Experiments on Nucleation in Different Flow Regimes Summary of ...

Experiments

on Nucleation Summary P.I.: Robert

Period

of Research:

in Different

Flow Regimes

of Research J. Bayuzick

June 1, 1996 to April

Vanderbilt University 610 Olin Hall 2400 Highland Ave. Nashville, TN 37240 Gram Numb,_i-: NCC8- i 0 i

30, 1999

Introduction The vast majority Understanding

of metallic

determines

the properties

stable

forms

solid

undercooling in order Early

differential

As such,

in nucleation

kinetics

were

dispersed

in a medium,

behavior.

Statistics

experiment,

are derived

determinations. the release

assumption

of isothermality

With

controlled

on a single

experiments

on single

measured must

exceptionally

Experimental Levitation

affects

are

the nucleation

observed

in a single

adds to the uncertainty

can be controlled

quite

of particles

approach

nucleation

to the study one sample

well before

of the the onset

complicates

have

of nucleation

to nucleation

process

fully developed

the analysis

of Skripov

are directly

observable.

The nucleation

pyrometry,

the mass

on the sample.

of

the

temperature

is known,

to isolate

[7]. in a multiple

of nucleation of these

can be

and post processing

are that temperature

and it is not possible

from

[8]. The advantage

of the sample

The disadvantages

kinetics repeatedly

can be derived

the suggestions

of refractory

on single experiments

samples.

materials Two

are possible;

in ultra high vacuum

experimental

processing

were conducted for contaminants

on zirconium. Liquid zirconium contained in the bulk material

environment. of molten

based

zirconium,

kinetic

experiments

theory

[9]. The advantage

levitation

in low earth orbit on TEMPUS

Oxides,

experiments

methods

electrostatic

electromagnetic

Ground

have

materials

during

of the nucleation

The authors

high precision,

techniques

Since

and

measurement

specific

heterogeneous

dispersions.

processing

studies

the surface

which

[ 1-6].

analysis

Method

high vacuum

vacuum

of particles

to undercool

following

optical

can be conducted

have

kinetic

sample. samples

These

methods

thermal

experiments.

another

it is possible

is that the samples

sites as in droplet

these

has enabled

by noneontact

analysis

of fusion

such that the statistics

experiments experiments

temperature heat

during

techniques

manner,

though

of the latent

processing

levitation

studies. interface

size distribution

phenomena

dispersion

differential

experiments.

of the emulsion/metal

a finite

nucleation

by droplet

recently

with these

the first

of

and alloys.

used for kinetic

from the large number

have

Even

nucleation,

been

are difficulties

the character

but dispersions

Containerless

have

there

and more

in turn,

where

the degree

to understand

in metals

phase. which

is nucleation,

determine

accomplished

and others,

calorimetry

however,

kinetics

it is important

formation

from the liquid

trol microstructure,

of solidification

Nucleation

or glass

scanning success;

kinetic

selection.

was used by Tumbull

to con

The genesis

phase.

solidification

experiments

are solidified

is essential

the liquid

and phase

Dilitometry

materials

process

of materials.

from

to control

enjoyed

engineering

the solidification

nitrides,

with electrostatic

are viable

based

to conduct

where

ultra

experiments

[9]. Such experiments,

do not exist in the melt, and vacuum

levitation

and yield results

in ground

an avenue identified

reported

and here,

is an excellent solvent and has a high solubility as well as those contaminants found in the

and carbides

for the materials

provides

have been

which

have

levels shown

used

in the liquid prior to nucleation. The purpose of nucleation examine the effects of fluid flow on nucleation.

in this study.

that the statistical

are consistent

of low earth orbit experiments

and do not form on

with classical

is the ability experiments

to vary

nucleation

nucleation

the flow conditions

in TEMPUS

was to

The primary

evidence

is not necessary mechanism Simply

to make

stated,

distribution

for a change

to know

the comparison

if the nucleation

of nucleation

Null hypothesis significant

in nucleation

the functional

difference

of nucleation is different

The null hypothesis The mean

nucleation

mean

therefore

B are identical.

