physical metallurgy 14 th lecture ms&e 410 d.ast dast@ccmr.cornell.edu 255 4140

Physical Metallurgy14 th Lecture

MS&E 410

D.Ast

dast@ccmr.cornell.edu

255 4140

Solidification

1. Overview of Metal processing

Melt

Cast

Roll Draw

Sheet Wires

Powder Metallurgy starts with powders. Ni powder is made decomposing Nickel Carbonyl, other powders electro-chemically

Notes

Pig Iron is high Carbon

Converter blows oxygen through melt, reducing C.

Mini-Mill: Scrap and ElectricityBig Mill: Iron ore, coal, limestone

Stocked billets reheated (US), German mills use hot billets (continuos processing)

• Not Alloy Hot Rolled Sheets and Plates

· Not Alloy Hot Rolled Narrow Strip

· Not Alloy Hot Rolled Flat Products

· Cold Rolled Sheets

· Electrical Sheets (other than GOES)

· Metallic Coated Sheets

· Organic Coated Sheets

· Tin Mill Products

· Quarto Plates

· Wide Flats

· Non Alloy Merchants Bars and Light Sections

· Alloy Merchant Bars and Light Sections

· Rebars

· Stainless Bars and Light Shapes

· Stainless Wire Rod

· Stainless Steel Wire

· Fittings (<609.6 mm)

· Flanges (Other than stainless steel)

· Gas Pipes

· Hollow sections• Fittings (<609.6 mm)

· Flanges (Other than stainless steel)

· Gas Pipes

· Hollow sections

Products

2001 Data

US production 36 b$, exported to Europe 0.9b$ EU production 66 b$, exported to US 7.5 b$

S.A. production 11 b$, exported to US 3.9 b$ China production 73 b$, exported to US 5.3

Europe (including Russia) ~ 3 times USA

The Bill Gates of his times

…he too, started a foundation

…his house, too was huge

Excursion into the Glory Days of US Steel

Liquid Metals (Melts)

Liquid melts can be modeled as “solids with vacancies” or as stuffed full with dislocation loops that can climb with a

velocity limited by the diffusion of vacancies to and from these hypothetical dislocation loops

Liquids as “solids with ~ 5% vacancies, or 1013 dislo/cm2

• maximum speed of solidification as climb of dislocation loops

vmax D/b 10-5 (cm2/s) /2.10-8 5 m/s

D diffusion coefficient in liquids (generally 10-5); b Burgers vector

• Enthalpy of melting => breaking one of 12 (fcc) or 8 (but remember second nearest neighbors count in bcc !) => Hm

Predicts that if I cool a metal faster than several meters per second it will freeze into a metallic glass.

3. Nucleation

Can be homogeneous or heterogeneous

Nucleus of critical size

Strain energy (liquid) 0, 500 ergs/cm2 , Hm 1eV/atom, hence G is zero at Tm and increases linearly with undercooling as m . In Hg, at m=0.2, the critical nucleus size is 200 atoms.

David Turnbull

Became famous by studying homogeneous nucleation in Hg at GE and moved to Harvard (see Chalmers). I I put this paper on our the website

Once upon a time you could do fundamental research at an industrial research lab.

Phase diagrams are equilibrium diagrams - do not contain kinetics

Heterogeneous nucleation rate can be calculated if surface energy with nucleating foreign substance is known (see Turnbull paper

m

switch

The Cu-Ni phase diagram. There is spinodal at low T.

Amount of undercooling depends on impurities and cooling rate.

Images show that the “first formed nuclei” are coated with an alloy containing less Ni - lowering Ts

- as you would predict from the phase diagram

Metallographic image of Cu60Ni40

Note that under equilibrium you would have a single homogeneous solution. The phase diagram does not kinetics.

Heterogeneous Nucleation

4. Crystal Growth

Extremely well understood in Si.

There is nothing we do not know..

Low T High T

Low Gv High Gv

Driving force is G which increases linearly in T below the melting point.

Control over the thermal gradient is crucial.

G

Undercooling required

Counteracting heat of solidification => needs to be removed from interface

Removal of heat of solidification via

• Radiation

• Conductance

is the rate limiting step in single crystal growth of Si.

Rate Theory

Similar to diffusion derivation

Forward jump => attachment

Backward jump => detachment

Gradient in free energy, not from concentration but from T

Maximum Rate

When not limited by T removal (splash cooling), upper limit is 10 ..20 m/sec for reasons discussed previously. Limit set by Diffusion coefficient divided by “atom size”

Attachment of adatoms

Preferred sites are kinks in surface steps and screw dislocations.

High index planes are difficult to grow - ask me why

Spiral, spirals everywhere..

The growth velocity depends on direction.

High index plans tend to grow faster than low index planes because they are less closed packed. But they are also tighter stacked, so..

T is degree of undercooling

Spiral Growth

Crystal growth rate is proportional to T (which sets the arrival rate)

At constant incorporation rate angular velocity increases linearly to center

? Haasen’s book says T1

Many real systems tend to be diffuse - because it eliminates the difficulty of finding kinks and ledges.

Si is an exception because it has a different coordination number in the solid and liquid

In situ, high T, x-ray imaging shows that liquid droplets are occasionally caught behind the crystallization front.

