- Email: [email protected]
Kirkendall effect and diffusion in the gold-platinum system—I
KIRKENDALL
EFFECT
AND
GOLD-PLATINUM THE
KIRKENDALL A.
DIFFUSION
IN THE
SYSTEM-I EFFECT*
BOLKt
The Kirkendall effect has been studied in the gold-platinum system, one of the rare systems with a miscibility gap in the solid state. The effect has been measured as a function of time and temperature in a great number of “sandwich” couples. These couples consisted of pure gold and pure platinum, polycrystalline and singlecrystalline, and of pure gold and a gold-rich alloy with 73.5 at.% gold. It could be established, as a consequence of the obtained accuracy of the measurements, that the difference in magnitude of the effect in couples with polycrystalline platinum and in couples with singlecrystalline platinum has a physical significance. It has been interpreted in terms of an extra diffusion transport along the grain boundaries in polycrystalline platinum. Besides the Kirkendall effect the phenomena associated with this effect, such as porosity, dimensional and structural changes, has been studied as well as the phase-boundary displacement.
EFFET
KIRKENDALL
ET
DIFFUSION
DANS
LE
SYSTEME
OR-PLATINE-I
L’auteur a Btudie l’effet Kirkendall dans le systeme or-platine, l’un des rares systemes qui presentent une lacune de miscibilite it 1’Ptat solide. L’effet a et& mesure en fonction du temps et de la temperature dans un grand nombre de couples “en sandwich”. Ces couples Btaient constitues d’or pur et de platine pur, polycristallin et monocristallin et d’or pur et d’un alliage riche en or a 73,5 at y0 d’or. 11 semble qu’on puisse conclure, en tenant compte de la precision obtenue dans les mesures que la difference de la grandeur de l’effet constatee entre les couples avec platine polycristallin et les couples avec platine monocristallin, ait une signification physique. Cette difference est interpretee comme resultant dune diffusion additionnelle le long des frontieres de grains dans le platine polycristallin. Outre l’effet Kirkendall, les phenomenes associes b cet e&t, tels que la porosite, les modifications de dimensions et de structures, ont 6th Studies en meme temps que les deplacements de front&es de phases.
KIRKENDALL-EFFEKT
UND DIFFUSION BEIM DER KIRKENDALL-EFFEKT
SYSTEM
GOLD-PLATIN-I
Bairn System Gold-Platin, einem der wenigen Systeme mit einer Mischungsliicke im fasten Zustand, wurde der Kirkendall-Effekt untersucht. Er wurde in Abhangigkeit von Zeit und Temperatur an einer groDen Zahl von “sandwich’‘-Probenpaaren gemessen. Die Paare bestanden aus reinem Gold und reinem Platin, polykristallin und einkristallin, und aus reinem Gold und einer goldreichen Legierung mit 73.5 Atom% Gold. Die Messungen waren so genau, da13 der Unterschied der GroDe des Effekts bei Paaren mit polykristallinem Platin und solchen mit einkristallinem Platin einwandfrei nachgewiesen werden konnta. Er wurde gedeutet auf Grund einer zusatzlichen Diffusion entlang den Korngrenzen in polykristallinem Platin. Neben dem Kirkendall-Effekt wurden die damit zusammenhlingenden Erscheinungen-Porositat, Anderungen von Ausdehnung und Struktur-sowie die Verschiebung der Phasengrenze untersucht.
A.
The discovery
INTRODUCTION
of the Kirkendall
effect in 1947 by
of Smigelskas
and Kirkendall
face between
the two halves
that the marked interof a diffusion couple
Smigelskas and Kirkendallo)
was a good motive for a
(consisting
comprehensive
in the field of the inter-
a-brass side of the couple, it was possible to describe
Before 1947 a diffusion
the diffusion by means of two diffusion coefficients.
investigation
diffusion of metals and alloys. process
was
described
by
means
coefficient only (see Matanot2));
of one diffusion
These well-known intrinsic
after the observation
METALLURGICA,
VOL.
9, JULY
1961
moves towards the
or partial
diffusion coeffi-
cients, referring to the two components which take part in the diffusion process, can be calculated from an
* This paper contains a part of the author’s thesis, Delft 1959. Received April 22, 1960; revised October 25 1960. 7 Laboratory for Physical Chemistry, Technical University, Delft, Holland. Now at Philips’ Research Laboratories, Eindhoven, Holland. ACTA
of copper and a-brass)
observed Kirkendall effect (see Darkenc3), Hartley
and
Crank(*), and Seitzc5)). The problem of the interdiffusion of two metals and/ or alloys is much more complicated if phase boundaries
632
BOLK:
and intermetallic the process.
KIRKENDALL
phases come into existence
EFFECT
during
Until now nearly all investigations
been carried out with continuous
have
metal systems or in
IN
Au-Pt
the difference between the initial concentrations be large.
of a phase boundary
(i.e. a discontinuity
such parts of binary metal syst ems,in which a continuous series of solid solutions can be formed during the
are chosen on opposite
diffusion.
An advantage
Only a few investigators
have made their
in systems with miscibility
gaps in the
The
following
discontinuous
investigated:
Ag-Zn
Lohmann”),
Al-Be
Ag-Mg
by
Hickso”), Cu-Zn
by Biickle’@ by
Heumann Cu-Sb
by
systems and and
by Seith and Kottmann@),
Kottmann@),
Fe-MO
by Oknow
Cr-Fe
by
Heinemannor),
couple
in continuous systems will for the
at elevated
temper-
whichisresponsiblefor
of the equilibrium
phases at the phase
diffusion
equations
rate-determining
is that the
process.
This
is
already the case after a short diffusion time. The
gold-platinum
investigation
per
system
on account
was
for
this
of one mis-
difference
of the
is favourable
for the appearance
effect. derived
from
obtained from experiments
these
values,
between the initial concentrations
however, is unfavourable
of the marker interface.
changes,
effect,
such
as
be
are not very pronounced.
of a large
An advantage
accompanying
porosity
of
This condition,
for the appearance
would be that the phenomena endall
can
in diffusion couples with a
the two halves of the diffusion couple.
and
the Kirk-
dimensional
In the opposite
case, a large difference between the two concentrations will be favourable for a large displacement of the marker interface. However, the porosity and similar phenomena
will be very pronounced,
the reliability coefficients.
of the calculated
which decreases
values of the diffusion
We have meant to lay stress on the Kirkendall and the accompanying
phenomena,
for about
at 1200°C for 2 hr and
In this way small pieces of the
quenched in icewater.
Two such
metals of the size of a button were obtained.
a thickness of about 1 mm and sawn into platelets of about
1 x 3 x 5 mm.
Another
button
of platinum
and the buttons of the alloys were sawn directly into platelets
of
the
same
size.
The
platelets
were
turned off carefully to make them plane parallel and between filter papers. graph showed
A back reflection X-ray photo-
that the surface of the platelets
deformed
To eliminate
as a consequence
secondary
reactions
effect
which means that
wau
of the turning during
the dif-
fusion process the platelets were heated at 1200°C for 100 hr, the gold platelets at 1055°C.
Reliable values for the diffusion coefficients and for
displacement
crucibles
furnace at a temper-
which took place in about 3 hr,
the alloys were homogenized
off.
(1769%) which
small difference
They were melted in alumina
After cooling,
melting points of gold (1063°C) and platinum
makes one expect a great difference in mobility,
quantities
of
by Drijfhout,
then cleaned with soap, alcohol and water and dried
chosen
of the existence
1 hr.
somewhat
the
with a purity
been supplied
kept in the molten state at this temperature
cibility gap only (Fig. l), while the great difference in
Kirkendall
have
cent,
buttons of pure gold and pure platinum were rolled to
of the diffusion time. The condition for the application is the
PROCEDURE
placed in a vacuum graphite-tube
and
This reaction we assume to be independent
of the fundamental
EXPERIMENTAL
The metals gold and platinum, 99.99
A second process which takes place is the so-
called phase-boundaryreaction,
diffusion
B.
