Solidification/Nucleation

By

Dr. Hanadi Salem

2

Solidification

After Callister

1. Nucleation 2. Crystallization

3. Grain formation 4. Solidified grains

Nuclei

Introduction • Solidification by phase transition is modelled as

two stage

– Nucleation

• Homogeneous nucleation: The formation of solid phase nuclei in a

solidifying pure metal which proceeds spontaneously. The pure metal supplies atoms for nucleation.

• Heterogeneous nucleation: The formation of solid phase nuclei in a

solidifying liquid at the interfaces of solid impurities. The impurities act as stress

regions, initiating more nucleation sites.

– Growth

Solidification

• Two types of solidification

Viscosity vs. temperature in: (a) Glass formation. (b) Metal casting.

Homogeneous nucleation

r r

Homogeneous nucleation

• No preferred nucleation sites

– Spontaneous

– Random

• Those of preferred sites

– Boundary

– Surface

– Inclusion, …

3.1 Homogeneous Nucleation – Driving Force

Table 8.1 Major Types of Phase Transformations

Type of Transformation Example

1. Vapor liquid Condensation of moisture

2. Vapor solid Formation of frost on a window

3. Liquid crystal Formation of ice on a lake

4. Crystal 1 crystal 2

(a) Precipitation Formulation of Fe3C on cooling austenite

(b) Allotropic α-Fe γ-Fe at 910 ºC

(c) Recrystallization Cold-worked Cu new grains at high

temperatures

From J.D. Verhoeven, “Fundamentals of Physical Metallurgy,” Wiley, 1974

3.1 Homogeneous Nucleation – Driving Force

Table 8.2 Degree of Complexity Involved in Phase Transformations

(a) Structure change

(b) Structure change + composition change

(c) Structure change + strain formation

(d) Structure change + strain formation + composition change

From J.D. Verhoeven, “Fundamentals of Physical Metallurgy,” Wiley, 1974

9

Homogeneous Nucleation

• Assume that the new, product phase appears as spherical particles.

• Free energy released by transformation is proportional to the volume.

• Free energy consumed by creation of interface is proportional to the surface area of particle and the interfacial energy, g.

• Net change in free energy per particle, ∆Gr: ∆Gr = -4π/3 r3 ∆GV + 4πr2 g.

• Differentiate to find the stationary point (at which the rate of change of free energy turns negative).

10

Critical radius, free energy • It starts by spontaneous cluster of atoms coming

closer to form bonding once the surrounding temperature drops with a specie magnitude = amount of undercooling = ∆T

• The clustered atoms are assumed to be spherical. An energy is released to the system = ∆Gv (-ve).

• The cluster is stable if its radius r r* (nulclei)

• The cluster is unstable if radius r r* (embryo)

• A solid-liquid interface is formed at the cluster boundaries, which absorbs heat from the surroundings (+ve).

• d(∆Gr) = 0 = -4π/ r*2 ∆G* + 8πr*g.

• From this we find the critical radius and critical free energy. r* = 2g/∆GV

•

∆G* = 16πg3/3∆GV2

• Crucial difference from solidification: the role of elastic energy!

Not at ∆Gr=0!!!

Local free energy change

1. Liquid to solid 2. Interface

Metal solidification

• Nucleation

• Growth

r r

Local free energy change

1. Liquid to solid 2. Interface

Parameters

For FCC Copper, r*1 nm, which contains 310 Cu atoms in each nucleus.

Effect of Undercooling

• Nucleation rate

• Number of nuclei

• Stable Nuclei size (r*)

• Final grain size

Heterogeneous nucleation

• Nucleation site

– Mold walls

– Inclusion

– Interface

– Surface

– Impurity

Heterogeneous nucleation

Liquid

Inclusion

Nucleus IL

NL

IN

R

r

h

a

The free energy needed for heterogeneous is a function of the contact angle :

The barrier energy needed for heterogeneous nucleation is reduced, and less supercooling is needed. The wetting angle determines the ease of nucleation by reducing the energy needed.

Heterogeneous

nucleation barrier

Homogeneous

nucleation barrier

Homogeneous vs. Heterogeneous Nucleation

Inoculating agents

• Small interface energy

– Similar crystal structure

– Similar lattice distance

– Same physical properties

– Same chemical properties

– Nanoscale

– Uniformly distributed

– Higher Tm

• Small interface energy

– Similar crystal structure

– Similar lattice distance

– Same physical properties

– Same chemical properties

What are the controlling parameters homogeneous nucleation vs. heterogeneous nucleation for Pure solids, alloys and unpure

pure ones.

