Controlled porosity by an extreme kirkendall effect

CONTROLLED

POROSITY

BY

AN

FRITZ

EXTREME

KIRKENDALL

EFFECT*7

ALDINGER:

Homogenizing of diffusion couples with spherical symmetry results in formation of hollow spheres if the mutual diffuaivities of the two components differ by a considerable amount. The particles grow as diffusion from the component of the core into the coating material occurs. 4n additional expansion takes place due to isotropic expansion of the coating shell resulting in an increasing inner radius of the spherical shell. Theoretical considerations show that isotropic growth (the ratio of shell thickness to shell radius being constant) leads to formation of infinitely large hollou particles if the starting coating thickness approaches zero. Sintering of nickel- or cobalt-coated beryllium powder compacts results in volume growth of several hundred per cent and densities of less than 0.5 g/cm3. The deviations of the experimental data from the ideal isotropic model calculations are explained by the non-uniformity of the applied coatings and by the closing of open porosity between particles in the compacts. (‘ON’VROLE

DE

LA

POROSITF:

PAR

CN

EPFET

EXTRfiME

DE

KIRKENDALL

L’homogbnC-isation dc couples de diffusion B sym8trie sphbrique m&c B la formation de .sphcrvs c.reuses si les tliffusivit6s mutuelles des deux romposants diffPrent d’une quantit6 considkrable. Lcs partirnles grossissent & mrsure qur sp produit la diffusion rlrpuis lc composant du noyau vers lo mat&inu IIC couvert,urc. Une expansion iaotrope dc la paroi de recouvrement about&ant, g l’augmentation de rayon int&ieur ale la paroi spheriqur cr& une expansion additionnelle. Des ronsid&ations theoriques montront que la vroissance isotrope (le rapport, de l’epais8eur de la paroi & son myon rest,ant constant) m8ne h la formation de part,irules creuses infiniment granden si l’hpaissrur dc la couche de rouverture au depart tend vers e&o. Lo frittago tic composhs de pourlrc de b6rgllium rerouvert de nikel ou cobalt, provoclue unc, croissancc cn volume de l’ordre de plusieurs centaines de fois et donne dcs densit& inf&icures h 0,s g/ems. Lrs auteurs justifient lcs &arts constat& entre les rbsultats expPrimentaux et les ralruls du modtile isotrope ideal par la non uniformit, des recouvremcnt,s appliq&s rt par IH bouchage tlrs poroaitbs ouvertcs c*lltrr IRS pa&rules dans les compo&s. EXTREMER

KIRKENDALL-EFFEKT

ZUR TROLLIERTER

HERSTELLUNG POROSITWT

VON

GEFBGEN

%IIT

KON-

Es wird gezeigt, da5 sich beim Homogenisieren van kugelsymmetrischen Diffusionspaaren hohls Teilchen bilden, wenn die partiellen Diffusionskoeffizienten hinreichend verschieden sind. Die iiu5eren Abmessungen der hohlen Teilchen werden in dem Ma5e gr65er, wie erstens das Kernmaterial in die Schicht diffundiert und zweitens eine damit verbundene isotrope Ausdehnung jedes Volumenelements der Schicht infolge der Sttitzwirkung zu einer zusittzlichen Vergr65erung des hohlen Teilchens fiihrt. Eine ideale Stiitzwirkung liegt “or, wenn das Verhllltnis aus Schiohtdicke und Radius des Teilchens sind im Extremfall unendlich w&hrend des Homogenisierens konstant ist. Unter dieser Voraussetzung gro5e hohle Teilchen zu erwarten, wenn die Ausgangsschicht,dicke gegen Null geht. Am Beispiel van pulvermetallurgisoh hergestellten Proben aus mit Nickel oder Kobalt beschichtetcm Berylliumpulver wird gezeigt, da5 Volumenzunahmen van mehreren hundert Prozent auftreten und Werkstoffe mit Dichten <0.5 g/cm3 entstehen. Die Abweichungen der experimentellen Werte vom idealen Wachstum sind auf ungleichm&iljige Beschichtung und ein teilweises Dichtsintern der Porosit,&t zwischen den Teilchen zuriickzufiihren.