Amsterdam.
in discontinuous
of a diffusion
boundary.
takes place as it
systems.
and Heumann and
to the diffusion
the diffusion
the occurrence
the diffusion
and Morozo3)
not be the only process which is responsible atures.
decreased;
ature of about 150-200°C above the melting points and
In contradistinction
behaviour
gap.
of a phase boundary
and
Fe-Xi by Fitzero4). systems,
sides of the miscibility
of the appearance
were in two separate one-phase
Descamps@),
Kottmanna’),
Heumann
been
and Heumann
Buckle
and
have
in the concen-
curve) that the two concentrations
is that the difference between the two concentrations is actually
solid state.
must
Moreover, it is necessary for the appearance
tration penetration
experiments
633
SYSTEM
after this treatment The not-rolled
The crystal size
is given in Table 1.
platinum
platelets are nearly single
crystals with one or two grain boundaries The diffusion couples (sandwich-type) in the welding-apparatus
only.
were prepared
shown in Fig. 2 at a temper-
ature of about 80-100°C below the temperature to be applied in the diffusion experiments, and under a pressure of about loo-350
atm.
The temperature
was
maintained by means of internal heating with a current of about 100 A. Two platelets with the highest concentration
of gold
were welded
on both
sides of the Quartz
platelet with the lowest concentration of gold. fibers (5-10 ,u) were used as marker material.
In this type of diffusion couple the “interface” reference to which the displacement
with
of the markers can
be measured lies in the middle between the two marker After welding the couples were made
interfaces.
parallel on the lathe, embedded
in urea-formaldehyde
G34
ACTA
METALLURGICA,
VOL.
9,
1961
1769
1600-
1500-
1400b-
I-1300-
1200-
/ / 1100-
IWO-
9oLJ0
20
Pt
40
60
Weight % Au
AU
FIG. 1. The gold-platinum system (according to Darling et CSZ.“~)).
and polished with Cr,O,-, Al,Os- and diamond-suspensions. The distance between the two marker interfaces TABLE 1. Average crystal size of gold, platinum and the gold-platinum alloys
Composition Rolled gold Rolled platinum Not-rolled platinum 73.5 at.% Au alloy 66.7 at.% Au alloy 13.5 at. y. Au alloy
Crystal size (cm) 7-8
x 10-z
< 10-Z
3 x 10-l 5 x 10-a 5 x 10-s
5 x 10-s
was measured by means of a microscope with a movable object-table with a very accurate micrometer. Diffusion took place in a furnace which was controlled within about &‘C and whose temperature has been measured with an accuracy of +2”C. After a certain diffusion time the diffusion couple was again embedded in urea-formaldehyde and, after polishing, the marker distance measured, The marker displacement was caloulsted from AM=-
4 - 4
BOLK:
KIRKENDALL
EFFECT
where d, = initial distance between the two marker interfaces, d, = the distance after a diffusion time t. The interdiffusion of gold and platinum has been studied in a number of diffusion couples listed in Table 2.
IN
Au-Pt
TABLE 2.
3* 4 : zi 9 11 12 13 14 15 16 :;: 19 24 25 26 21 28 30
31 40 41 42 43 44 4: 41 50 51 52 54
(_
Diffusion temp. (“C)
Type of couple
~1038 ~1038 -1002 -1020 NlOOO 1020 1020 970 970 970 1055 1055 926 926 1055 1055 1020 1020 970 970 926 926 NlOlO -1020 1020 1055 1055 1020 1020 970 970 926 926 1000 1000 1000 1000
A/PO/A A/PO/A A/PO/A AlLIlA Li/Pb/LB A/PG/A A/PG/A A/PO/A A/PG/A A/PG/A A/PG/A A/PG/A A/PG/A AiPGiA A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PG/A A/PG/A AIPGIA AiLliA AjLliA A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/PG/A A/L3/A L2/PG/L2 A/PO/A
-
Fm. 2. The welding apparatus. C. RESULTS
The displacements of the marker interfaces are given in Figs. 3-6 as a function of the square root of the diffusion time t. It appears that the straight lines, calculated with the method of the root mean squares, do not go through the point (0; O).* This is due to the fact that the markers are pressed completely into the soft gold during the welding as can be seen from Fig. 7. The straight line can be expressed by A,=al/t+b
635
The diffusion couples investigated, with diffusion temperatures
Number
;:
SYSTEM
(1)
where a is the slope of the straight line and where b is the length cut from the AM-axis. We think that b is the distance over which the concentration cM of the * In the first papers concerning the Kirkendall effect in the gold-platinum system by the present authorI1s~1s’the curves through the points are not straight lines. These tirst measurements have not been carried out by means of the microscope described in Section B and the specimens were not heated in a controlled furnace. The investigations with specimen 54 shows (Fig. 6) that the points lie on a straight line within the experimental error. The deviation of the curves from a straight line in Fig. 2 of the paper mentioned above has no physical significance.
A = rolled gold PG = rolled platinum PO = not-rolled platinum Ll = 73.5 at.% Au-alloy L2 = 66.7 at.% Au-alloy L3 = 13.5 at.% Au-alloy The sign N indicates that the diffusion couple has been heated in a non-controlled furnace. The accuracy of the temperature is about 10°C in these cases. * The results obtained with this specimen have already been published by the author.(iBJPJ
marker interface must be displaced before the markers move proportionally to the diffusion time t. The calculation of b for each specimen shows that the values are spread randomly around the mean value 6 = -5.8 /J. All displacements have been corrected with this mean value, after which the straight line has been recalculated. Then we obtain:
(2) From the standard deviation of every series of plotted points the standard deviation, era,, of a’ can be calculated. The values for equation (2) and the standard deviation of every series are given in Table 3 and Table 4. Together with the measurements of the marker
636
ACTA
METALLURGICA,
vTtime
Fig. 3, series I, type A/PG/A. FIGS.
3,
4
and
t,
VOL.
9,
1961
hr
Fig. 4, series II, type A/PO/A.
Fig. 5, series III, type A/Ll/A.
The marker displacement Aar as a function of the square root of the diffusion time t at four diffusion temperatures.
5.
25c
2oc
l5C
x
Phase 9
;
boundary
~Markw
interface
IOC
AlPGlA AIPG(A 50
0
lr&” /
AlPGlA A fL31A
IrB
5
A iPO[A
97O~i A
IO
fi
time 1,
lb).
(POIA
I5
hr
Fm. 6. The marker displacement Ax in diffusion couples of various types as a function of the square root of the diffusion time t.
FIG. 7. Diffusion couple 9 before (a) and after (b) a diffusion time of 100 hr. x 150
BOLK:
Type of couple
Number of couple
Diff. time t (hr)
12 13 6
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
1055
I(A/PG/A)
1020
: 11 14 15 16 17 18
970 926 1055
II(A/PO/A)
1020
;: 25 26 27 40 41 42 43 44 4.5 46 47
970 926 1055
III(A/Ll/A)
IN
Au-Pt
=
I
Temp. (“C)
EFFECT
637
SYSTEM
:A for the diffusion counles of the series I(A/PC . I A), II(A/PO/A)
TABLE 3. Dienlacement
I__.__
KIRKENDALL
1020 970 926
I
and III(A/Ll/A)
r;
Std. deviation (20.84 (20.76 (17.80 (17.5” (12.4O (12.15 (8.0* (8.22 (19.62 (19.05 (15.0s (14.00 (9.48
+ 0.28) * O.l*) f 0.19) k 0.14) & 0.3O) * 0.12) & 0.16) & 0.06) -& 0.07) & 0.1”) * 0.13) & 0.19) & 0.19)
(p)
A#
3.9
1.’ 2.9 0.9
/
2.4 2.9 2.8 2.9
16 217
(14.80 (12.57 (12.2’ (7.94
& + 5 *
1.’ 0.8 1.1 1.’ 2.5 2.2
0.13) 0.06) 0.08) 0.13)
0.0207
0.0208 0.0208 0.0178 0.0176 0.0124 0.0122 0.008 1 0.0082 0.0196 0.0191 0.0150 0.0140 0.0095 0.0097 0.0068 0.0068 0.0143 0.0148 0.0126 0.0122 0.0079 0.0082 0.0068 0.0064
2.3
’
AM b4-t
(cm) *
--
3.7 2.5 2.0
1.0 1.3 1.’
