Vacancy supersaturation

A low deposition velocity in combination with a high vacancy supersaturation caused by the ion bombardment creates conditions for the intensive diffusion of aluminum atoms into a chromium coating. 

First-order kinetics were assumed for the elimination of vacancy supersaturation 5, which assumes that elimination takes place on fixed sinks. The characteristic process frequency factor is given by kom = Pvi Om, where Pv is the effective sink density. For a dislocation density J = lO cmcm", as expected in the present material and using the conventional relation Pv = 27r6 5/ln(rs/rc) in which Tg is the average distance between dislocations, Vc the capture radius of the dislocation and b the atom jump distance, pv = 4.3 x 10 at" is obtained. This value, in conjunction with the values calculated for uom, gives kom = 6.7 x 10, 13 X 10 and 2.3 x 10 s" for 19, 13 and 6.5% Al. Furthermore, under nonisother-mal conditions, S = exp(—/com i(-E m)- Curves for S and Xi, plotted against T are shown in Fig. 12. For illustration purposes only, an 5 curve was plotted for a deformed material with 6 = 10 cmcm, which corresponds to pv = 10 at . For such a specimen, it can be inferred that stage 1 should go to completion at a lower temperature. 

Comparison of both x, and S curves, confirms that stage 1 effectively corresponds to an SRO process assisted by excess vacancies, because in all cases it goes to completion just as the vacancy supersaturation vanishes. Moreover, both curves exhibit symmetrical kinetic paths. It is then inferred, necessarily, that during stage 2 the ordering process must be completed, assisted by equilibrium vacancies and by vacancy complexes which were not yet eliminated during stage 1. 

Suppose, for instance, that the B component is considerably more mobile than the A component. Then the emergence of the R lamella (enriched with the B component) and the P lamella (depleted with the B component) in the unstable alloy causes a more intensive flux of the B component from P to R than the opposite A component flux from R to P. Thus, the vacancy flux from R to P (i.e., opposite to the direction of a more mobile component s (the B one) diffusion) must arise. This must result in vacancy supersaturation in P and vacancy depletion in R. 

The Laplace tension and compression of the compound layer due to curvatures of internal and outer interfaces have been taken into account in the analysis. However, vacancy supersaturation is assumed to be outside the compound layer (in the B-core) at the initial stage of reaction, so voids can be nucleated. Curvature effects on vacancy concentration exist, so the difference of vacancy concentrations at the internal and external boundaries of the compound cannot be neglected. On the basis of the Gibbs-Thomson effect, the equilibrium vacancy concentration at the internal boundary of the compound layer is higher than that at the planar free surface... 

Conventionally, the critical void size is determined only by vacancy supersaturation and temperature. In our case, the concept of a critical size should be reconsidered. Void behavior, besides local vacancy concentration, is also determined by the gradients of vacancies and the main component, so that a thermodynamically stable void might be kinetically unstable. The approximate criterion of central void growth is given by Equation 7.145. 

The formation stage starts from a vacancy supersaturation just under the interface and formation of multiple tiny nanovoids in this region, with bridges in-between providing mass transfer to the remaining metallic core. This feature was established only by MC simulations, since our phenomenological model is... 

Finally, and what is precisely the cause of swelling, the preferred elimination of interstitials on biased sinks in favor of interstitials rather than vacancies, as some dislocations. This allows vacancy supersaturations to exist and, thus, cavities to nucleate and grow. 

The swelling of nonfissile materials in fast neutron fluxes has only recently been discovered (76). In spite of this its importance has already stimulated much work. Theories have been advanced for the nucleation and growth of voids under the vacancy supersaturation produced by the radiation field (77-79). Experimental data is available from EBR-II components for cold-worked and solution treated 304 and 316 stainless steels (80, 81) and from irradiations in DFR for a range of potential clad alloys (82, 83). Claudson has fitted EBR-II data to empirical relations, e.g., the swelling for 20% cold-worked stainless steel is given by (81)... 

If, within the diffusion zone, there is no active vacancy source or sink, then no drift of lattice planes could occur and the difference in the diffusion fluxes of substitutional chemical species would result in vacancy supersaturation and build-up of local stress states within the diffusion zone. Return to local equilibrium in a stress-free state could be achieved by the nucleation of pores leading to the well-known Kirkendall porosity (Fig. 2.2d). All intermediate situations are possible depending on local stress states and the density, distribution and efficiency of vacancy sources or sinks. However, it should be emphasized that complete Kirkendall shift would occur only in stress-free systems in local equihbrium. Therefore, all obstacles to the free relative displacement of lattice planes would lead to local non-equilibrium. Such a situation corresponds to the build-up of stress states that modify the conditions of local equilibrium and the action of vacancy sources or sinks these stress states must therefore be taken into account to define and analyse these local conditions and their spatial and temporal evolutions. 

Typical surfaces observed in Ising model simulations are illustrated in Fig. 2. The size and extent of adatom and vacancy clusters increases with the temperature. Above a transition temperature (T. 62 for the surface illustrated), the clusters percolate. That is, some of the clusters link up to produce a connected network over the entire surface. Above Tj, crystal growth can proceed without two-dimensional nucleation, since large clusters are an inherent part of the interface structure. Finite growth rates are expected at arbitrarily small values of the supersaturation. 

