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“Perfect Crystals?”

“Perfect Crystals?”. A Little Thermo Free Energies & Entropy Defects in a “Perfect” Crystal Atoms Vibrating in a Well Diffusion Hopping Concentration Gradients HW #4 Due 2/11/03 Exam #1 Date Change to Thurs. 2/27 from Thurs. 3/6. Thursday, Feb. 4, 2003.

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“Perfect Crystals?”

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  1. “Perfect Crystals?” • A Little Thermo • Free Energies & Entropy • Defects in a “Perfect” Crystal Atoms Vibrating in a Well • Diffusion • Hopping • Concentration Gradients • HW #4 Due 2/11/03 • Exam #1 Date Change to Thurs. 2/27 from Thurs. 3/6 Thursday, Feb. 4, 2003 MATS275: INTRODUCTION TO MATERIALS SCIENCE

  2. Crystal Structures • BCC • FCC • HCP • CsCl • NaCl • Diamond Cubic • Zinc Blende • Fluorite (CaF2) • Crystobalite (SiO2) • Ice (snowflakes)

  3. Defects • Zero Dimensional • Vacancies • Interstitials • Impurities • One Dimensional • Dislocations • Two Dimensional • Planar • Three Dimensional • Amorphous Mat’ls

  4. Zero Dimensional Defects • These are in order of prevalence in nature from most to least • V: Vacancy • S: Substitutional Atom • I: Interstitial atom • J: Self-Interstitial atom • These can also be divided into intrinsic defects (native to the material) and extrinsic defects (other atoms than the lattice)

  5. Unknown Point Defects on Cu D. Eigler, IBM Almaden Research Center

  6. D. Eigler, IBM Almaden Research Center

  7. Clean Si (111) - 7 x 7 reconstruction Si surface reacted with Br2 (top layer stripped away, Br terminated surface) Courtesy: J.J. Boland, UNC Dept. of Chemistry

  8. Vacancies Remove atom from regular lattice site to surface - requires an activation energy EV

  9. A Little Thermo • Reaction Gibb’s Free Energy

  10. A Little Thermo • Reaction • Spontaneous if G<0 • Exothermic if H<0 • G = H - T S Entropy Enthalpy Gibb’s Free Energy

  11. Minimization of DG

  12. At Equilibrium and note that ni / N is the concentration of defects. (N is the total number of lattice sites) So we can write this expression: where ce is the equilibrium concentration.

  13. Vacancies • The vacancy activation energy for VAl in Aluminum is 0.76 eV. At 400°C, the fraction of Al sites that are vacant is 2.29 x 10-5. What fraction are vacant at 660°C?

  14. Aluminum Vacancy Concentration mp Al ~ 940 K

  15. Aluminum Vacancy Concentration

  16. Defect Complexes Schottky Frenkel

  17. Impurities • Add a different atom to the lattice • Form a solid solution • INTERSTITIAL • RANDOM • ORDERED Ex) AuCu3 - at T<390°C Cu occupies face centers of FCC, above that Cu and Au are randomly distributed SUBSTITUTIONAL

  18. Liquid Solutions: Molecular Mixing Alcohol Water H2O Molecule (Solvent) C2H5OH Molecule (Solute) Mixing on the Molecular Scale

  19. Solid Solution: Bronze Copper Atoms (Solvent) Tin Atoms (Solute) A 10% Cu / Sn alloy (bronze)

  20. Hume-Rothery Rules • What can be substitutional? • Atomic size difference <15% • Same crystal structure • Similar electronegativities • Same valence • EXAMPLE - Cu and Ni • rCu=0.128nm, rNi=0.125 (2.3% diff) • both fcc • ENCu=1.90, ENNi=1.91 • Valences: Cu +1 +2, Ni +2

  21. ImpuritiesIonic Materials • Put Cd in AgCl • Cd wants to be +2, Ag is +1... -1 +2

  22. T Dependence of D H in Fe C in Fe Fe in Fe Al in Al2O3 O in Al2O3

  23. Activation Energyvs. Melting Point 300 Fe 250 Cu 200 Self-Diffusion Activation Energy 150 Al Pb Mg 100 Zn 50 0 0 500 1000 1500 2000 Melting Point (C)

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