Vacancy interaction

M. Porta, C. Frontera, F. Vives, T. Castan. Effect of the vacancy interaction on antiphase domain growth in a two-dimensional binary alloy. Phys Rev B 56 5261, 1997. 

Let us consider a crystal similar to that discussed in Sections 1,3.3 and 1.3.4, which, in this case, shows a larger deviation from stoichiometry. It is appropriate to assume that there are no interstitial atoms in this case, because the Frenkel type defect has a tendency to decrease deviation. Consider a crystal in which M occupies sites in N lattice points and X occupies sites in N lattice points. It is necessary to take the vacancy-vacancy interaction energy into consideration, because the concentration of vacancies is higher. The method of calculation of free energy (enthalpy) related to is shown in Fig. 1.12. The total free energy of the crystal may be written... 

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... 

The value of sj v is almost constant (6-7 kcal mol" ) in the measured temperature range and the positive value means that the vacancy-vacancy interaction is repulsive. On the other hand, the value of (/iNis + ) changes sign from minus to plus with increasing temperature. Upon substituting eqns (1.145) for (jUnjs + fi ) and, from eqns (1.146) and (1.147), eqn (1.145) can be rewritten as the relation between y, Uj, and T, as shown in Fig. 1.36. The curves for phase boundaries (thicker curves), i.e. the upper curve for coexistent condensed phases (Ni. S phase + adjacent sulfur rich phase) and the lower curve for coexistent condensed phases (Ni. S phase + adjacent sulfur poor phase), were taken from Refs 26 and 27, in which the temperature dependence of Ps. for coexistent samples was investigated in detail. (As mentioned in Section 1.2, the relationship between the equilibrium sulfur pressure for coexistent condensed phases and temperature must show one to one correspondence. Rau calculated <5 in Nij S for the coexistent phases by substitution of the data from refs 26 and 27 for Os and T into eqn (1.145).)... 

The parameter x corresponds to the chemical composition, since Y in the notation MXy is equal to 8/(4 4- x). a is the ratio of the inter-layer to intra-layer vacancy-vacancy interaction and t is the measure of temperature. 

In this structure there are perovskite layers of ABO3 separated by AO rock salt layers. It is this layered structure that allows great flexibility in the oxygen stoichiometry of these materials. It is possible to incorporate excess oxygen (5 > 0) in the unusual form of interstitial oxygens, which provide an alternative to the vacancy-based conduction mechanism present in the perovskite and fluorite oxides, where the dopant-vacancy interactions can limit the observed conductivity. The mobility of the oxide ions in these materials occurs mainly through an interstitialcy mechanism in the aZ)-plane, although evidence of low Ea for the conduction in the c-direction via a Frenkel mechanism has also been reported. ... 

The nature and strength of vacancy-vacancy interactions have scarcely been investigated, although they drive the thermodynamics of vacancy ordering on defective surfaces, and are thus key quantities to understand the numerous reconstructions observed on surfaces annealed in vacuum [1,2]. However, the ordering process may be inhibited by kinetic effects, relying on parameters, such as the activation energy for vacancy diffusion and the temperature. On MgO(lOO), vacancies have been found to weakly repell... 

Overall, the results from the cathode-only KMC simulations [118-120] were found to be qualitatively consistent with experimental trends, with a great deal of the atomistic-level details preserved. However, in order to improve the results, and approach quantitative agreement with experiments, additional features must be incorporated, such as the anode-side reactions, correlation of the ion-vacancy and vacancy-vacancy interactions, grain boundaries, and explicit structural treatment of the anode and cathode. In order to incorporate some of these necessary features, two KMC-based SOFC simulation studies have recently emerged [126,127] along with some close experimental collaboration [128], In all of these more recent studies, a complete SOFC model (anode+cathode) was assembled. 

La Magna A., Coffa S. and Colombo L., Role of Extended Vacancy-Vacancy Interaction on the Ripening of Voids in Silicon, Phys. Rev. Lett. 82, 1720 (1999). 

Diffusion in NijAl has been studied by few investigators - in particular Chou and Chou (1985) and Hoshino et al. (1988) -and has been reviewed and discussed with respect to mechanisms and defects (Bakker, 1984 Wever et al., 1989 Stoloff, 1989). The constitutional defects are antistructure atoms on both sides of stoichiometry, i.e. Al on Ni sites and Ni on Al sites, and the concentration of constitutional, i.e. ather-mal, vacancies is very small. The vacancy content of 6 x 10 at the melting temperature and the vacancy formation enthalpy of 1.60 eV correspond to the respective values for Ni, i.e. the vacancy behavior of NijAI is similar to that of pure metals (Schaefer et al., 1992). The diffusion of Ni in NijAl is not very different from that in pure Ni and at high temperatures it is insensitive to deviations from stoichiometry. The diffusion of Al in NijAl is less well studied because a tracer is not readily available. Defects may interact with dissolved third elements which affects diffusion. In particular vacancies interact with B which is needed for ductilization , and this leads to a complex dependence of the Ni diffusion coefficient on the Al and B content of NijAl (Hoshino etal., 1988). Data for the diffusion of the third elements, Co, Cr, or Ti, in Nij Al are available (Minamino etal., 1992). 

R241 A. Somoza and A. Dupasquier, Vacancies in Aluminium and Solute-Vacancy Interactions in Aluminium Alloys , in Fundamentals of Aluminium Metallurgy Production, Processing and Applications, ed. R. Lumley, Woodhead Publishing Ltd., Cambridge, UK, 2011, p. 386. 

Urquidi, M. and Macdonald, D.D. (1985) Solute-vacancy interaction model and the effect of minor alloying elements on the initiation of pitting corrosion. Journal of The Electrochemical Society, 132, 555-558. 

The data were analyzed by using 3 models for the point defect population, and this permitted a detailed interpretation to be made of Ca/vacancy interactions. It was shown that the contribution made by was negligible, and that interacted... 

By further analyzing the data, some insight into the impurity/vacancy interactions was obtained. This suggested that Co interacted quite strongly with Vjqj" during... 

Numerous studies have attempted to elucidate the role of Mo in the passivity of stainless steel. It has been proposed from XPS studies that Mo forms a solid solution with CrOOH with the result tiiat Mo is inhibited from dissolving trans-passively [9]. Others have proposed that active sites are rapidly covered with molybdenum oxyhydroxide or molybdate salts, thereby inhibiting localized corrosion [10]. Yet another study proposed that molybdate is formed by oxidation of an Mo dissolution product [11]. The oxyanion is then precipitated preferentially at active sites, where repassivation follows. It has also been proposed that in an oxide lattice dominated by three-valent species of Cr and Fe, ferrous ions will be accompanied by point defects. These defects are conjectured to be canceled by the presence of four- and six-valent Mo species [1]. Hence, the more defect-free film will be less able to be penetrated by aggressive anions. A theoretical study proposed a solute vacancy interaction model in which Mo " is assumed to interact electrostatically with oppositely charged cation vacancies [ 12]. As a consequence, the cation vacancy flux is gradually reduced in the passive film from the solution side to the metal-film interface, thus hindering vacancy condensation at the metal-oxide interface, which the authors postulate acts as a precursor for localized film breakdown [12]. 

Within the previous formalism, we can easily introduce atom-vacancy interactions. These interactions tire a simple way to take into account the electronic relaxations around the vacancy. Without them, the vacancy formation energy E(T in a pure metal would necessarily equal the cohesive energy E(r = 0.69 eV [30] and = 3.36 eV for fee Al). 

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