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Lecture 03
 

Lecture 03

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    Lecture 03 Lecture 03 Presentation Transcript

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