--~
3.4
0.676 0.0194 0.0190 0.0156 0.0146 0.0096 0.0082 0.0072 0.0068 0.0199 0.0209 0.0163 0.0156 0.0113 0.0115 0.0079 0.0076
= .-.-* Calculated from equation (2) for t = 100 hr. 7 Deduced from the concentration penetration curves (see Part II). TABLE 4. Displacement
I Type of couple A/PG/A A/PG/A A/PG/A A/L3/A A/PO/A A/PO/S
Temp. (“C) -1020 NlOlO 1000 1000 1000 970
* Calculated from equation
I
Number of couple 30 28 50 51 54 8
for diffusion couples of various types .~_ Diff. time t (hr) 100 100 100 100 400
(16.8l (15.50 (15.49 (13.56 (12.64 (9.72
100
displacement
Temp. (“C) I-1010 -1020 1020 1000 1000
1.6
0.0168 0.0155 0.0155 0.0136 0.0126 0.0097
&- 0.12) + 0.14) + 0.29) f 0.03) f 0.21) + 0.2’)
;:“, 0.3 2.9 3.6
Diff. time t (hr)
28
100 100 100 100 400
z 51 54
I
I
Number of couple
.-.-* Calculated from equation
A.#’ (cm)*
AP.b. in various diffusion couples
I
A/PG/A A/PG/A A/PG/A AILS/A A/PO/A
Std. deviation (p)
_
(2) for t = 100 hr.
TABLE 5. Phase-boundary Type of couple
n’(p/hr”“)
(t’( p/h+‘*) (2.14 (2.2’ (2.00 (2.7’ (1.58 _:-
* & + + f
Std. deviation (p)
0.04) 0.04) 0.11) 0.1’) 0.03)
1.6 1* 1:1
- .~__..__ Id
sidered concentration sionless constant
range. Together with the dimen-
(Fig. 8). The straight lines can be drawn through the point (0; 0). The values are given in Table 5. The diffusion coefficient D can be written as = D,(c) exp
0.0021 0.0023 0.0021 0.0028 0.0016
0.6 0.6
(2) for t = 100 hr.
displacements the displacement Ap,b_of the phase boundary has been measured in some diffusion couples
W4
AD.b. (cm)*
k-4?(c)/~~l.
K=xa
(3)
Now we assume D,(c) (the frequency factor) and Q(c) (the activation energy) to be constants in the con-
(4)
Dt
we obtain x = 1/(D,K)
dt exp [-Q/2ET]
Alw = K,y’t
exp [--&,/2RT].
so that
From this equation
the values of K,
(5)
and QM can be
638
ACTA
METALLURGICA,
40
30
P 20 9"
VOL.
9,
1961
of series I and II they are in good agreement with the directly observed displacements. For the couples of series III they are about 2040 per cent greater than the directly observed values, so that secondary reactions have taken part in the process, which have influenced the direct measurements. For series III the indirect observed displacements have been used for the calculation of K, and QM. The displacements in the couples 2830 and 50 of the A/PG/A type of series I and in the couples 8 and 54 of the A/PO/A type of series II (Table 4), which have not -4.400
IO
-4.600
0
Jf time1, hr The phase boundary displacement Ap.b. in couples of various types as a function of the square root of the diffusion time t. Fxo. 8.
calculated by plotting log ( A,“/z/t) as a function of the reciprocal temperature (Fig. 9). The calculated values are given in Table 6 together with the standard deviations of the activation energies.
k ; -4.700 9 3
-4.600
D. DISCUSSION
A very pronounced displacement (in the order of about 50-200 ,u in 100 hr) of the marker interface has been observed. The displacement takes place in the direction of the highest concentration of gold, from which we can conclude that gold is the faster diffusing component. The displacement in couple 5 (gold rich alloy against not-rolled platinum) appeared to be only about 10 ,u in 870 hr or about 3 p in 100 hr, which is very small compared with the displacements in other types of couples. The displacements deduced from the concentration penetration curves of the couples from the series I, II and III are assembled in Table 3.* For the couples TABLE 6. The values of&x, KM and aearcalculated from the displacement AM by means of equation (5) Series
* The concentration penetration curves will be discussed in Part II.
I
I
I
\I
\\
-4.900
-5.CXXl~ 750
Bo
I/TXIO+4 FIG. 9. Log(Ax/l/t) plotted as a function of the reciprocal temperature.
been used for the calculation of KM and QM, are in good agreement with the calculated lines of Fig. 8. The displacements in diffusion couples consisting of gold and rolled polycrystalline platinum (crystal size < low2 cm) turn out to be about lo-20 per cent greater than those in couples consisting of gold and nearly single crystalline platinum (crystal size 3.10-l cm). This effect, moreover, is dependent on the diffusion temperature. In consequence of the accuracy of observation attained by us these observed differences must be real. We interpret them as a consequence of an extra diffusion transport along the grain boundaries in polyorystalline platinum. In 1951 Le Claire and Barne@) observed that markers lying opposite to a
BOLK:
KIRKENDALL
EFFECT
grain boundary were displaced over a greater distance than markers lying farther from a grain boundary. From a number of investigations (17)in the field of selfdiffusion, it appears that a grain boundary contribution can be detected and measured when the annealing temperature is between 0.50-0.90 of the melting point of the system. Taking in our case for the melting point that of the alloy with the concentration of the marker interface (since the difference between the partial diffusion coeffmients there is responsible for the appearance of the Kirkendall effect), our annealing temperatures are N 0.85-0.94 of the melting point. We can conclude from these values that a measurable transport can take place along the grain boundaries. However, the diffusion temperatures are too high to expect grain boundary diffusion only, which is a necessary condition for the calculation of the grain boundary diffusion coefficient as done by the referred investigators. From the values of K, and QM for the series I and II (Table 6) and using formula (5) the marker displacement AM-s.,,. can be calculated, in so far as it is an effect of the grain boundary diffusion only. At 1055 and 926°C the grain boundary displacement is 11.5 and 20.9 per cent, respectively of the total marker displacement in polycrystalline platinum. These percentages are in agreement with the fact that the contribution of
IN
Au-Pt
639
SYSTEM
the grain boundary diffusion to the total diffusion is decreasing with increasing temperatures. The marker displacements at these temperatures are 23.9 and 17 p, respectively. From these values we can calculate K M_g,b.and QM_q.b,,thus giving the relation between A M_g.b.,t and T: 300/2RT].
A M_g.b,= 9 x 10h51/t exp [-16
We hereby assumed that the log (AM-,&Z/t)-l/T relation may be rendered by a straight line. The ratio between the activation
energy for volume
selfdiffusion
and that of grain boundary
determined
by the authors
from 0.40-0.70.(17)
mentioned
In our investigation
selfdiffusion
above varies the ratio turns
out to be 0.36. The activation
energy in the polycrystalline
line platinum, preceding
which is not astonishing
calculation
size is nearly
in view of the
and the fact that the crystal
the same in both alloy and platinum
(Table 1). In Fig.
10 the results concerning
effect in the gold-platinum
system
together
with those
systems.
For this purpose the values of log (AM/l/t)
of practically
concerning
the Kirkendall are summarized
the effect
in other
all known effects are given as a function
of the reciprocal
temperature.
