Vacancies metal

They allow non-metal vacancies (i.e., carbon) in the lattice. 

Flux of metal atoms (or of metal vacancies in reverse direction)... 

Figure 1.3 Point defects in a crystal of a pure compound, MX, VM, a metal vacancy Vx a nonmetal vacancy Mj, a metal (self-)interstitial and Xs a nonmetal (self-)interstitial.

Metal vacancy at metal (M) site VM Nonmetal vacancy at nonmetal (Y) site Vy... 

The compound will be stoichiometric, with an exact composition of MX10ooo when the number of metal vacancies is equal to the number of nonmetal vacancies. At the same time, the number of electrons and holes will be equal. In an inorganic compound, which is an insulator or poor semiconductor with a fairly large band-gap, the number of point defects is greater than the number of intrinsic electrons or holes. To illustrate the procedure, suppose that the values for the equilibrium constants describing Schottky disorder, Ks, and intrinsic electron and hole numbers, Kc, are... 

As the pressure diminishes far below that of the stoichiometric point, the number of metal vacancies and holes will continue to fall and the electroneutrality equation chosen, Eq. (7.16), will no longer be representative. A more appropriate form of the electroneutrality equation for the low-pressure region ignores the minority defects, which are now metal vacancies and holes, to give... 

The high-pressure region is associated with the electroneutrality equation [h ] = 2[V ]. Holes predominate, so that the material is a p-type semiconductor in this regime. In addition, the conductivity will increase as the g power of the partial pressure of the gaseous X2 component increases. The number of metal vacancies (and nonmetal excess) will increase as the partial pressure of the gaseous X2 component increases and the phase will be distinctly nonstoichiometric. There is a high concentration of cation vacancies that would be expected to enhance cation diffusion. 

Derive the polynomial expressions for the concentration dependence of electrons, metal vacancies, and anion vacancies for a compound MX showing Schottky equilibrium (Section 7.9.4). Insert values of the equilibrium constants to obtain polynomial expressions for the cases where electronic defects dominate. 

Further reduction of manganese ions and the generation of oxygen vacancies could take place only after all metal vacancies are consumed under cathodic polarization. However, the oxygen vacancy formation and the removal of cation vacancies may not be the only explanation for the hysteresis behavior as shown recently by Wang and Jiang [35],... 

The driving force for isoselective propagation results from steric and electrostatic interactions between the substituent of the incoming monomer and the ligands of the transition metal. The chirality of the active site dictates that monomer coordinate to the transition metal vacancy primarily through one of the two enantiofaces. Actives sites XXI and XXII each yield isotactic polymer molecules through nearly exclusive coordination with the re and si monomer enantioface, respectively, or vice versa. That is, we may not know which enantio-face will coordinate with XXI and which enantioface with XXII, but it is clear that only one of the enantiofaces will coordinate with XXI while the opposite enantioface will coordinate with XXn. This is the catalyst (initiator) site control or enantiomorphic site control model for isoselective polymerization. 

Partial pressure of oxygen controls the nature of defects and nonstoichiometry in metal oxides. The defects responsible for nonstoichiometry and the corresponding oxidation or reduction of cations can be described in terms of quasichemical defect reactions. Let us consider the example of transition metal monoxides, M, 0 (M = Mn, Fe, Co, Ni), which exhibit metal-deficient nonstoichiometry. For the formation of metal vacancies in M, 0, the following equations can be written ... 

A plot of AGq versus In x would be linear, the slope giving n the value of n gives information about the types of defects involved. For doubly ionized metal vacancies, Vm , m = 6 for Vm, m = 4 and so on. Isothermal AGq — In x plots can be constructed from equilibrium thermogravimetric data or electrochemical measurements. A typical AGqj — log X plot for the Fe, 0 system is shown in Fig. 5.4, where n values corresponding to various regions are indicated. We see that n = 6 applies when X 0.09, while n = 5, corresponding to pairs, also applies close to this... 

Frenkel type in which metal atoms on regular sites move to interstitial sites, leaving metal vacancies, i.e. (M = MJ (Fig. 1.9(b)). Anti-Frenkel type defects, in which anion atoms on regular sites move to interstitial sites, are also possible, but are rarely observed because the ionic radii of anions are usually larger than those of the metals under consideration. Frenkel type is stoichiometric. 