More generally, co is independent of the external gas pressure k is the Boltzmann constant (1.38 x 10 erg deg ) and T is the temperature in Kelvin. Furthermore, the equilibrium between co and a collapsed CS plane fault is maintained by exchange at dislocations bounding the CS planes. Clearly, this equilibrium cannot be maintained except by the nucleation of a dislocation loop and such a process requires a supersaturation of vacancies and CS planes eliminate supersaturation of anion vacancies (Gai 1981, Gai et al 1982). Thus we introduce the concept of supersaturation of oxygen point defects in the reacting catalytic oxides, which contributes to the driving force for the nucleation of CS planes. From thermodynamics. 

The results indicate that a supersaturation of vacancies, c/co — 10, at the catalyst s surface is required to nucleate CS planes in M0O3 catalysts. CS planes are formed by the elimination of anion vacancies in supersaturation (where the supersaturation is defined relative to the background concentration of anion vacancies in equilibrium with CS planes, as described earlier) (Gai 1981, Gai et al 1982). The driving force for the nucleation of the CS fault is the difference between the chemical stress due to the supersaturation of anion vacancies of the faulted (defective) structure and the force required to create the fault. The estimate of Co is consistent with the equilibrium concentration of anion vacancies found in electron beam heating studies of M0O3 in vacuum (Bursill 1969). 

Dynamic ETEM experiments on CS defects have shown mat mey consume anion vacancies and grow (figure 3.7). These correlation studies indicate mat CS planes are secondary or detrimental to catalytic reactivity. They eliminate anion vacancies by accommodating the supersaturation of the vacancies in the reacting oxide catalyst and me catalyst reactivity (selectivity) begins to decrease with the onset of CS formation, i.e. CS planes are the consequence of catalyst reduction reactions rather than the origins of catalytic reactivity (Gai 1981,1992, 1993, Gai etfl/ 1982). 

The results that CS planes (which eliminate anion vacancies in supersaturation by shearing and collapsing the lattice) are detrimental to catalysis are also consistent with me fact mat if the catalyst structure continues to collapse to form CS planes, after a period of time me catalyst is no longer an efficient oxidation catalyst. An efficient catalyst is essential for prolonged catalytic activity. This has led to me discovery of a novel glide shear mechanism (Gai et al 1995, Gai 1997). The role of mis mechanism in mixed-metal practical (commercial) catalysts will be examined when we discuss butane oxidation technology. 

As described in section 3.3, correlation studies between CS plane defects observed by ETEM and and parallel reaction chemistry (under conditions similar to those used in ETEM) indicate that the CS planes which eliminate supersaturation of anion vacancies are a consequence of catalytic activity and not active oxygen exchange sites for catalysis as was originally believed. They are secondary or detrimental to catalysis. The correlation results strongly suggest that anion point defects are active centres in the rapid diffusion of oxygen in... 

Of particular interest in kinetics is the non-conservative dislocation motion (climb). The net force on a dislocation line in the climb direction (per unit length) consists of two parts Kei is the force due to elastic interactions (Peach-Koehler force), Kcbcm is the force due to the deviation from SE equilibrium in the dislocation-free bulk relative to the established equilibrium at the dislocation line. Sites of repeatable growth (kinks, jogs) allow fast equilibration at the dislocation. For example, if cv is the supersaturated concentration and c is the equilibrium concentration of vacancies, (in the sense of an osmotic pressure) is... 

Several points are to be noted. Firstly, pores and changes of sample dimension have been observed at and near interdiffusion zones [R. Busch, V. Ruth (1991)]. Pore formation is witness to a certain point defect supersaturation and indicates that sinks and sources for point defects are not sufficiently effective to maintain local defect equilibrium. Secondly, it is not necessary to assume a vacancy mechanism for atomic motion in order to invoke a Kirkendall effect. Finally, external observers would still see a marker movement (markers connected by lattice planes) in spite of bA = bB (no Kirkendall effect) if Vm depends on composition. The consequences of a variable molar volume for the determination of diffusion coefficients in binary systems have been thoroughly discussed (F. Sauer, V. Freise (1962) C. Wagner (1969) H. Schmalzried (1981)]. 

The Kirkendall effect alters the structure of the diffusion zone in crystalline materials. In many cases, the small supersaturation of vacancies on the side losing mass by fast diffusion causes the excess vacancies to precipitate out in the form of small voids, and the region becomes porous [11], Also, the plastic flow maintains a constant cross section in the diffusion zone because of compatibility stresses. These stresses induce dislocation multiplication and the formation of cellular dislocation structures in the diffusion zone. Similar dislocation structures are associated with high-temperature plastic deformation in the absence of diffusion [12-14]. 

R.W. Balluffi. The supersaturation and precipitation of vacancies during diffusion. Acta Metall., 2(2) 194-202, 1954. 

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

Vacancy quenching experiments where the destruction rate at climbing dislocations of supersaturated vacancies obtained by quenching the metal from an elevated temperature is measured (see the analysis of this phenomenon in the following section)... 

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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