Since the density of liquid Si > solid Si, they freeze by sending out Si self interstitials

5. Heat Transfer Effects

Small undercooling

Small T gradient

Protrusions into liquid encounter higher T, nucleation rate decreases

Stable x-stal front

• Heat of solidification produces a local bump in T profile

• Negative dT/dx in liquid => unstable

• Any statistical protrusion of S/L interface into L will speed up

Factors favoring Dendritic Growth

High solidification rate => High heat of solidification

Inefficient heat removal

Self heating forces dendrite to seek cooler areas via branches

Cobalt Samarium Copper

Note:

3-D structure

2-D image !

Dentric Growth of solar silicon

How it works

The dendritic web process for growing long thin ribbon crystals of silicon and other semiconductors is described. Growth is initiated from a thin wirelike dendrite seed which is brought into contact with the melt surface. Initially, the seed grows laterally to form a button at the melt surface; when the seed is withdrawn, needlelike dendrites propagate from each end of the button into the melt, and the web portion of the crystal is formed by the solidification of the liquid film supported by the button and the bounding dendrites. Apparatus used for dendritic web growth, material characteristics, and the two distinctly different mechanisms involved in the growth of a single crystal are examined. The performance of solar cells fabricated from dendritic web material is indistinguishable from the performance of cells fabricated from Czochralski grown material. (Seidensticker 1977)

Useful dendrites

Self test

Why does the snow flake have a dendrite structure ?

And why are the branches offset … rather than mirror symmetric ?

6 . Solidification of alloys

Alloy with higher “Tm composition” precipitates first, followed by “lower Tm” compositions. At infinite times, diffusion will homogenize it

Notes

• Coring => Kinetic effect

• Casting => Spatially inhomogeneous cooling => coring

Two useful equations:

a) if convection mixing in liquid, but no diffusion in solid, concentration in solid, cs

(1)

b) If no convection in liquid, no diffusion in solid, concentration,c, of liquid in front of solid

(2)

f is the fraction of liquid solidified, k is partition coefficient

Notes

The first equation is the Scheil equation and the basis for zone refining.

k is the ratio of the slopes of solidus and liquidus

k is determined by making linear fits

Quantitative dendrite formation due to supercooling

• Negative dT/dx in liquid is rare - much rarer then dendrites

• Higher concentration of impurities in front of growing . Crystal (snow plowing), lowering Ts

• “ Dissolved impurity profile” leads to to dendrite growth . even if temperature profile in melt has a positive slope

• Quantitative evaluation by taking equation 2 and a linear fit . to liquidus line (I.e. linear depression of Tm with concentration

• Well known annoyance to crystal growers trying to grow . heavily doped Si single crystals

Constitutional supercooling

Temperature in liquid increases linearly with distance from interface.

Temperature at which liquid freezes increases with distance (less “snow plowing” pile up)

Smallest T slope to suppress constitutional supercooling

Critical T gradient depends on solidification velocity,v, see also eq. 2

Excursion into practical metallurgy: welding superalloys

Lower gradient => cellular

Higher T gradient=> dendritic

Growth Velocity of Dendrite as function of undercooling

• Tip of growing dendrite must have radius of curvature of critical nucleus size, r* - otherwise it would either shrink or grow. As r* = 2/Gv = 2/T (is a constant) dendrite radius proportional to 1/T

• Let tip - hypothetically - grow or shrink => consider heat balance

Hence v 1/(T/r) T2

Cellular dendritic growth Notes

• High undercooling => high growth velocity => high surface to volume required to shed heat => high snow plowing, I.e. segregation

• Low growth velocity => reverse of above

•Dendrite at lower velocity sheds less heat

• Less surface area needed - bulges will do

• Hottest point

• Alloying elements lowering melting point “core” towards bottom of cusps

• Bottom of cups freeze last, incorporate Tm lowering impurities

Simple view

The quantitative theory is rather difficult and concludes that the dendrite spacing is not an equilibrium value but history dependent (how growth velocity was changed). I put a copy of it on our Website - should you be interested.

The segregation of impurity into cell walls has interesting

consequences.

Consider 2-D growth (EFG growth of Solar Silicon)

• The periodic trail of impurities triggers the formation of twins

• The result is an array of twin boundaries parallel to the ribbon

Liquid Silicon is pulled up by capillary forces between high purity graphite dies and pulled as a thin sheet from the top of the die. The method avoids the wasteful cutting of Si single crystals into wafers

Excursion into Low Cost Solar Silicon Growth

Etched High resolution Raman

High resolution TEM showed that the lattice distance of the {111} twin planes in EFG material is reduced by about 15%, as compared to the regular silicon–silicon bond length across the twin plane. This can be explained by the insertion of a single carbon layer on the (111) twin plane (Fig. 8) [10]. Ab-initio simulations of the total energy of the proposed lattice structure and the comparison with high resolution electron microscopy (HREM) images are in

quantitative agreement with the model [26].

The twin boundaries are single layer insertion of Carbon atoms.

The carbon atoms originate from the graphite die (the surface of which converts to SiC)

Lower pulling speeds would reduce dendritic growth front but would worsen throughput => increase cost

C is more soluble in liquid than in solid Si

At three-phase eutectic equilibrium (SiC) + Si (liquid) + Si (solid), the C solubility is ~ 9 at. ppm in the solid and ~ 260 at. ppm in the liquid.

Why Carbon “drops out”

The End