However,

temperature

in experiment

A and experiment

B are different.

and HI supported,

then the means

rate as a function

limit theorem

states

particularly in invoking

distributions

Results

of the parent distributions

of temperature

that the means

those

energies,

limit theorem,

and the means

from a population

distributed.

at low activation

are different

and

is different.

of samples

is not normally

the central

are necessary,

distribution

Two

(HI) is:

even if the population

distributions,

conditions.

a

the null hypothesis.

A and experiment

the nucleation

The central

reflects

in experiment

nucleation

normally,

Nucleation

will be distributed

temperature

are not normally

no assumptions

of two samples

about

distributed.

the underlying

can be compared

by using

Student's

experiments

on

"t"

[ 10].

and Conclusions

Statistical

distributions

TEMPUS

during

power field.

temperature

hypothesis

If rio is rejected

then the parent

of two samples

for two experimental using

conditions.

is different.

in means

of means

It

(Ho) is:

and, the altemate The

flow

conditions,

undercooling

distributions

by analysis

undercooling.

or the operative

two different

for two experimental

if the difference

of parent

sets of data (A and B) can be compared

rate equation, under

and the mean

is used to determine in the means

is a shift in the mean

behavior

rate is different

events

testing

behavior

form of the nucleation

was

the MSL-1

set to the lowest

One sample

variables supply sample,

settings

except

were

used;

numbers

corresponding The experiments

on space

power

melted

of about were

and cooled power

power

flow calculations

interspersed

power

to minimize

holding

on cooling.

capable

for the lower with flows

is continuing which

all experimental different

positioning

rate for this sample

any effect

positioner

power

of approximately to characterize

is know

to be greater

of sample

the heater

from the positioning

Two

of stable

cooling

free cooling

came

50Ks _, and at the high positioner

flow regime

200111 ]. Modeling positioner

to freezing,

radiation

rate was

During

to the sample

settings

The pure

the cooling

in "free cooling" Columbia.

input

positioner

power.

was in the laminar

to the higher

shuttle

and the power

the lowest

rate was 48Ks 1. Fluid liquid

were generated

for the positioner

and a high positioner

undercooled Reynolds

mission value,

was repeatedly

constant

At the low positioner cooling

of undercoolings

power of the was 53Ks 1. power

indicate

the the

4 cm s "_and the flow regime

than the low power.

history

on the comparison.

The distributions shown

ofundercoolings

in figure

hypothesis change

1. A t-test for mean undercooling

and rejects

the alternate

in the nucleation determinations

expression

[12] are given

based experiments to those

in table I. These

uncertainty

Other experiments undercooled

were

melt

caused

surface

temperatures which,

to determine

at the desired

experiments

was within

near the melting

the classical

temperature

and pulsing

were followed

of the temperature

The maximum

and cooling

tension

of the

and viscosity modulation

or modulation

of the distributions

temperature,

at heater voltages

calorimetry was used to

of the heater was used

of the sample.

by free cooling

the bounds

mean

in the ESL if volume

melt, the heater power

the temperature

are

in the electrostatic

by noncontact

in the undercooled

values

values

sample

on MSL-I.

the surface

with ground

(ESL) tg). The kinetic

to be lower because achieved

the null

is no significant

nucleation

are consistent

levitator

the heat capacity

or to modulate

(and heater powers)

in all cases

assuming

translations

there

tested.

on a machined

to the maximum

fits are

level supports

and are lower than the maximum are believed

kinetic

revealed

determinations

obtained

experiments

oscillations

kinetic

by sample

scale

conducted

these

hold liquid samples to excite

samples,

[13], and to examine

[ 14]. To accomplish

experiments

using the electrostatic

determinations

undercoolings from MSL-1 rate are considered.

at the 95% confidence These

from the distributions,

K_=1043, AG*=88kT)

The kinetic

measurement

made

for arc melted

and the nucleation

in the range of flow conditions

on zirconium

(ATmean=348K, levitator.

hypothesis.

behavior

The kinetic

similar

for these experiments

Experiments

to the nucleation

in the previous above

at low

temperature,

experiments.

