Affect of Variables on Recrystallization

1. Minimum amount of deformation is required2. The smaller the deformation, the higher the temperature

required for recrystallization3. 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. The recrystallization temperature decreases with increasing purity of the metal. Solid solution alloying additions ALWAYS raise the recrystallization temperature.

7. The amount of deformation required to produce equivalent recrystallization behavior increases with increased working temperature

8. 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

(oC) (K) (oC) (K)Lead -4 269 327 600 45%Tin -4 269 232 505 53%Zinc 10 283 420 693 41%Aluminum (99.999 wt%) 80 353 660 933 38%Copper (99.999 wt%) 120 393 1085 1358 29%Brass (60 Cu - 40 Zn) 475 748 900 1173 64%Nickel (99.99 wt%) 370 643 1455 1728 37%Iron 450 723 1538 1811 40%Tungsten 1200 1473 3410 3683 40%

Recrystallization T Melting Point Homologous TemperatureElement (Alloy)

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

http://www.albany.edu/geosciences/wdm/wdmoviep.html

• 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

After 8 s,580ºC

After 15 min,580ºC

0.6 mm 0.6 mm

Grain Growth – How does it occurGrain size is the mean diameter of an aggregate of grainsAs grains grow the number of grains decreases but the mean diameter continues to grow

Mathematical RelationshipsEmpirical Relationship:

Ktdd no

n elapsed time

coefficient dependenton 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

21

ktD

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, G:

G = H – TSG = Go – RTlnQ

• Gibb’s Free Energy is used to determine if a reaction will occur – must be negative

• At equilibrium – G = 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

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…

Gibbs Phase Rule:

P + F = C + 2

P: Number of PhasesF: Degrees of Freedom(What variables may be independently changed without altering state of system)C: Number of Components

Invariant point – no degrees of freedom

Curves represent chemical reaction that describes a phase transformation

Definition of Solubility Limit

• Solubility Limit: Max concentration for which only a single phase solution occurs.

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.

65

Sucrose/Water Phase Diagram

Pure

Su

gar

Tem

pera

ture

(°C

)

0 20 40 60 80 100Co =Composition (wt% sugar)

L (liquid solution

i.e., syrup)

Solubility Limit L

(liquid) + S

(solid sugar)20

40

60

80

100

Pure

W

ater

Effect of T & Composition (Co)• Changing T can change # of phases:

Adapted from Fig. 9.1, Callister 7e.

D (100°C,90)2 phases

B (100°C,70)1 phase

path A to B.• Changing Co can change # of phases: path B to D.

A (20°C,70)2 phases

70 80 1006040200

Tem

pera

ture

(°C

)

Co =Composition (wt% sugar)

L (liquid solution

i.e., syrup)

20

100

40

60

80

0

L (liquid)

+ S

(solid sugar)

water-sugarsystem

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

CrystalStructure

electroneg r (nm)

Ni FCC 1.9 0.1246Cu 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.

Simple solution system (e.g., Ni-Cu solution)

• 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: 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?