It appears from this
-6.OC
t
6
6
IO
12
14
16
I/T x104
FIG. 10. 2
Survey
of the Kirkendall
alloy
with 73.5 at. y& gold is just the same as in polycrystal-
effect in vmious systems; reciprocal temperature.
log (Ax/dt)
as a function
of the
640
ACTA
METALLURGICA,
figure that the Kirkendall effect in the gold-platinum system is about 30,000 times smaller than that in the copper-zinc system, at least if compared at the same temperature (400°C). In Part II the magnitude of an observed Kirkendall effect is expressed in a numerical quantity based on the ratio between the partial diffusion coefficients, thus comparing the marker displacement with the diffusion amount. It appears from the experiments (Fig. 8) that the phase-boundary displacement Ap.b. is proportional with the square root of the diffusion time. When the phase-boundary reaction is rate-determining, the phase-boundary displacement will be a function of this reaction. Assuming the rate of this reaction to be independent of the diffusion time, which means that a certain amount of the one phase will be transformed into the other phase in unit time and at any moment of the process, the phase boundary will move proportionally to the diffusion time. When the diffusion is process-determining the phase boundary reaction will be a reaction which follows the diffusion process. Since the course of this process is proportional to the square root of the diffusion time, the phase boundary reaction, i.e. the phase boundary displacement, will do the same. So we may conclude that the diffusion has been rate-determining, although this conclusion need not be valid for the beginning of the process when the concentration gradient is very high. Our accuracy was not sufficient to measure a beginning effect.
FIG. 11.
Electrolytica;llypolished surface of diffusion couple 17. x 54
VOL.
9,
1961
E. PHENOMENOLOGICAL OF
THE
OBSERVATIONS
INTERDIFFUSION AND
OF
GOLD
PLATINUM
Besides the Kirkendall effect some accompanying phenomena can be observed such as porosity, dimensional changes and structural changes. (1) Porosity It appears from very many theoretical and experimental investigations that the kinetics of the pore formation is very complicated. Summarizing these investigations one can say that porosity occurs if the vacancy concentration lies above the equilibrium value and if nuclei are present. Moreover, the pore formation is influenced by internal stresses. We succeeded in making the pores visible by a very careful electrolytical polishing technique with a concentrated solution of ferric-chloride in concentrated hydrochloric acid and a current density of about 50 mA/cm z. In all types of diffusion couples employed porosity has been observed. Fig. 11 shows the electrolytically polished surface of diffusion couple 17. A mechanically polished surface does not show any porosity as a consequence of the filling-up of the pores by the soft gold. The porosity distribution and the size of the pores has been especially studied in diffusion couple 8. The distribution was determined by turning off the couple carefully parallel to the marker interface and polishing the surface. From a microphotograph (Fig. 12) the percentage of the pores could be measured.
FIG. 12. Twenty-five per cent porosity in an interface .*.. .. . ..^
BOLK: MARKER d I
KIRKENDALL
EFFECT
INTERFACE
IE
Au-Pt
SYSTEM
It can be observed
641
from the intersections
of the
pores with the polished surface of the diffusion couple
I
that they are of octahedral
shape.
Their average size
is about 25 p. (2) Other phenomena Several other phenomena have been observed during the interdiffusion in lateral
-i-
surface
of gold and platinum, such as changes
dimensions
gonization nounced. increases.
IO4
of the pores is given in Fig. 13.
shows that the porosity with the concentration
is about It
is mainly present at the gold
side of the marker interface.
By comparing
penetration
Fig. 13
curve of the dif-
fusion couples 24 and 25 (same type, diffusion temper-
in lateral
dimensions
decreases,
60-70 ,u and the decrease
The occurrence
about
internal stresses cause deformation the surface layer of the diffusion
porosity lies in nearly pure gold. penetration
in the
For this reason we do
to correct
the concentration
curves for the presence of the pores.
It appears from Fig. 12 that the pores are bounded by crystallographic earlier
by
Buckle
planes. and
This has been observed
Blinc20), in Al-Cu
couples and by Barnesc2n in Cu-Ni nomenon
has been explained
of the anisotropy
couples.
3040
p.
This defor-
mation results in a gliding along crystal planes. The polygonization
is also a consequence
Fig. 16(a) is a microphotograph
of diffusion boundary
lying
intermediate
to the direction
between
and the marker interface.
of internal
of an electrothe phase
Fig. 16(b) is an
enlarged von Laue spot of a similar surface.
The spot
is split up into parts, a criterion for polygonization. It is not known at this present time which precise
diffusion
atomic
The phe-
mentioned
by Geguzin(22) by means
of the surface tension.
side it couples
of the crystals in
couple.
lytically polished surface perpendicular
not think it necessary
pro-
of glide steps makes one suspect that
already
the maximum
are very
with diffusion
stresses.
Even
at the
at the platinum
Some experiments
ature and time) it appears that the pores are formed in pure gold.
steps
heated at 1055°C during 100 hr show that the increase
FIG. 13. The porosity distribution in diffusion couple 8.
The distribution
glide
(Fig. 15) and poly-
At the gold side of the marker interface the
lateral dimension cmx
la),
couples
(Fig. 16).
The changes
x,
(Fig.
of the diffusion
mechanism above.
nism is responsible
is responsible
for the phenomena
We believe that the same mechafor the porosity formation
the other phenomena.
FIG. 14. Change of lateral dimensions in diffusion couple 1 after 360 hr. x 63
and for
ACTA
642
FIG. 15.
METALLURGICA,
VOL.
9,
1961
Glide steps at the surface of a couple.
x430
3. L. S. DARKEN, TT~~s. Amer. Inst. Min. (M&K) ETZ~S 175, 184 (1948). 4. G. S. HARTLEY and J. CRANK, Trans. Faraday Sot. 45, 801 (1949). 5. F. SEITZ, Phys. Rev. 74, 1513 (1948); Acta Cry&, Kopenh.
3, 355 (1950). 6. H. BUCKLE, 2. Met&k. 37, 175 (1946). 7. Th. HEUMANN and P. LOHMANN, 2.
(a)
Elektrochem.
59,
849 8. H. B+KLE (1955). and J. DESCAMPS, Rev. M&all. 48, 569 (1951). 9. TH. HEUMANN and A. KOTTMANN, 2. MetaUk. 44. 139
11953).
10. i. C.’ HICKS, !&an% Amer. Inst. Min. (Met&) Engrs 113, 163 (1934). 11. TH. HEUMANN and F. HEINEMANN, 2. Elektrochem. 80.
1160 (1956). 12. W. SEITE and
A.
KOTTMANN, Angew.
Chem. 64, 379
(1952).
13. M. G. OKNOW and L. S. MOROZ, Zh. Tekh. Fiz. 11, 593 (1941). 14. E. FITZER. 2. Met&k. 44. 462 (1953). 15. A. S. D&LINO, R. A. %INT~RN and J. C. CHASTON, J. Inst. Met. 81, 125 (1952). 16. A. D. LE CLAIRE and R. S. BARNES, J. Metals, N. Y. 3.
(bl
1060 (1951). 17. R. E. HOFFMANN and D. TURNBULL, J. Appl. 634 (1951). B. OKKERSE, Thesis, Delft (1954). E. S. WAJDA, Acta Met. 2, 184 (1954).
Phys. 22,
E. S. WAJDA, G. A. SHIRN and H. B. HUNTINGTON, Acta Met. 3, 39 (1955). S. YUKAWA and M. J. SINNOTT, J. Metal8 N.Y. 7, 996 (1955). W. R. UPTHEGROVE and M. J. SINNOTT, Trans. A?ner. Sot. Metals 50, 30 (1957).
S. Z. BOKSTEIN, S. T. KISHKIN and L. M. MOROZ, Int. in Sci. Res. Paris, 1957, UNESCORapp. No. 193. A. BOLK, Actn Met. 6, 59 (1958). A, BOLK and T. J. TIEDEMA, La Diffusion dans 1~9Mdtaux p. 91. Philips Techn. Library, Eindhoven (1957). H. Bii~~~~~and J. BLIN, J. Inst. Met. 80, 385 (1951). R. S. BARNES, PTOC. Phys. SW., BBS, 512 ~~ Lond. _ -______ _ (1952). ..__-. YA. E. GEGUZIN, Dokl. Akad. Nauk SSSH 100,255 (1955).
Conf. on Radio-Isotopes
FIG+. 16. (a) Polygonizetion. (b) Von Laue spot.
x430
18. 19. 20.
REFERENCES 1. A. D. SMI~ELSKAS and E. 0. KIRKENDALL, Trans. Amer.
Inat. Min. (Met&.) Engrs 171, 130 (1947). 2. C. MATANO, J. Phys. Japan 8, 109 (1933).
