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Nagy El-Kaddah

MTE 449 Powder Metallurgy

Chapter 4

Solidification and Microstructure ofAtomized Powders

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Analysis of Solidification Processes

To produce the desired microstructure of the powder in

atomization processes, one need to control process

variables that influence the rate of solidification of the

atomized droplets

The first step toward this goal is to identify key

solidification parameters through the analysis of heat

transfer processes and nucleation and growth kinetics inthe droplet

Due to complexity of solidification phenomena, the

analysis should involve every available experimentallydeveloped relationships for describing microstructure

features of the material system

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Formulation of Heat Transfer Problem for a Droplet

For an atomized metal droplet in tens of microns size range, due to high

thermal conductivity, the rate of heat flow from the droplet to the surround iscontrolled principally by convective resistance with practically no temperature

gradient in the droplet.

By assuming that the droplet is space wise isothermal and temperature varying

only with time, from overall energy balance, the temperature history of the

droplet is given by

)()();()(

)(

)(

2244

,

,

**

ooradoradorad

oconvconv

ssp

sl

sl

p

llp

pradconvp

TTTThTThTTq

TThq

TTc

TTT

TT

Lc

TTc

CqqA

td

TdCV

+===

=

>>

+

=+=

where V and A are volume and surface area of the droplet, Cp is specific heat, L

is latent heat of fusion, To is room temperature, hconv and hradare convective and

radiation heat transfer coefficients, is Stefan-Boltzmann constant and is

emissivity of material

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Calculation of Cooling Rate and Solidification Time

Cooling Rate

Calculation of the cooling rate to predict the grain structure of solidified the

particle is based on the cooling rate of the droplet at the liquidus temperature

(TM), which may be written as

)()(

6

,

oMradconv

VlpTThhDc

k

td

Td

+=

where DV is equivalent volume diameter and k is shape factor. The convective

heat transfer coefficient, hconv, may be estimated from the following correlation

g

ggp

g

Vgg

g

Vconv

K

cDV

K

DhNu

Nu

,

3/1805.0

PrRe

PrRe0266.0

====

The temperature history of droplet during cooling from its initial temperature toits freezing temperature is given by

where KV is thermal conductivity of the surrounding gas

+=

Vlp

radconv

oi

o

Dc

thhk

TT

TT

,

)(6exp

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Calculation of Cooling Rate and Solidification Time (cont.)

Solidification time

Solidification time is the time taken to cool the droplet to the liquidus

temperature and to freeze the droplet.

The cooling time can be evaluated from temperature history equation when

the droplet reached TM

Since the latent heat is much higher than the specific heat, the freezing time

can be directly estimated by equating total heat losses to total heat released

during solidification

+=

oM

oi

radconv

Vlp

CTT

TT

hhk

Dct ln

)(6

,

)()(6 oMradconv

Vf

TThhk

DLt

+=

From these two equation the solidification time is

+

+

=

)(

ln

)(6

,

oMoM

oilp

radconv

VS

TT

L

TT

TTc

hhk

Dt

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Prediction of Grain Structure

For all solidification processes except rotating disk, the structure of solidified

powders is dendritic, and dependence of the secondary arm spacing, whichrelates to the grain size, on the cooling rate (class 8) is given by

where C and n are constants specific to the alloy.

The value of n is between 0.5 and 1

n

dt

dTC

=

From the above analysis, the process variables affecting cooling rate, and

hence the grain structure are

Size of the droplet

Droplet velocity

Temperature of the melt

Gas used in the atomization chamber

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Typical Cooling Rates and Microstructure Characteristics

of Atomized Steel Powders

Process D50, m , m dT/dt, C/s h, J/m2.s.CGas atomization 75 2 2. 104 1. 103

Centrifugal atomization 150 3 5. 103

5. 103

Water atomization 1000 7 4. 102 3. 103

Melt explosion 650 7 4. 102 2. 103

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Nucleation and Growth Kinetics

Solidification starts with nucleation of the solid in the melt and followed by

growth of formed nuclei.Nucleation

It is a non-equilibrium process, and transformation of the liquid to solid takes

place in under cooled liquid below its melting points.

The deviation of the bulk free energy of the liquid from its equilibrium value at

the melting point (Gv =Go T) causes the atoms to form solid clusters in themelt (homogeneous nucleation) or to deposit on the surface of dispersed solid

phases such as nonmetallic inclusions in the melt (heterogeneous nucleation)Homogeneous Nucleation Theory

Clustering of the atoms is a probabilistic process involving clustering few atoms

to form a solid phase and the growth of the cluster (diffusion).

This process involves an increase of the energy of the cluster due to the

formation a new surface (surface energy)

As a result not all formed clusters survive, only the ones (nuclei) which do not

increase the energy of the system

N l i d G h Ki i ( )

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Nucleation and Growth Kinetics (cont.)

The rate nucleation is determined from

1. Extent of deviation from equilibrium state, i.e. (Gv)2. Rate of growth of initially formed cluster to its critical size

Undercooling has opposite effects on these two kinetic parameters.

Higher undercooling favors formation of clusters through Gv, and hindersgrowth by slowing mobility of atoms

=

Tk

E

TTHk

TII

f

Mo exp

3

16exp

22

23

043

4 23 =+ RGR v

where Io is nucleation rate constant andE is activationenergy for atom motion

Maximum nucleation rate occur at moderate

undercooling High undercooling suppress nucleation and

favors solidification of amorphous metals

nucleation

rate, I

Homogeneous Nucleation Theory (cont.)

The condition for formation of a stable cluster

vGR

=

3 The critical size nucleus

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Nucleation and Growth Kinetics

Heterogeneous Nucleation

The heterogeneous solid phases in melt act as nuclei if they overcome interfacialbarrier to form a grow on them

Based on this concept a number of models were proposed to predict nucleation

rate in terms to

Number of available heterogeneous particles in the melt (Ns)

Undercooling of the melt and empirical growth rate constants ().

Hunts model

Growth Kinetics

The growth of formed nuclei is described empirically in terms of undercooling

2TdtdR =

=2

21 exp

T

NI s

The nucleation and growth theories are foundation of all solidification models

for predicting grain and microstructure of solidified materials.

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Time-Temperature-Transformation (TTT) diagram

The TTT diagram provides a

practical way to predict solidified

phases and their amounts for any

material during cooling

It maps the times for nuclei toform and to grow in crystalline

phase as function of temperature.

The shortest nucleation time is

intermediate undercooling wherenucleation rate is maximum.

The form phases are determined

from superimposing the cooling

rate from heat transfer analysis

path i normal cooling, crystalline solid

path ii rapid solidification, amorphous solid

path iii partial transformation, mixed microstructure; some crystals and some amorphouspath iv atomization with intermediate quench - gives all amorphous

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Effect of Particle Size on Amorphous/Crystalline Ratio

Smaller particles have higher cooling rates than larger ones

They are more likely to experience high undercooling which favors

solidification of amorphous structure

The percentage of amorphous phase increases with

Decreasing particle size Increasing heat transfer coefficient by using gases with higher thermal

conductivity such as H2 and He.