Lecture 02


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Lecture 02

  1. 1. Today’s objectives-Ceramic Structures <ul><li>Lattice and basis </li></ul><ul><li>How do you estimate the crystal structure for a ceramic? </li></ul><ul><li>What are the common crystal structures for ceramics? </li></ul>
  2. 2. CERAMIC BONDING • Bonding: --Mostly ionic, some covalent. --% ionic character increases with difference in electronegativity. Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond , 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. • Large vs small ionic bond character:
  3. 3. Rules for Ionic Structures • Rule 1: Charge Neutrality : --Net charge in the structure should be zero. --General form:
  4. 4. <ul><li>What is the charge on: </li></ul><ul><li>K Mg Na Li Si </li></ul><ul><li>What is the charge on: </li></ul><ul><li>Cl O S P N </li></ul><ul><li>What are the formulas for: </li></ul><ul><li>KCl MgO NaS LiP SiN </li></ul>Examples: K m Cl p , Mg m O p , Na m S p , Li m P p , Si m N p
  5. 5. More rules for Ionic Structures <ul><li>Q2) How do the atoms (ions) fill space in a crystal? </li></ul>• Stable structures: --maximize the # of nearest oppositely charged neighbors. Adapted from Fig. 12.1, Callister 6e.
  6. 6. COORDINATION # AND IONIC RADII • Coordination # increases with: Issue: How many anions can you arrange around a cation? Adapted from Table 12.2, Callister 6e. There are many possibilities—how do we generally determine which is appropriate? And what do we call them? Binary Trigonal Tetrahedral Octahedral Cubic
  7. 7. Defining Radius Ratio Rules <ul><li>What is the ideal size of a cation that will just fit into this site (octahedral)? </li></ul>a) Sketch the hard spheres b) Do some basic geometry (leg length w/r radii) c) Do some math r a r c r a 2r c
  8. 8. EX: PREDICTING STRUCTURE OF FeO • On the basis of ionic radii, what crystal structure would you predict for FeO? <ul><li>What does the chemical formula tell us? </li></ul><ul><li>What are the ionic radii? </li></ul><ul><li>What is the radius ratio (cation/anion) </li></ul>0.414 was ideal for octahedral (CN6), so what does this value do for us? • Answer: Data from Table 12.3, Callister 6e.
  9. 9. Radius Ratio Rules <ul><li>based on the ratio for FeO of 0.550: </li></ul><ul><ul><li>coord # = 6 </li></ul></ul>
  10. 10. Which crystal structures are appropriate?
  11. 11. 2-d Lattices <ul><li>A lattice repeats in all directions, and defines the symmetry. </li></ul>square centered
  12. 12. 2-d Lattice and Basis <ul><li>Anions at lattice positions (0,0) </li></ul><ul><li>Cations at (½,0) </li></ul>square Lattice: Basis: centered
  13. 13. 2-d Lattice and Basis <ul><li>Anions at square lattice positions (0,0) </li></ul><ul><li>Cations at (0,½) </li></ul>square Lattice: Basis: <ul><li>Cations at (½,0) </li></ul>
  14. 14. Simple ceramic unit cells: CsCl <ul><li>Based on Simple Cubic Lattice with a basis of: </li></ul><ul><li>Cl anions at the SC points </li></ul><ul><li>Cs cations at the center [offset by (½, ½, ½)] </li></ul>
  15. 15. NaCl <ul><li>Based on FCC Lattice with a basis of: </li></ul><ul><li>Cl anions at the FCC points </li></ul><ul><li>Na cations at the center [offset by (½, 0, 0)] </li></ul>
  16. 16. Other Common Ceramic unit cells <ul><li>Based on FCC Lattice with a basis of: </li></ul><ul><li>anions at the FCC points </li></ul><ul><li>cations at (¼,¼,¼) </li></ul>
  17. 17. Perovskite <ul><li>Based on SC Lattice with a basis of: </li></ul><ul><li>Big cation at the SC points </li></ul><ul><li>Small cation at (½,½,½) </li></ul><ul><li>Anion at (½,½,0) </li></ul>
  18. 18. A m X p STRUCTURES • Consider CaF 2 : • Based on this ratio, coord # = 8 and structure = CsCl. • BUT: there are half as many Ca 2+ as F - ions—how can we accommodate this? CsCl structure w/only half of cation sites occupied. Adapted from Fig. 12.5, Callister 6e. m is not equal to p
  19. 19. Silicon oxides Building Block: SiO 4 4-
  20. 20. Quartz, SiO 2 Hexagonal - Trigonal trapezohedral
  21. 21. SiO x There are three polymorphs of SiO 2 : Quartz, Cristobalite, and Tridymite
  22. 22. Glasses <ul><li>CaO and Na 2 O are examples of network modifiers . Cations modify the SiO 4 4- network. </li></ul><ul><li>TiO 2 and Al 2 O 3 are intermediates . Become part of or stabilize SiO 4 4- network. </li></ul><ul><li>B 2 O 3 and GeO 2 , are network formers , like SiO 4 4- . </li></ul><ul><li>Addition of modifiers and intermediates lower the melting point (and viscocity) of network formers. </li></ul>
  23. 23. Glasses Can we form glass structures in metals? YES, you need to cool them very fast, 10 6o C/sec…
  24. 24. Glass Production
  25. 25. Carbon
  26. 26. Crystals often indicate crystal structure
  27. 27. SUMMARY <ul><li>• Ceramic materials have both covalent & ionic bonding. </li></ul><ul><li>• Structures are based on: </li></ul><ul><li>-- charge neutrality </li></ul><ul><li>--maximizing # of nearest oppositely charged neighbors. </li></ul><ul><li>• Structures may be predicted based on: </li></ul><ul><li>--ratio of cations to anions. </li></ul><ul><li>--ratio of cation to anion radii. </li></ul><ul><li>The rules and crystal structures are strange for C and glasses. </li></ul>Defects in ceramics, glasses Chapter sections: 12.5 + 3.7-10 Reading for next class