Small vacancy clusters

Carter et alJ used PALA and hardness measurements coupled with postirradiation annealing (PIA) to study irradiation damage in two low-Cu plates and two high-Cu welds. The results from the irradiated plate were consistent with the presence of matrix damage clusters such as vacancies or very small vacancy clusters. 

The lifetimes of positrons trapped in small vacancy clusters were calculated using the LDA approach. As the lattice relaxation around the cluster has a relatively small influence on positron annihilation parameters, it was not included in the calculations. The results show that the lifetime of a positron trapped by a divacancy does not differ a lot from that trapped by a monovacancy (it increases by about 10 ps for Fe and 20 ps for Al). However, the lifetime increases rapidly when the cluster grows into a two-dimensional trivacancy and then into a three-dimensional tetravacancy [72]. For large clusters, the lifetime saturates at around 500 ps. The dependence of the positron lifetime in vacancy clusters on the free volume of the cluster expressed as the number of vacancies comprising the cluster is shown in Figure 4.32. 

In order to elucidate whether such a precipitate can trap positrons, the positron affinities A+ for the host material and the precipitate were calculated [154], The A+ values were found to be relatively high and the positron lifetimes very short for perfect MC carbides. This fact confirms that perfect MC (M s Cr, V, Ti, Mn, Fe, Zr, Nb) carbides are very dense materials that cannot trap positrons when embedded in the Fe matrix. In general, from a PAS point of view, radiation damage can be interpreted as a combination of radiation-induced point defects, dislocations and small vacancy clusters [129,130] that occur mainly in the region of the precipitate-matrix interface. 

The swelling rate as a function of dose is negligible below an incubation dose, followed by a rapid acceleration (transient regime) after which the sweUing rate tends toward a constant value. The incubation dose is sensitive to a number of parameters such as temperature, dose rate, chemical composition/microstructure, and gas content (in particular He produced by transmutation). Indeed it has been shown that the presence of gases stabilizes the three-dimensional geometry for small vacancy clusters and thus promotes the nucleation of voids [44,45]. 

Fig. 21. Defects formed by condensation of vacancies onto dislocation loops formed by collapse of small vacancy clusters, (a) Dislocation loops in 99.999% Al, quenched from 610°C into liquid N2, then aged 1 hr at — 80°C and 2 hr at 60°C. The defect is a Frank sessile dislocation enclosing an intrinsic stacking fault. Magnification 27,000 x. From Dr. K. Y. Chen, Northwestern University, Evanston, Illinois, (b) Stacking fault tetrahedra in 99.999% Au quenched from 1038° into -35°C brine and aged at 25°C. The tetrahedra (some are truncated) are bound by intrinsic stacking faults and dislocations at the edges called stair rod dislocations. Magnification 70,000 X. From Dr. J. A. McComb, Northwestern University, Evanston, Illinois.

The third term in Eq. 7, K, is the contribution to the basal plane thermal resistance due to defect scattering. Neutron irradiation causes various types of defects to be produced depending on the irradiation temperature. These defects are very effective in scattering phonons, even at flux levels which would be considered modest for most nuclear applications, and quickly dominate the other terms in Eq. 7. Several types of in-adiation-induced defects have been identified in graphite. For irradiation temperatures lower than 650°C, simple point defects in the form of vacancies or interstitials, along with small interstitial clusters, are the predominant defects. Moreover, at an irradiation temperatui-e near 150°C [17] the defect which dominates the thermal resistance is the lattice vacancy. 

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. 

As a continuum approximation, this approach should break down by the atomistic level. For islands it is presumably inappropriate for the small clusters imaged with FIM. More importantly, in many cases the stiffness may not be nearly anisotropic, as we have assumed it to be in our analysis. Then, as perhaps for Ag( 100) islands, new mechanisms may play a role. For vacancy clusters, there can be trapping in corners in systems that might seem to be cases of PD from consideration of vicinal surfaces. 