3.4 Nucleation in the Solid State

MMAT 305

Fig. 3.48 For a coherent thin disc there is little misfit parallel to the plane of the disc. Maximum misfit is perpendicular to the disc.

Fig. 3.47 The origin of coherency strains. The number of lattice points in the hole is conserved.

(a) (b) (c)

Powder Synthesis

Powder Synthesis

Wet chemical synthesis methods constitute excellent routes to a wide range of ceramic powders, inorganic materials and nanostructures. Wet chemical synthesis routes are therefore an important part of our ceramic powder and material synthesis program. To be able provide high quality ceramic powders for our activities we have installed a pilot scale spray pyrolysis equipment where a precursor solution is atomized into a furnace for the formation of oxide powder. Fine ceramic powder is obtained after milling and mild calcination of the powder. By this equipment we can produce several kilogram of high quality powder per day of almost any composition. The precursors used are aqueous solutions of salts (nitrates, acetates, etc) or complexed cations with citric or other acid, EDTA , etc. Examples of powders that have been made include a large number of pure and doped compounds within the coboltite, ferrate, manganite, titanate, nickelate, cerate, niobate, tantalate and zirconate-systems. The powders have been produced for a number of purposes ranging from the processing of high density polycrystalline bulk materials, via thin films to powders used for catalytic purposes.

Powder production techniques

• Any fusible material can be atomized: • Several techniques have been developed which permit large production rates of

powdered particles, often with considerable control over the size ranges of the final particle size population.

• Comminution: grinding, chemical reactions, or electrolytic deposition. Several of the melting and mechanical procedures are clearly adaptable to operations in space or on the Moon.

• Powders of the elements Ti, V, Th, Nb, Ta, Ca, and U have been produced by high-temperature reduction of the correrresponding nitrides and carbides.

• Fe, Ni, U, and Be submicron powders are obtained by reducing metallic oxalates and formates.

• Exceedingly fine particles also have been prepared by directing a stream of molten metal through a high-temperature plasma jet orflame, simultaneously atomizing and comminuting the material.

• On Earth various chemical- and flame-associated powdering processes are adopted in part to prevent serious degradation of particle surfaces by atmospheric oxygen.

Atomization • by forcing a molten metal stream through an orifice at moderate pressures.

• A gas is introduced into the metal stream just before it leaves the nozzle, serving to create turbulence as the entrained gas expands (due to heating) and exits into a large collection volume exterior to the orifice.

• The collection volume is filled with gas to promote further turbulence of the molten metal jet.

• On Earth, air and powder streams are segregated using gravity or cyclonic separation.

• Most atomized powders are annealed, which helps reduce the oxide and carbon content.

• The water atomized particles are smaller, cleaner, and nonporous and have a greater breadth of size, which allows better compacting.

• The usual performance index used is the Reynolds number

R = fvd/n,

• where f = fluid density, v = velocity of the exit stream, d = diameter of the opening, and n = absolute viscosity.

• Drawback: it is difficult to eject metals through orifices smaller than a few

millimeters in diameter, which in practice limits the minimum size of powder grains to approximately 10 μm.

Centrifugal disintegration: o Centrifugal disintegration of molten particles offers one way

around these problems

o Metal to be powdered is formed into a rod which is introduced into a chamber through a rapidly rotating spindle.

o Opposite the spindle tip is an electrode from which an arc is established which heats the metal rod.

o As the tip material fuses, the rapid rod rotation throws off tiny melt droplets which solidify before hitting the chamber walls.

o A circulating gas sweeps particles from the chamber. The chamber wall could be rotated to force new powders into remote collection vessels (DeCarmo, 1979),

Powder compaction

• The density of the compacted powder is directly proportional to the amount of pressure applied.

• Typical pressures range from 80 psi to 1000 psi, pressures from 1000 psi to 1,000,000 psi have been obtained.

• Pressure of 10 tons/in² to 50 tons/in² are commonly used for metal powder compaction.

• Isostatic pressing

Sintering

heating used for bonding of individual particles and once

cooled the powder has bonded to form a solid piece.