Since

the

Kirkendall’l) a diffusion

original

work

by

many investigations couple

Smigelskas

and

have shown that in

pores are generated

in the com-

Although

the observed

ponent with higher diffusivity.

geneities like impurities, and

these

Simultaneously of excess

only a fraction of the value calculated from the mass transports involved. This is explained by a retarded

shrinkage

and heterogeneous

diffusion

varies considerably

nucleation

the Gibbs-Thompson-equation cleation

process.

for homogeneous

of pores an excess vacancy

twice the equilibrium

vacancy

According

concentration

concentration

may

micropores not

or microcracks@)

formc4)

in high

purity

materials that do not contain imperfections.

it usually makes up

pore volume

pores

boundaries

to

with pore

formation

annihilation

vacancies

at edge dislocations and grain This will lead to is likely to occur.

of the faster couple.

diffusing

In a planar

component

diffusion

in the

couple

the

resulting lattice strain can be released in a direction

nuof

parallel

to the concentration

pendicular

or more

direction,

gradient.

however,

In the per-

a plane stress field will

is required.c2) A much lower excess vacancy concentration of only about 0.01 must be expected.(3)

be generated. Even with a relatively small number of annihilated vacancies the tensile stresses so created

Thus, pores can be generated

are considerable

exclusively

at hetero-

*

Received December I, 1973. t This paper was presented at the “Hauptversammlung DGM”, Villach, Austria (June 1973). 2 Max-Planck-Institut fiir Metallforschung, Institut Werkstoffwissenschaften, Stuttgart, Germany. ACTA

METALLURGICA,

VOL.

22, JULY

1974

: at an excess vacancy

c, of 0.1 per cent they are comparable stres&

der

and hence

plastic

flow

concentration to the yield

results.(6)

On the

other hand the excess vacancy concentration is also influenced by an applied stress CT. As a consequence

fiir 923

ACTA

METALLURGICA,

TABI.E 1. The Be-alloy

VOL.

22,

1974

powders investigated .~.:-----

Alloy content (at. %) (vol. %)

Alloying (coating) element

CO $ Ni Ni Ni Ni h-i Ni _-._~_.________I___ of’ tjhis

the

radius

decreased,f’*s)

y is the surface

where

formation can

(R,)

tension.

even

be

reduced

In diffusion

couples

by

d*+ (E’m)

(%)

0.04

5.25 ;::

1.3 7.25 2.8

0.07 0.38 0.14

0.5 0.5 I

s 108 38

0.53 0.61 1.18 1.88 2.24 3.34

:.5

205 262 138 88 66 38

9.5 10.3 18.7 27.8 31.3 42.5

which

_^__-.

can grow

to t,he relation

can be suppressed

Volume growth

0.9

7.2 8.0 14.6 22.2 25.4 35.3

pores

of

according

St,arting thickness

0.7

CO

.--_

-.-

Density (g/cm9

_-.

2 3 3.5 5 .._____

1.24 0.99 0.74 0.56 0.47 0.87 1.33 1.60 2.20

__

is

a = 2y/R,

This means that pore or the number

of pores

applying

external

an

pressure.(9) peculiar

consequence

of spherical of

the

symmetry,

mechanisms

as a

outlined

above, hollow spheres are formed. In this paper the mechanisms involved in this process as well as experimental results on beryllium-nickel and beryliiumcobalt aBoys will be described. Furthermore deviations are characterized irregularly

shaped

uniformIy

which arise from the use of

coated

particles

instead

of ideal

coated spheres.

Flo.

I

Formation of a hollow sphere in a diffusion couple with spherical geometry (schematic).

smaller than of atoms A and B, shrinkage occur because edge

of annihilation

dislocations

and

stress is generated

of A will

of excess vacancies

grain

boundaries.

at

A radial

in space A :

EXPERIMENTAL

Equi-axed

beryllium powder (Kawecki

of an aserage the

starting

particle

BeryIco P 8)

size of 33.5 fiurn was used as

mat’erial.

