Chapter 10: Phase Diagrams and Microstructures

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Chapter 10 Phase Diagrams and Microstructures

• Temperature vs. composition behavior of the
  various
• alloy constitutes the phases.
• Allows design and control of heat treatment by
  controlling
• equilibrium and non-equilibrium structure.
• Structure (phases and microstructure) often
  controls properties
• of materials, and, therefore, depends on thermal
  history.

• Objectives
• Read and evaluate phases present at T.
• Determine composition of phases and phase
  fraction.
• Know difference between types of reactions,
  e.g., eutectic, eutectoid, proeutectoid.
• Make a schematic diagram of microstructure.

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Phase Diagrams Issues to Address
When we combine two elements, what equilibrium
state do we get?
In particular, if we specify... --a
composition (e.g., wtA - wtB), and --a
temperature (T)
then... How many phases do we get? What
is the composition of each phase? How much of
each phase do we get?
Ordered Phase
Solid-solution Phase
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Example Phase (T-c) Diagram Cu-Zn
Solution solid, liquid, or gas solutions,
single phase Mixture more than one phase
liquid
bcc-ss
fcc-ss
2-phase
hcp-ss
hcp
bcc CsCl
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Solubility Limit in Phase Diagram
Solubility Limit Max concentration for
which only a solution occurs.
Ex Water-Sugar
Q What is solubility limit at 20oC? Answer
65wt sugar. If Co lt 65wt sugar syrup
If Co gt 65wt sugar syrup sugar.
Adapted from Fig. 10.1, Callister Rethwisch 3e.
Solubility limit increases with T e.g.,
if T 100C, solubility limit 80wt sugar.
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Components and Phases
Components elements or compounds that are
mixed initially (e.g., Al and Cu) Phases
physically and chemically distinct material
regions that result (e.g., a and b).
Aluminum-Copper Alloy
Adapted from chapter-opening photograph, Chapter
9, Callister, Materials Science Engineering An
Introduction, 3e.
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Temperature (T) and Composition (C) Effects
Changing T can change of phases path A to
B. Changing Co can change of phases path B
to D.
water- sugar system
Adapted from Fig. 10.1, Callister Rethwisch 3e.
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Criteria for Solid Solubility recall
Hume-Rothery rules
Simple system (e.g., Ni-Cu solution)

• Both have the same crystal structure (FCC) and
  have similar electronegativities and
  atomic radii (W. Hume Rothery rules)
  suggesting high mutual solubility.

• Ni and Cu are totally soluble in one another
  for all proportions.

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Cu-Ni Phase Diagram T vs. c (wt or at)
Tell us about phases as function of T, Co, P.
For this course --binary systems just
2 components. --independent variables T and
Co (P 1atm is always used).
-- isomorphous i.e., complete solubility of one
component in another a phase field extends from
0 to 100 wt Ni.
Adapted from Fig. 10.3(a), Callister Rethwisch
3e. (Fig. 10.3(a) is adapted from Phase Diagrams
of Binary Nickel Alloys, P. Nash (Ed.), ASM
International, Materials Park, OH (1991).
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Phase Diagrams and types of phases
Rule 1 If we know T and Co, then we know
--the and types of phases present.
Examples
Cu-Ni phase diagram
A(1100C, 60 wt Ni)
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Phase Diagrams composition of phases
Rule 2 If we know T and Co, then we know
--the composition of each phase.
Examples
Consider C0 35 wt Ni
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Phase Diagrams wt. fraction of phases
Rule 3 If we know T and C0, then can
determine -- the weight fraction of each
phase.
Examples
Consider C0 35 wt Ni
W wt. fraction of phase out of whole.
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The Lever Rule
Sum of weight fractions
Conservation of mass (Ni)
Combine above equations
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The Lever Rule an interpretation

• Tie line connects the phases in equilibrium
  with each other also sometimes called an
  isotherm

What fraction of each phase?
Think of tie line as a lever
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Phase and Microstructure (equilibrium) Example
Cooling in Cu-Ni Binary
Consider microstuctural changes that accompany
the cooling of a C0 35 wt Ni alloy

• From liquid, solid phase nucleates.
• From solid, other phases can nucleate.
• Like ice, many grains of solid form.
• wt of SOLUTE given by line dropped from
  boundaries
• Fraction of PHASES present given by the lever
  rule.
• Microstructure different depending on cool
  slowly or quench.

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Phases and Microstructure (non-equilibrium)

• Upon cooling quickly (i.e. nonequilibrium),
  microstructure has range of composition depending
  on when it was formed.
• Inside nucleus of solid phase higher composition
  (in Cu-Ni case) due to its creation at higher T.
• Outside part of growing solid phase nucleus has
  lower composition due to its forming at lower T.

Core-like development
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Cored versus Equilibrium Phases
Ca changes as we solidify. Cu-Ni case
First a to solidify has Ca 46 wt Ni. Last a to
solidify has Ca 35 wt Ni.
Slow rate of cooling Equilibrium structure
Fast rate of cooling Cored structure
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Recall Mechanical Properties of Cu-Ni
Effect of solid solution strengthening on
--Ductility (EL,AR)
--Tensile strength (TS)
-Peak as a function of Co
-Minimum as a function of Co
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Binary-Eutectic Systems
has a special composition with a minimum melting
T.

