Today’s objectives:  Directions, Planes, and Defects <ul><li>Know how to determine standard directions and planes (100, 11...
Crystallographic Directions and Planes <ul><li>Terminology </li></ul><ul><ul><li>Directions [] </li></ul></ul><ul><ul><li>...
[Directions] <ul><li>[100] </li></ul><ul><li>[110] </li></ul><ul><li>[111] </li></ul><ul><li>[021] </li></ul><ul><li>[011]...
more [Directions] <ul><li>[100] </li></ul><ul><li>[011] </li></ul><ul><li>[011] </li></ul><ul><li>For negative directions:...
more <Directions> <ul><li><100> </li></ul><ul><li>[100] </li></ul><ul><li>[010] </li></ul><ul><li>[001] </li></ul><ul><li>...
(Planes) <ul><li>(xyz) </li></ul><ul><li>(100) </li></ul><ul><li>(110) </li></ul><ul><li>(111) </li></ul><ul><li>(100) </l...
more {Planes} <ul><li>{xyz} </li></ul><ul><li>{100} </li></ul><ul><li>{110} </li></ul><ul><li>{100} </li></ul>x y z
For a simple cubic lattice and (0,0,0) basis: <ul><li>Along (xyz) plane </li></ul><ul><li>(100) </li></ul><ul><li>(110) </...
For CsCl (simple cubic lattice,  basis of Cl-(0,0,0) and Cs-(½½,½)) <ul><li>Along (xyz) plane </li></ul><ul><li>(100) </li...
Others <ul><li>Be able to draw the (001), (110), and (111) planes of  </li></ul><ul><ul><li>CsCl </li></ul></ul><ul><ul><l...
Interstitial sites for cations
Vacancies and Interstitials <ul><li>Anion interstitials are unlikely (usually the anions are already larger than the catio...
Defect Concentrations •  Frenkel Defect -- a cation is out of place. •  Shottky Defect -- a paired set of cation and anion...
Correlated Defects Defects usually add/subtract charge; thus, Coulombic forces attract them, and conveniently  stoichiomet...
Multivalent self-Defects Multivalent defects occur often for certain metal ions, primarily transition metals. This will le...
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...
IMPURITIES •  Impurities must satisfy  charge balance •  Ex:  NaCl Instead of the anion vacancy, we could have a cation in...
Charge Balancing Cations Anions Na + Cl - Substitutional- ”aliovalent” Vacancy Initial Compound: NaCl K F V Na V Cl Extra ...
Charge Balancing Cations Anions Zn 2+ S 2- Substitutional-aliovalent Vacancy Initial Compound: ZnS Ca O V Zn V S Extra Cha...
Dopants vs. Impurities <ul><li>Dopants: Purposefully added to tailor properties. </li></ul><ul><ul><li>n and p type semico...
SUMMARY <ul><li>•  Defects </li></ul><ul><li>--exist in many forms (know these) </li></ul><ul><li>--must preserve charge n...
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Lecture 03

