ENGR 145: Chemistry of Materials

1
Additional Information for Exam 3

• Covers lectures 19 25 and the associated
  reading assignments
• Arrive 5 minutes before the start of the exam
• Closed-book, closed notes
• Bring
• Calculators (memories cleared)
• Notes on a 3 x 5 card
• Periodic table (handed out in recitation)
• Provided
• Fundamental constants

2
Reading Assignments for Exam 3

• Lecture 19 Enthalpy Changes in Nonreacting
  Systems
• OGN 5.4-5.6 7.2, 7.3, 7.5
• Lecture 20 Spontaneous Processes Thermodynamic
  Equilibrium
• OGN 7.5, 8.1, 8.3, 8.5-8.7
• Lecture 21 Chemical Equilibrium
• OGN 9.1-9.2 eq. 9.4 9.6
• Lecture 22 Two-Component Systems Continuous
  Solid Solutions
• Callister 9.1-9.6
• Lecture 23 Two-Component Systems Eutectics
• Callister 9.7
• Lecture 24 Equilibrium vs. Nonequilibrium
  Solidification
• Callister 9.6-9.7 lecture slides
• Lecture 25 Role of Bonding in Binary Systems
  Practice Problems
• Lecture slides

3
First Law of Thermodynamics OGN 7.3

• Heat and work are forms in which energy is
  transferred into or out of a system
• The first law of thermodynamics describes the net
  change in energy ?E transferred between a system
  and its surroundings
• q heat into system w work done by
  surroundings
• One type of work change in volume ?Vsurr (
  ?Vsys) at constant pressure P
• Net change in energy of system at constant
  pressure

4
Calorimetry Two Approaches OGN 7.3
OGN Fig. 7.6
?HP M ? cS ? ?T
5
One-Component Phase Diagrams OGN Ch. 5

• Similar one-component diagrams for many different
  substances

OGN Fig. 5.21
6
Zeroes of Enthalpy and Entropy

• Elements in standard states at 298.15 K have H
  0
• Pure substances in equilibrium form as T ? 0 K
  have S ? 0

7
Enthalpy vs. T for a Phase Transition

• H vs. T for melting of a solid or freezing of a
  liquid
• Slopes heat capacities (Which is larger? Why?)
• ?H _at_ Tm ?Hf

Cliq
?Hf
enthalpy
Csolid
8
Computing Entropy Changes OGN 8.5

• How to compute ?S for a process
• Examples for several types of processes OGN 8.5
• ?S in n moles of a single nonreacting phase
  during a ?T (P const)
• ?S for a phase transition

9
Gibbs Free Energy for a Phase Transition OGN
8.7
At constant T and P
spontaneous(may happen)
reversible (may go either way)
non-spontaneous (can happen only with energy
input from surroundings)
10
?G for a Phase Transition OGN 8.7

• Example melting freezing of H2O

?Gfreezinggt0
?Gfreezinglt0
At 0C (273 K)
OGN Fig. 8.10
11
?G for a Chemical Reaction OGN 8.7

• Competition between
• the change in enthalpy (?H) and the change in
  entropy (?S)
• At eqm, ?G 0 ? Teqm ?H /?S
• At other temperatures, sign of ?G depends on
  signs of ?H and ?S

12
?G, K, T (OGN eq. 9.4)

• The temperature dependence of K is linked to ?G
• for reaction aA bB ? cC dD with Gibbs f.e. ?G
• K exp?G/RT or
• ?G lt 0 ? K gtgt 1 ? C and D are predominant
• ?G gt 0 ? K is small A and B are predominant

for solutions
for gases
13
Examples of Le Châteliers Principle

• Ti(s) O2(g) ? TiO2(s)
• Reaction consumes gas from left to right
• P? ? reaction shifts to right (i.e., to relieve
  pressure)
• pO2? ? reaction shifts to right (i.e., to consume
  oxygen)
• ?Hf,298 944.7 kJ mol1 (exothermic) ?Sf,298
  185.33 J mol1 K1 (lt0, as expected
  why?)?Gf,298 889.4 kJ mol1 K pO21
  exp?G/RT K' exp?H/RT
• T? ? K? ? reaction shifts to left (to less heat
  given off) (toward reduction of the oxide to
  metal)

14
Lever Rule Callister 9.6

• Tie line tells
• phases present (L, ?)
• their compositions (CL, Ca)
• how much of each phase is present for a given
  overall composition C0 the lever rule

liquidus curve
solidus curve
Callister Fig. 9.2b
15
Review Equilibrium Solidification of a Solid
Solution

• Assume equilibrium is reached at each temperature
• Above liquidus T 100 liquid
• Initial formation of solid
• Continued growth of solid
• Solidification of last liquid
• Below solidus T 100 solid
• Note
• Composition of liquid changes from 35 wt Ni to
  23 wt Ni
• Composition of solid changes from 49 wt Ni to
  35 wt Ni
• These processes take time

16
Nonequilibrium Solidification of a Solid Solution

• Start from 100 liquid
• Initial solid forms eqm compn
• Additional solid eqm compn at surface only
• Average solid compn is Ni-rich (dotted line)
• ? remaining liquid is Cu-rich
• Last liquid has a lower liquidus temperature than
  at eqm
• Grains have compositional gradients from interior
  to grain boundary
• On reheating, grain boundaries may melt
  prematurely

17
The Pb-Sn System Callister 9.7

• Solidification of 15 wt Sn, 85 wt Pb
• 100 liquid
• L??
• 100 ?
• So far, process is same as solidification of a
  continuous solid solution
• ? ? ??
• Solvus reaction
• ? precipitates inside ? grains

Callister Fig. 9.10
18
The Pb-Sn System Callister 9.7

• Solidification of eutectic liquid (CE)
• L ? ? ? at TE
• Characteristic lamellar (layered) microstructure
• Individual eutectic colonies nucleate and grow
  until they impinge on each other

Callister Fig. 9.11
Callister Fig. 9.12
19
The Pb-Sn System Callister 9.7

• Solidification of 40 wtSn, 60 wt Pb
• A hypoeutectic composition (C lt CE)
• 100 liquid
• Primary ? forms
• Last primary forms
• Eutectic reaction

Callister Fig. 9.14
Callister Fig. 9.15
20
Real Data EMSE 270, Spring 06

• Hypoeutectic Pb-Sn alloy at still higher
  magnification. Light phase ? (Pb-rich) dark
  phase ? (Sn-rich)

? precip-itates in primary ? why?
eutectic