7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

1/7

1

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

2

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

2/7

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 .

3

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

4

Phase diagram

Image from http://www.che.tohoku.ac.jp/~scf/

about/about%20sc%20fluid-E.htm

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

3/7

5

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

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

4/7

A Broader Perspective:

Consider the Earth

7

One-Component Phase Diagrams

iron SiO2

8

Al lotropic : when an element has

several phases

BCC

=BCC,

=FCC,

=BCC, =austenite

Figure 7.2-2 & 7.7-3

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

5/7

One-Component Phase Diagrams

9

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

10

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

6/7

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?

11

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

12

7/24/2019 Chapter7: Phase Equilibria and Diagrams part 1

7/7

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.

13

Cu-Ni: Binary Isomorphous Alloy Example

Cu-Ni: Binary Isomorphous Alloy Example

14