21. 22.
EFFECT
AND
GOLD-PLATINUM THE
KIRKENDALL A.
DIFFUSION
IN THE
SYSTEM-I EFFECT*
BOLKt
The Kirkendall effect has been studied in the gold-platinum system, one of the rare systems with a miscibility gap in the solid state. The effect has been measured as a function of time and temperature in a great number of “sandwich” couples. These couples consisted of pure gold and pure platinum, polycrystalline and singlecrystalline, and of pure gold and a gold-rich alloy with 73.5 at.% gold. It could be established, as a consequence of the obtained accuracy of the measurements, that the difference in magnitude of the effect in couples with polycrystalline platinum and in couples with singlecrystalline platinum has a physical significance. It has been interpreted in terms of an extra diffusion transport along the grain boundaries in polycrystalline platinum. Besides the Kirkendall effect the phenomena associated with this effect, such as porosity, dimensional and structural changes, has been studied as well as the phase-boundary displacement.
EFFET
KIRKENDALL
ET
DIFFUSION
DANS
LE
SYSTEME
OR-PLATINE-I
L’auteur a Btudie l’effet Kirkendall dans le systeme or-platine, l’un des rares systemes qui presentent une lacune de miscibilite it 1’Ptat solide. L’effet a et& mesure en fonction du temps et de la temperature dans un grand nombre de couples “en sandwich”. Ces couples Btaient constitues d’or pur et de platine pur, polycristallin et monocristallin et d’or pur et d’un alliage riche en or a 73,5 at y0 d’or. 11 semble qu’on puisse conclure, en tenant compte de la precision obtenue dans les mesures que la difference de la grandeur de l’effet constatee entre les couples avec platine polycristallin et les couples avec platine monocristallin, ait une signification physique. Cette difference est interpretee comme resultant dune diffusion additionnelle le long des frontieres de grains dans le platine polycristallin. Outre l’effet Kirkendall, les phenomenes associes b cet e&t, tels que la porosite, les modifications de dimensions et de structures, ont 6th Studies en meme temps que les deplacements de front&es de phases.
KIRKENDALL-EFFEKT
UND DIFFUSION BEIM DER KIRKENDALL-EFFEKT
SYSTEM
GOLD-PLATIN-I
Bairn System Gold-Platin, einem der wenigen Systeme mit einer Mischungsliicke im fasten Zustand, wurde der Kirkendall-Effekt untersucht. Er wurde in Abhangigkeit von Zeit und Temperatur an einer groDen Zahl von “sandwich’‘-Probenpaaren gemessen. Die Paare bestanden aus reinem Gold und reinem Platin, polykristallin und einkristallin, und aus reinem Gold und einer goldreichen Legierung mit 73.5 Atom% Gold. Die Messungen waren so genau, da13 der Unterschied der GroDe des Effekts bei Paaren mit polykristallinem Platin und solchen mit einkristallinem Platin einwandfrei nachgewiesen werden konnta. Er wurde gedeutet auf Grund einer zusatzlichen Diffusion entlang den Korngrenzen in polykristallinem Platin. Neben dem Kirkendall-Effekt wurden die damit zusammenhlingenden Erscheinungen-Porositat, Anderungen von Ausdehnung und Struktur-sowie die Verschiebung der Phasengrenze untersucht.
A.
The discovery
INTRODUCTION
of the Kirkendall
effect in 1947 by
of Smigelskas
and Kirkendall
face between
the two halves
that the marked interof a diffusion couple
Smigelskas and Kirkendallo)
was a good motive for a
(consisting
comprehensive
in the field of the inter-
a-brass side of the couple, it was possible to describe
Before 1947 a diffusion
the diffusion by means of two diffusion coefficients.
investigation
diffusion of metals and alloys. process
was
described
by
means
coefficient only (see Matanot2));
of one diffusion
These well-known intrinsic
after the observation
METALLURGICA,
VOL.
9, JULY
1961
moves towards the
or partial
diffusion coeffi-
cients, referring to the two components which take part in the diffusion process, can be calculated from an
* This paper contains a part of the author’s thesis, Delft 1959. Received April 22, 1960; revised October 25 1960. 7 Laboratory for Physical Chemistry, Technical University, Delft, Holland. Now at Philips’ Research Laboratories, Eindhoven, Holland. ACTA
of copper and a-brass)
observed Kirkendall effect (see Darkenc3), Hartley
and
Crank(*), and Seitzc5)). The problem of the interdiffusion of two metals and/ or alloys is much more complicated if phase boundaries
632
BOLK:
and intermetallic the process.
KIRKENDALL
phases come into existence
EFFECT
during
Until now nearly all investigations
been carried out with continuous
have
metal systems or in
IN
Au-Pt
the difference between the initial concentrations be large.
of a phase boundary
(i.e. a discontinuity
such parts of binary metal syst ems,in which a continuous series of solid solutions can be formed during the
are chosen on opposite
diffusion.
An advantage
Only a few investigators
have made their
in systems with miscibility
gaps in the
The
following
discontinuous
investigated:
Ag-Zn
Lohmann”),
Al-Be
Ag-Mg
by
Hickso”), Cu-Zn
by Biickle’@ by
Heumann Cu-Sb
by
systems and and
by Seith and Kottmann@),
Kottmann@),
Fe-MO
by Oknow
Cr-Fe
by
Heinemannor),
couple
in continuous systems will for the
at elevated
temper-
whichisresponsiblefor
of the equilibrium
phases at the phase
diffusion
equations
rate-determining
is that the
process.
This
is
already the case after a short diffusion time. The
gold-platinum
investigation
per
system
on account
was
for
this
of one mis-
difference
of the
is favourable
for the appearance
effect. derived
from
obtained from experiments
these
values,
between the initial concentrations
however, is unfavourable
of the marker interface.
changes,
effect,
such
as
be
are not very pronounced.
of a large
An advantage
accompanying
porosity
of
This condition,
for the appearance
would be that the phenomena endall
can
in diffusion couples with a
the two halves of the diffusion couple.
and
the Kirk-
dimensional
In the opposite
case, a large difference between the two concentrations will be favourable for a large displacement of the marker interface. However, the porosity and similar phenomena
will be very pronounced,
the reliability coefficients.
of the calculated
which decreases
values of the diffusion
We have meant to lay stress on the Kirkendall and the accompanying
phenomena,
for about
at 1200°C for 2 hr and
In this way small pieces of the
quenched in icewater.
Two such
metals of the size of a button were obtained.
a thickness of about 1 mm and sawn into platelets of about
1 x 3 x 5 mm.
Another
button
of platinum
and the buttons of the alloys were sawn directly into platelets
of
the
same
size.
The
platelets
were
turned off carefully to make them plane parallel and between filter papers. graph showed
A back reflection X-ray photo-
that the surface of the platelets
deformed
To eliminate
as a consequence
secondary
reactions
effect
which means that
wau
of the turning during
the dif-
fusion process the platelets were heated at 1200°C for 100 hr, the gold platelets at 1055°C.
Reliable values for the diffusion coefficients and for
displacement
crucibles
furnace at a temper-
which took place in about 3 hr,
the alloys were homogenized
off.
(1769%) which
small difference
They were melted in alumina
After cooling,
melting points of gold (1063°C) and platinum
makes one expect a great difference in mobility,
quantities
of
by Drijfhout,
then cleaned with soap, alcohol and water and dried
chosen
of the existence
1 hr.
somewhat
the
with a purity
been supplied
kept in the molten state at this temperature
cibility gap only (Fig. l), while the great difference in
Kirkendall
have
cent,
buttons of pure gold and pure platinum were rolled to
of the diffusion time. The condition for the application is the
PROCEDURE
placed in a vacuum graphite-tube
and
This reaction we assume to be independent
of the fundamental
EXPERIMENTAL
The metals gold and platinum, 99.99
A second process which takes place is the so-
called phase-boundaryreaction,
diffusion
B.
