Transcript Document 7376650

Introduction to Materials Science, Chapter 9, Phase Diagrams
Chapter Outline: Phase Diagrams
Microstructure + Phase Transformations
in Multicomponent Systems
 Definitions and basic concepts
 Phases and microstructure
 Binary isomorphous systems (complete solid
solubility)
 Binary eutectic systems (limited solid solubility)
 Binary systems with intermediate phases/compounds
 The iron-carbon system (steel and cast iron)
Not tested: The Gibbs Phase Rule
University of Virginia, Dept. of Materials Science and Engineering
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Components and Phases
Component - chemical species
(Fe + C in steel; H2O + NaCl in salt water).
Binary alloy 2 two components,
Ternary alloy – 3, etc.
Phase – a portion with distinct,
uniform
physical
or
chemical
characteristics
Single-phase system: Homogeneous.
Two or more phases
Mixture or Heterogeneous system.
e.g. water + ice, separated by a phase
boundary
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Solubility Limit
Solvent - host or major component
Solute - minor component (Chapter 4).
Solubility Limit = maximum amount that
can be dissolved in a phase
(e.g. alcohol has unlimited solubility in
water, sugar has a limited solubility, oil is
insoluble).
Same concepts for solids: Cu and Ni are
mutually soluble in any amount (unlimited
solid solubility), while C has a limited
solubility in Fe.
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Microstructure
Properties of an alloy depend on proportions of the
phases and on how they are arranged at the
microscopic level.
Microstructure: number of phases, their
proportions, and their arrangements
Microstructure of cast Iron
Alloy of Fe with 4 wt.% C. There are several
phases. The long gray regions are flakes of
graphite. The matrix is a fine mixture of BCC Fe
and Fe3C compound.
Phase diagrams
microstructures
help
understand
and
predict
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Equilibrium and Metastable States
Equilibrium: at constant temperature,
pressure and composition system is stable
(Equilibrium is achieved given sufficient time,
but that may be very long. )
Metastable: System appears to be stable
Equilibrium  minimum in the free energy.
• Stable equilibrium is state
with minimum free energy.
• Metastable state is a local
minimum of free energy.
Free Energy
• Under conditions of constant temperature,
pressure and composition, change is toward
lower free energy.
equilibrium
metastable
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Phase diagram
Phase diagram - combinations of temperature, pressure
or composition for which specific phases exist at
equilibrium
H2O: diagram shows temperature and pressure at
which ice (solid),water (liquid) and steam (gas) exist.
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Phase diagram
Show what phases exist at equilibrium
and what transformations we can
expect when we change T, P, or
composition
Consider binary alloys only
Pressure constant at one atmosphere.
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Binary Isomorphous System (I)
Assume Complete Solubility
L
+L

Three phases :
Liquid (L) , solid + liquid (+L), solid ()
Liquidus line separates liquid from liquid + solid
Solidus line separates solid from liquid + solid
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Binary Isomorphous Systems (II)
Cu-Ni
Complete solubility occurs because Cu and Ni have
the same crystal structure (FCC), similar radii,
electronegativity and valence
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Binary Isomorphous System (III)
One-component: melting occurs at a well-defined
temperature.
Multi-component: melting occurs over range of
temperatures between solidus and liquidus lines.
Solid and liquid phases are in equilibrium in this
temperature range.
L
Liquid solution
+L

Liquid solution
+
Crystallites of
Solid solution
Polycrystal
Solid solution
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Interpretation of Phase Diagrams
Given:
temperature + composition 
determine
1) Phases present
2) Compositions of phases
3) Relative fractions of phases
Composition in a two phase region:
1. Locate composition and temperature
2. Draw tie line or isotherm
3. Note intersection with phase boundaries
4. Read compositions at the intersections
Liquid and solid phases have these compositions
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Introduction to Materials Science, Chapter 9, Phase Diagrams
The Lever Rule
Amounts of each phase in two phase region
Locate composition and temperature
Draw tie line or isotherm
Fraction of a phase = length of tie line to
other phase boundary divided by the
length of tie line
The lever rule is a mechanical
analogy to the mass balance
calculation. The tie line in the
two-phase region is analogous
to a lever balanced on a
fulcrum.
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Introduction to Materials Science, Chapter 9, Phase Diagrams
The Lever Rule
Mass fractions: WL = S / (R+S) = (C- Co) / (C - CL)
W = R / (R+S) = (Co - CL) / (C - CL)
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Derivation of the lever rule
W and WL are fractions of  and L phases
1) All material is in one phase or the other:
W + WL = 1
2) Composition equal composition in one
phase + composition second phase
at given T:
Co = WC + WLCL
3) Solution gives Lever rule.
WL = (C- Co) / (C - CL)
W = (Co - CL) / (C - CL)
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Phase compositions and amounts. An example.
Co = 35 wt. %, CL = 31.5 wt. %, C = 42.5 wt. %
Mass fractions: WL = (C- Co) / (C - CL) = 0.68
W = (Co - CL) / (C - CL) = 0.32
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Introduction to Materials Science, Chapter 9, Phase Diagrams
Microstructure in isomorphous alloys
Equilibrium (very slow) cooling
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