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Materials Science and Engineering A 473 (2008) 206–212

Kinetics of heterogeneous nucleation of gas-atomizedSn–5 mass%Pb droplets

Shu Li a, Ping Wu a, Wei Zhou a, Teiichi Ando b,∗a Department of Applied Physics, School of Science, Tianjin University, Tianjin 300072, China

b Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115, USA

Received 21 November 2006; received in revised form 15 March 2007; accepted 21 March 2007

bstract

A method for predicting the nucleation kinetics of gas-atomized droplets has been developed by combining models predicting the nucleationemperature of cooling droplets with a model simulating the droplet motion and cooling in gas atomization. Application to a Sn–5 mass%Pblloy has yielded continuous-cooling transformation (CCT) diagrams for the heterogeneous droplet nucleation in helium gas atomization. Bothnternal nucleation caused by a catalyst present in the melt and surface nucleation caused by oxidation are considered. Droplets atomized at a

igh atomizing gas velocity get around surface oxidation and nucleate internally at high supercoolings. Low atomization gas velocities promotexidation-catalyzed nucleation which leads to lower supercoolings. The developed method enables improved screening of atomized powders forritical applications where stringent control of powder microstructure is required. 2007 Elsevier B.V. All rights reserved.

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eywords: Gas atomization; Droplet nucleation; CCT diagram

. Introduction

Gas atomization provides an essential means for metallicowder production and is the most widely used commercial rapidolidification process (RSP) for constitutionally complex alloysuch as tool steels and nickel-based superalloys [1–3] because ofts ability to mass-produce high-performance pre-alloyed pow-ers at low cost.

Gas atomization, however, inherently produces droplets ofon-uniform diameters that must solidify at different coolingates. Therefore, atomized powders are often sieved to removeowder particles of undesirable mesh sizes in order to guar-ntee product quality. Such sieving is justified primarily onhe basis of empirical relationships between cooling rates and

icrostructural parameters such as the secondary dendrite armpacing (SDAS) [4]. This, however, is misleading because its the prior supercooling, and not necessarily the cooling rate,

hat determines the extent of rapid solidification during recales-ence [5–9]. Droplet supercooling is determined by the kineticsf droplet nucleation that depend upon the complex interplay

∗ Corresponding author. Tel.: +1 617 373 3811; fax: +1 617 373 2921.E-mail address: tando@coe.neu.edu (T. Ando).

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921-5093/$ – see front matter © 2007 Elsevier B.V. All rights reserved.oi:10.1016/j.msea.2007.03.109

mong the potency and density of nucleation catalysts androplet cooling conditions [9]. Droplets of the same size mayucleate at different temperatures if produced under differenttomizing conditions or from different melt stocks. Therefore,n ability to predict the complex nucleation behavior of atom-zed droplets is essential in screening atomized powders intoroducts of desired quality.

The nucleation of molten alloy droplets has been studiedxtensively using various techniques including hot-stage dropletispersion methods [10–12], emulsification methods [13–17],evitation melting methods [18–20] and drop tower methods21,22]. Most of these studies, however, only address the nucle-tion of small stationary droplets except for the ones that usedrop tower methods. Recently, the nucleation kinetics of travel-ng Sn–5 mass%Pb droplets have been studied using a controlledapillary jet breakup process [23] that can generate a steamf mono-disperse droplets [24–28]. The determined nucleationinetics were presented in the form of continuous-cooling trans-ormation (CCT) diagrams specific to the capillary jet breakuprocess, for both surface and internal heterogeneous nucleation

26,28,29].

The latter models can also predict nucleation temperatureor any other droplet solidification process provided that theroplet cooling schedule is known. The present study combines

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S. Li et al. / Materials Science an

he nucleation-temperature computation models [26,28,29] andmodel for droplet cooling in gas-atomization [30] to pre-

ict the nucleation kinetics of gas-atomized Sn–5 mass%Pbroplets in relation to the droplet diameter, the atomizingas velocity and the oxygen potential in the atmosphere.he ultimate goal of the study is to provide a theoreticalasis for the screening of gas-atomized powders and opti-izing process parameters for maximum yields of useful

owders.