Amsterdam.
in discontinuous
of a diffusion
boundary.
takes place as it
systems.
and Heumann and
to the diffusion
the diffusion
the occurrence
the diffusion
and Morozo3)
not be the only process which is responsible atures.
decreased;
ature of about 150-200°C above the melting points and
In contradistinction
behaviour
gap.
of a phase boundary
and
Fe-Xi by Fitzero4). systems,
sides of the miscibility
of the appearance
were in two separate one-phase
Descamps@),
Kottmanna’),
Heumann
been
and Heumann
Buckle
and
have
in the concen-
curve) that the two concentrations
is that the difference between the two concentrations is actually
solid state.
must
Moreover, it is necessary for the appearance
tration penetration
experiments
633
SYSTEM
after this treatment The not-rolled
The crystal size
is given in Table 1.
platinum
platelets are nearly single
crystals with one or two grain boundaries The diffusion couples (sandwich-type) in the welding-apparatus
only.
were prepared
shown in Fig. 2 at a temper-
ature of about 80-100°C below the temperature to be applied in the diffusion experiments, and under a pressure of about loo-350
atm.
The temperature
was
maintained by means of internal heating with a current of about 100 A. Two platelets with the highest concentration
of gold
were welded
on both
sides of the Quartz
platelet with the lowest concentration of gold. fibers (5-10 ,u) were used as marker material.
In this type of diffusion couple the “interface” reference to which the displacement
with
of the markers can
be measured lies in the middle between the two marker After welding the couples were made
interfaces.
parallel on the lathe, embedded
in urea-formaldehyde
G34
ACTA
METALLURGICA,
VOL.
9,
1961
1769
1600-
1500-
1400b-
I-1300-
1200-
/ / 1100-
IWO-
9oLJ0
20
Pt
40
60
Weight % Au
AU
FIG. 1. The gold-platinum system (according to Darling et CSZ.“~)).
and polished with Cr,O,-, Al,Os- and diamond-suspensions. The distance between the two marker interfaces TABLE 1. Average crystal size of gold, platinum and the gold-platinum alloys
Composition Rolled gold Rolled platinum Not-rolled platinum 73.5 at.% Au alloy 66.7 at.% Au alloy 13.5 at. y. Au alloy
Crystal size (cm) 7-8
x 10-z
< 10-Z
3 x 10-l 5 x 10-a 5 x 10-s
5 x 10-s
was measured by means of a microscope with a movable object-table with a very accurate micrometer. Diffusion took place in a furnace which was controlled within about &‘C and whose temperature has been measured with an accuracy of +2”C. After a certain diffusion time the diffusion couple was again embedded in urea-formaldehyde and, after polishing, the marker distance measured, The marker displacement was caloulsted from AM=-
4 - 4
BOLK:
KIRKENDALL
EFFECT
where d, = initial distance between the two marker interfaces, d, = the distance after a diffusion time t. The interdiffusion of gold and platinum has been studied in a number of diffusion couples listed in Table 2.
IN
Au-Pt
TABLE 2.
3* 4 : zi 9 11 12 13 14 15 16 :;: 19 24 25 26 21 28 30
31 40 41 42 43 44 4: 41 50 51 52 54
(_
Diffusion temp. (“C)
Type of couple
~1038 ~1038 -1002 -1020 NlOOO 1020 1020 970 970 970 1055 1055 926 926 1055 1055 1020 1020 970 970 926 926 NlOlO -1020 1020 1055 1055 1020 1020 970 970 926 926 1000 1000 1000 1000
A/PO/A A/PO/A A/PO/A AlLIlA Li/Pb/LB A/PG/A A/PG/A A/PO/A A/PG/A A/PG/A A/PG/A A/PG/A A/PG/A AiPGiA A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PO/A A/PG/A A/PG/A AIPGIA AiLliA AjLliA A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/Ll/A A/PG/A A/L3/A L2/PG/L2 A/PO/A
-
Fm. 2. The welding apparatus. C. RESULTS
The displacements of the marker interfaces are given in Figs. 3-6 as a function of the square root of the diffusion time t. It appears that the straight lines, calculated with the method of the root mean squares, do not go through the point (0; O).* This is due to the fact that the markers are pressed completely into the soft gold during the welding as can be seen from Fig. 7. The straight line can be expressed by A,=al/t+b
635
The diffusion couples investigated, with diffusion temperatures
Number
;:
SYSTEM
(1)
where a is the slope of the straight line and where b is the length cut from the AM-axis. We think that b is the distance over which the concentration cM of the * In the first papers concerning the Kirkendall effect in the gold-platinum system by the present authorI1s~1s’the curves through the points are not straight lines. These tirst measurements have not been carried out by means of the microscope described in Section B and the specimens were not heated in a controlled furnace. The investigations with specimen 54 shows (Fig. 6) that the points lie on a straight line within the experimental error. The deviation of the curves from a straight line in Fig. 2 of the paper mentioned above has no physical significance.
A = rolled gold PG = rolled platinum PO = not-rolled platinum Ll = 73.5 at.% Au-alloy L2 = 66.7 at.% Au-alloy L3 = 13.5 at.% Au-alloy The sign N indicates that the diffusion couple has been heated in a non-controlled furnace. The accuracy of the temperature is about 10°C in these cases. * The results obtained with this specimen have already been published by the author.(iBJPJ
marker interface must be displaced before the markers move proportionally to the diffusion time t. The calculation of b for each specimen shows that the values are spread randomly around the mean value 6 = -5.8 /J. All displacements have been corrected with this mean value, after which the straight line has been recalculated. Then we obtain:
(2) From the standard deviation of every series of plotted points the standard deviation, era,, of a’ can be calculated. The values for equation (2) and the standard deviation of every series are given in Table 3 and Table 4. Together with the measurements of the marker
636
ACTA
METALLURGICA,
vTtime
Fig. 3, series I, type A/PG/A. FIGS.
3,
4
and
t,
VOL.
9,
1961
hr
Fig. 4, series II, type A/PO/A.
Fig. 5, series III, type A/Ll/A.
The marker displacement Aar as a function of the square root of the diffusion time t at four diffusion temperatures.
5.
25c
2oc
l5C
x
Phase 9
;
boundary
~Markw
interface
IOC
AlPGlA AIPG(A 50
0
lr&” /
AlPGlA A fL31A
IrB
5
A iPO[A
97O~i A
IO
fi
time 1,
lb).
(POIA
I5
hr
Fm. 6. The marker displacement Ax in diffusion couples of various types as a function of the square root of the diffusion time t.
FIG. 7. Diffusion couple 9 before (a) and after (b) a diffusion time of 100 hr. x 150
BOLK:
Type of couple
Number of couple
Diff. time t (hr)
12 13 6
100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100
1055
I(A/PG/A)
1020
: 11 14 15 16 17 18
970 926 1055
II(A/PO/A)
1020
;: 25 26 27 40 41 42 43 44 4.5 46 47
970 926 1055
III(A/Ll/A)
IN
Au-Pt
=
I
Temp. (“C)
EFFECT
637
SYSTEM
:A for the diffusion counles of the series I(A/PC . I A), II(A/PO/A)
TABLE 3. Dienlacement
I__.__
KIRKENDALL
1020 970 926
I
and III(A/Ll/A)
r;
Std. deviation (20.84 (20.76 (17.80 (17.5” (12.4O (12.15 (8.0* (8.22 (19.62 (19.05 (15.0s (14.00 (9.48
+ 0.28) * O.l*) f 0.19) k 0.14) & 0.3O) * 0.12) & 0.16) & 0.06) -& 0.07) & 0.1”) * 0.13) & 0.19) & 0.19)
(p)
A#
3.9
1.’ 2.9 0.9
/
2.4 2.9 2.8 2.9
16 217
(14.80 (12.57 (12.2’ (7.94
& + 5 *
1.’ 0.8 1.1 1.’ 2.5 2.2
0.13) 0.06) 0.08) 0.13)
0.0207
0.0208 0.0208 0.0178 0.0176 0.0124 0.0122 0.008 1 0.0082 0.0196 0.0191 0.0150 0.0140 0.0095 0.0097 0.0068 0.0068 0.0143 0.0148 0.0126 0.0122 0.0079 0.0082 0.0068 0.0064
2.3
’
AM b4-t
(cm) *
--
3.7 2.5 2.0
1.0 1.3 1.’