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Lecture 03

  1. 1. Today’s objectives: Directions, Planes, and Defects <ul><li>Know how to determine standard directions and planes (100, 110, and 111) of basic ceramic crystal structures. </li></ul><ul><li>What types of ionic defects are common for ceramics? </li></ul><ul><li>How can a ceramic be made to be non-stoichiometric? </li></ul><ul><li>How do substitutional impurities affect stoichiometry? </li></ul><ul><li>How is charge neutrality maintained in ionic structures? </li></ul><ul><li>What is the distinction between dopants and impurities? </li></ul>
  2. 2. Crystallographic Directions and Planes <ul><li>Terminology </li></ul><ul><ul><li>Directions [] </li></ul></ul><ul><ul><li>Planes () </li></ul></ul><ul><ul><li>Families of directions <> </li></ul></ul><ul><ul><li>Families of equivalent planes {} </li></ul></ul><ul><ul><li>(100)=“bar one zero zero” and NOT “one bar zero zero” </li></ul></ul>
  3. 3. [Directions] <ul><li>[100] </li></ul><ul><li>[110] </li></ul><ul><li>[111] </li></ul><ul><li>[021] </li></ul><ul><li>[011] </li></ul><ul><li>[200] </li></ul><ul><li>[210] </li></ul><ul><li>Draw cell + origin </li></ul><ul><li>Draw vector </li></ul><ul><li>“ reduce” to smallest integer values </li></ul><ul><li>[xyz] </li></ul>x y z
  4. 4. more [Directions] <ul><li>[100] </li></ul><ul><li>[011] </li></ul><ul><li>[011] </li></ul><ul><li>For negative directions: </li></ul><ul><li>Add more unit cells. </li></ul><ul><li>OR </li></ul><ul><li>Shift the origin. </li></ul>x y z
  5. 5. more <Directions> <ul><li><100> </li></ul><ul><li>[100] </li></ul><ul><li>[010] </li></ul><ul><li>[001] </li></ul><ul><li>[100] </li></ul><ul><li>[010] </li></ul><ul><li>[001] </li></ul>A <family of directions> includes all possible directions with the same basic coordinates. x y z
  6. 6. (Planes) <ul><li>(xyz) </li></ul><ul><li>(100) </li></ul><ul><li>(110) </li></ul><ul><li>(111) </li></ul><ul><li>(100) </li></ul><ul><li>(020) </li></ul><ul><li>(040) </li></ul><ul><li>Draw the origin, cell, and normal vector (direction). </li></ul><ul><li>Draw the plane at a distance from the origin of 1/sqrt(a 2 +b 2 +c 2 ). </li></ul>x y z
  7. 7. more {Planes} <ul><li>{xyz} </li></ul><ul><li>{100} </li></ul><ul><li>{110} </li></ul><ul><li>{100} </li></ul>x y z
  8. 8. For a simple cubic lattice and (0,0,0) basis: <ul><li>Along (xyz) plane </li></ul><ul><li>(100) </li></ul><ul><li>(110) </li></ul><ul><li>(111) </li></ul>x y z ± ± - + +
  9. 9. For CsCl (simple cubic lattice, basis of Cl-(0,0,0) and Cs-(½½,½)) <ul><li>Along (xyz) plane </li></ul><ul><li>(100) </li></ul><ul><li>(110) </li></ul><ul><li>(111) </li></ul>x y z ± ± - + ++ ++ ± ± ±
  10. 10. Others <ul><li>Be able to draw the (001), (110), and (111) planes of </li></ul><ul><ul><li>CsCl </li></ul></ul><ul><ul><li>NaCl </li></ul></ul><ul><ul><li>ZnS </li></ul></ul><ul><ul><li>Perovskite (BaTiO 3 ) </li></ul></ul><ul><ul><li>CaF 2 </li></ul></ul><ul><ul><li>etc. . </li></ul></ul>
  11. 11. Interstitial sites for cations
  12. 12. Vacancies and Interstitials <ul><li>Anion interstitials are unlikely (usually the anions are already larger than the cations, leaving little room to squeeze in an extra anion). </li></ul><ul><li>Vacancies and interstitials often occur in pairs, maintaining stoichiometry . </li></ul>Stoichiometry: Maintaining a simple ratio of cations and anions (independent of charge neutrality which always must be maintained)
  13. 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. 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. 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. 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. 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. 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. 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 -
  20. 20. Dopants vs. Impurities <ul><li>Dopants: Purposefully added to tailor properties. </li></ul><ul><ul><li>n and p type semiconductors (add P or B to Si) </li></ul></ul><ul><ul><li>Si atom density is 10 23 atoms/cm 3 , while dopants from 10 15 to 10 21 are used for modern Si semiconductor devices. </li></ul></ul><ul><li>Impurities: Cannot remove so come up with ways to live with them. </li></ul><ul><ul><li>In the initial raw materials </li></ul></ul><ul><ul><li>Processing related </li></ul></ul><ul><ul><li>Too costly to remove (usually a matter of energy, but sometimes also of environmental cost) </li></ul></ul>
  21. 21. SUMMARY <ul><li>• Defects </li></ul><ul><li>--exist in many forms (know these) </li></ul><ul><li>--must preserve charge neutrality </li></ul><ul><li>--have a concentration that varies exponentially with Temp. </li></ul><ul><li>--may modify stoichiometry </li></ul><ul><li>--may be considered to be dopants or impurities </li></ul><ul><li>--be able to accommodate a flaw with other defects to balance the charge. </li></ul><ul><li>Directions and Planes </li></ul><ul><li>--be able to identify and draw directions and planes. </li></ul><ul><li>--be able to draw lattice and atom positions for {100}, {110}, and {111} planes of standard ceramic crystal structures. </li></ul>Mechanical Properties Chapter sections: 8.4,12.8-12.11 Reading for next class

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