• Ex Cu-Ag
• 3 single-phase regions
• (L, ?, ?)
• Limited solubility
• ? mostly Cu
• ? mostly Ag
• TE no liquid below TE.
• cE composition for min. melting T (Eutectic).

Eutectic direct from liquid to 2-phase solid
upon cooling L ? ? ?
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Solder for electronics
Example 1 Lead-Tin (Pb-Sn) Eutectic Diagram
For a 40wtSn-60wtPb alloy at 150oC,
determine... --phases present a b
--compositions of phases
Ca 11 wt Sn
Cb 99 wt Sn
-- relative amount of each phase
Use the Lever Rule
Adapted from Fig. 10.8, Callister Rethwisch 3e.

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Example 2 Pb-Sn Eutectic System
For a 40 wt Sn-60 wt Pb alloy at 220C,
determine -- phases present
a L
-- phase compositions
Ca 17 wt Sn
CL 46 wt Sn
-- relative amt of phases
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Microstructure for Eutectic Diagrams Pb-Sn
For alloys with C0 lt 2 wt Sn Result at
room temperature -- polycrystalline with
grains of a phase having C0
Note liquid-to-solid creates grain boundaries.
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Microstructure for Eutectic Diagrams Pb-Sn
For alloys with 2 wt Sn lt C0 lt 18.3 wt
Sn Result at Ts in a b range --
polycrystalline with a grains and small
b-phase particles
Note Solubility depends on T.
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Microstructure at Eutectic
For alloy of composition C0 CE Result
Eutectic microstructure (lamellar structure)
-- alternating layers (lamellae) of a and b
phases.
Light Sn-rich Dark Pb-rich
Adapted from Fig. 10.13, Callister Rethwisch
3e.
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Lamellar Eutectic Structure
Diffusion local
Adapted from Figs. 10.14 10.15, Callister
Rethwisch 3e.
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Microstructure below Eutectic (hypoeutectic)
For alloys for 18.3wtSn lt Co lt 61.9wtSn
Result a crystals and a eutectic microstructure
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Solder Lead-Tin (Pb-Sn) microstructure

• For 50 wt Pb alloy
• Lead-rich ? phase (dark)
• Lamellar eutectic structure
• of Sn-rich ? phase (light).

L
L ?
?
?
? ?
Why is Liquid-phase 62.9wtSn and ?-phase
16.3wtSn at 180 C? For fraction of total ?
phase (both eutectic and primary), use the Lever
Rule.
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Hypoeutectic Hypereutectic
Adapted from Fig. 10.8, Callister Rethwisch
3e.
(Figs. 10.14 and 10.17 from Metals Handbook, 9th
ed., Vol. 9, Metallography and Microstructures,
American Society for Metals, Materials Park, OH,
1985.)
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Intermetallic Compounds
Adapted from Fig. 10.20, Callister Rethwisch
3e.
Intermetallic compounds exists as a line on the
phase diagram - not an area - because of
stoichiometry (i.e. c of a compound is a fixed
value).
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Eutectic, Eutectoid, Peritectic

• Eutectic - liquid transforms to two solid phases
• L ? ? (For Pb-Sn, 183?C, 61.9 wt
  Sn)

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Eutectoid, Peritectic
Cu-Zn Phase diagram
Adapted from Fig. 10.21, Callister Rethwisch
3e.
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Ceramic Phase Diagrams
MgO-Al2O3 diagram
Adapted from Fig. 10.24, Callister Rethwisch
3e.
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Iron-Carbon (Fe-C) Phase Diagram
2 points
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Hypoeutectoid Steel
Adapted from Figs. 10.28 and 10.33
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Hypoeutectoid Steel
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Hypereutectoid Steel
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Hypereutectoid Steel
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Example Problem Steel

• For a 99.6 wt Fe-0.40 wt C steel at a
  temperature just below the eutectoid, determine
  the following
• The compositions of Fe3C and ferrite (?).
• The amount of cementite (in grams) that forms in
  100 g of steel.
• The amounts of pearlite and proeutectoid ferrite
  (?) in the 100 g.

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Solution to Problem
a) Use RS tie line just below Eutectoid
Ca 0.022 wt CCFe3C 6.70 wt C

• Use lever rule with the tie line shown

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Solution to Problem
c) Using the VX tie line just above the
eutectoid and realizing that
C0 0.40 wt CCa 0.022 wt CCpearlite C?
0.76 wt C
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Alloying Steel With More Elements
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Summary Phase Diagrams and Microstructures
Phase (T vs c) diagrams are useful to
determine
- the number and types of phases, - the wt of
each phase, - and the composition of each phase
for a given T and composition of the system.
Alloying to produce a solid solution usually
- increases the tensile strength (TS) -
decreases the ductility.
Binary eutectics and binary eutectoids allow
for a range of microstructures. - Alloy
composition and annealing temperature and time
determine possible microstructure(s). Slow vs.
Fast. - In 2-phase regions, use lever rule to
get wt of phases. - Varying microstructure
affects mechanical properties.