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The diffusion of antimony in tin at elevated temperatures
Scripta
METALLURGICA
Vol. 4, pp. 9 4 7 - 9 5 2 , 1970 P r i n t e d in the U n i t e d S t a t e s
Pergamon
Press,
Inc.
TIIE DIFFUSION OF ANTIMONY IN TIN AT ELEVATED TEMPERATURES
R. H. Packwood + and R. W. Smith* Research Scientist, Department of Energy, Mines and Resources, Ottawa, Canada. Professor of Metallurgy and Metallurgical Engineering, Queen's University, Kingston, Ontario, Canada. (Received
September
9,
1970)
Introduction When a dilute alloy freezes, the solid-liquid interface may become constitutionally supercooled(l).
This causes it to adopt a non-planar morphology, usually consisting of a
regular array of projections.
It is found that there is often considerable solute segregation
associated with this mode of freezing.
Should the solute reduce the melting point of the
solvent (i.e., distribution coefficient (k) < I) then the lower-melting point solute-rich liquid will accumulate around the base of any projection.
The earlier presence during freezing
of grooves on the interface is often revealed on a microsection behind and parallel to the interface as a regular ' honeycombe-like' array of segregation boundaries (leading to its usual description as the cellular substructure).
Upon continued crystal growth, the segregated
solute tends to disperse and to such an extent that all traces of the original cellular substructure may have disappeared by the time the interface has advanced 2 or 3 cm.(2). However, the situation for k > 1 solute, i.e., solute which raises the melting point of the solvent and therefore tends to avoid the cellular boundaries, is very different.(3) Very little change in the segregation pattern appears to take place during subsequent crystal growth.
One of the systems examined was that of antimony as a solute in tin.
Since little
diffusion data was available, in an attempt to account for this apparently anomalous diffusion behaviour, it was decided to determine the diffusion coefficient for the diffusion of antimony in tin and dilute tin antimony alloys.
The purpose of this paper is to report some of the
diffusion data obtained in these experiments. Experimental M e t h o d The short right-cylindrical single crystal specimens, 1 cm. diameter, required for these diffusion studies were produced by the Bridgman-technique using a split graphite mold and a seed crystal.
After the seed crystal had been placed in position the split was sealed with
'aquadag' to avoid strays originating in the 'flashing'.
Suitable growth conditions were
selected to produce specimens with the 'C' - crystal - axis perpendicular to the cylinder axis and containing no obvious substructure.
The compositions used were pure tin (Pass - 'S',
947
948
DIFFUSION
OF Sb
99.999% Sn) and 0.2 wt.% antimony in tin. saw(4) using 50% HNO 3. (5).
IN Sn
Vol.
4, No.
12
Pure tin crystals were sectioned with an acid
One end of each specimen was then 'spark-planed' to a fine satin finish
The alloy crystals proved almost impossible to cut with the acid saw and so were spark
sectioned.
Removal of the resulting rough surface finish was then effected by spark-planing
to a depth of 1 m.m.
The face into which the radio-isotope was to be incorporated was then
electro-polished, electro-etched, to check monocrystallinity and finally lightly ground to ensure a true planar condition.
All other faces were covered with 'Laconit' laquer.
The isotope use~ 124 Sb, has a half life of 60 days and emits a variety of high energy y-radiation during B- decay to 124Te.
It was obtained from U.K.A.E.A. (Amersham)
of antimony chloride in 5N, HCI., specific activity 200 mc/g. Sb.
in the form
After dilution, the isotope
was deposited on the exposed surfaces of the immersed specimens by electro-replacement.
The
masking lacquer was then removed and the specimens wrapped face to face in aluminium foil and sealed under argon in a thin wall copper-vessel.
Diffusion-annealing was carried out in a high
thermal mass oil bath, the temperature of which could be controlled to ± 0.01°C.
On removal
the specimens were quenched in water. To section a specimen it was first mounted in a jewellers chuck, the plane of the active-face positioned to ± .001 n~n. and 1 mm. machined from the specimen sides (in the directior low + high activity).
A perspex collecting vessel was then placed in position and the turnings
from each cut collected directly in the polythene bottles in which they were to be weighed and their activity determined using a Geiger-counting facility.
