MS115a Principles of Materials Science Fall 2012 Instructor: –Prof. Sossina M. Haile –307 Steele Laboratories, x2958, Class Meetings: MWF 11am-noon; 080 Moore; to 12:30pm?? Teaching Assistant: –Alex Zevalkink, 317 Steele, x4804, 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

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

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

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

Course Structure Homework: weekly50% –Assigned Wednesdays –Due following Wednesday, 5pm –Place in course mailbox, 3 rd floor Steele Midterm HW: Oct 31 - Nov 615% –Solo homework Final: Dec % –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; this exception includes solutions from earlier in the year.

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 K M L Q.N. nK, L, M “shell” n = 1, 2, 3  radius ls, p, d “orbital” l = 0, 1 …. n -1 mp x, p y, p z “orientation” m = - l, - l +1, … 0,... l -1, l s spin s = ± ½ K-shell: n = 1  l =  1s  m = 0 s = ± ½ L-shell: n = 2  l = {0, 1}  2s, 2p m = 0m = {-1, 0, 1}  p x. p y. p z Chemical notation

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,..

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

electronegativity

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) Types of Chemical Bonds Isotropic, filled outer shells e-

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 (x A – x B ) 2 ) –x A, x B = electronegativities Some properties from “bond-energy” curve

Some Properties E R (interatomic distance) long range attraction short range repulsion E = E R + E A E0E0 R0R0 E 0 :decrease in energy due to bond formation this much energy is required to break the bond define as bond energy sets the melting temperature R 0 : interatomic distance that minimizes E is the equilibrium bond distance The bond energy curve

E R (interatomic distance) E = E R + E A Heat the material More Properties E thermal = k b T T  R 0  as T  Asymmetry in E(R) sets thermal expansion coefficient

E R (interatomic distance) F = dE/dR Some Mechanical Properties E0E0 R0R0 F attractive repulsive R (interatomic distance) The bond force curve at R 0 no net force (equilibrium bond distance) R0R0 Elastic constants relate stress to strain Stress – related to force Strain – related to displacement F = k  x stress*area strain*length stress  k strain k Elastic constants given by slope of B.F. curve at R 0 given by curvature of B.E. curve at R 0

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 bonding electrons = n bonds Example: carbon (C) –6 electrons total: 1s 2 2s 2 2p 2 –2s 2 2p 2  N = 4  n = 4 s orbital p orbitals – solution: sp 2 or sp 3 hybrization    how can carbon atoms fill p x, p y and p z orbitals if the other element is also electronegative? bonding electrons bonds

Hybridized Bonds one s + three p orbitals  4 (x 2) electron states (resulting orbital is a combination) sp 3 hybridization             diamond also methane: CH 4 Elemental carbon (no other elements)

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