G T , P 0
Equilibrium between two solution phases in a binary system
G n1 , n2
total Gibbs energy
G n1 , n2 G n1 , n2
additivity
Gibbs energy of the
fist phase
Gibbs energy of the
second phase
Let us use molar Gibbs energies instead of total Gib

Problem A
The exponent n in the JMAK equation f 1 exp Kt n , which is habitually used to describe
experimental data on isothermal recrystallization, is always a positive integer number.
True
X False
Problem B
Recovery always precedes recrystallization; th

Spinodal decomposition
Nucleation within a solid-solution alloy requires that in certain regions of the solid solution the
composition must change and these regions of new composition must be stable. In the classical
theory of nucleation it is assumed tha

Page 1 of 4
Name
Student number
MATLS 3T04 "Phase Transformation Instructor:
Dr. D.V. Malakhov
Day class
Duration of examination: 3 hours
McMaster University nal examination December 14, 2006
This examination paper includes 5 pages and 9 questions. You ar

Recovery
We will examine a number of different types of solidsolid phase transformations that allow us to control
the structure of alloys. The first of these is recrystallization. The general phenomenon of recrystallization
may be described as follows. Fi

Order-disorder transformations
Describing ordering using a two-sublattice model
A
1 y
By
p
A1 z B z q
Major constituents are bolded. In plain English, A wants to go to the 1st sublattice, and B prefers
to reside on the 2nd sublattice.
There is a reason

There is a mistake in this document. Can you find it?
Scheil model of solidification
Basic assumptions:
1. No diffusion in the solid state
2. No concentration gradients in the liquid phase
3. Equilibrium at the interface
CL
A dz
volume
CS
A dz
number of

Before we start talking about the gradient energy and strain energy, let us recall what we already
know.
We derived an extremely important equation, which related the total flux of the second
T
component, J 2 , to the mutual mobility, M , the molar volume

Nucleation of martensite
Our first task is to find the side surface of the spherical cup shown in Figure 1.
h
2a
Figure 1. A spherical cup
a R cos
(1)
dh
cos
(2)
dl
dS 2 a dl
(3)
Substitution of (1) and (2) in (3) yields:
dS 2 R cos
dh
2 Rdh
cos
dh

Volume and surface area of a spherical cap via integration
Let us inspect Figure 1 and recall that:
b
V f x dx
2
(1)
a
b
S 2 f x 1 f x dx
2
(2)
a
Figure 1
Let us make use of (1) and (2) for deriving the volume and the surface area 1 of a spherical cap sho

Fundamentals of homogeneous solidification
Let us imagine that a cluster (nucleus) containing n moles appeared in the liquid phase.
G n
J
cluster
mole
cluster
surface
S
L
2
G
n G (T ) G (T ) 4 r
J cm2
J
positive if T Tm and
cm 2 cluster
cluster
negativ

Fundamentals of heterogeneous nucleation
Spherical cap
Let us inspect Figure 1 and recall that:
b
V f x dx
2
(1)
a
b
S 2 f x 1 f x dx
2
(2)
a
Figure 1
Let us make use of (1) and (2) for deriving the volume and the surface area 1 of a spherical cap shown i

Thermodynamic aspects of the formation of GP zones in AlCu alloys
Inspect Figure 1-Figure 4 and ensure that you understand what is shown in them.
THERMO-CALC (2013.11.05:16.14) :
THERMO-CALC (2013.11.05:16.16) :
DATABASE:USER
DATABASE:USER
P=1E5, N=1
P=1E

MATLS 3T04 "Phase Transformations"
Experiment A: Solidification and Casting
Lab Quiz
1. The solidification process, as heat is extracted out through the wall:
a. Starts from the center and proceeds outward
b. Proceeds inward from mold wall
c. Starts from

MATLS 3T04 "Phase Transformations"
Experiment A: Solidification and Casting
Lab Quiz
1. The solidification process, as heat is extracted out through the wall:
a. Starts from the center and proceeds outward
b. Proceeds inward from mold wall
c. Starts from