Statistics were always better than
2%. Experimental Results and Discussions Fick's law of diffusion, when applied to the present situation, shows that the concentration (C) of an isotope at some point (X) within a cylindrical specimen is given by
C = (Co/(~Dt)½)
exp (-x2/4Dt)
C
is the initial amount of isotope deposited, D is the diffusion coefficient and t is time of o anneal. The specific activity of a thin section is directly proportional to the concentration of isotope.
Hence a plot of In (activity) with x 2 should yield a straight line of slope - 1/4
Dr. Figure 1 shows a typical plot of log C versus x 2, where 'C' is the counting rate per minute per gramme and 'x' is the section-depth in centimeters.
It is seen to be a curve.
The
steeper part is due to bulk diffusion, however, the proportion of the remainder varies from specimen to specimen and is therefore presumably related to the previous treatment.
Spark
machining will produce irregular arrays of dislocations which on annealing could promote local recrystallisation or possibly the establishment of low-angle boundaries penetrating a variety of distances into the body of the crystal.
The x 2 varialion would favour the partial recrys-
tallisation proposal but the distribution of dislocations is not known and so cannot be ruled
Vol.
4, No.
12
DIFFUSION
OF
Sb
IN SN
949
-[ Experime.tal point with error bars
10'
Locus of 1/2 log C versus x" 1 Distribution due to bulk diffusion 2 Distribution due to enhanced diffusion
a--a
o ~0
o a
0
o
~x,,,,, °
10(
102 40
80
I 160
120
I 200
240
x 2 x 106 (cm 1)
Figure 1
Diffusion of 124Sb into Sn-O.2 wt.% Sb at 209°C (time 1.616 x 105 sees.)
out.
(A similar tail has been reported for the diffusion of gold in sodium(6).)
This would
suggest that the curve results from the superimposition of two linear variations of log C versus 2 x , namely, that resulting from bulk diffusion and that due to the previous treatment. The magnitudes of these two contributions may be estimated as follows. To reduce the curve to its components, a plot of ½ log C versus x 2 is made (line aa, Fig. I).
On this must lie the intersection of the linear plots for each contribution, i.e., at
some point along the specimen axis both transport mechanisms will have contributed equally to producing the inferred antimony concentration.
Test lines are then drawn-in to denote each
contribution and the fit checked by summation.
The slope of each line is proportional to the
value of the diffusion coefficient (D) for that process. Table I shows the D-values which have been deduced graphically from the experimental results of this study.
The proportions of each contribution are also noted.
The diffusion coefficient increases with increase in temperature, usually obeying the Arrhenius-type relation D = D e -Q/RT O
where D O is the diffusion constant, Q is the activation energy, R is the gas constant and T is the absolute temperature.
In view of the limited data available no attempt has been made to
950
DIFFUSION
determine D O and q.
OF Sb
IN Sn
Vol.
4, No.
12
However, the Q for the self-diffusion of tin, approximately 25 kcal/gm
atom(7,8), has been included in figure 2. tentative conclusions
The general spread of the results only permits the
that the diffusion of Sb 124 in tin and 0.2 wt.% Sb-Sn, and tin in tin are
not wildly different and that entended anneals should be applied in order to fully develop the effects of latent damage.
W°m
W-,I --Q
of 25 kcaL/g, atom i Z.O
0 I Z~;
I 2.W 1o a
-~- ('K ~)
Figure 2
Variation of the diffusion coefficient with temperature, It is interesting llel
1 i.e., log10 D vs. ~.
1 t o n o t e t h a t loglOD vs ~ p l o t can a l s o be r e s o l v e d i n t o two p a r a -
l i n e s o f a p p r o x i m a t e l y 12 kcal/gm atom, o b t a i n e d by a v e r a g i n g t h e r e s u l t s
Sn a t 209°C and u s i n g t h e e x p r e s s i o n lOgloD = lOgl0D o -
fo'r Sb 124 i n t o
lOgl0e ~.
A d e t a i I e d a n a l y s i s o f the s o l u t e h o m o g e n i s a t i o n o c c u r i n g d u r i n g c e l l u l a r growth and t h e a s s o c i a t e d c r y s t a l s u b s t r u c t u r e f o r m a t i o n i s t o appear e l s e w h e r e . Acknowledgements The e x p e r i m e n t a l work was c a r r i e d - o u t w h i l s t t h e Authors were a t t h e U n i v e r s i t y o f Birmingham, England.
The Authors wish t o acknowledge t h e i r i n d e b t e d n e s s to t h e U n i v e r s i t y f o r
Vol.
