11. Interstitial sites for cations

13. Defect Concentrations • Frenkel Defect -- a cation is out of place. • Shottky Defect -- a paired set of cation and anion vacancies. • Equilibrium concentration of defects Adapted from Fig. 13.20, Callister 5e. (Fig. 13.20 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials , Vol. 1, Structure , John Wiley and Sons, Inc., p. 78.) See Fig. 12.21, Callister 6e . As temperature increases, so does the vacancy and interstitial concentration. Thus, the properties can change (this is often a major limitation but sometimes a benefit). Why not an anionic Frenkel?.

14. Correlated Defects Defects usually add/subtract charge; thus, Coulombic forces attract them, and conveniently stoichiometry is maintained. Why will defects sometimes hang out together (‘correlation’)?

15. Multivalent self-Defects Multivalent defects occur often for certain metal ions, primarily transition metals. This will lead to non -stoichiometry . Fe x O

16. Impurity defects Cationic Ca instead of Na in NaCl B instead of Si in SiO 2 Anionic O instead of Cl in NaCl O instead of N in GaN Charge neutrality must be maintained. Thus, if a substitutional impurity has a different charge than the substituted ion, another defect (or defects) must be present to balance it out. Non-stoichiometry often results.

17. IMPURITIES • Impurities must satisfy charge balance • Ex: NaCl Instead of the anion vacancy, we could have a cation interstitial. Why not the same for the cation impurity? • Substitutional cation impurity • Substitutional anion impurity

18. Charge Balancing Cations Anions Na + Cl - Substitutional- ”aliovalent” Vacancy Initial Compound: NaCl K F V Na V Cl Extra Charge? Extra Charge? none none 1 too few e - 1 extra e - Interstitial (self or impurity) Na i Cl i 1 extra e - 1 too few e - BUT unlikely Substitutional- 2 higher charges Al P 2 too many 2 too few Substitutional- 1 higher charge (or multivalent) Ca O 1 extra e - 1 too few e -

19. Charge Balancing Cations Anions Zn 2+ S 2- Substitutional-aliovalent Vacancy Initial Compound: ZnS Ca O V Zn V S Extra Charge? Extra Charge? none none 2 too few e - 2 extra e - Interstitial (self or impurity) Zn i S i 2 extra e - NEVER Substitutional- 1 lower charge K Br 1 too few e- 1 too many e- Mix and match defects to maintain charge neutrality, but recognize that multiple defects (especially different kinds) generally diminish properties. Substitutional- 1 higher charge (or multivalent) Al As 1 extra e - 1 too few e -