MS115a Principles of Materials Science
Fall 2011
• Instructor:
– Prof. Sossina M. Haile
– 307 Steele Laboratories, x2958, smhaile@caltech.edu
• http://addis.caltech.edu/teaching/MS115a/MS115a.html
• Class Meetings:
M 9-10am; W 11am-noon; F 9-10am 214 Steele
• Teaching Assistants:
– Balaji Gopal (BG) Chiranjeevi, 302 Steele, x2777, bcg@caltech.edu
– Áron Varga, 326 Steele, x4814, avarga@caltech.edu
•
•
•
•
TA Office Hours:
TBA (likely Tuesdays)
Required Text:
“Understanding Solids” R. Tilley
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
MS 115a
MS 115b
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 TA mailbox, 3rd floor Steele
• Midterm HW: Oct 26 - Nov 1
15%
– Solo homework
• Final:
– Take home
Dec 7 - 09
35%
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
L
1
M
2
3
Q.N.
Chemical notation
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
spin
s=±½
s
K-shell: n = 1  l = 0  1s  m = 0
L-shell: n = 2  l = {0, 1}  2s, 2p
m=0
s=±½
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
• 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
Isotropic, filled outer shells
• Electronegative/Electropositive
– Metallic
• Electropositive – give up electrons
– Colavent
• Electronegative – want electrons
• Shared electrons along bond direction
• Secondary
+
-
+
-
+
-
+
-
+
+
+
+
– Fluctuating/instantaneous dipoles
+
– Permanent dipoles (H-bonds)
+
ee-
e+
+
+
+
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 electrons = n bonds
• Example: carbon (C)
how can carbon atoms fill px, py and pz
orbitals if the other element is also
electronegative?
– 6 electrons: 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
Hybridized Bonds
• Elemental carbon (no other elements)
sp3 hybridization
diamond






 
 

also methane: CH4
one s + three p orbitals  4 (x 2) electron states
(resulting orbital is a combination)
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
short range repulsion
~
E
1
R
The bond energy curve
E = ER + EA
n
R0
R (interatomic distance)
E0
long range attraction
~
1
R
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 = E R + EA
E
R (interatomic distance)
R0  as T 
T
Ethermal = kbT
Asymmetry in E(R) sets thermal expansion coefficient
Some Mechanical Properties
E
R (interatomic distance)
R0
attractive
E0
F = dE/dR
F
at R0 no net force
(equilibrium bond distance)
Elastic constants relate stress to strain
Stress – related to force
Strain – related to displacement
repulsive
k
R0
The bond force curve
F = k Dx
stress*area
R (interatomic distance)
strain*length
stress  k strain
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
Metallic Structures
• Goal: Achieve as many bonds as possible
• Treat as the close-packing of hard spheres
1-D
2-D
Definitions
• Lattice point
• Unit cell
• Lattice parameters
• Atoms per unit cell
• Fractional coordinates
• Symmetry operations
• Coordination number