Although individual point defects, such as vacancies and interstitial atoms, cannot be seen by these contrast mechanisms, we can observe certain clusters of defects. For example, if a number of vacancies cluster together (condense) on a single atomic plane, then the planes above and below will collapse, forming an edge dislocation loop (as shown in Figure 5.5). Sometimes small voids (or gas bubbles) that have a negligible strain field are present in a crystal. These features can be observed because... 

The chemical shift of the line at -0.1 ppm indicates a hydrogen-bonded water cluster, while the peak at -3.9 ppm results from monomers or small mul-timers. The authors suggested that the monomolecular species are in one of two sites, an octahedral void or a small vacancy left by a missing fullerene cage. The remaining signal at -0.1 ppm comes from large water clusters. Support for this conclusion comes from four observations ... 

Fig. 2.2. (a) STM image of small Au clusters on Ti02. Vacancies are marked with squares, (b) Simulated STM image of a single Au atom trapped in an oxygen vacancy, (c) Line profiles comparing DFT theoretical and experimental results. Reproduced from [34]. Copyright 2003 American Physical Society... 

In this chapter, we have concentrated on MgO, one of the most studied and better understood oxide materials. We have shown that even on such a simple nontransition metal oxide about a dozen of different surface defect centers have been identified and described in the literature. Each of these centers has a somewhat different behavior toward adsorbed metal atoms. It becomes immediately clear that the precise assignment of the defect sites involved in the interaction, nucleation, and growth of the cluster is a formidable task. Nevertheless, thanks to the combined use of theory and experiment, the progress in this direction has been particularly significant and promising. For instance, a lot of evidence has been accumulated that points toward the role of the oxygen vacancies, the F centers. At the moment, these sites seem the most likely sites for nucleation and growth of small metal clusters. 

Even well-made TS-1 contains a small fraction of Si-vacancy defects [73,74]. Consistent with FTIR results on H2O2/TS-I [75], previous DPT calculations on nondefect (tetrapodal) and metal-vacancy defect (tripodal) Ti sites in TS-1 suggested that H2O2 attack on Ti-defect sites leads to Ti-OOH species (and water), while H2O2 attack on Ti-nondefect sites is kinetically and thermodynamically less favorable [76]. Moreover, Ti-OOH species can catalyze propylene epoxidation to PO [76-78]. Recent QM/MM calculations on adsorption of Aui 5 clusters inside the TS-1 pores suggest that the Ti-defect site is also the most favorable binding site for small Au clusters [66]. Therefore, defects in TS-1 are likely to stabilize adsorbed Au clusters and prevent sintering. 

The solubility of inert gas atoms (such as xenon, krypton and radon) in inorganic solids is small. The inert gases are trapped at lattice defects such as vacancy clusters, grain boundaries and pores. The defects in the solids can serve both as traps and as diffusion paths for the inert gas. A survey of the influence of various factors on the migration of inert gases in solids is given in a monograph by Balek [1]. 

Since electrons with MeV order energies can produce uniform damage to a depth in the order of mm, tensile tests can be conducted as macroscopic mechanical testing. SAXS or SANS can be conducted as well as TEM, atom probe tomography analysis and positron annihilation spectroscopy measurements. In HVEM irradiation, time-dependent evolution of individual defect clusters such as an interstitial loop or a vacancy cluster can be investigated in an irradiated spot area. Microanalysis using an electron beam probe such as energy dispersive X-ray analysis is also applicable in the beam spot area. However, other analyses or measurements on such small areas are difficult to carry out. 

There are very few data on the effect of irradiation temperature for example, fewer, larger dislocation loops are produced in high-purity Fe as the irradiation temperature increases. In CMn steels, loops are only seen after high-temperature, high dose irradiations. The small size of the vacancy clusters observed in RPV steels by positron annihilation, and poor correlations between hardening recovery and PA signal recovery, indicate to some workers that the defect clusters responsible for RPV steel hardening are predominantly interstitial in nature. ° ... 

---