4, No.
12
DIFFUSION
OF
Sb
IN Sn
951
the provision of laboratory facilities and to the (then)Ministry of avaiation for financial assistance . References i.
Rutter, J. W., and Chalmers, B., 1953, Can. J. Phys., 31, 15.
2.
Damiano, V. V., and Tint, G. S., 1961, Acta Met., ~, 177.
3.
Hunt, M. D., 1965, Ph.D., Thesis, Birmingham University.
4.
Hunt, M. D., Spittle, J. A., and Smith, R. W., 1967, J. Sci. Inst., 44, 230.
5.
Packwood, R. H., and Smith, R. W., 1967, J. Sci. Instrum., 44, 1057.
6.
Barr, L. W., Mundy, G. N., and Smith, F. A., 1966, Phil. Mag., 14, 1299.
7.
Meakin, J. D., and Klokholm, E., 1960, Trans. A.I.M.E., 218, 463.
8.
Packwood, R. H., 1964, Ph.D. Thesis, Birmingham University.
Table 1 Diffusion of Sb 124 into Tin and 0.2 wt% Sb-Sn parallel to the C axis
Base Material
Temperature (°C)
0.2 wt% Sb-Sn
200.75
"
209.1
D (bulk) (cm2sec -I) 7.5 + 0.7 x 10 -12 (94%) 2.12 + 0.2 x I0 -II (99%)
D (damage)
(cm2sec -1)
9 . 2 + 0.9 x 10 -11 1.95 + 0 . 3 x 10
-10 -10
(6%) (1%)
"
209.73
1.84 + 0.15 x 10 -4 (99.8%)
5.39 + 0.4 x i0
"
224.1
2.79 + 0.3 x i0 -II (95%)
1.02 + 0.3 x I0 -I0 (5%)
209.1
1.93 _+ 0.2 x i0 -II (99.6%)
1.41 _+ -.3 x i0 -I0 (0.4%)
"
209.73
3.54 + 0.3 x i0 -II (96%)
2.88 _+ 0.4 x I0 -I0 (4%)
"
228.75
5.07 _+ 0.5 x I0 -ll (94%)
1.51 + 0.5 A i0 -I0 (6%)
Sn (99.999%)
(0.2%)
METALLURGICA
Vol. 4, pp. 9 4 7 - 9 5 2 , 1970 P r i n t e d in the U n i t e d S t a t e s
Pergamon
Press,
Inc.
TIIE DIFFUSION OF ANTIMONY IN TIN AT ELEVATED TEMPERATURES
R. H. Packwood + and R. W. Smith* Research Scientist, Department of Energy, Mines and Resources, Ottawa, Canada. Professor of Metallurgy and Metallurgical Engineering, Queen's University, Kingston, Ontario, Canada. (Received
September
9,
1970)
Introduction When a dilute alloy freezes, the solid-liquid interface may become constitutionally supercooled(l).
This causes it to adopt a non-planar morphology, usually consisting of a
regular array of projections.
It is found that there is often considerable solute segregation
associated with this mode of freezing.
Should the solute reduce the melting point of the
solvent (i.e., distribution coefficient (k) < I) then the lower-melting point solute-rich liquid will accumulate around the base of any projection.
The earlier presence during freezing
of grooves on the interface is often revealed on a microsection behind and parallel to the interface as a regular ' honeycombe-like' array of segregation boundaries (leading to its usual description as the cellular substructure).
Upon continued crystal growth, the segregated
solute tends to disperse and to such an extent that all traces of the original cellular substructure may have disappeared by the time the interface has advanced 2 or 3 cm.(2). However, the situation for k > 1 solute, i.e., solute which raises the melting point of the solvent and therefore tends to avoid the cellular boundaries, is very different.(3) Very little change in the segregation pattern appears to take place during subsequent crystal growth.
One of the systems examined was that of antimony as a solute in tin.
Since little
diffusion data was available, in an attempt to account for this apparently anomalous diffusion behaviour, it was decided to determine the diffusion coefficient for the diffusion of antimony in tin and dilute tin antimony alloys.
The purpose of this paper is to report some of the
diffusion data obtained in these experiments. Experimental M e t h o d The short right-cylindrical single crystal specimens, 1 cm. diameter, required for these diffusion studies were produced by the Bridgman-technique using a split graphite mold and a seed crystal.