In

220 V, the undercooling

of

the samples was significantly limited as shown in figure 2. At 220 V heater the flows are estimated to be 50 cm s_. Analysis by Hyers and Trapaga indicates that at these flows the dynamic cause

pressure

cavitation

pressures

is equal to the static pressure in fluid flows

to raise the melting

nucleation

of the solid

Additional

evidence

compilation measuring average standard

by cavitation hemispherical

and TEMPUS

creates

the Clapyeron

is known

equation

such that

temperature

emissivity

of Zr pendant

temperature.

(Cp/e)

in figure

experiments.

determinations

from the drop

drops, the free fall time to recalescence

In 135 experiments

to 0.057

g) were evaluated

radiation

equation

solving

cooling

(1 o). The TEMPUS

determinations apparently

except

13-15%

temperature

for Cp/e. The average

modulation

with masses

for the experiment

modulation a smaller

of

boxcar value

at the melting

in

Cp/_ in the measured

experiment

at the melting

modulation

in temperature

curves

over the temperature the bounds

temperature.

indicate

In essence,

for the applied

power

is

that there is no

the melting modulation.

to the

other

range and do not support the findings temperature.

mass

range was

of these

This determination

determinations

by

around 0.23 g, the

fit of the cooling

Cp/e data falls within

higher than the rest of the data. Other

dependence

data showed

by a sliding

A

3. The drop tube data was derived

ratio of specific heat to total hemispherical emissivity was 1.57 with a one sigma deviation of 0.03. In the electrostatic levitator, 332 cooling curves (four samples,

1.54 _+0.12

to

sufficient

can be found in the modulation

is shown

range from 0.013

TEMPUS

through

bubbles

which

[ 16-18].

heat/total

and the nucleation

a condition

of cavitation

point of the material

occurs

levitator

the release

vacuum,

[15]. The collapse

of nucleation

of specific

tube, electrostatic

in the samples,

of the

temperature The

temperature frequency

modulations

in this experiment

of O.1Hz. A cyclic

subsequent

remelting

provides

were

1OK above

phase transformation

including

a heat source

during cooling

explains the decrease in the temperature modulation is consistent with the above fluid flow calculations. These

experiments

indicate

phenomenon

occurs,

undercooling

in the higher

induced

the melting

point.

at a

and

and a heat sink during melting

on nucleation

nucleation

temperature

by cavitation

around the melting

that fluid flow has no effect

and that cavitation

below

nucleation

which

This explanation

until the cavitation

is responsible

for limiting

bulk

flow regimes.

References 1.

D. Tumbull,

J. Chem.

Phys.,

20 (3), 411 (1952).

2.

D. Turnbull,

J. Chem.

Phys.

18, 198 (1950).

3.

J.J. Richmond,

Processing: MD, 4.

J.H. Perepezko, Solidified

136, ASTM-STP

and K.P. Cooper,

III" (R. Mehrabian,

S.E. LeBeau, Powder

W.T.

Kim, D.L.

6.

G.A. Merry

7.

C.W.

Zhang

209 (1994). V.P. Skripov,

W.H.

in "Current

and H.J. Scheel,

9.

Morton,

W.H.

1903 (1998). G.K. Bhattacharyya

and Sons,

New

York,

Acta.

ed.),

in "Rapid

pp. 90-95,

Solidification

NBS,

Gaithersburg,

Alloys"

(M.E.

in Materials

Conference

Jr., eds.),

Science,

Holland

Robinson,

Crystal

Publishing

A. Rulison,

"Statistical

(1991).

Methods

Mat.

Growth

Sci. Eng.

in Materials,

Co., New J. Watkins,

York, Acta

and Concepts",

1977.

11.

