MS115a Principles of Materials ScienceFall 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

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– 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– 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 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

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

• 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

• 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-

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

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