It

was

either

coated

with

(,!Z = Young’s crack

modulus).

separating

the

two

This stress can lead to a components

which

then

act,s as a nucleus for vacancy annihilation. If by cobalt by evaporation or plat,ed with nickel by some lnechanisln a Now of atoms A t,o the inner chemical reduction with hydrazine from an amrn~)~liu~n surface of the alloy layer is maintained, the cracksolution. The chemical analysis data and the coating thickness cl, calculated from it are given in Table 1. initiated pore layer (P’ in Fig. 1) will grow until finally a hollow sphere of radius r,, and shell thickness Because of their similar behavior the cobalt- and nickel-alloys The

are described

coated

powders

and discussed together.

were compacted

in a st,atic

press (3% MN/mZf and then sint,ered in a dilatomater. Even the small stress of approx. in

the

samples change.

volume

by

the

Therefore

dilatometer

out parallel

affects

their

FORMATION

powder

coated

anneal

at 1110 K.

experi-

PARTICLES

by a layer of component

If the diffusivity

beryllium

B with a thick-

of atoms B and A is much

made

was observed from

irregular

In Fig. 2(a) the microstructure

heat treat-

to the dilat’orneter

HOLLOW

powder particles.

of processes

compacts

from 870 to X320 K

I shows a diffusion couple of spherical consisting of component A with radius r,,

surrounded ness d,.

OF

sequence in

after cold compaction

me.nts.

F’igure symmetry

The described experimentally

shown

“pressureless”

ments at, t~Illperat,ures ranging wrre carried

3 . fO” N/m2 created

d, results.

with

The pore

7 vol. %

followed layer

nickel

of a is

by a 30 min can be clearly

discerned.

After 300 min at 1220 K completely hollow particles are obtained (Fig. Zb). The beryllium has completely diffused into the out,er shell which consi& of a sat,urated solid solut,ion of nickel in beryllium (light grey) and a small amount of a Be,,fr;& intermetallic compound (white). Figure 3 shows scanniilg efectron micrographs. Figure 3(a) shows a core of beryllium still present in the center

ALDINGER:

CONTROLLED

POROSITY

BY

AX

EXTREME

KIRKENDALL

925

EFFECT

3(b)

FIG. 3. Scanning

electron micrographs of fract,ure SWfaces of a reaction sintered beryllium alloy (18.5 vol.% Ni) (a) Hollow particle with core still present; 800 x ; (b) Hollow particle after reaction is completed; 800 x

of the

particle

while

Fig.

3(b)

shows

a completely

hollow particle. The necessary crack

mass transfer

transport

condensation

2(b) Fro. 2. Microstructure of compacted (325 MN/m*) and sintered beryllium powder coated with 7 vol.‘h Ni. (a) 30 min/lllO K; 145 x ; (b) 300 min/1220 K; 145 X.

FIG. 3(a)

spreading surface bridges

by

of the

evaporation

and

is much too slow to explain the observed

growth rate of the pore layer. via remaining

after formation

of beryllium

bridges

of beryllium diffusion

is

Transport

of material

by rapid

on the inner shell surface a more

are seen in the scanning

of a beryllium-cobalt

by diffusion

followed

likely

electron

alloy particle

by

process.

Such micrograph

(Fig. 4).

FIG. 4. Scanning electron micrograph of reaction sintered and fractured beryllium alloy (2.8 ~01.0,~Co): 800 x.

ACTA

926

XETALLURGICA,

VOL.

22,

1974

Considering the usually small changes in atomi volume during homogeneization in metallic systems (for Be-Ni see (11))a 1’mear relationship holds between total composition and density pL of the alloy, thus equation (4) is simplified, AV

(5)

iy=

or AV -~-, Vo

OO

03

INi)

Volume

Fraction,v,

tf

14

FIG. 5. Volume growth during heat treatment of nickeland cobalt-~r~lliurn alloys as theo~tieal~~ calculated and experim&taIly observed. _

VOLUME

GROWTH DURING THE FORMATION OF HOLLOW PARTICLES

Two simple models are used t#odescribe quantitatively the growth during the homogeneization of multicomponent systems under the assumption that shape of the particles is maintained. In both models the total mass is constant. The first model assumes that the pore finally generated takes up the volume of componentS A: p, = r, = cons& (1) (r, and r,, are specified in Fig. 1). From this follows the proportionality between volume increase of the system and volume content of component A, v,, if during homogeneization the partial volume of atoms A and B does not change: Afrv ‘v,=vA* The experimentally observed volume growth for Be-Ni alloys exceeds the value given by equation (2) up to a factor 3 as shown in l?ig. 5 resulting in samples with densities around 0.5 g/cm3 (Table l).(lO) In the second model each volume element of layer B is assumed to grow isotropically by the A atoms diffusing into it. Then, the inner radius of the shell inoreases steadily during the reaction : d-2 = re In this case the volume