. Models

The nucleation temperature of an alloy droplet, TN, dependsn the droplet size, the cooling condition (schedule) and theensity and potency of heterogeneous nucleation catalysts. Theensity and potency of nucleation catalysts depends on alloyurity and may vary from an alloy melt to another. Oxide for-ation on the surface of the droplet may also increase the

otency for surface nucleation [24,31,32]. In any droplet solid-fication process, the droplet size and cooling conditions cane varied independently, for example by using different cool-ng media, such as argon and helium. Even with the sameooling gas, different droplet solidification processes produceifferent droplet cooling schedules. For example, in centrifu-al atomization, droplets, once they are formed, only deceleratehile traveling in a stationary gas atmosphere. This causes the

onvective cooling rate to decrease monotonically with time.n gas atomization, however, the relative velocity between theroplet and the gas (which determines the instantaneous con-ective cooling rate) has a high initial value but decreasesharply to a minimum as the droplet is accelerated to theas velocity, and increases again as the gas velocity quicklyttenuates while the droplet decelerates more slowly due tonertia effects. This produces complex cooling schedules forroplets in a gas-atomized spray as addressed by Liu et al.n their modeling of the droplet cooling in gas atomization30].

The nucleation-temperature prediction models presented inefs. [26,28,29] treat the droplet size, the cooling condition

schedule) and the density and potency of heterogeneous nucle-tion catalysts as de-coupled parameters, and therefore arepplicable to the complex conditions of droplet cooling encoun-ered in gas atomization. These models and Liu et al.’s modelor the cooling of gas-atomized droplets [30] are first out-ined below and then applied to the nucleation of gas-atomizedn–5 mass%Pb droplets in the sections that follow.

.1. Prediction of nucleation temperature

.1.1. Oxidation-catalyzed surface nucleationThe nucleation of a solid in a liquid usually takes place hetero-

eneously, either within or on the surface of the liquid. Internalucleation is catalyzed by a heterogeneous nucleant that pre-

xists in the liquid, but surface nucleation may be caused byxide formation on the surface of the melt [25,31,32]. The ear-iest model for the prediction of TN for the surface nucleationf a cooling liquid was presented by Dong et al. [26] in which

Tmi

ineering A 473 (2008) 206–212 207

ontinuous-cooling nucleation kinetics are computed from

TN

TL

axM

(TL − T )2 exp

[− Q

RT− N

T (TL − T )2

] (dt

dT

)dT = 1

(1)

here a is the surface area of the liquid, x the fraction of theurface that is potent for nucleation, Q the activation energy forhe diffusion in the liquid, TL the liquidus temperature of thelloy, dt/dT the inverse of the instantaneous cooling rate, and Mnd N are material-specific constants. The values of M and N areetermined for the alloy of interest by substituting experimentalN data and cooling schedules in Eq. (1).

Using Eq. (1) for oxidation-catalyzed surface nucleationequires an expression for x which should increase from zerooward unity as oxidation proceeds. Assuming that the oxida-ion on the liquid surface proceeds by the nucleation and growthf disk-shaped oxide islands, Li et al. obtained [29]:

= 1 − exp

{−

∫ T

T0

PO2C exp

(− E

RTi

)π

×[∫ T

Ti

�G · exp

(− E

RT

) (dt

dT

)dT

]2 (dt

dTi

)dTi

}(2)

here T0 is the initial temperature, PO2 the oxygen partial pres-ure in the gas, E and �G are the activation energy and drivingorce for oxidation, respectively, and C is a constant specific tohe oxidation reaction of concern. Substituting Eq. (2) in Eq. (1)ields an equation for oxidation-catalyzed surface nucleation ofdroplet that contains four constants, M, N, C and E. The four

onstants are first determined for the alloy of interest by sub-tituting four sets of experimental TN data obtained for knownroplet cooling schedules, i.e., T0 and dt/dT. Eq. (2) then predictsN for any cooling schedule.

.1.2. Internal nucleationThe nucleation of a solid in a molten droplet may also be

atalyzed by an internal nucleant. Wu and Ando re-write Eq. (1)or such internal heterogeneous nucleation as [28]:

TN

TL

vdM∗

(TL − T )2 exp

[− Q

RT− N∗

T (TL − T )2

]dt

dTdT = 1 (3)

here vd is the volume of the melt (droplet) and M* and N*re constants whose values are specific to the alloy of inter-st. Solving Eq. (3) with two sets of experimental nucleationata and cooling schedules yields the values of M* and N*hich are then used in Eq. (3) to compute TN for any cooling

chedule.