R. W. Hyers

and G. Trapaga,

MIT,

12.

D. Tumbull,

and J.C. Fisher,

J. Chem.

13. 14.

I. Egry; J. Mat. Sci. 26 (1991) H.J. Fecht and W.L. Johnson;

15.

I.S. Pearsall;

16.

J.D. Hunt

17.

R. Hickling;

Nature,

18.

J.J. Frawley

and W.J.

I. Mech.

July

J. Appl.

v. 206, no.4987 Childs;

personal Phys.,

communication. 17 (1), 71 (1949).

2997-3003. Rev. Sci. Instrum.

E., CME,

and K.A. Jackson;

pp. 118-

p. 1447.

and M.B.

R.J. Bayuzick,

and R.A. Johnson;

2487

V. 32, no. 9 (1984)

p. 328, North

Hofmeister,

in "ASTM

Fine and E.A. Starke,

Met. Trans. A 22A,

R.J. Bayuzick,

Topics

eds.),

and G.J. Hildeman,

1985. Metall.

Hofmeister,

2" (E. Kaldis C.W.

PA,

and B. Cantor,

and H. Reiss,

Morton,

B.A. Mueller,

Aluminum

890. Philadelphia,

5.

(6), 10.

S.E. LeBeau,

and Technologies

1982.

on Rapidly

(1-2), 8.

J.H. Perepezko,

Principles

Trans.

V. 65, no. 5 (1991)

1974, p. 79. Phys.

V. 37, no. 1 (1966)

(1965)

p. 915.

AIME,

v. 242, Feb.

p.254.

1968, p.256.

p. 1299.

A178 Vol.

1977. Mater.,

John

46

Wiley

Table I: Results Classical

of kinetic

Tumbull-Fisher

determinations ex _ression

Positioner Power

of nucleation

distributions

from MSL-I

was used to fit the distributions. Mean

Undercooling ATavg± 1o (K)

log Kv (o=3.0)

AG' (kT) (0--7.0)

Low

333.8.4- 4.8

29

62

High

334.7 4- 3.2

34

72

tat} ,=l.=,m

¢... (1)

IJJ (1) m

tO ¢.3

09

310

320

330

340

Undercooling Figure

1" Two distributions

1R. The Low Positioner the High

Positioner

R. The

from "flee

distribution

is believed

cooling"

350

(K) experiments

is in the laminar

to be in a transitional

on MSL-

flow regime flow

regime.

and

35o[_ o_ _/// _12oo _oo±.,1o..°_..,_ ° / / /I ,ooo _= _s°/ °_'""'-'_ II I f _oo=="g 2o0t

"="'°"'"

(">

//.

/

I

150

-_ :_

J_ 100 /

"'W/

C_o..=.b,r=1

_

_. 8

Tooos

t.-

_ .....+ ,oo --!E

/ /

IZ_F,_,.I

a

50

200

0

0 0

100

200

300

Applied Heater Voltage (V)

Figure

2: Undercooling

obtained

samples

as a function

of applied

positioner

voltages

are represented

from all TEMPUS heater

voltage.

as one point

quadrant

of the graph.

The right ordinate

the drop.

The curved

lines are the relations

for a spherical sample, laminar flow models.

oblate

and prolate

experiments

The distributions

on two zirconium with differing

with error bars in the upper

is the calculated between ellipsoids

minimum

heater

voltage

applied

left hand

pressure

difference

and minimum

(-)-5% deformation)

calculated

1.601.50-

J=

_-._= "_ E 1.4ot3,, 1.30

18'00

19'00

20'00

2100

22'00

Temperature (K) Figure thick

3: The ESL data as a function black

line. The average

of temperature

ESL data over

is plotted

the temperature

represented

with filled squares.

The drop tube data temperature

represented

with a thin straight

line and the mean

as open given

squares.

as filled

The modulation circles.

calorimetry

range

and one sigma

results

as the is

range

is

points

from TEMPUS

are

pressure using

in