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MS115a Principles of Materials Science Fall 2012. Instructor: Prof. Sossina M. Haile 307 Steele Laboratories, x2958, [email protected] http://addis.caltech.edu/teaching/MS115a/MS115a.html Class Meetings: MWF 11am-noon; 080 Moore; to 12:30pm?? Teaching Assistant:

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ms115a principles of materials science fall 2012
MS115a Principles of Materials ScienceFall 2012
  • Instructor:
  • http://addis.caltech.edu/teaching/MS115a/MS115a.html
  • Class Meetings: MWF 11am-noon; 080 Moore; to 12:30pm??
  • Teaching Assistant:
  • 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
what is materials science

Chemistry / Composition

Processing

+

Structure

Properties / Performance

What is Materials Science?

?

?

kinetics

thermodynamics

(MS 115b)

MS 115a

course content
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 content1
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
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
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
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
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}

structure of the atom1
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
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
types of chemical bonds

+

-

+

-

+

-

+

-

+

+

+

+

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

chemical bonding1
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
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

more properties
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

some mechanical properties
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

covalent bonds
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

hybridized bonds

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)

summary
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
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