.2. Droplet flight dynamics and cooling in gas atomization

The cooling schedule of the droplets in gas atomization, i.e.,0 and dt/dT in Eqs. (1) and (2), can be calculated with theodel presented by Liu et al. [30]. In their model, the gas flow

s assumed to be laminar so that the velocity of a droplet traveling

2 nd Engineering A 473 (2008) 206–212

i

wtditEf

h

wvof

−

wT

3

3

tTipcgtsVttf

3

auidiecba

Fig. 1. Calculated velocities of helium gas-atomized Sn–5 mass%Pb dropletsof various diameters. The gas velocity is reproduced from Ref. [30] (initial gasvelocity = 1700 m/s).

Table 1Thermophysical data required in Eqs. (4)–(6) obtained from Ref. [30]

Property Symbol Value Unit

Density of particlea ρd 7298 kg m−3

Gas density (helium) ρg 0.18 kg m−3

Added mass effect coefficient CA 0.5 –Thermal conductivity (helium) kg 0.2 W m−1 K−1

Dynamic viscosity (helium) ηg 2.5 × 10−5 Pa sHeat capacity (helium) Cg 950 J m−3 K−1

Heat capacity of particle Cp 176 J m−3 K−1

S

htFcalculated from Eq. (6) with the values of h and Tg = 298 K.A strong dependence of cooling rate on droplet diameter isapparent.

08 S. Li et al. / Materials Science a

n the gas is calculated from [33]:

4

3πr3

ddVd

dt= 4

3πr3

d(ρd − ρg)g − Cdπr2d

2ρgV |V |

−4

3CAπr3

dρpdV

dt(4)

here rd is the droplet radius, ρd the density of the droplet, ρghe density of the gas, g the gravitational acceleration, Cd therag coefficient, CA the added mass effect constant [33], and Vs the relative velocity defined as the droplet velocity (Vd) minushe gas velocity (Vg). With the relative velocity calculated fromq. (4), the convective heat transfer coefficient, h, is calculated

rom the Ranz–Marshall equation [34]:

= kg

D

[2.0 + 0.6

(VDρg

ηg

)1/2(Cgηg

Kg

)1/3]

(5)

here kg, ηg, and Cg are, respectively, the thermal conductivity,iscosity and heat capacity of the gas and D is the diameterf the droplet. The droplet temperature T is then calculatedrom

vdρdCpdT

dt= a[εδ(T 4 − T 4

g ) + h(T − Tg)] (6)

here ε is the emissivity, δ the Stephan–Boltzmann constant andg is the temperature of the gas.

. Application to gas-atomized Sn–5 mass%Pb droplets

.1. Droplet motion

The above models were combined to predict the nucleationemperatures of helium gas-atomized Sn–5 mass%Pb droplets.he gas velocity, Vg, in gas atomization depends on the atom-

zing gas pressure and the type of atomizing nozzle used. Fromitot-tube pressure measurements and isentropic gas dynamicsalculations, Liu et al. [30] were able to estimate Vg for heliumas in ultrasonic gas atomization [35] as a function of the dis-ance from the atomizing nozzle. The results indicated that aupersonic zone existed within about 15 cm of the nozzle whereg had a high constant value of about 1700 m/s and that beyond

his zone Vg rapidly decreased to below 100 m/s. Fig. 1 showshe Vg as a function of the distance from the nozzle reproducedrom Liu et al.’s work.

.2. Droplet temperature

Fig. 1 also shows the velocity of Sn–5 wt.%Pb helium gas-tomized droplets, Vd, calculated for various droplet diameterssing the profile of Vg in Fig. 1 and the thermophysical data givenn Table 1. As expected, Vd increases with decreasing dropletiameter. Also, droplets, regardless of their size, are acceleratednitially until their velocity reaches the gas velocity and decel-

rated as the gas falls behind the droplets. Consequently, theonvective heat transfer coefficient, h, has a high initial valueut decreases rapidly as the droplet catches up with the gasnd sharply increases again as Vd exceeds Vg. Fig. 2 shows the

Fai

tephan–Boltzmann constant δ 5.67 × 10−8 W m−2 K−4

a Calculated for Sn–5 mass%Pb by the rule of mixture.

calculated with Eq. (5) as a function of the distance fromhe nozzle for Sn–5 mass%Pb droplets of various diameters.ig. 3 shows the cooling curves of the Sn–5 mass%Pb droplets

ig. 2. Heat transfer coefficient calculated as a function of the distance fromtomization nozzle for different Sn–5 mass%Pb droplets (initial gas veloc-ty = 1700 m/s).

