Intrinsic defect clusters

The most important application to be considered under this heading is the calculation of intrinsic defect concentrations in dilute solid solutions. If the solution is so dilute that only the leading terms in the various cluster expansions need be retained then the results required are slight generalizations of those above and follow at once from the notation for the general results. For example, the equilibrium concentration of vacancies in a dilute solution of a single solute, s, is found from Eqs. (74a) and (75) to be... 

In this section we are concerned with the properties of intrinsic Schottky and Frenkel disorder in pure ionic conducting crystals and with the same systems doped with aliovalent cations. As already remarked in Section I, the properties of uni-univalent crystals, e.g. sodium choride and silver bromide which contain Schottky and cationic Frenkel disorder respectively, doped with divalent cation impurities are of particular interest. At low concentrations the impurity is incorporated substitutionally together with an additional cation vacancy to preserve electrical neutrality. At sufficiently low temperatures the concentration of intrinsic defects in a doped crystal is negligible compared with the concentration of added defects. We shall first mention briefly the theoretical methods used for such systems and then review the use of the cluster formalism. 

Abstract. An embedded-cluster approximation is adopted for simulating the heterolytic dissociation of hydrogen at two intrinsic defects on the (001) surface of magnesium oxide the isolated anion vacancy, and the tub divacancy. The dissociation process is shown to be critically dependent on the structure of the electrostatic field at the surface both as concerns energetics and final configuration. 

Presence of these interstices provides to the fluorite stmcture extremely specific features. In UO2 particularly, it allows for placement of some radioactive decay products, these sites are responsible for existence of hyperstoichiometric UO2+X phase, where the extra oxygen ions fill the empty interstitial sites in the fluorite lattice etc. First case is extremely important in radiation damaged UO2. Second one is cmcial in oxidation of pure UO2 in atmospheric conditions. Diffusion of atmospheric oxygen into the bulk of crystal brings excess oxygens into empty interstices. These become filled more or less randomly only at low x, at higher concentration of extra anions they form different types of clusters, including so-called 2 2 2 Willis dimers Willis), tetra- and pentameric defects clusters of cuboctahedral symmetry Allen and Tempest). Last defects appear due to interaction of extra anions with intrinsic crystal FP defects (anion Frenkel pairs, i.e. anion vacancies and anion interstitials). 

Once the cluster expansion of the partition function has been made the remaining thermodynamic functions can be obtained as cluster expansions by taking suitable derivatives. Of particular interest are the expressions for the equilibrium concentrations of intrinsic point defects for the various types of lattice disorder. Since the partition function is a function of Nx, N2, V, and T, it is convenient for the derivation of these expressions to introduce defect chemical potentials for each of the species in the set (Nj + N2) defined, by analogy with ordinary Gibbs chemical potentials (cf. Section I), by the relation... 

Here we want to mention some other transition-metal systems which have been studied by chemists, whereas the work on M11F2 and ruby has mainly been done by physicists. In Cr(urea) 6I3 energy transfer from the intrinsic Cr ions to Cr " ions near defects has been shown to occur . The traps are very shallow 13 and 49 cm for the more important ones. The intrinsic Cr luminescence increases rapidly with increasing temperature. It is interesting to note that in the diluted system Al(urea)6l3—Cr the Cr + are not distributed at random. They strongly tend to cluster. Energy migration in these clusters has been shown to occur. 

The photophysical processes of semiconductor nanoclusters are discussed in this section. The absorption of a photon by a semiconductor cluster creates an electron-hole pair bounded by Coulomb interaction, generally referred to as an exciton. The peak of the exciton emission band should overlap with the peak of the absorption band, that is, the Franck-Condon shift should be small or absent. The exciton can decay either nonradiatively or radiative-ly. The excitation can also be trapped by various impurities states (Figure 10). If the impurity atom replaces one of the constituent atoms of the crystal and provides the crystal with additional electrons, then the impurity is a donor. If the impurity atom provides less electrons than the atom it replaces, it is an acceptor. When the impurity is lodged in an interstitial position, it acts as a donor. A missing atom in the crystal results in a vacancy which deprives the crystal of electrons and makes the vacancy an acceptor. In a nanocluster, there may be intrinsic surface states which can act as either donors or acceptors. Radiative transitions can occur from these impurity states, as shown in Figure 10. The spectral position of the defect-related emission band usually shows significant red-shift from the exciton absorption band. 

Although the appearance of red-shifted, broad-band luminescence is usually attributed to the presence of defects, this is not always so. As the size of the cluster becomes smaller, the concept of defect becomes meaningless. Red-shifted luminescence may be due to an intrinsic excited state of the cluster which is significantly distorted from the ground state. This is quite common for molecules. Since the surface structures of most of the semiconductor clusters synthesized to date are not precisely known, in most cases it is difficult to establish whether the observed red-shifted luminescence band is due to defects or the intrinsic excited state. 

This chapter proceeds with a general discussion of the overall catalytic cycle and Sabatier s principle in order to illustrate the comparison of relative kinetic and thermodynamic steps in the overall cycle. This is followed by a fundamental discussion of the intrinsic surface chemistry and the application of transition state theory to the description of the surface reactivity. We discuss the important problem of the pressure and material gap in relating intrinsic rates with overall catalytic behavior and then describe the influence of the tatic reaction environment including promoters, cluster size, support, defects, ensemble, coadsorption and stereochemistry. Lastly, we discuss the transient changes to the surface structure as well as intermediates and their influence on catalytic performance. 

---