MS115a Principles of Materials Science Fall 2010 Instructor: Prof. Sossina M. Haile 307 Steele Laboratories, x2958, smhaile@caltech.edu http://addis.caltech.edu/teaching/MS115a/MS115a.html Class Meetings: MWF 9-10am, 214 Steele Teaching Assistants: Nick Heinz, 303 Steele, x1711, heinz@caltech.edu Balaji Gopal (BG) Chiranjeevi, 302 Steele, x2777, bcg@caltech.edu TA Office Hours: TBA (likely Tuesdays) Required Text: None Recommended Text: “Intro to Mat Sci for Engineers” Shackelford Reserved Texts: SFL “The Principles of Engineering Materials,” Barrett, Nix & Tetelman “Phase Transformations in Metals and Alloys,” Porter & Easterling “Quantum Chemistry,” Levine

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

Course Content Introduction to Materials Science Structure Chemistry + Processing  Structure  Properties Structure Structure of the Atom & Introduction to 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

Course Content Electrons in Solids Thermodynamics 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

Course Structure Homework: weekly 50% Midterm HW: Oct 27 - Nov 2 15% Assigned Wednesdays Due following Wednesday, 5pm Place in TA mailbox, 3rd floor Steele Midterm HW: Oct 27 - Nov 2 15% Solo homework Final: Dec 8 - 10 35% Take home

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.

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, including ones from earlier in the year.

Structure of the Atom “Electron in a box” – use quantum mechanics to solve electron wave functions Electron quantum numbers, orbitals Electrical properties Qualitative description of chemical bonding Electrons ‘orbit’ atomic nucleus Q.N. n K, L, M “shell” n = 1, 2, 3  radius l s, p, d “orbital” l = 0, 1 …. n-1 m px, py, pz “orientation” m = -l, -l + 1, …0,...l - 1, l s spin s = ± ½ 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} m = 0 m = {-1, 0, 1}  px. py. pz

Structure of the Atom Electrons occupy these orbitals Pauling 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,..

Chemical Bonding Noble gases: filled outer shell, limited chemistry 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

electronegativity

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 + - + e-

Some Properties The bond energy curve E = ER + EA E E0 R0 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 formation this much energy is required to break the bond define as bond energy sets the melting temperature

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

Some Mechanical Properties 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 = k Dx F k stress*area strain*length R0 R (interatomic distance) stress  k strain repulsive Elastic constants given by slope of B.F. curve at R0 given by curvature of B.E. curve at R0

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 correlation between the type of bond and the value of the property