Av

vo-

.PB

-

PL

2d = const. 70 growth is

+ !!A .

v, 1-

2?4

This analysis yields increasing volume growth as the content of component A increases and infinite growth for V~ --f 0 (see dotted curve in Fig. 5). A comparison between equation (6) and growth measurements of beryllium-nickel compacts shows that the observed values are smaller than the calculated volume changes (Fig. 5). The analysis applies, however, qualitatively and is able to explain volume changes of several hundred per cent. DISCUSSION

A number of parameters influences the volume growth of coated particles and powder compacts and their various cont’ributions interact in a rather complicated way in reducing the volume growth described by equation (6) : (a) The diffusion of shell mat,erial int,o the core causes a decrease in t’he inner diameter of the hollow particle. (b) Deviations from the ideal geometry, for example porous (see P” in Fig. 6), incomplete or nonuniform coating, will lead to directional volume growt,h and an apparent coating thickness, in the compact do+, which is larger than the thickness calculated from the chemical analysis data do (Fig. 6). According to equation (5) increased coating thickness causes decreased volume growth. B

(3)

?b3

(4)

PL (~0+ doj3 - ro3 PL (pA, ps and pL are the densities of component A, B and the alloy L, respectively).

FIG. 6. Parameters which ini%mneo volume growth of oorsted particles. (a) Incomplete coating; (b) three kinds of porosity.

ALDINGER:

C~~TRObLED

POROSITY

BY

AN

EXTREME

KIRKENRALL

EFFECT

927

k 0

3

2

I

4

6

5

de inpm FIG. 7. Measured thickness of nickel coating (do+) of compacted (325 MN/m2) particles as a function of coating thickness calculated from chemical analysis (d,).

(e) The

pore

particles

can

volume

fraction

decrease

due

to

P"

between

normal

solid

sintering while the model assumes (d) Stresses in the alloyed flow decreasing be created

the inner radius.

volume

const

PO" =

layer may cause plastic These stresses can

by several mechanisms.

individual

the state

For example

an

element on the inside of the alloy

shell can be locked by other elements which grow at a rate ; or interface

slower ponents,

layers

grain boundaries

between

or micropores

the com-

in the ahoy

layer can cause an uneven d~ffusional flow and hence

8(b)

uneven volume growth. (e) For a coating thickness independent size differences in chemical composition particles

to

mutual

locking

grow

different

amounts.

and impediment

of particle will cause This

of growth

causes

in a real

compact. The deviations isotropic

of our experimental

growth

during reaction

tions (4-6) respectively

results

described

from

by equa-

(Fig. 5): can be explained

by

these l~~echanisms. The diffusion rates in the beryllium nickel system differ by a factor of 2OO,(11) therefore up to

effect (a) will be negligible.

a beryllium

content

mainly by mechanism of open porosity

(b) and (o), i.e. due to closing

P"'during

that the apparent

sintering and to the fact

shell thickness

the gross composition

The deviation

of 90 vol. % is caused

cl,,+ is larger than

suggests (Table 1).

In Fig. 7 d,,+ as observed in cold compacted is compared data.

with d, calculated

The two quantities

samples

from chemical analysis

are related by the empirical

equation do+ = 4 pm + +a$.

(7)

This difference is mainly due to a porosity P" (Fig. 6) as a result of the electroless plating process by which the nickel coating was applied. As shown in Fig. 8(a)

Fra. 8. Scanning electron micrographs of nickel coatings and alloyed shells. (a) Nickel coating, 42.5 vol.% Ni; 2500 x ; (b) Alloy shell after pressing (325 MWjmz) and reaction sintering; 500 x ; (c) Nickel ooating, 9.5 vol.‘$$; 500s.

the nickel layer consists of a loose packing of very fine grains each having a diameter of approx. Gj,um. is decreased After heat t#reatment this porosity considerably (Fig. Sb). The decrease of P"'ends up in a decreased volume growth AV’ described by AP’

= AV -

V,

eI'," f V,+ . P,"'

(8)

ACTA

928

V, and V,+ are the theoretical

where AV

and

the

V, + AV’ P,‘”

METALLURGICA,

the

experimentally

volume

the particles

fractions

of

at the beginning

respectively.

the

By considering

equation

equation

pores

BeNi

and

between

and end of the process,

Due t,o the deviations

and pore shrinkage

1974

volume

and P,‘”

at the end of the reaction,

22,

V, +

volume

measured

VOL.

from ideal coating

(5) must be changed.

