Vacancies simple metals

After characterizing this type of nanocatalyst consisting of metal atoms trapped on oxygen vacancies, simple reactions like acetylene polymerization or CO oxidation can be studied by means of temperature programmed reaction studies and infrared spectroscopy. 

The electronic structure of a solid determines, to a large extent, the subsequent fate of the excited state produced when a photon is absorbed. It is convenient to distinguish at the outset between the excitation of electrons in a simple metal on the one hand and in a semiconductor or insulator on the other. Figure 1 contrasts the two cases. Excitation of an electron from a filled state in a metal leaves an electron vacancy below the Fermi level that can be filled rapidly by electrons from higher occupied energy levels. The... 

A Frenkel defect forms when an atom (ion) goes into an interstitial site leaving behind a vacancy and therefore consists of a defect pair of an interstitial atom and its vacancy. For a simple metal oxide compound MO with full ionization, its formation equation is expressed as... 

For a range of simple substitutional solid solutions to form, certain requirements must be met. First, the ions that replace each other must be isovalent. If this were not the case, other structural changes (e.g., vacancies or interstitials) would be required to maintain electroneutrality. Second, the ions that replace each other must be fairly similar in size. From a review of the experimental results on metal alloy formation, it has been suggested that 15% size difference can be tolerated for the formation of a substantial range of substitutional solid solutions. For solid solutions in nomnetal-lic systems, the limiting difference in size appears to be somewhat larger than 15%, although it is very difficult to quantify this. To a certain extent, this is because it is difficult to quantify the sizes of the ions themselves, but also because solid solution formation is very temperature dependent. 

The activity of the transition metals, especially for the chemisorption of molecular hydrogen and in hydrogenation reactions has been correlated, in the past, with the existence of partially filled d bands. Many alloy studies were prompted by the expectation that catalytic activity would change abruptly once these vacancies were filled by alloying with a group IB metal. Examples of such behavior have been collected together for the Pd-Au system (1). It is to be expected also that various complications might superimpose on the simple activity patterns observed for primitive... 

When the random-walk model is expanded to take into account the real structures of solids, it becomes apparent that diffusion in crystals is dependent upon point defect populations. To give a simple example, imagine a crystal such as that of a metal in which all of the atom sites are occupied. Inherently, diffusion from one normally occupied site to another would be impossible in such a crystal and a random walk cannot occur at all. However, diffusion can occur if a population of defects such as vacancies exists. In this case, atoms can jump from a normal site into a neighboring vacancy and so gradually move through the crystal. Movement of a diffusing atom into a vacant site corresponds to movement of the vacancy in the other direction (Fig. 5.7). In practice, it is often very convenient, in problems where vacancy diffusion occurs, to ignore atom movement and to focus attention upon the diffusion of the vacancies as if they were real particles. This process is therefore frequently referred to as vacancy diffusion... 

The discussion of the defects in FeO has so far been only structural. Now we turn our attention to the balancing of the charges within the crystal. In principle the compensation for the iron deficiency can be made either by oxidation of some Fe(II) ions or by reduction of some oxide anions. It is energetically more favourable to oxidise Fe(II). For each Fe vacancy, two Fe cations must be oxidised to Fe ". In the overwhelming majority of cases, defect creation involves changes in the cation oxidation state. In the case of metal excess in simple compounds, we would usually expect to find that neighbouring cation(s) would be reduced. 

As mentioned previously (see Section 1.3.5) the binary M-X system shows a phase separation phenomenon in which the phase decomposes into two phases, having lower and higher concentrations of vacancies, below the critical temperature f, under the condition < 0, i.e. there is an attractive force between vacancies. In Section 1.3.5 it was not possible to refer to the details of those structures, because the model was less than simple. In any case, it can be safely said that if s < 0, vacancies cluster at low temperatures (from a thermodynamic point of view). Here let us briefly review the non-stoichiometry of 3d transition metal monoxides Mj- O, and then discuss the Fej system as a typical example of the clustering of vacancies in detail. 

One typical way to improve the catalyst system was directed at the multi-component bismuth molybdate catalyst having scheelite structure (85), where metal cations other than molybdenum and bismuth usually have ionic radii larger than 0.9 A. It is important that the a-phase of bismuth molybdate has a distorted scheelite structure. Thus, metal molybdates of third and fourth metal elements having scheelite structure easily form mixed-metal scheelite crystals or solid solution with the a-phase of bismuth molybdates. Thus, the catalyst structure of the scheelite-type multicomponent bismuth molybdate is rather simple and composed of a single phase or double phases including many lattice vacancies. On the other hand, another type of multi-component bismuth molybdate is composed mainly of the metal cation additives having ionic radii smaller than 0.8 A. Different from the scheelite-type multicomponent bismuth molybdates, the latter catalyst system is never composed of a simple phase but is made up of many kinds of different crys-... 

When a metal crystal free of applied stress and containing screw dislocation segments is quenched so that supersaturated vacancies are produced, the screw segments are converted into helices by climb. Show that the converted helices can be at equilibrium with a certain concentration of supersaturated vacancies and find an expression for this critical concentration in terms of appropriate parameters of the system. Use the simple line-tension approximation leading to Eq. 11.12. We note that the helix will grow by climb if the vacancy concentration in the crystal exceeds this critical concentration and will contract if it falls below it. 

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