Precipitate Free Zone
To show the formation of precipitate free zones due to grain boundar
ies acting as sinks for vacancies as well as heterogeneous nucleation
sites
Education Level : UG
Course Name: Phase transformations and heat
treatment
LO’s for prior viewing : Precipitate growth
Authors
Amol Subhedar
(Under guidance of Prof. M P Gururajan )
Learning Objectives
After interacting with this Learning Object, the learner will be
able to:
1. Identify precipitate free zones
2. Explain how precipitate free zones are formed
3. Explain the effect of quenching rate on the formation of
precipitate free zone
1
2
Definitions of the components/Keywords:
Precipitation – The formation of a second
phase in a solid through nucleation and growth
Grain boundary - The interface between two
grains, or crystallites, in a polycrystalline
material
Vacancy – Absence of atom in lattice
3
Nucleation - Extremely localized formation of a
distinct thermodynamic phase.
Quenching - Rapid cooling of a material
4
5
Heterogeneous nucleation – Nucleation of a
phase on the defects
PFZ – Precipitate free zone; a zone near a
grain boundary and is free of precipitates
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2
3
Definitions of the components/Keywords:
Solute atoms: Atoms of the second phase
which is formed as precipitates
: Critical vacancy supersaturation i.e.
vacancy concentration above which nucleation
is possible.
Xv – vacancy concentration
- Equilibrium vacancy concentration at
grain boundary
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5
1
Master Layout 1:Typical precipitate morphology
near grain boundary
Step 1: Area near grain boundary is free of precipitate
2
Precipitate
3
4
5
Grain Boundary
Step 1
Description of the activity Audio narration
Draw a rectangle and
divide it in middle by
vertical straight line
Draw two dotted line at
some distance from
centre line dividing area
in 4 parts. Name centre
vertical solid line as
“Grain boundary”. Draw
small circles in first and
fourth part in red colour.
Draw three ellipse on
central solid line in red
colour.
Animation time : 2
seconds
Consider area near a
grain boundary.
Precipitates are
shown with red
ellipse and circles.
Precipitate density is
very low near grain
boundary but is high
on grain boundary itself
and at some distance
from it. So there is
region of nearly zero
precipitate shown as
dotted lines. In next
step we will see how
it is formed.
Text to be displayed
1
Master Layout 2: Formation of precipitate free zone
Step 1:Vacancy distribution near grain boundary area
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3
4
Vacancy
Grain boundary
5
Image on right is copyrighted.
Please redraw
Step 1
Description of the activity Audio narration
Draw a rectangle and divide
it in middle by vertical
straight line Draw two
dotted line at some distance
from centre line dividing
area in 4 parts. In first and
fourth rectangle part draw
large number of dots. In
second and third region
draw very few dots. Name
any dot as “vacancy” and
centre vertical solid line as
“Grain boundary”.
Redraw the figure on right
(it is copyrighted). Equation
for plotting can be used y =
5 – exp(-0.5*abs(x -8))
where x varies from 0 to 16.
Do not show numbers on
axis. Draw a dotted vertical
line on x = 8
Consider area near a
grain boundary. Note the
very low concentration
area of vacancies near
grain boundary as grain
boundary acts as sink of
vacancies. Variation of
vacancy concentration is
also shown in graph.
Text to be displayed
Step 1: (Continued...)
Description of the activity Audio narration
Points for plotting the graph
(7,4.393), (6,
4.632),(5,4.778), (4,4.864),
(0,4.981),(8,4), (9,4.393),
(10, 4.632),(11,4.778),
(12,4.864), (16,4.981)
Animation time : 3 seconds
Text to be displayed
1
Step 2:
Start of nucleation process
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3
4
Grain boundary
Vacancy
Nucleation starts on vacancies
5
Decomposition of α into
β+α
Step 2
Description of the activity Audio narration
Remove the graph on
right side and decrease
number of dots by nearly
1/3.
Now as parent phase
alpha is cooled below
transition temperature
precipitation starts and
parent phase alpha
In place of graph draw a decomposes into alpha
rectangle and inside it
+ beta phase. vacancies
draw a part of circle as
act as nucleation site for
shown. Mark circular
homogeneous
region as α+β and rest nucleation. Also Grain
boundary itself act as
part as α. Draw a
site for heterogeneous
arrow pointing
downwards.
nucleation. Since area
Animation time : 3
near grain boundary is
seconds
devoid of vacancies very
small number of nuclei
appear in this region.
