ten orders smaller than that at 4.2 K, while the measured values coincide. The diffusion coefficient of the D atoms in the D2 crystal is also the same for 1.9 and 4.2 K. It is 4 orders of magnitude smaller (3 x 10 cm /s) than the diffusion coefficient for H in H2 [Lee et al. 1987]. 

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