(8) and using d,+ instead of

Volume

d, we get -1= vo

Perfect

1 -- Pp”’

agreement

experimental (Fig.

FIG. 10. Free

Plrrt .

1 -

AV’

(To + 4l+)3 (To + do+)” ~ r:

between

results

equation

is obtained

9) if k = (1 -

P,“‘)/(l

0.71 and d,+ is taken

from

P,“‘)

-

is caused (Fig.

interrupted however,

the coating

is chosen

as

This also

of the thin nickel

can occur; thickness

the coating

in coated

is

areas,

a,,+ is larger than d,

and this causes reduced growth. sequence of the incomplete

the

(Figs. 5 and 9).

In areas where

no growth

and

90 vol. o/0 Be a sudden

by irregularities 8~).

(9)

(7).

drop in the growth curve is observed coatings

(9)

l.

up to 90 vol. ‘A Be

equation

can be seen in Fig. 5. Above This

-

coating

An additional

con-

up to 10 vol. ‘A Ni

is that there is no or less support between the isolated grains of the shell (Fig. SC) during reaction required for isotropic In

growth.

addition

decreasing

to

volume

these growth

morphological

reasons

must be expected

a

nickel force

the

Equation (9 k = 0,71 and d&\/Z +Ll3d. q

Be-Ni

approaches formation

simultaneously

reduced

The position

the

porosity

formation

(Fig.

volume (Fig.

is

growth in a

5)

cannot

be

of the free energy

10) or the

concentration

of

of inter-

with low diffusion rates reducing

sintering

of the powder

Williams

and Jones,‘13) but solely by morphological

details

discussed

above.

compact

as suggested

More definitive

by

statements

about the influence of other parameters (constitutional conditions, sure,

powder

sample

characteristics,

geometry

and

compacting

reaction

will be made after investigations

pres-

temperature)

on carefully selectSed

model systems are concluded. ACKNOWLEDGEMENTS

wishes to thank

Dr. G. Petzow

Dr. H. E. Exner for their encouragement

(12LO”Kl

the driving

Kirkendall

diagram

by the maximum

as the

1

beryllium-

(Fig. 10).

explained

metallic compounds

in

zero because of

of the maximum

growth-concentration

The author -

vB,

energy of formation nickel system.“2J

content for

Fraction,

lating comments.

Financial

support

ministerium

Forschung

und

resented

by

fiir Dr.

Weltraumforschung

Pippig

of

the

and

and st’imu-

by the BundesTechnologie Gesellschaft

mbH is gratefully

repfiir

acknowledged.

REFERENCES

0' 0

I 1

’ ,r.+h3‘_ ’ lr. +dB3-

’

r.3

FIG. 9. Observed and calculated volume growth of reaction sintered beryllium-nickel alloys.

1. A. D. SMIGELSKAS and E. 0. KIRKENDAI,L, Trans. dlXB 171, 130 (1947). 2. F. SEITZ, Acta Met. 1, 355 (1953). 3. R. W. BALLUFFI, Acta Met. 2, 194 (1954). 4. R. RESNICK and L. SEIGLE, Trans. AIME 209, 87 (1957). 5. J. A. BRINKMAN, Acta Met. 3, 141 (1955). 6. V. Y. Doo and R. W. BALUFFI, Acta Met. 6, 428 (1958). 7. R. W. BALLUFFI and L. L. SEIGLE, Acta Met. 5,449 (1957). 8. D. HILL and D. RIMMER, Phil. Mag. 4, 673 (1959). 9. R. S. BARNES and D. J. MAZEP, Acta Met. 6, 1 (1958). 10. F. ALDINGER, Powd. Met. Int. 9, (2) (1974). 11. S. H. GELLES. Thesis. Massachusetts Institute of Technology (1957). 12. R. HVLTGREN et al., Selected Values of Thermodynamic Properties of Met& and Alloys. Wiley (1963). 13. J. WILLIAMS and J. W. S. JOXES, Powd. Met. 5, 45 (1960).