Text to be displayed
Step 3:
Formation of precipitate free zone
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2
Precipitate
3
4
5
Precipitate free zone
Grain boundary
Step 3
Description of the activity Audio narration
Increase the size of dots
(while reducing their
number) as shown in
figure and name the
circles as precipitate.
Name the region
between two dotted lines
as precipitate free zone.
Draw 4 arrow on each
side of central solid line
pointing towards line.
Draw 3 ellipse on the
central solid line at equal
spacing.
Animation time : 4
seconds
As nuclei at grain
boundary starts to grow
area near grain
boundary gets depleted
in vacancies as well as
in solute. Thus growth
of any nuclei in area
near grain boundary is
suppressed due to lack
of solute. Direction of
arrows show solute atom
movement towards
precipitates on grain
boundary
The region near grain
boundary thus is nearly
free of precipitates, this
region is known as
precipitate free zone.
Text to be displayed
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2
3
4
5
Master Layout 3: Effect of quench rate on PFZ
area
Step 1: Greater the quench rate lesser the PFZ
Step 1
Description of the activity Audio narration
Draw X axis as distance
and Y axis as . Draw
two curves
a) Y = 5 - exp(-1*abs(x8))
b) Y = 5 - exp(0.5*abs(x-8))
in the range [0:16]. Mark
curve (a) as fast
quench and (b) as
slow quench.
Draw a dotted horizontal
line at Xv = 2.5.
Mark It as
. This
line will Cut two curves
a and b At two points
each. Draw Vertical lines
from these points and
mark them as PFZ
Animation time : 4
seconds
High quench rates
leads in reduction of
the width of the
vacancy
concentration profile
thus reducing
precipitate free zone
area. The reason for
this reduction in the
width of precipitate
free zone is that
diffusion distance
varies as square root
of Dt, Where D is
diffusivity
and t is quench time.
Text to be displayed
Step 1(continued...)
Description of the activity Audio narration
Points for plotting graph:
For plotting (b) :
(7,4.393), (6,
4.632),(5,4.778),
(4,4.864),
(0,4.981),(8,4),
(9,4.393), (10,
4.632),(11,4.778),
(12,4.864),
(16,4.981)
For plotting (a);
(0, 5), (4, 4.999),(5,
4.9975),(6, 4.981),
(7,4.864), (8,4),
(9,4.864), (10,4.981),
(11, 4.9975), (12,
4.999), (16,5)
Text to be displayed
Questions
1. Which of the following is not heterogeneous
nucleation site?
a) Vacancies
b) Grain boundary
c) Solute atoms
2. Which of following curve can approximate
Vacancy concentration versus distance from grain
boundary. Note that curve is symmetric about
grain boundary and asymptotically converges to
some value at large distance. Assume grain
boundary is at x = x0 , d, K are constants and abs
represents absolute value
a) Y = K – exp(-d*abs[x-x0])
b) Y = exp(d*abs[x-x0])
c) Y = K – exp(-d*[x-x0])
3. Grain boundaries act as homogeneous nucleation
sites. True or false?
4. If the quenching rate is high, the width of the
precipitate free zone is high. True or false?
5. The precipitate free zone width will be large if the
diffusivity of the solute atoms are small. True or
false?
Answers
1. Solute atoms. Other are example of
heterogeneous vacancies.
2. Y = K – exp(-d*abs[x-x0]), where grain boundary
is at x0 and d, K are constants.
3. False. Grain boundary act as heterogeneous site
for nucleation.
4. False. When quench rate is high solute atoms get
less time to diffuse through resulting lesser
width.
5. False. Width of precipitate free zone varies as
√Dt, where D is diffusivity and t is time.
Links for further reading
Reference websites:
1.
http://www.msm.cam.ac.uk/phase-trans/abstracts/pfz.html
1. Books:
1. D. Porter, K. Easterling, M. Sherif, Phase Transformations in
Metals and Alloys, Third Edition (2009), CRS Press.
Research papers:
Summary
1.
2.
3.
4.
Grain boundary acts as sink for vacancies.
Grain boundary itself can act as potential
heterogeneous nucleation site.
Excess vacancies can act as potential heterogeneous
nucleation site.
Width of Precipitate free zone can be minimized by
using high quench rates.