MS115a Principles of Materials Science Fall 2012

1. MS115a Principles of Materials ScienceFall 2012 • Instructor: • Prof. Sossina M. Haile • 307 Steele Laboratories, x2958, smhaile@caltech.edu • http://addis.caltech.edu/teaching/MS115a/MS115a.html • Class Meetings: MWF 11am-noon; 080 Moore; to 12:30pm?? • Teaching Assistant: • Alex Zevalkink, 317 Steele, x4804, azw@caltech.edu • TA Office Hours: TBA (likely Tuesdays) • All recommended and reference texts on reserve in SFL • Recommended: • “Understanding Solids,” Tilley; “Intro to Mat Sci for Engineers,” Shackelford • Additional references: • “The Principles of Engineering Materials,” Barrett, Nix & Tetelman • “Phase Transformations in Metals and Alloys,” Porter & Easterling • “Quantum Chemistry,” Levine

2. Chemistry / Composition Processing + Structure Properties / Performance What is Materials Science?  ? ?  kinetics thermodynamics (MS 115b) MS 115a

3. Course Content • Introduction to Materials Science • Chemistry + Processing  Structure  Properties • Structure • Review: Structure of the Atom & Chemical Bonding • Crystalline Structure • Structural Characterization (X-ray diffraction) • Amorphous Structure • Microstructure • Defects in Crystalline Solids, Connections to Properties • Point Defects (0-D) and Diffusion & Ionic Conductivity • Dislocations (1-D) and Mechanical Deformation • Surfaces and interfaces (2-D) • Volume Defects (3-D) and Fracture

4. Course Content • Electrons in Solids • Chemical Bonding, Revisited • Band Structure • Electronic Conductivity: Metals vs. Insulators • Thermodynamics • 1st and 2nd Laws • Gibb’s Free Energy • Phase Diagrams • Some Other Properties Along the Way • Thermal: Thermal Expansion, Heat Capacity, Thermal Conductivity • Optical: Refraction, Reflection; Absorption, Transmission, Scattering, Color • Conceptual vs. Highly Mathematical

5. Course Structure • Homework: weekly 50% • Assigned Wednesdays • Due following Wednesday, 5pm • Place in course mailbox, 3rd floor Steele • Midterm HW: Oct 31 - Nov 6 15% • Solo homework • Final: Dec 12 - 14 35% • Take home

6. HW Collaboration Policy • Students are encouraged to discuss and work on problems together. • During discussion, you may make/take notes • However, do not bring and/or exchange written solutions or attempted solutions you generated prior to the discussion. • If you’ve worked the problem out and you plan to help a friend, you should know the solution cold. • Do not consult old problem sets, exams or their solutions. • Solutions will be handed out on Friday, or possibly Monday. Assignments turned in late, but before solutions are available, will receive 2/3 credit. Assignments will not be accepted after solutions are handed out.

7. Midterm Homework • In lieu of a midterm exam there will be homework to be performed on an individual basis. This homework must be completed without collaborative discussion. • The problem set will focus primarily on recent lectures, but material from early topics may also be included. • Similar to other homeworks, you will have one week to complete the assignment. • You are permitted to utilize all available resources, with the exception of previous solutions; this exception includes solutions from earlier in the year.

9. Structure of the Atom • “Electron in a box” – use quantum mechanics to solve electron wave functions • Electron quantum numbers: describe orbitals • Electrical properties • Qualitative description of chemical bonding • Electrons ‘orbit’ atomic nucleus Chemical notation K L 1 M 2 K-shell: n = 1  l = 0  1s  m = 0 s = ± ½ 3  2s, 2p L-shell: n = 2  l = {0, 1}  px. py. pz m = 0 m = {-1, 0, 1}

10. Structure of the Atom • Electrons occupy these orbitals • Pauli exclusion principle • Only one electron with a given set of QNs • For a multi-electron atom, fill up orbitals beginning with lowest energy & go up • Order: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s,..

11. Chemical Bonding • Atoms  Molecules  Solids • Bonds form so as to produce filled outer shells • Some atoms are a few electrons short • Electronegative: readily pick up a few electrons from other atoms, become negatively charged • Some atoms have a few electrons too many • Electropositive: readily give up a few electrons to other atoms, become positively charged • Noble gases: filled outer shell, limited chemistry

12. electronegativity

13. + - + - + - + - + + + + e- e- + + + e- + + + Types of Chemical Bonds • Primary • Ionic • Electronegative/Electropositive • Metallic • Electropositive – give up electrons • Colavent • Electronegative – want electrons • Shared electrons along bond direction • Secondary • Fluctuating/instantaneous dipoles • Permanent dipoles (H-bonds) Isotropic, filled outer shells

14. Chemical Bonding • Covalent – between electronegative elements • Metallic – between electropositive elements • Ionic – between different elements with differing electronegativities • Clear distinction between metallic & non-metallic • Ionic & covalent – somewhat qualitative boundary • ‘% ionic chararacter”: 1 – exp( -¼ (xA – xB)2) • xA, xB = electronegativities • Some properties from “bond-energy” curve

15. Some Properties The bond energy curve short range repulsion E = ER + EA E R0 R (interatomic distance) E0 long range attraction R0 : interatomic distance that minimizes E is the equilibrium bond distance E0 : decrease in energy due to bond formationthis much energy is required to break the bond define as bond energy sets the melting temperature

16. More Properties Heat the material E = ER + EA E R (interatomic distance) R0 as T  T  Ethermal = kbT Asymmetry in E(R) sets thermal expansion coefficient

17. Some Mechanical Properties E R (interatomic distance) R0 E0 F = dE/dR The bond force curve Elastic constants relate stress to strain Stress – related to force Strain – related to displacement at R0 no net force (equilibrium bond distance) attractive F = kDx F k stress*area strain*length R0 stress k strain R (interatomic distance) repulsive Elastic constants given by slope of B.F. curve at R0 given by curvature of B.E. curve at R0

18. Covalent Bonds • Locally well-defined orbitals • Elements with electrons up to 2p or 3p states • Filled outer shell  octet rule (s + p  8 states) • Rule: 8 – N bondingelectrons = n bonds • Example: carbon (C) • 6 electrons total: 1s22s22p2 • 2s22p2N = 4 n = 4 how can carbon atoms fill px, py and pz orbitals if the other element is also electronegative? bonds bonding electrons s orbital p orbitals     • solution: sp2 or sp3 hybrization http://www.emc.maricopa.edu/faculty/farabee/BIOBK/orbitals.gif

19. diamond         Hybridized Bonds • Elemental carbon (no other elements) sp3 hybridization     also methane: CH4 one s + three p orbitals  4 (x 2) electron states (resulting orbital is a combination)

20. Summary • Nature of the bonds formed depends on the chemical nature of the elements (as given by placement on the periodic table) • Bond energy / bond force curve gives • Equilibrium bond distance • Melt temperature • Thermal expansion coefficient • Elastic constants • In general, there is not a direct correlation between type of bond and value of properties