S. Li et al. / Materials Science and Engineering A 473 (2008) 206–212 209

Fh

3

vidnobvioawbcspdob(tadMn

TNb

E

123456

Table 3Values of material-specific constants in Eqs. (1)–(3) calculated from the data inTable 2

Constant Value Unit

M 2.7268 × 1015 K2 m−2 s−1

N 1.8467 × 106 K3

C 3.0063 × 1011 mol2 m−2 s−3 N−2 P−1O2

E 4.493 × 104 J/molMN

Ti

3

fstftat(rwa

3

pvelocities of 1700, 1000, 500 and 200 m/s. These initial veloc-ities were chosen to cover more ordinary atomizing conditionsas well as the extreme ones that may be encountered in high-pressure gas atomization. Since measured values of Vg are

ig. 3. Calculated cooling curves of the Sn–5 mass%Pb droplets generated byelium gas atomization (initial gas velocity = 1700 m/s).

.3. Material-specific constants

The calculated cooling curves (schedules) in Fig. 3 give thealues of dt/dT as a function of T and thus permit calculat-ng the nucleation temperature for gas-atomized Sn–5 mass%Pbroplets from Eqs. (1) and (2) for oxidation-catalyzed surfaceucleation, or from Eq. (3) for internal nucleation. The valuesf the constants, M, N, C and E, or M* and N*, however, need toe determined first. This can be achieved by substituting knownalues of TN and dt/dT in Eqs. (1) and (3) or Eq. (3) and solv-ng the equations for the constants. Such nucleation data werebtained in previous studies with a high-purity Sn–5 mass%Pblloy containing less than 0.25 mass% impurities [24–27] inhich the nucleation kinetics of mono-size droplets generatedy controlled capillary jet breakup [23] were determined byalorimetric measurements [24] and droplet in-flight coolingimulation [36]. The reported nucleation temperatures, com-iled in Table 2, indicate that the nucleation of Sn–5 mass%Pbroplets is catalyzed by surface oxidation in the presence ofxygen in the atmosphere (Experiments 1–4) but is triggeredy an internal catalyst when a reducing atmosphere was usedExperiments 5 and 6). Therefore, the surface oxide gives riseo a higher nucleation potency than the internal catalyst in this

lloy. Li et al. [29] and Wu and Ando [28] used the nucleationata and cooling schedule simulations to calculate the constants, N, C and E for surface nucleation and M* and N* for inter-

al nucleation. The calculated values of the constants, listed in

able 2ucleation temperatures and supercoolings of Sn–5 mass%Pb droplets producedy capillary jet breakup in different gas atmospheres

xp. no. Dropletdia. (�m)

Atmosphere TN (K) �T (K) Reference

185 N2–166 ppm O2 472 27 [26]185 N2–35 ppm O2 425 74 [24]155 N2–166 ppm O2 421 78 [26]155 N2–35 ppm O2 393 106 [24]185 N2–2% H2 353 146 [26]155 N2–2% H2 334 165 [27]

Fca

* 9.618 × 1021 K2 m−3 s−1

* 2.82 × 107 K3

able 3, are therefore specific to the Sn–5 mass%Pb alloy usedn [26,28].

.4. Fraction oxidized, x

With the value of C in Table 3, the fraction of the melt sur-ace that is oxidized (and has hence become potent to causeurface nucleation) can be calculated using Eq. (2). Fig. 4 showshe variations of fraction oxidized, x, during cooling calculatedor a 500 �m Sn–5 mass%Pb droplet at various oxygen concen-rations. The dependence of x on the oxygen concentration ispparent. It should be noted that Eq. (2) does implicitly involvehe droplet diameter since the calculation of dt/dT from Eqs.4)–(6) requires to specify the droplet diameter. Since the coolingate decreases with increasing droplet diameter, larger dropletsill have larger values of x than smaller droplets when compared

t the same oxygen concentration.

.5. Prediction of nucleation kinetics

With the above scheme, nucleation temperatures were com-uted for Sn–5 mass%Pb droplets atomized at initial gas

ig. 4. Fraction oxidized x as a function of temperature at different oxygen con-entrations calculated for 500 �m Sn–5 mass%Pb droplets helium gas-atomizedt an initial gas velocity of 1700 m/s.