Experiment B
_
1.
a)
b)
c)
d)
Which of following are nature polymers?
Enzyme
Polyethylene
Rayon
Bakelite
2.
a)
b)
c)
Copolymers contain_.
Single repeating monomer
Only two repeating monomers
More than two repeating monomers
3.
a)
b)
c)
Which polymers can

Name:_
Student No.:_
Experiment C Quiz: Phase Transformations and Age Hardening in Non
Ferrous Alloys
1.
Of the following phase transformations:
i. Precipitation Reactions
ii. Eutectoid Transformations
iii. Ordering Reactions
iv. Massive Transformations
v

Pre-Lab Quiz: Experiment D
Name:
Student Number:
1) What does eutectoid transformation indicate?
a) Liquid1 Solid1 + Liquid2
b) Solid1 Solid2 + Solid3
c) Liquid1 Liquid2 + Liquid3
d) Liquid Solid
2) What kind of curve will you get if you plot the pearlite

Name _
(dont write down your student number!)
MATLS 3T04 Phase Transformations 2013-2014
Test 4
This test includes 3 pages, 8 multiple choice problems and 4 conventional problems.
Multiple choice problems (6 marks per each problem)
Problem A
The exponent

Thermodynamics of massive transformations
Consider the phase diagram shown in Figure 1.
T
a
b
TH
c
d
TL
e
f
x
x0
Figure 1
We are interested in two isothermal processes.
Process 1 (complete transformation)
x
x x0 The equilibrium state of the system
x0

Nucleation of pearlite
Cementite
Cementite
Figure 1
N pearlite
number of pearlite nuclei formed
V t
(1)
nucleation rate
of pearlite
Inspect Figure 1 and realize that the formation of the pearlite nucleus is identified with the
nucleation of ferrite nex

Gibbs-Thomson equation
Figure 1
G
G P 0 G x x x
x x
G
G P P G x x x
x x
G
G
G P P G P 0 G x x x G x x x
x x
x x
(1)
P Vm
Let us use our favourite ultimate weapon by decomposing G in the Taylors series in the
vicinity of x :
G
G
x x

Mathematical model of decarburization
It is convenient to start the analysis of decarburization in multicomponent steels with the
simplest possible case decarburization in the binary Fe-C alloy.
A conventional metastable diagram of the Fe-C system is pres

Eutectoid transformations
Eutectic structures at off-eutectic compositions (a reminder)
Figure 1. An off-eutectic
Figure 2. Solute buildup required for growth of a
composition C0
regular eutectic structure at off-eutectic composition
Consider an alloy of

Influence of external pressure on phase equilibria
Firstly, we will be concerned with the case when all phases are under the same pressure. Then, it
will be explained what influence curved interfaces may have upon pressures inside various
phases.
Let us c

Classification of precipitates
Chunky precipitates
Grain-boundary allotriomorphs
In this case, the precipitates form as elongated chunky blocks in the grain boundaries (Figure 1).
Idiomorphs
The precipitates form as a more equiaxed chunk, which can appear

Different contributions to the molar Gibbs energy of a binary
solution
Let us, for the sake of determinacy, assume that we are interested in the molar Gibbs energy of a
binary liquid solution. Firs and foremost, it must be comprehended that the term the m

Eutectic growth
Area of one interface bc
Number of interfaces 2
a
spacing
a
Total area of all interfcaes 2 bc
a
2 bc
2
Total area of all interfaces in unit volume
abc
Surface energy per unit volume
2
Contribution to the Gibbs energy per one mole of eut

A preparatory step
Adz
C1
n1
dz
volume
J1
C1 C1
v
dt
Adt
Adt
velocity with which the body moves
Adz
C2
n2
dz
volume
J2
C2
C2
v
dt
Adt
Adt
velocity with which the body moves
Flux associate with the macroscopic motion of the whole body (drift) can be

MATLS 3T04 Phase Transformations 2013-2014
DMs solutions of Test 3 problems
Problem 1
a
C
L
b
C
L
c
C
L
d
C
L
T1 is supercooling needed to create interfaces; T2 is supercooling needed to drive diffusion.
C1
C L C L
min
1
C L C L
C2
Problem 2
If