Host lattice

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. 

A wide variety of guest molecules may be trapped by the Wemer-type crystalline host lattice, ranging, eg, from noble gases to condensed aromatic hydrocarbons. These clathrates may be formed from solution or by sorption. Kinetics of sorption—desorption have been studied (83). 

Shielding and Stabilization. Inclusion compounds may be used as sources and reservoirs of unstable species. The inner phases of inclusion compounds uniquely constrain guest movements, provide a medium for reactions, and shelter molecules that self-destmct in the bulk phase or transform and react under atmospheric conditions. Clathrate hosts have been shown to stabiLhe molecules in unusual conformations that can only be obtained in the host lattice (138) and to stabiLhe free radicals (139) and other reactive species (1) similar to the use of matrix isolation techniques. Inclusion compounds do, however, have the great advantage that they can be used over a relatively wide temperature range. Cyclobutadiene, pursued for over a century has been generated photochemicaHy inside a carcerand container (see (17) Fig. 5) where it is protected from dimerization and from reactants by its surrounding shell (140). 

When the host is a single oxide, incorporation is best achieved during a high temperature phase transition of the host lattice such as when Ti02 goes from anatase to mtile, or during formation from carbonates or other salts. 

In pigments, 2irconium sHicate serves as the host lattice for various chromophores, such as vanadium, praseodymium, iron, etc. Zirconium sHicate crystals are usuaHy formed in situ during pigment preparation by a high temperature reaction of Zr02 and Si02 ... 

The most important rechargeable lithium batteries are those using a soHd positive electrode within which the lithium ion is capable of intercalating. These intercalation, or insertion, electrodes function by allowing the interstitial introduction of the LE ion into a host lattice (16,17). The general reaction can be represented by the equation ... 

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. 

Extension to interstitial alloys can be accomplished without violating the one-to-one correspondence assumption. All atoms around the interstitial can be related to host lattice positions, see the lower defect in Fig. 1, while the host is treated as having no scatterer in the corresponding interstice. Nevertheless a rather serious problem arises, because the more complicated integral... 

A common feature of all clathrates discussed so far is a host lattice, by itself thermodynamically unstable, which is stabilized by inclusion of the second component. The forces binding this component must be similar in nature to the intermolecular forces in liquids. It seems natural, therefore, to regard a clathrate compound as a solid solution of the second component in the (meta-stable) host lattice. 

In the present review a description is given of the phase behavior of clathrates on the basis of a solution theory. The treatment is restricted to those cases where the empty host lattice ( solvent") is indeed unstable, although many of the present considerations also apply to the few cases known where the host lattice is stable. An example of the latter is the chroman complex first discovered by Dianin9 and recently examined by Baker and McOmie and Powell and Wett ers.34... 

Although it is difficult to predict exactly which solute molecules will form clathrate solutions in any given host lattice, the general principle is quite clear. All molecules which fit into the cavities will be able to stabilize the host lattice, unless they show a specific chemical interaction with the solvent molecules. HC1 (or the other hydrogen halides), for instance, does not form a clathrate with water, but rather the stoichiometric compounds HC1 H20,... 

Let us consider a clathrate crystal consisting of a cage-forming substance Q and a number of encaged compounds ( solutes ) A, B,. . ., M. The substance Q has two forms a stable modification, which under given conditions may be either crystalline (a) or liquid (L), and a metastable modification (ft) enclosing cavities of different types 1,. . ., n which acts as host lattice ( solvent ) in the clathrate. The number of cavities of type i per molecule of Q is denoted by vt. For hydroquinone v — for gas hydrates of Structure I 1/23 and v2 = 3/23, for those of Structure II vx = 2/17 and v2 = 1/17. 

The assumptions (a) - (d) are believed to give an adequate description of the physical situation in the great majority of clathrates. Assumption (a) implies that the spectrum of the host lattice is not affected by the presence of the solute molecules. Little is known about this, but since the host lattice in general is a com-... 

TABLE II. Thermodynamic Properties of the Metastable Host Lattice, Relative to the Stable a-Modification... 

Nuclear magnetic resonance spectroscopy of the solutes in clathrates and low temperature specific heat measurements are thought to be particularly promising methods for providing more detailed information on the rotational freedom of the solute molecules and their interaction with the host lattice. The absence of electron paramagnetic resonance of the oxygen molecule in a hydroquinone clathrate has already been explained on the basis of weak orientational effects by Meyer, O Brien, and van Vleck.18... 

The second way in which an electroactive species such as lithium can be incorporated into the structure of an electrode is by a topotactic insertion reaction. In this case the guest species is relatively mobile and enters the crystal structure of the host phase so that no significant change in the structural configuration of the host lattice occurs. 

During electrochemical reduction (charge) of the carbon host, lithium cations from the electrolyte penetrate into the carbon and form a lithiated carbon Li rCn. The corresponding negative charges are accepted by the carbon host lattice. As for any other electrochemical insertion process, the prerequisite for the formation of lithiated carbons is a host material that exhibits mixed (electronic and ionic) conductance. 

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