Irradiation point defect concentration

Defect structure of neutron-irradiated Fe-Cr alloys contains free vacancies, SIA, VC, pure dislocation loops, dislocation loops decorated by Cr atoms, and vacancy-Cr complexes as well as Cr precipitates depending on the irradiation regime (Malerba et al. 2008). The CD model in our study is close to the model proposed by Christien and Barbu (2004), where the CD simulations are first performed for the free vacancies, SIAC, and point defect clusters and then for the precipitates, taking into account the steady state values of the free point defects concentrations obtained in the first step. In addition, we take into account the Cr-effect on the SIA diffusivity according to the density functional theory (DFT) calculations (Terentyev et al. 2008). 

We conclude that a crystal which is continuously irradiated with particles of sufficient kinetic energy and in which no further reactions (e.g., phase formations) take place becomes more and more supersaturated with point defects. Recombination starts if the defects can move fast enough by thermal activation. A steady state is reached when the rates of defect production and annihilation (by recombination) are equal. In the homogeneous crystal, the change in local defect concentration (cd) over time is given by (see Section 5.3.3)... 

Figure 13-2. Concentration of point defects (cv, c) due to irradiation as a function of time (schematic).

Of special interest in the recent years was the kinetics of defect radiation-induced aggregation in a form of colloids-, in alkali halides MeX irradiated at high temperatures and high doses bubbles filled with X2 gas and metal particles with several nanometers in size were observed [58] more than once. Several theoretical formalisms were developed for describing this phenomenon, which could be classified as three general categories (i) macroscopic theory [59-62], which is based on the rate equations for macroscopic defect concentrations (ii) mesoscopic theory [63-65] operating with space-dependent local concentrations of point defects, and lastly (iii) discussed in Section 7.1 microscopic theory based on the hierarchy of equations for many-particle densities (in principle, it is infinite and contains complete information about all kinds of spatial correlation within different clusters of defects). 

The current majority opinion is that both types of point defects are important. Thermal equilibrium concentrations of point defects at the melting point are orders of magnitude lower in Si than in metals. Therefore, a direct determination of their nature by Simmons-Balluffi-type experiments (26) has not been possible. The accuracy of calculated enthalpies of formation and migration is within 1 eV, and the calculations do not help in distinguishing between the dominance of vacancies or interstitials in diffusion. The interpretation of low-temperature experiments on the migration of irradiation-induced point defects is complicated by the occurrence of radiation-induced migration of self-interstitials (27, 28). 

Nonequihbrium concentrations of point defects can be introduced by materials processing (e.g. rapid quenching or irradiation treatment), in which case they are classified as extrinsic. Extrinsic defects can also be introduced chemically. Often times, nonstoichiometry results from extrinsic point defects, and its extent may be measmed by the defect concentration. Many transition metal compounds are nonstoichiometric because the transition metal is present in more than one oxidation state. For example, some of the metal ions may be oxidized to a higher valence state. This requires either the introduction of cation vacancies or the creation of anion interstitials in order to maintain charge neutrality. The possibility for mixed-valency is not a prerequisite for nonstoichiometry, however. In the alkah hahdes, extra alkah metal atoms can diffuse into the lattice, giving (5 metal atoms ionize and force an equal number... 

Up to now, our equations have been continuum-level descriptions of mass flow. As with the other transport properties discussed in this chapter, however, the primary objective here is to examine the microscopic, or atomistic, descriptions, a topic that is now taken up. The transport of matter through a solid is a good example of a phenomenon mediated by point defects. Diffusion is the result of a concentration gradient of solute atoms, vacancies (unoccupied lattice, or solvent atom, sites), or interstitials (atoms residing between lattice sites). An equilibrium concentration of vacancies and interstitials are introduced into a lattice by thermal vibrations, for it is known from the theory of specific heat, atoms in a crystal oscillate around their equilibrium positions. Nonequilibrium concentrations can be introduced by materials processing (e.g. rapid quenching or irradiation treatment). 

There are two types of lattice defects that occur in all real crystals and at very high concentration in irradiated crystals. These are known as point defects and line defects. Point defects occur as the result of displacements of atoms from their normal lattice sites. The displaced atoms usually occupy sites that are not in the lattice framework they are then known as interstitials. The empty lattice site left behind by the interstitial is called a vacancy. Avacancy produced by displacement of an anion or cation, along with its interstitial ion, is called a Frenkel pair, or simply a... 

Upon irradiation, on the contrary to the passivation treatment, the protons penetrate far behind the QD layer md do not exhibit any passivation effect. In contrast, the irradiation, producing a uniform defect concentration up to the depth of several 10 pm, reduces the intensities of all spectral components mentioned above, but to a different extent. So, it almost removes the B dots from the spectrum. Besides, the irradiation introduces well-known point defects with sharp NP lines (C, G and W) [5, 6] and a very broad band, also of defect origin. It is seen in Fig. 1 (c) for the lowest dose that the PL from the WL and bulk Si disappears whereas the PL from the QDs persists. This behavior clearly proves a higher radiation resistance of the dots as compared to the quantum wells and bulk material. At the highest dose (2 x 10 p/cm ) the QD PL is quenched too, and only sharp NP lines and the broad band of defect origin are observed. The spectra of the dots irradiated to low doses can be separated from the defect spectra by subtracting the spectrum of this heavily irradiated sample normalized to the intensity of a distinct feature, e.g., of the C-line (Fig. 3c). 

Radiation more effectively increases the concentration of point defects than an increase in temperature. To study the effect of point defects on mechanical properties, such as strength or hardness-related features, large amounts of point defects are preferable. Therefore, radiation is useful for studying the effects of point defects in crystals and studies on the effects of point defects are done on irradiated materials. 

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