After the seed crystal had been placed in position the split was sealed with
'aquadag' to avoid strays originating in the 'flashing'.
Suitable growth conditions were
selected to produce specimens with the 'C' - crystal - axis perpendicular to the cylinder axis and containing no obvious substructure.
The compositions used were pure tin (Pass - 'S',
947
948
DIFFUSION
OF Sb
99.999% Sn) and 0.2 wt.% antimony in tin. saw(4) using 50% HNO 3. (5).
IN Sn
Vol.
4, No.
12
Pure tin crystals were sectioned with an acid
One end of each specimen was then 'spark-planed' to a fine satin finish
The alloy crystals proved almost impossible to cut with the acid saw and so were spark
sectioned.
Removal of the resulting rough surface finish was then effected by spark-planing
to a depth of 1 m.m.
The face into which the radio-isotope was to be incorporated was then
electro-polished, electro-etched, to check monocrystallinity and finally lightly ground to ensure a true planar condition.
All other faces were covered with 'Laconit' laquer.
The isotope use~ 124 Sb, has a half life of 60 days and emits a variety of high energy y-radiation during B- decay to 124Te.
It was obtained from U.K.A.E.A. (Amersham)
of antimony chloride in 5N, HCI., specific activity 200 mc/g. Sb.
in the form
After dilution, the isotope
was deposited on the exposed surfaces of the immersed specimens by electro-replacement.
The
masking lacquer was then removed and the specimens wrapped face to face in aluminium foil and sealed under argon in a thin wall copper-vessel.
Diffusion-annealing was carried out in a high
thermal mass oil bath, the temperature of which could be controlled to ± 0.01°C.
On removal
the specimens were quenched in water. To section a specimen it was first mounted in a jewellers chuck, the plane of the active-face positioned to ± .001 n~n. and 1 mm. machined from the specimen sides (in the directior low + high activity).
A perspex collecting vessel was then placed in position and the turnings
from each cut collected directly in the polythene bottles in which they were to be weighed and their activity determined using a Geiger-counting facility.
Statistics were always better than
2%. Experimental Results and Discussions Fick's law of diffusion, when applied to the present situation, shows that the concentration (C) of an isotope at some point (X) within a cylindrical specimen is given by
C = (Co/(~Dt)½)
exp (-x2/4Dt)
C
is the initial amount of isotope deposited, D is the diffusion coefficient and t is time of o anneal. The specific activity of a thin section is directly proportional to the concentration of isotope.
Hence a plot of In (activity) with x 2 should yield a straight line of slope - 1/4
Dr. Figure 1 shows a typical plot of log C versus x 2, where 'C' is the counting rate per minute per gramme and 'x' is the section-depth in centimeters.
It is seen to be a curve.
The
steeper part is due to bulk diffusion, however, the proportion of the remainder varies from specimen to specimen and is therefore presumably related to the previous treatment.
Spark
machining will produce irregular arrays of dislocations which on annealing could promote local recrystallisation or possibly the establishment of low-angle boundaries penetrating a variety of distances into the body of the crystal.
The x 2 varialion would favour the partial recrys-
tallisation proposal but the distribution of dislocations is not known and so cannot be ruled
Vol.
4, No.
12
DIFFUSION
OF
Sb
IN SN
949
-[ Experime.tal point with error bars
10'
Locus of 1/2 log C versus x" 1 Distribution due to bulk diffusion 2 Distribution due to enhanced diffusion
a--a
o ~0
o a
0
o
~x,,,,, °
10(
102 40
80
I 160
120
I 200
240
x 2 x 106 (cm 1)
Figure 1
Diffusion of 124Sb into Sn-O.2 wt.% Sb at 209°C (time 1.616 x 105 sees.)
out.
(A similar tail has been reported for the diffusion of gold in sodium(6).)
This would
suggest that the curve results from the superimposition of two linear variations of log C versus 2 x , namely, that resulting from bulk diffusion and that due to the previous treatment. The magnitudes of these two contributions may be estimated as follows. To reduce the curve to its components, a plot of ½ log C versus x 2 is made (line aa, Fig. I).
On this must lie the intersection of the linear plots for each contribution, i.e., at
some point along the specimen axis both transport mechanisms will have contributed equally to producing the inferred antimony concentration.
Test lines are then drawn-in to denote each
contribution and the fit checked by summation.
The slope of each line is proportional to the
value of the diffusion coefficient (D) for that process. Table I shows the D-values which have been deduced graphically from the experimental results of this study.
