Host crystals

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Examples of the hydroquinone inclusion compounds (91,93) are those formed with HCl, H2S, SO2, CH OH, HCOOH, CH CN (but not with C2H 0H, CH COOH or any other nitrile), benzene, thiophene, CH, noble gases, and other substances that can fit and remain inside the 0.4 nm cavities of the host crystals. That is, clathration of hydroquinone is essentially physical in nature, not chemical. A less than stoichiometric ratio of the guest may result, indicating that not all void spaces are occupied during formation of the framework. Hydroquinone clathrates are very stable at atmospheric pressure and room temperature. Thermodynamic studies suggest them to be entropic in nature (88). 

The term solid-state laser refers to lasers that use solids as their active medium. However, two kinds of materials are required a host crystal and an impurity dopant. The dopant is selected for its ability to form a population inversion. The Nd YAG laser, for example, uses a small number of neodymium ions as a dopant in the solid YAG (yttrium-aluminum-gar-net) crystal. Solid-state lasers are pumped with an outside source such as a flash lamp, arc lamp, or another laser. This energy is then absorbed by the dopant, raising the atoms to an excited state. Solid-state lasers are sought after because the active medium is relatively easy to handle and store. Also, because the wavelength they produce is within the transmission range of glass, they can be used with fiber optics. 

Nonstoichiometric Compounds Intrinsic defects are stoichiometric defects (i.e., they do not involve any change in overall composition). Defects can also be nonstoichiometric. In the case of extrinsic defects where the host crystal is doped with aliovalent impurities, the solid so formed is a nonstoichiometric compound because the ratio of the atomic components is no longer the simple integer. There is also... 

Figure 5. Variation in apparent lattice-site Young s Modulus ) with molar anorthite content of the host crystal for the plagioclase partitioning experiments of Blundy and Wood (1994)., Ej and...

Insertion (intercalation) compounds. Insertion compounds are defined as products of a reversible reaction of suitable crystalline host materials with guest molecules (ions). Guests are introduced into the host lattice, whose structure is virtually intact except for a possible increase of some lattice constants. This reaction is called topotactic. A special case of topotactic insertion is reaction with host crystals possessing stacked layered structure. In this case, we speak about intercalation (from the Latin verb intercalare, used originally for inserting an extra month, mensis intercalarius, into the calendar). 

Fig. 9. Stereoview of the inclusion compound between host 5 (extended conformation) and 2 mol of N,N-dimethylacetamide (denoted by S ) + 2 mol of water (isolated circles). In the crystal structure there are hydrogen bonds between the solvent molecules and the —COOH and > S02 groups of the host (crystal data a = 14.838, b = 14.818, c — 14.500 A, a = p = y = 90°, space group...

This host network, termed the helical tubuland structure type 7,8), is unique. The walls of the canals are lined only by aliphatic hydrocarbon, and the hydrogen bonded spines are insulated from the guest canals. Powder diffraction and IR measurements indicate that when 1 is crystallised from acetonitrile the same host crystal structure occurs, but devoid of guest. This has the unusually low calculated density, 1.02 g cm 3. 

The melting point of the empty host crystals is 189-191 °C. Therefore it was apparent that this is an independently stable host structure containing large yet chemically inert guest canals, in which guest species cannot interfere with the strong hydrogen bonds which maintain the host network. 

As mentioned above alkali halide crystals are strongly hardened by small additions of divalent impurities. Data are available for 12 cases, the host crystals NaCl, NaBr, KC1, and KBr with additions of Ca2+, Sr2+, and Ba2+ (Chin, et al., 1973). It was found that the hardness increases depend only on the concentrations of the additions and not on the divalent specie (Ca, Sr, or Ba). However, a dependence on the valence (1, 2, or 3) is observed. It was also found that hardness increment is proportional to the square root of the concentration, (C1/2). 

Radon forms a series of clathrate compounds (inclusion compounds) similar to those of argon, krypton, and xenon. These can be prepared by mixing trace amounts of radon with macro amounts of host substances and allowing the mixtures to crystallize. No chemical bonds are formed the radon is merely trapped in the lattice of surrounding atoms it therefore escapes when the host crystal melts or dissolves. Compounds prepared in this manner include radon hydrate, Rn 6H20 (Nikitin, 1936) radon-phenol clathrate, Rn 3C H 0H (Nikitin and Kovalskaya, 1952) radon-p-chlorophenol clathrate, Rn 3p-ClC H 0H (Nikitin and Ioffe, 1952) and radon-p-cresol clathrate, Rn bp-CH C H OH (Trofimov and Kazankin, 1966). Radon has also been reported to co-crystallize with sulfur dioxide, carbon dioxide, hydrogen chloride, and hydrogen sulfide (Nikitin, 1939). 

In a supercell geometry, which seems to have become the method of choice these days, the impurity is surrounded by a finite number of semiconductor atoms, and what whole structure is periodically repeated (e.g., Pickett et al., 1979 Van de Walle et al., 1989). This allows the use of various techniques that require translational periodicity of the system. Provided the impurities are sufficiently well separated, properties of a single isolated impurity can be derived. Supercells containing 16 or 32 atoms have typically been found to be sufficient for such purposes (Van de Walle et al., 1989). The band structure of the host crystal is well described. 

Another approach that provides a good desciption of the band structure of the host crystal is based on the Green s function determined for the perfect crystal. This function is then used to calculate changes induced by the presence of the defect (e.g., Rodriguez et al., 1979 Katayama-Yoshida and Shindo, 1983). The Green s function approach seems to be more cumbersome and less physically transparent that the supercell technique. 

The total energy of the system is one of the most important results obtained from any of the calculational techniques. To study the behavior of an impurity (in a particular charge state) in a semiconductor one needs to know the total energy of many different configurations, in which the impurity is located at different sites in the host crystal. Specific sites in the diamond or zinc-blende structure have been extensively studied because of their relatively high symmetry. Figure 1 shows their location in a three-dimensional view. In Fig. 2, some sites are indicated in a (110) plane... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

Diphenylmethylene is certainly the most exhaustively studied of the aromatic carbenes. Low temperature epr spectroscopy (Trozzolo et al., 1962) clearly established the ground state of this carbene as the triplet. The optical spectrum of the triplet was recorded first in a 1,1-diphenylethylene host crystal (Closs et al., 1966) and later in frozen solvents (Trozzolo and Gibbons, 1967). 

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