Defects in Ceramics • Point defects • Line Defects - Dislocations • Surface Defects - Grain Boundaries • Majority of this chapter is on point defects.
Why bother? • Point defects dictate several properties: • Diffusion which then determines sintering and sometimes creep • Electrical conductivity • Dielectric constants • Most dramatic example: YBa2Cu3O7 • Metal oxidation • Solid electrolytes
Thermodynamics of Point Defect Formation Or why vacancies are an unavoidable: a thermodynamic necessity… Approach: find an expression for G of perfect crystal and one for defective crystal; the one with the lower (more negative G) wins…
Perfect Crystal Gperf = Hperf - T Sperf S = Scofig + ST
Defective Crystal If it costs, hd to form one defect, how much for nv defects Assume all atoms near a vacancy now vibrate with a different frequency, ’. Thus
Drum roll comes here…. • Lets plot this function ….. Ignore 2nd term.
Types of Point Defects in Ionic Solids • Stoichiometric Defects: • Do not change the chemistry of crystal. Egs. Schottky and Frenkel • Non-stoichiometric Defects • Change the chemistry of the crystal • Electronic Defects: electrons and holes • Extrinsic Defects • Aka impurities
Examples • Examples: What are defects that can occur in pure Al2O3…. • Vacancy on Al: • Vacancy of O:
Al interstitials ? • O interstitials? • Add CaCl2 to NaCl • Add KCl to NaCl
For an MaXb compound For example in Al2O3: should always be true even in hell.
Stoichiometric Defects and Reactions Stoichiometric defect reactions do NOT change the chemistry of the crystal
Schottky Defect Reaction In MOMO oxide: In M2O3 oxide: In MOOMOO oxide:
Thermo of Schottky Defects • Find minimum in free energy then:
Square brackets denote mole fractions of defects! They are dimensionless!
Frenkel Defects • Frenkel defect for a trivalent cation: Mass balance? Charge balance? Site ratio preserved?
Antistructure Defects • Impossible in ionic solids. • Even if they form are not that important
Nonstoichiometric Defect ReactionsBy definition result in changes in chemistry Mass B? Charge B? Site ratio?
MISI Placing any oxide in a low oxygen partial pressure environment at high temperatures results in the loss of oxygen… You get Swiss cheese… Placing any oxide in a high oxygen partial pressure environment at high temperatures results in the gain of oxygen… You can get Unswiss cheese…