The proportions of each contribution are also noted.
The diffusion coefficient increases with increase in temperature, usually obeying the Arrhenius-type relation D = D e -Q/RT O
where D O is the diffusion constant, Q is the activation energy, R is the gas constant and T is the absolute temperature.
In view of the limited data available no attempt has been made to
950
DIFFUSION
determine D O and q.
OF Sb
IN Sn
Vol.
4, No.
12
However, the Q for the self-diffusion of tin, approximately 25 kcal/gm
atom(7,8), has been included in figure 2. tentative conclusions
The general spread of the results only permits the
that the diffusion of Sb 124 in tin and 0.2 wt.% Sb-Sn, and tin in tin are
not wildly different and that entended anneals should be applied in order to fully develop the effects of latent damage.
W°m
W-,I --Q
of 25 kcaL/g, atom i Z.O
0 I Z~;
I 2.W 1o a
-~- ('K ~)
Figure 2
Variation of the diffusion coefficient with temperature, It is interesting llel
1 i.e., log10 D vs. ~.
1 t o n o t e t h a t loglOD vs ~ p l o t can a l s o be r e s o l v e d i n t o two p a r a -
l i n e s o f a p p r o x i m a t e l y 12 kcal/gm atom, o b t a i n e d by a v e r a g i n g t h e r e s u l t s
Sn a t 209°C and u s i n g t h e e x p r e s s i o n lOgloD = lOgl0D o -
fo'r Sb 124 i n t o
lOgl0e ~.
A d e t a i I e d a n a l y s i s o f the s o l u t e h o m o g e n i s a t i o n o c c u r i n g d u r i n g c e l l u l a r growth and t h e a s s o c i a t e d c r y s t a l s u b s t r u c t u r e f o r m a t i o n i s t o appear e l s e w h e r e . Acknowledgements The e x p e r i m e n t a l work was c a r r i e d - o u t w h i l s t t h e Authors were a t t h e U n i v e r s i t y o f Birmingham, England.
The Authors wish t o acknowledge t h e i r i n d e b t e d n e s s to t h e U n i v e r s i t y f o r
Vol.
4, No.
12
DIFFUSION
OF
Sb
IN Sn
951
the provision of laboratory facilities and to the (then)Ministry of avaiation for financial assistance . References i.
Rutter, J. W., and Chalmers, B., 1953, Can. J. Phys., 31, 15.
2.
Damiano, V. V., and Tint, G. S., 1961, Acta Met., ~, 177.
3.
Hunt, M. D., 1965, Ph.D., Thesis, Birmingham University.
4.
Hunt, M. D., Spittle, J. A., and Smith, R. W., 1967, J. Sci. Inst., 44, 230.
5.
Packwood, R. H., and Smith, R. W., 1967, J. Sci. Instrum., 44, 1057.
6.
Barr, L. W., Mundy, G. N., and Smith, F. A., 1966, Phil. Mag., 14, 1299.
7.
Meakin, J. D., and Klokholm, E., 1960, Trans. A.I.M.E., 218, 463.
8.
Packwood, R. H., 1964, Ph.D. Thesis, Birmingham University.
Table 1 Diffusion of Sb 124 into Tin and 0.2 wt% Sb-Sn parallel to the C axis
Base Material
Temperature (°C)
0.2 wt% Sb-Sn
200.75
"
209.1
D (bulk) (cm2sec -I) 7.5 + 0.7 x 10 -12 (94%) 2.12 + 0.2 x I0 -II (99%)
D (damage)
(cm2sec -1)
9 . 2 + 0.9 x 10 -11 1.95 + 0 . 3 x 10
-10 -10
(6%) (1%)
"
209.73
1.84 + 0.15 x 10 -4 (99.8%)
5.39 + 0.4 x i0
"
224.1
2.79 + 0.3 x i0 -II (95%)
1.02 + 0.3 x I0 -I0 (5%)
209.1
1.93 _+ 0.2 x i0 -II (99.6%)
1.41 _+ -.3 x i0 -I0 (0.4%)
"
209.73
3.54 + 0.3 x i0 -II (96%)
2.88 _+ 0.4 x I0 -I0 (4%)
"
228.75
5.07 _+ 0.5 x I0 -ll (94%)
1.51 + 0.5 A i0 -I0 (6%)
Sn (99.999%)
(0.2%)