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7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1
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MSE 2001 C
Fall 2015
Chapter 7
Phase Equilibria and
Phase Diagrams
Chapter 7Objectives of the class
Gibbs phase rule
Introduction to phase diagram
Practice phase diagram
Lever rule
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A chemically and structurally homogeneous region of a
material.
A part of a system, physically distinct, macroscopically
homogeneous, and of fixed or variable composition.
It is mechanically separable from the rest of the system.
That is, a phase is a region within which all the intensive
variables vary cont inuously, whereas at least some of them
have discont inuities at the borders between phases.
Ex: ice water = ice + water
2 phases: solid phase + liquid phase
I want to drink 2-phase system consisting
of solid water and liquid water .
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Phase
Graphical representation of the combination of temperature,
pressure, composition, or other variables for which specific
phases exist at equilibrium.
Phase diagram of Water (H2O) Phase diagram of
Carbon dioxide (CO2)
State point: a position on the phase diagram
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Phase diagram
Image from http://www.che.tohoku.ac.jp/~scf/
about/about%20sc%20fluid-E.htm
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Gibbs Phase Rule
F = C - P + 2
where F = number of independent state variables or
degrees of freedomC = number of components
P = number of phases that coexist in
equilibrium
If pressure is kept constant (say at 1 atm.)
F = C - P + 1
One-Component Phase Diagrams: Water
Gibbs phase rule for systems in equilibrium:
* Component: a chemical species whose concentration in a phasecan be varied independently of the other species concentration
* Number of degrees of freedom in equilibrium: the number ofvariables (P, T, or composition) that can be independent ly
adjusted w ithout disturbing equilibrium. 6
F = 2
F = 1
F = 0
F = 2
F = 2
F = C P + 2F: Degrees of freedom
C: # of Components
P: # of phases
* Triple point: F=0 (= invariant point)
0.00603 atm
0.0098oC
* Critical point: F=0
Solid
373.946 C
217.7 atmFigure 7.2-1
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A Broader Perspective:
Consider the Earth
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One-Component Phase Diagrams
iron SiO2
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Al lotropic : when an element has
several phases
BCC
=BCC,
=FCC,
=BCC, =austenite
Figure 7.2-2 & 7.7-3
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One-Component Phase Diagrams
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Carbon
104 atm ~ Gpa
At RT, ~2 GPa,
graphite diamond
Industrial diamond:
at high T, high P
polycrystalline
Solubility
Unlimited solubility Limited solubility No solubility
Alcohol + Water Salt + Water Oil + Water
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Issues to address
When we combine two elements... what equilibrium state would we expect to get?
In particular, if we specify...-- a composition (e.g., wt% Cu - wt% Ni), and
-- a temperature (T ) and/or a Pressure (P)
then...How many phases do we get?
What is the composition of each phase?
How much of each phase do we get?
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Copper (Cu) and Nickel (Ni) are mutually
soluble in any amount
* unlimited solid solubility
* Satisfies Hume-Rothery rule
Carbon (C) has a limited solubil ity in Iron (Fe).
Similar concepts apply to solid solutions
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Binary Isomorphous Alloy Systems
A mixture of two metals is called a binary alloy
and constitutes a two-component system.
Each metallic element in an alloy is called aseparate component.
Isomorphous systems contain metals which are
completely soluble in each other and have a
single type of crystal structure.
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Cu-Ni: Binary Isomorphous Alloy Example
Cu-Ni: Binary Isomorphous Alloy Example
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