1. Affect of Variables on Recrystallization
Minimum amount of deformation is required
The smaller the deformation, the higher the temperature required for recrystallization
Increasing annealing time decreases required recrystallization temperature. Temperature is more important than time. Doubling annealing time is approximately equivalent to increasing annealing temperature 10oC
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.
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.

2. Affect of Variables on Recrystallization
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.

3. Recrystallization Temperature

4. 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
Why? Grain boundary area (and therefore energy) is reduced

5. Grain Growth – How does it occur
After 8 s,
580ºC
After 15 min,
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
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

6. Mathematical Relationships
Empirical Relationship:
elapsed time
coefficient dependent
on material and T.
grain diam.
at time t.
exponent typ. ~ 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.

7. Equilibrium Phase Diagrams

8. 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

9. 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.

10. 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…

11. Definition of Solubility Limit
Sucrose/Water Phase Diagram
Pure
Sugar
Temperature (°C) 20 40 60 80
100 Co
=Composition (wt% sugar) L
(liquid solution
i.e., syrup)
Solubility
Limit
(liquid) + S
(solid
sugar) 4 6 8 10
Water
• Solubility Limit:
Max concentration for
which only a single phase solution occurs. 65
Question: What is the
solubility limit at 20°C?
Answer: 65 wt% sugar.
If Co < 65 wt% sugar: syrup
If Co > 65 wt% sugar: syrup + sugar.

12. 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)
1 phase
D (100°C,90)
2 phases 70 80
100 60 40 20
Temperature (°C) Co
=Composition (wt% sugar) L (
liquid solution
i.e., syrup)
(liquid) + S
(solid
sugar)
water-
sugar
system
A (20°C,70)
2 phases
Adapted from Fig. 9.1,
Callister 7e.

13. 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

14. Fully Miscible Solution
Simple solution system (e.g., Ni-Cu solution)
Crystal
Structure
electroneg
r (nm) Ni
FCC
1.9
0.1246 Cu
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

15. 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?