--~
3.4
0.676 0.0194 0.0190 0.0156 0.0146 0.0096 0.0082 0.0072 0.0068 0.0199 0.0209 0.0163 0.0156 0.0113 0.0115 0.0079 0.0076
= .-.-* Calculated from equation (2) for t = 100 hr. 7 Deduced from the concentration penetration curves (see Part II). TABLE 4. Displacement
I Type of couple A/PG/A A/PG/A A/PG/A A/L3/A A/PO/A A/PO/S
Temp. (“C) -1020 NlOlO 1000 1000 1000 970
* Calculated from equation
I
Number of couple 30 28 50 51 54 8
for diffusion couples of various types .~_ Diff. time t (hr) 100 100 100 100 400
(16.8l (15.50 (15.49 (13.56 (12.64 (9.72
100
displacement
Temp. (“C) I-1010 -1020 1020 1000 1000
1.6
0.0168 0.0155 0.0155 0.0136 0.0126 0.0097
&- 0.12) + 0.14) + 0.29) f 0.03) f 0.21) + 0.2’)
;:“, 0.3 2.9 3.6
Diff. time t (hr)
28
100 100 100 100 400
z 51 54
I
I
Number of couple
.-.-* Calculated from equation
A.#’ (cm)*
AP.b. in various diffusion couples
I
A/PG/A A/PG/A A/PG/A AILS/A A/PO/A
Std. deviation (p)
_
(2) for t = 100 hr.
TABLE 5. Phase-boundary Type of couple
n’(p/hr”“)
(t’( p/h+‘*) (2.14 (2.2’ (2.00 (2.7’ (1.58 _:-
* & + + f
Std. deviation (p)
0.04) 0.04) 0.11) 0.1’) 0.03)
1.6 1* 1:1
- .~__..__ Id
sidered concentration sionless constant
range. Together with the dimen-
(Fig. 8). The straight lines can be drawn through the point (0; 0). The values are given in Table 5. The diffusion coefficient D can be written as = D,(c) exp
0.0021 0.0023 0.0021 0.0028 0.0016
0.6 0.6
(2) for t = 100 hr.
displacements the displacement Ap,b_of the phase boundary has been measured in some diffusion couples
W4
AD.b. (cm)*
k-4?(c)/~~l.
K=xa
(3)
Now we assume D,(c) (the frequency factor) and Q(c) (the activation energy) to be constants in the con-
(4)
Dt
we obtain x = 1/(D,K)
dt exp [-Q/2ET]
Alw = K,y’t
exp [--&,/2RT].
so that
From this equation
the values of K,
(5)
and QM can be
638
ACTA
METALLURGICA,
40
30
P 20 9"
VOL.
9,
1961
of series I and II they are in good agreement with the directly observed displacements. For the couples of series III they are about 2040 per cent greater than the directly observed values, so that secondary reactions have taken part in the process, which have influenced the direct measurements. For series III the indirect observed displacements have been used for the calculation of K, and QM. The displacements in the couples 2830 and 50 of the A/PG/A type of series I and in the couples 8 and 54 of the A/PO/A type of series II (Table 4), which have not -4.400
IO
-4.600
0
Jf time1, hr The phase boundary displacement Ap.b. in couples of various types as a function of the square root of the diffusion time t. Fxo. 8.
calculated by plotting log ( A,“/z/t) as a function of the reciprocal temperature (Fig. 9). The calculated values are given in Table 6 together with the standard deviations of the activation energies.
k ; -4.700 9 3
-4.600
D. DISCUSSION
A very pronounced displacement (in the order of about 50-200 ,u in 100 hr) of the marker interface has been observed. The displacement takes place in the direction of the highest concentration of gold, from which we can conclude that gold is the faster diffusing component. The displacement in couple 5 (gold rich alloy against not-rolled platinum) appeared to be only about 10 ,u in 870 hr or about 3 p in 100 hr, which is very small compared with the displacements in other types of couples. The displacements deduced from the concentration penetration curves of the couples from the series I, II and III are assembled in Table 3.* For the couples TABLE 6. The values of&x, KM and aearcalculated from the displacement AM by means of equation (5) Series
* The concentration penetration curves will be discussed in Part II.
I
I
I
\I
\\
-4.900
-5.CXXl~ 750
Bo
I/TXIO+4 FIG. 9. Log(Ax/l/t) plotted as a function of the reciprocal temperature.
been used for the calculation of KM and QM, are in good agreement with the calculated lines of Fig. 8. The displacements in diffusion couples consisting of gold and rolled polycrystalline platinum (crystal size < low2 cm) turn out to be about lo-20 per cent greater than those in couples consisting of gold and nearly single crystalline platinum (crystal size 3.10-l cm). This effect, moreover, is dependent on the diffusion temperature. In consequence of the accuracy of observation attained by us these observed differences must be real. We interpret them as a consequence of an extra diffusion transport along the grain boundaries in polyorystalline platinum. In 1951 Le Claire and Barne@) observed that markers lying opposite to a
BOLK:
KIRKENDALL
EFFECT
grain boundary were displaced over a greater distance than markers lying farther from a grain boundary. From a number of investigations (17)in the field of selfdiffusion, it appears that a grain boundary contribution can be detected and measured when the annealing temperature is between 0.50-0.90 of the melting point of the system. Taking in our case for the melting point that of the alloy with the concentration of the marker interface (since the difference between the partial diffusion coeffmients there is responsible for the appearance of the Kirkendall effect), our annealing temperatures are N 0.85-0.94 of the melting point. We can conclude from these values that a measurable transport can take place along the grain boundaries. However, the diffusion temperatures are too high to expect grain boundary diffusion only, which is a necessary condition for the calculation of the grain boundary diffusion coefficient as done by the referred investigators. From the values of K, and QM for the series I and II (Table 6) and using formula (5) the marker displacement AM-s.,,. can be calculated, in so far as it is an effect of the grain boundary diffusion only. At 1055 and 926°C the grain boundary displacement is 11.5 and 20.9 per cent, respectively of the total marker displacement in polycrystalline platinum. These percentages are in agreement with the fact that the contribution of
IN
Au-Pt
639
SYSTEM
the grain boundary diffusion to the total diffusion is decreasing with increasing temperatures. The marker displacements at these temperatures are 23.9 and 17 p, respectively. From these values we can calculate K M_g,b.and QM_q.b,,thus giving the relation between A M_g.b.,t and T: 300/2RT].
A M_g.b,= 9 x 10h51/t exp [-16
We hereby assumed that the log (AM-,&Z/t)-l/T relation may be rendered by a straight line. The ratio between the activation
energy for volume
selfdiffusion
and that of grain boundary
determined
by the authors
from 0.40-0.70.(17)
mentioned
In our investigation
selfdiffusion
above varies the ratio turns
out to be 0.36. The activation
energy in the polycrystalline
line platinum, preceding
which is not astonishing
calculation
size is nearly
in view of the
and the fact that the crystal
the same in both alloy and platinum
(Table 1). In Fig.
10 the results concerning
effect in the gold-platinum
system
together
with those
systems.
For this purpose the values of log (AM/l/t)
of practically
concerning
the Kirkendall are summarized
the effect
in other
all known effects are given as a function
of the reciprocal
temperature.