Small deviation from stoichiometry. I. Metal vacancies... 

Let us consider the compounds which show a small deviation from the stoichiometric composition and whose non-stoichiometry is derived from metal vacancies. The free energy of these compounds, which take the composition MX in the ideal or non-defect state, can be calculated by the method proposed by Libowitz. To readers who are well acquainted with the Fowler-Guggenheim style of statistical thermodynamics, the method here adopted may not be quite satisfactory however, the Libowitz method is understandable even to beginners who know only elementary thermodynamics and statistical mechanics. It goes without saying that the result calculated by the Libowitz method is essentially coincident with that calculated by the Fowler-Guggenheim method. 

Consider a crystal Mj X which contains both metal vacancies and interstitial metal atoms in low concentration, i.e. M occupies lattice points in N lattice sites of metal, X occupies N in N lattice sites (generally, N, N, but in this calculation we assume = Nf and, moreover, interstitial M occupies in Na, where a is a constant which is fixed by crystal structure. If the conditions N N — N ), (N — N ), N are satisfied, it is not necessary to take the interaction energy between defects, as mentioned below, into consideration. The free energy of the crystal may be written as... 

Fig. 1.12 Interaction energy, s , between metal vacancies and its calculation, (a) denotes the interaction energy (enthalpy) between the first nearest vacancies, (b) A metal vacancy has metal sites as first nearest neighbours (labelled 1 ). The probability of being a vacancy in a metal site equals (N — Aml/A. The interaction energy between a metal vacancy and its first nearest neighbour vacancies is The total...

Consider a crystal of composition M0.5X, the metal vacancies are regularly arranged among the lattice sites at lower temperatures, shown in Fig. 1.18 as a basic model of a vacancy-ordered structure with a two-dimensional lattice (in this figure, the anion atoms are omitted for clarity). This structure is realized if the composition of the crystal is Mq 5X, and metal atoms M fully occupy the B-sites and metal vacancies fully occupy the A-sites, this only occurs at absolute zero temperature (perfect order). The occupation probabilities, p and Pg, denote the ratio of number of metal atoms on the A-sites (ma) to the number of lattice points of the A-sites ( 1V) and the ratio of number of metal atoms on the B-sites (Ug) to the number of lattice points of the B-sites (ilV), respectively. Thus p and pg can be expressed as... 

Next let us discuss the electronic defects associated with point defects in semiconductive or insulating compounds, which lead to non-stoichiometry. Consider a NiO crystal, which has a NaCl-type structure, as NiO can be regarded as an ionic crystal, the valence states of Ni and O are Ni and O , respectively. We assume that the non-stoichiometry originates only from metal vacancies. Generation of metal defects in NiO may be expressed by a chemical reaction similar to eqn (1.119), i.e. 

Fig. 1.23 Electro-neutrality of NiO with two metal vacancies. A perfect crystal (a) is oxidized to crystal (b) or (c). In crystal (b), there are two metal vacancies with 2 charge. In crystal (c), there are two metal vacancies with neutral charge and four metal ions with excess charge (-I- 3). (b) and (c) are alternative representations of the oxidized crystal.

This situation can be expressed in terms of the band model as shown in Fig. 1.24. Stoichiometric NiO is an intrinsic semiconductor, having an energy gap of Eq (=Eq—E ). Non-stoichiometric Nij O, which has metal vacancies or electronic defects, has an acceptor level A between the valence... 

Rau analysed these data on the assumption that Nii S has defects only in the metal sites, i.e. metal vacancies, and these vacancies are distributed randomly with vacancy-vacancy interaction , see Section 1.3.5. Because this assumption is the same as that adopted in Section 1.3.5, we can apply eqn (1.90) to this problem. On replacing and N/N by 8 (in the NiAs type structure, a metal has 8 near neighbour metals separated by the same metal-metal distance) and y (by doing this, d in eqn (1.90) equals (y — l)/y) in the equation, we have... 

As described in Section 1,1, both the procedures of changing Po. at fixed temperature and changing temperature at fixed Po. control the nonstoichiometry in Nii O, Let us consider the relation between a and 3 in Nil O, in which the non-stoichiometry S is believed to originate from metal vacancies. By use of the notation based on the effective charge, described in Section 1,3,7, the chemical equilibrium between the oxygen gas in the atmosphere and the oxygen in the solid may be expressed as... 

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