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

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: 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

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

ML

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

K-shell: n = 1 l = 0

1

32

1s m = 0 s = ± ½

L-shell: n = 2 l = {0, 1} 2s, 2p

m = 0 m = {-1, 0, 1} px. py. pz

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-

e-

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 (xA – xB)2)

– xA, xB = electronegativities

• Some properties from “bond-energy” curve

Some Properties

E

R (interatomic distance)long range attraction

1~

R

short range repulsion1

~nR E = ER + EA

E0

R0

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

R0 : interatomic distance that minimizes E

is the equilibrium bond distance

The bond energy curve

E

R (interatomic distance)

E = ER + EA

Heat the material

More Properties

Ethermal = kbTT

R0 as T

Asymmetry in E(R) sets thermal expansion coefficient

ER (interatomic distance)

F = dE/dR

Some Mechanical Properties

E0

R0

Fattr

activ

ere

puls

ive

R (interatomic distance)

The bond force curve

at R0 no net force (equilibrium bond distance)

R0

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 R0

given by curvature of B.E. curve at R0

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: 1s22s22p2

– 2s22p2 N = 4 n = 4

s orbital p orbitals

– solution: sp2 or sp3 hybrization

http://www.emc.maricopa.edu/faculty/farabee/BIOBK/orbitals.gif

how can carbon atoms fill px, py and pz 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)

sp3 hybridization

diamond

also methane: CH4

• 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