Affect of Variables on Recrystallization
1. Minimum amount of deformation is required
2. The smaller the deformation, the higher the temperature
required for recrystallization
3. Increasing annealing time decreases required recrystallization
temperature. Temperature is more important than time.
Doubling annealing time is approximately equivalent to
increasing annealing temperature 10oC
4. Final grain size depends most on the degree of deformation
and to lesser extent on the annealing temperature. The
greater the deformation & the lower the annealing temp., the
smaller the recrystallized grain size.
5. The larger the original grain size, the greater the amount of
cold work required to produce same recrystallization temp.
Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.
Affect of Variables on Recrystallization
6.
7.
8.
The recrystallization temperature decreases with increasing
purity of the metal. Solid solution alloying additions
ALWAYS raise the recrystallization temperature.
The amount of deformation required to produce equivalent
recrystallization behavior increases with increased working
temperature
For a given reduction in cross-section – different metal
working processes produce different effective deformations.
Therefore, identical recrystallization behavior may not be
obtained.
Source: G. Dieter, Mechanical Metallurgy, 3rd Edition, McGraw-Hill, 1986.
Recrystallization Temperature
Element (Alloy)
Recrystallization T
(K)
269
269
283
(oC)
327
232
420
Homologous
Temperature
600
505
693
45%
53%
41%
80
353
660
933
38%
120
475
370
450
1200
393
748
643
723
1473
1085
900
1455
1538
3410
1358
1173
1728
1811
3683
29%
64%
37%
40%
40%
Lead
Tin
Zinc
(oC)
-4
-4
10
Aluminum (99.999 wt%)
Copper (99.999 wt%)
Brass (60 Cu - 40 Zn)
Nickel (99.99 wt%)
Iron
Tungsten
Melting Point
(K)
Grain Growth
• If you expose any crystalline material to a high enough
temperature to allow diffusivity and atomic mobility then
you will have grain growth.
• Specifically, the average grain size will increase with
time at temperature
Movie
http://www.albany.edu/geosciences/wdm/wdmoviep.html
• Why? Grain boundary area (and therefore energy) is
reduced
Grain Growth – How does it occur
0.6 mm
After 8 s,
580ºC
0.6 mm
Grain size is the mean diameter of
an aggregate of grains
As grains grow the number of
grains decreases but the mean
diameter continues to grow
After 15 min,
580ºC
• Larger grains consume smaller ones.
• Grain boundaries have curvature
• Migration of atoms across grain boundaries always moves
toward the center of curvature
• Small grains that are not hexagonal and have corners at angles
less than 120o (a perfect hexagon has 120o) tend to have center
of curvature towards center of grain – they shrink
• Big grains, or grains with more than 6 sides grow
Mathematical Relationships
Empirical Relationship:
exponent typ. ~ 2
grain diam.
n
d
at time t.
 d on  Kt
coefficient dependent
on material and T.
elapsed time
D  kt
1
2
• Most reported experimental work does
not conform to grain growth equation
• Many of the data sets correspond to
empirical equation of the form
D = ktn
Where
 n is less than value ½
 n is not usually constant for given
metal or alloy with changes in T
Source: Reed-Hill & Abbaschian, Physical Metallurgy Principles, 3rd Edition, PWS Publishing Company, 1994.
Equilibrium Phase Diagrams
Definitions
• Component: Pure metal or compound from which an alloy is composed
– Components are Zn and Cu in Brass Diagram
– We have also used the terms solvent and solute when we were discussing
solid solutions
• Phase: A homogeneous portion of a system that has uniform physical
and chemical characteristics
– Every pure metal is a phase
– Every liquid, solid, or gaseous solution is a phase
– When two or more phases are present there is a boundary between the two
• Phase diagram: is a graphical representation of phase stability
– Phase stability is dependent on temperature, pressure, and composition
– Phase diagrams are constructed to show the interplay of these parameters
Definition of Equilibrium
• Definition of Gibb’s Free Energy, DG:
DG = DH – TDS
DG = DGo – RTlnQ
• Gibb’s Free Energy is used to determine if a reaction will occur –
must be negative
• At equilibrium – DG = 0, reaction rates forward and backward are
equal
• Phase equilibrium is stability in the chemical and physical makeup of
phases present with time
Solution thermodynamics can be used to derive
phase diagrams – not gonna happen here.
One Component Phase Diagram
Curves represent chemical reaction that describes a phase transformation
Gibbs Phase Rule:
P+F=C+2
P: Number of Phases
F: Degrees of Freedom
(What variables may be independently
changed without altering state of system)
C: Number of Components
Invariant point – no degrees of freedom
Beyond “critical point” physico-chemical properties of water and steam converge to the
point where they are identical. Beyond the critical point: "supercritical fluid".
Water phase diagram can be used to explain ice skating…
Definition of Solubility Limit
Sucrose/Water Phase Diagram
80
L
(liquid)
60
L
40
(liquid solution
i.e., syrup)
20
0
Pure
Water
Question: What is the
solubility limit at 20°C?
Solubility
Limit
+
S
(solid
sugar)
20
40
60 65 80
100
Co =Composition (wt% sugar)
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.
Pure
Sugar
Max concentration for
which only a single phase
solution occurs.
100
Temperature (°C)
• Solubility Limit:
Effect of T & Composition (Co)
• Changing T can change # of phases: path A to B.
• Changing Co can change # of phases: path B to D.
B (100°C,70) D (100°C,90)
1 phase
watersugar
system
Adapted from
Fig. 9.1,
Callister 7e.
Temperature (°C)
100
2 phases
L
80
(liquid)
60
L
(liquid solution
40
i.e., syrup)
20
0
0
+
S
(solid
sugar)
A (20°C,70)
2 phases
20
40
60 70 80
100
Co =Composition (wt% sugar)
Binary Phase Diagram
•
•
•
•
Hold pressure constant (typically 1 atm)
Allow temperature and composition to vary
Binary phase diagram has 2 components
Ternary phase diagram has 3 components (not going to
cover in this class)
• Maps of equilibrium phase structures
Fully Miscible Solution
Simple solution system (e.g., Ni-Cu solution)
Crystal
Structure
electroneg
r (nm)
Ni
FCC
1.9
0.1246
Cu
FCC
1.8
0.1278
• Both have the same crystal structure (FCC) and have similar
electronegativities and atomic radii (W. Hume – Rothery rules)
suggesting high mutual solubility.
• Ni and Cu are totally miscible at all mixture compositions – isomorphous
Copper-Nickel Binary Equilibrium Phase Diagram
• Solid solutions are typically
designated by lower case Greek
letters: a, B, g, etc.
• Liquidus line separates liquid
from two phase field
• Solidus line separates two
phase field from a solid solution
• Pure metals have melting points
• Alloys have melting ranges
What do we have? What’s the composition?