210 S. Li et al. / Materials Science and Engineering A 473 (2008) 206–212

Fig. 5. Gas velocity attenuation curves for initial velocities of 200, 500, 1000aTt

l5t1it1zncg

(Soa

FS1[

Fig. 7. Calculated CCT curves for the surface and internal nucleation ofSn–5 mass%Pb droplets helium gas-atomized at an initial gas velocity of1000 m/s. The droplet cooling curves were calculated with Liu et al.’s model[30].

nd 1700 m/s used in the computation of nucleation kinetics in the present study.he curves for 200, 500 and 1000 m/s were generated with exponential functions

hat mimic the curve for 1700 m/s determined by Liu et al. [30].

acking, the attenuations of Vg from the initial values of 1000,00 and 200 m/s were mathematically generated with exponen-ial decaying functions mimicking the one for the initial value of700 m/s determined by Liu et al. Fig. 5 shows the correspond-ng attenuations of Vg used in the computation of nucleationemperatures. The artificial curves for the initial gas velocities000, 500 and 200 m/s are given to exhibit no initial constantone. For more precise computations, actual attenuation curveseed to be determined for the specific atomizing technology andonditions of concern as done by Liu et al. for their ultrasonicas atomization experiment [30].

Figs. 6–9 show continuous-cooling transformation

CCT) diagrams for the nucleation of helium gas-atomizedn–5 mass%Pb droplets calculated for the initial gas velocitiesf 1700, 1000, 500 and 200 m/s, respectively. The CCT curvesre obtained as the trajectories of the points on droplet cooling

ig. 6. Calculated CCT curves for the surface and internal nucleation ofn–5 mass%Pb droplets helium gas-atomized at an initial gas velocity of700 m/s. The droplet cooling curves were calculated with Liu et al.’s model30].

Fig. 8. Calculated CCT curves for the surface and internal nucleation ofSn–5 mass%Pb droplets helium gas-atomized at an initial gas velocity of500 m/s. The droplet cooling curves were calculated with Liu et al.’s model[30].

Fig. 9. Calculated CCT curves for the surface and internal nucleation ofSn–5 mass%Pb droplets helium gas-atomized at an initial gas velocity of200 m/s. The droplet cooling curves were calculated with Liu et al.’s model[30].

d Engineering A 473 (2008) 206–212 211

cpfb3c

stattsisSw

tSaTgrifitowsdfg

stiwtraawcn

itcwiattat

Fig. 10. Oxidation-limited droplet supercooling vs. droplet diameter calculatedftO

isp

ondCltaios0Titfsbtcvmh

4

apa model simulating the droplet motion and cooling in gas atom-

S. Li et al. / Materials Science an

urves calculated with Eqs. (4)–(6) at which nucleation isredicted to takes place. Many cooling curves were calculatedor different droplet diameters to produce smooth CCT curvesut only five of such cooling curves, representing 150, 250,50, 500 and 750 �m droplets, are shown in the figures for alear view of the computation results.

The CCT curves were computed for both oxidation-catalyzedurface nucleation and internal nucleation using the values ofhe constants shown in Table 3 in Eqs. (1) and (2) or Eq. (3)nd therefore are specific to the Sn–5 mass%Pb alloy used inhe previous studies [24–27]. An observation common to all ofhe four gas velocity conditions is that the oxidation-catalyzedurface nucleation occurs at much higher temperatures than thenternal nucleation, indicating a higher nucleation potency of theurface oxide. Therefore, large supercoolings of gas-atomizedn–5 mass%Pb droplets would be obtained if surface oxidationere delayed or suppressed.The CCT diagram calculated for 1700 m/s, Fig. 6, shows

hat surface oxidation would not catalyze nucleation inn–5 mass%Pb droplets smaller than about 650 �m event a very high oxygen concentration of 20,000 ppm (2%).his suggests that oxidation-catalyzed surface nucleation ofas-atomized Sn–Pb droplets may be circumvented almostegardless of the oxygen concentration in the gas if the gas veloc-ty is sufficiently high. This is understood from Eq. (2) where theactor dt/dT, i.e., the inverse of the cooling rate, decreases withncreasing gas velocity, thereby decreasing the extent of oxida-ion, x. Low initial gas velocities, however, increase the chancef oxidation-catalyzed surface nucleation as seen in Figs. 7–9here the CCT curves calculated at 500, and 200 ppm O2 inter-

ect with the cooling curve of 750 �m droplets. The criticalroplet diameter above which nucleation is catalyzed by sur-ace oxidation progressively decreases with decreasing initialas velocity.

