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Diffusion Solids Fundamentals Diffusion Controlled Solid State Episode 2 Part 9

Tham khảo tài liệu 'diffusion solids fundamentals diffusion controlled solid state episode 2 part 9', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 26.2 Point Defects in Ionic Crystals 453 1. In undoped crystals with Schottky disorder charge neutrality requires equal site fractions of cation and anion vacancies. Then 0 0 exp llpA exp - p KPT . 26.3 y 2KB 2kbt 2. In undoped crystals with Frenkel disorder charge neutrality requires equal numbers of vacancies and interstitials. For Frenkel disorder in the cation sublattice we have c 0 CIc 0 exp exp - Fp VKFP T . 26.4 y 2kB J y 2KB-L J In Eqs. 26.3 and 26.4 the zero in the arguments of the site fractions refers to intrinsic conditions. Frenkel disorder in the anion sublattice can be treated in an analogous way. 3. If the formation enthalpies of Schottky and Frenkel pairs are similar cation vacancies anion vacancies and cation interstitials will be present. The relative concentrations of the various defects must then be determined by satisfying Eq. 26.1 and Eq. 26.2 simultaneously and in addition the condition of charge neutrality which requires that Cvc Cva Cic 26.5 provided all ions have the same charge. 4. Heterovalent doping of ionic crystals means that some of the matrix ions are replaced by foreign ions of different valence. For example if Ca2 ions replace a few Na ions in NaCl an equal number of cation vacancies must be added to preserve charge neutrality. Thus the equilibrium concentration of defects is determined by the arrangement which maintains charge neutrality and at the same time satisfies Eqs. 26.1 or 26.2 see below . Vacancy-pairs Relative to the perfect lattice cation and anion vacancies bear opposite charges and attract each other by Coulomb forces. When two Table 26.1. Dominant type of disorder in ionic crystals Material Structure Dominant disorder Alkali halides NaCl KCl . NaCl Schottky Alkaline earth oxides NaCl Schottky AgCl AgBr NaCl Cation Frenkel CsCl TlCl TlBr CsCl Schottky BeO MgO . Wurtzite Schottky Alkaline earth fluorites CeO2 ThO2 CaF2 Anion Frenkel 454 26 Ionic Crystals vacancies form a nearest-neighbour pair Vp in addition to .