It appears from this
-6.OC
t
6
6
IO
12
14
16
I/T x104
FIG. 10. 2
Survey
of the Kirkendall
alloy
with 73.5 at. y& gold is just the same as in polycrystal-
effect in vmious systems; reciprocal temperature.
log (Ax/dt)
as a function
of the
640
ACTA
METALLURGICA,
figure that the Kirkendall effect in the gold-platinum system is about 30,000 times smaller than that in the copper-zinc system, at least if compared at the same temperature (400°C). In Part II the magnitude of an observed Kirkendall effect is expressed in a numerical quantity based on the ratio between the partial diffusion coefficients, thus comparing the marker displacement with the diffusion amount. It appears from the experiments (Fig. 8) that the phase-boundary displacement Ap.b. is proportional with the square root of the diffusion time. When the phase-boundary reaction is rate-determining, the phase-boundary displacement will be a function of this reaction. Assuming the rate of this reaction to be independent of the diffusion time, which means that a certain amount of the one phase will be transformed into the other phase in unit time and at any moment of the process, the phase boundary will move proportionally to the diffusion time. When the diffusion is process-determining the phase boundary reaction will be a reaction which follows the diffusion process. Since the course of this process is proportional to the square root of the diffusion time, the phase boundary reaction, i.e. the phase boundary displacement, will do the same. So we may conclude that the diffusion has been rate-determining, although this conclusion need not be valid for the beginning of the process when the concentration gradient is very high. Our accuracy was not sufficient to measure a beginning effect.
FIG. 11.
Electrolytica;llypolished surface of diffusion couple 17. x 54
VOL.
9,
1961
E. PHENOMENOLOGICAL OF
THE
OBSERVATIONS
INTERDIFFUSION AND
OF
GOLD
PLATINUM
Besides the Kirkendall effect some accompanying phenomena can be observed such as porosity, dimensional changes and structural changes. (1) Porosity It appears from very many theoretical and experimental investigations that the kinetics of the pore formation is very complicated. Summarizing these investigations one can say that porosity occurs if the vacancy concentration lies above the equilibrium value and if nuclei are present. Moreover, the pore formation is influenced by internal stresses. We succeeded in making the pores visible by a very careful electrolytical polishing technique with a concentrated solution of ferric-chloride in concentrated hydrochloric acid and a current density of about 50 mA/cm z. In all types of diffusion couples employed porosity has been observed. Fig. 11 shows the electrolytically polished surface of diffusion couple 17. A mechanically polished surface does not show any porosity as a consequence of the filling-up of the pores by the soft gold. The porosity distribution and the size of the pores has been especially studied in diffusion couple 8. The distribution was determined by turning off the couple carefully parallel to the marker interface and polishing the surface. From a microphotograph (Fig. 12) the percentage of the pores could be measured.
FIG. 12. Twenty-five per cent porosity in an interface .*.. .. . ..^
BOLK: MARKER d I
KIRKENDALL
EFFECT
INTERFACE
IE
Au-Pt
SYSTEM
It can be observed
641
from the intersections
of the
pores with the polished surface of the diffusion couple
I
that they are of octahedral
shape.
Their average size
is about 25 p. (2) Other phenomena Several other phenomena have been observed during the interdiffusion in lateral
-i-
surface
of gold and platinum, such as changes
dimensions
gonization nounced. increases.
IO4
of the pores is given in Fig. 13.
shows that the porosity with the concentration
is about It
is mainly present at the gold
side of the marker interface.
By comparing
penetration
Fig. 13
curve of the dif-
fusion couples 24 and 25 (same type, diffusion temper-
in lateral
dimensions
decreases,
60-70 ,u and the decrease
The occurrence
about
internal stresses cause deformation the surface layer of the diffusion
porosity lies in nearly pure gold. penetration
in the
For this reason we do
to correct
the concentration
curves for the presence of the pores.
It appears from Fig. 12 that the pores are bounded by crystallographic earlier
by
Buckle
planes. and
This has been observed
Blinc20), in Al-Cu
couples and by Barnesc2n in Cu-Ni nomenon
has been explained
of the anisotropy
couples.
3040
p.
This defor-
mation results in a gliding along crystal planes. The polygonization
is also a consequence
Fig. 16(a) is a microphotograph
of diffusion boundary
lying
intermediate
to the direction
between
and the marker interface.
of internal
of an electrothe phase
Fig. 16(b) is an
enlarged von Laue spot of a similar surface.
The spot
is split up into parts, a criterion for polygonization. It is not known at this present time which precise
diffusion
atomic
The phe-
mentioned
by Geguzin(22) by means
of the surface tension.
side it couples
of the crystals in
couple.
lytically polished surface perpendicular
not think it necessary
pro-
of glide steps makes one suspect that
already
the maximum
are very
with diffusion
stresses.
Even
at the
at the platinum
Some experiments
ature and time) it appears that the pores are formed in pure gold.
steps
heated at 1055°C during 100 hr show that the increase
FIG. 13. The porosity distribution in diffusion couple 8.
The distribution
glide
(Fig. 15) and poly-
At the gold side of the marker interface the
lateral dimension cmx
la),
couples
(Fig. 16).
The changes
x,
(Fig.
of the diffusion
mechanism above.
nism is responsible
is responsible
for the phenomena
We believe that the same mechafor the porosity formation
the other phenomena.
FIG. 14. Change of lateral dimensions in diffusion couple 1 after 360 hr. x 63
and for
ACTA
642
FIG. 15.
METALLURGICA,
VOL.
9,
1961
Glide steps at the surface of a couple.
x430
3. L. S. DARKEN, TT~~s. Amer. Inst. Min. (M&K) ETZ~S 175, 184 (1948). 4. G. S. HARTLEY and J. CRANK, Trans. Faraday Sot. 45, 801 (1949). 5. F. SEITZ, Phys. Rev. 74, 1513 (1948); Acta Cry&, Kopenh.
3, 355 (1950). 6. H. BUCKLE, 2. Met&k. 37, 175 (1946). 7. Th. HEUMANN and P. LOHMANN, 2.
(a)
Elektrochem.
59,
849 8. H. B+KLE (1955). and J. DESCAMPS, Rev. M&all. 48, 569 (1951). 9. TH. HEUMANN and A. KOTTMANN, 2. MetaUk. 44. 139
11953).
10. i. C.’ HICKS, !&an% Amer. Inst. Min. (Met&) Engrs 113, 163 (1934). 11. TH. HEUMANN and F. HEINEMANN, 2. Elektrochem. 80.
1160 (1956). 12. W. SEITE and
A.
KOTTMANN, Angew.
Chem. 64, 379
(1952).
13. M. G. OKNOW and L. S. MOROZ, Zh. Tekh. Fiz. 11, 593 (1941). 14. E. FITZER. 2. Met&k. 44. 462 (1953). 15. A. S. D&LINO, R. A. %INT~RN and J. C. CHASTON, J. Inst. Met. 81, 125 (1952). 16. A. D. LE CLAIRE and R. S. BARNES, J. Metals, N. Y. 3.
(bl
1060 (1951). 17. R. E. HOFFMANN and D. TURNBULL, J. Appl. 634 (1951). B. OKKERSE, Thesis, Delft (1954). E. S. WAJDA, Acta Met. 2, 184 (1954).
Phys. 22,
E. S. WAJDA, G. A. SHIRN and H. B. HUNTINGTON, Acta Met. 3, 39 (1955). S. YUKAWA and M. J. SINNOTT, J. Metal8 N.Y. 7, 996 (1955). W. R. UPTHEGROVE and M. J. SINNOTT, Trans. A?ner. Sot. Metals 50, 30 (1957).
S. Z. BOKSTEIN, S. T. KISHKIN and L. M. MOROZ, Int. in Sci. Res. Paris, 1957, UNESCORapp. No. 193. A. BOLK, Actn Met. 6, 59 (1958). A, BOLK and T. J. TIEDEMA, La Diffusion dans 1~9Mdtaux p. 91. Philips Techn. Library, Eindhoven (1957). H. Bii~~~~~and J. BLIN, J. Inst. Met. 80, 385 (1951). R. S. BARNES, PTOC. Phys. SW., BBS, 512 ~~ Lond. _ -______ _ (1952). ..__-. YA. E. GEGUZIN, Dokl. Akad. Nauk SSSH 100,255 (1955).
Conf. on Radio-Isotopes
FIG+. 16. (a) Polygonizetion. (b) Von Laue spot.
x430
18. 19. 20.
REFERENCES 1. A. D. SMI~ELSKAS and E. 0. KIRKENDALL, Trans. Amer.
Inat. Min. (Met&.) Engrs 171, 130 (1947). 2. C. MATANO, J. Phys. Japan 8, 109 (1933).
21. 22.