Eq. (2) also suggests that the chance of oxidation-catalyzedurface nucleation decreases with decreasing oxygen concen-ration in the gas. In fact, large Sn–5 mass%Pb droplets, evenf they were atomized at a low initial gas velocity of 200 m/s,ould still be free of surface nucleation if the oxygen concentra-

ion were controlled below 200 ppm, Fig. 9. Therefore, it wouldelatively be easy to suppress oxidation-catalyzed surface nucle-tion in gas-atomized droplets of this particular Sn–5 mass%Pblloy. However, alloys that are more susceptible to oxidationould require a higher gas velocity and/or a lower oxygen con-

entration, or even a reducing atmosphere, to prevent prematureucleation due to oxidation.

Fig. 10 shows the oxidation-limited supercooling attainablen helium gas atomization with this Sn–5 mass%Pb alloy at ini-ial gas velocities of 1700, 1000, 500 and 200 m/s and oxygenontents of 200, 500 and 20,000 ppm O2 for the diameter rangehere surface nucleation may result. Strong effects of gas veloc-

ty and oxygen content on the oxidation-limited supercoolingre predicted, particularly toward the lower end of the diame-

er range shown. An important implication, which also applieso more readily oxidizing alloys, is that particles sieved fromn atomized powder may not be the same microstructurally ashose of comparable mesh sizes from another powder atom-

iicy

or helium gas-atomized Sn–5 mass%Pb droplets atomized at initial gas veloci-ies of 200, 500, 1000 and 1700 m/s in the presence of 20,000, 500 and 200 ppm

2.

zed at different gas velocities or oxygen contents, i.e., particleize-based powder screening may not guarantee product quality,articularly for fine RSP powders.

Figs. 6–9 also show CCT curves that represent the kineticsf nucleation caused by an internal catalyst. Internal heteroge-eous nucleation should depend on the melt volume (i.e., dropletiameter) and the cooling rate as seen in Eq. (3). The computedCT curves indeed indicate higher nucleation temperatures for

arger droplets. However, for a given droplet size, the nucleationime decreases with increasing gas velocity while the nucle-tion temperature increases only slightly. For example, at annitial gas velocity of 1700 m/s, a 350 �m droplet would requirenly 0.008 s to cool and internally nucleate at 345 K while theame droplet, at an initial gas velocity of 200 m/s, would need.0013 s to cool and nucleate at a similar temperature of 355 K.his is because the driving force for nucleation builds up faster

n a droplet cooled at a higher rate. Lower nucleation tempera-ures, and supercoolings well in excess of 150 K, are predictedor smaller droplets. It may even seem that very small dropletupercool with no limitations. The latter, however, would note seen in reality. Since the CCT curves were computed withhe values of M* and N* in Table 3, they refer to a specificatalyst that existed in the Sn–5 mass%Pb alloy used in the pre-ious studies [24–27]. Other catalysts with different potenciesay also exist in the alloy. Even if there were no other catalyst,

omogeneous nucleation must eventually set in.

. Summary

A method for predicting the nucleation kinetics of gas-tomized droplets has been developed by combining modelsredicting the nucleation temperature of cooling droplets with

zation. Both the internal nucleation caused by a catalyst presentn the melt and the surface nucleation caused by oxidation areonsidered. Application to a 99.75% pure Sn–5 mass%Pb alloyielded the following knowledge:

2 nd E

(

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A

Ntt(i(

R

[[[[[

[

[[

[

[

[

[[

[

[

[

[[

[[[

[[

12 S. Li et al. / Materials Science a

1) In helium gas atomization with a high gas velocity,Sn–5 mass%Pb droplets cool so fast that surface oxidation-catalyzed nucleation is not an issue unless the oxygencontent in the atomizing gas is very high or the dropletsare very large. Instead, droplets nucleate internally at highsupercoolings. In conventional gas atomization with a lowgas velocity, there may be enough time for an oxide tonucleate and grow on the droplet surface causing surfacenucleation at low supercoolings if droplets are sufficientlylarge.

2) Assessment of the supercooling of gas-atomized dropletsneeds to consider all of the variables that determine thesupercooling, namely the droplet size, the cooling condi-tion, and the potency and density of internal and surfacecatalysts. Gas-atomized powder particles of a given sizefrom different batches may have different microstructuresand therefore may not be mixed. The developed model pro-vides an improved method for screening atomized powdersfor critical applications where powder microstructures needto be stringently controlled.

cknowledgements

The authors would like to acknowledge the support of theational Natural Science Foundation of China (50674071),

he Tianjin Natural Science Foundation (06YFJZJC01300),he Program for New Century Excellent Talents in UniversityNCET) and the Platform Project of Tianjin for Innovationn Science and Technology and Environmental Construction06TXTJJC13900).

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