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Experimental measurement of chemical diffusivity of Tin in Lead
Scripta METALLURGICA
Vol. 21, pp. 153-156, 1987 Printed in the U.S.A.
Pergamon Journals, Ltd. All rights reserved
EXPERIMENTAL MEASUREMENTOF CHEMICAL DIFFUSIVITY OF TIN IN LEAD S. Mei, H. B. Huntington, C. K. Hu* and M. J. McBride**
Physics Department of Rensselaer Polytechnic Institute Troy, New York 12181 (Received October 6, 1986) (Revised November i0, 1986)
Introduction Lead solders, p a r t i c u l a r l y l e a d - t i n solders, are materials of considerable technological i n t e r e s t . From the standooint of atom movement studies of bulk soecimens only a few measurements [ i ] [2] [3] have been made. I t is known that t i n diffuses more r a o i d l y than lead in these a l l o y s . Because of the considerable use of these solders, i t seemed worthwhile to explore the behavior of the chemical d i f f u s i v i t y of t i n and also i t s thermodynamic f a c t or . The thermodynamic factor enters as a correction in the i n t e r o r e t a t i o n of the e f f e c t i v e charge numher Z* a as determined by the steady state technique measuring e l e c t r o m i g r a t i o n . Sample PreParation Two sample disks, 3 mm in thickness and 5 mm in diameter were Dreoared f i r s t , one of them pure Pb (Cominco 99.999%) and the other Pb + i0 at.% Sn a l l o y containinQ uniformly distributed 113Sn tracer. The press used is displayed in Fig. 1. Before being mounted between the Fig. 1
Helium
Press fo r preparation of d i f f u s i o n - c o u p l e ( I ) specimens, (2) pistons pressing pistons, the sample surfaces were etched in etching s o l u t i o n (2 Darts of acetic acid, 3 parts of hydrogen peroxide and 2 Darts of d i s t i l l e d water by volume), rinsed with d i s t i l l e d water and acetone. In order to protect the sample surfaces from being oxidized, the sample * IBM Thomas J. Watson Research and Development, Yorktown Heiqhts, New York ** General E l e c t r i c Company at Syracuse, New York
153 0036-9748/87 $3.00 + .00 Copyright (c) 1987 Pergamon Journals Ltd.
154
DIFFUSIVITY OF Sn IN Pb
Vol.
21, No.
2
was then quickly transferred into a helium atmosphere in the chamber of the tool while a thin layer of acetone s t i l l covered the whole sample surfaces. This procedure was important in preventing the formation of any surface oxide, which forms in a few seconds on exposing lead to a i r and causes a discontinuity in the diffusion p r o f i l e . After being carefully aligned to each other and dried under the protection of the helium gas, the specimens were pressed together and kept under high uniaxial pressure for 10 hours at room temperature. The two disks were then sintered t i g h t l y together in one sample disk. At the end of diffusion anneal, the tracer concentration p r o f i l e was obtained using the standard sequential-sectioning technique. The Boltzmann-Matano analysis [4] was emDloyed to determine the chemical d i f f u s i v ' i t y as a function of composition of Sn in Pb. Experimental Results Contrary to the fast diffusers which diffuse in lead by a type of i n t e r s t i t i a l mechanism, the diffusion of tiq in lead, where a vacancy mechanism dominates the process, is very slow (of the order of !) -9 mm2/sec at 250°C). The addition of t i n enhances the diffusion of t i n in lead. This impurity d i f f u s i o n enhancement is displayed in Fig. 2. The measurement of Dch of Sn in Pb-Sn alloy provided a result consistent with that observation. Fig. 2
Fiq. 3
10"13
10 m a f a ~ [nterfacl
8 6
C) LU U)
l~ 4
RUN # 1 Sn in Pb'Sn
0
~E
M 5 ~ S~ a 8 . 4 ~ Sn
rh
• 12~
2
Sn
1
2 X ( 1 0 -4
10-is
, 1.7
I
I/T
, J 1.8 ( 10 -3 K " )
M)
119
Tracer diffusion of t i n in lead-tin alloys
Concentration p r o f i l e of chemical diffusion of t i n in lead-tin alloy
In Fig. 3 one sees a typical run with a welded specimen. One can notice that the concentration p r o f i l e dropped down faster at lower t i n composition. Fiq. 4 depicts the Dch value calculated using the Boltzmann-Matano method as a function of t i n composition. The diffusion concentration p r o f i l e in Fig. 3 shows that no discontinuity resulted from the interface oxidation. Consequently, the helium gas protection in the sample preparation seems to be a successful technique. The Dch of t i n in Pb-Sn alloys at 250°C is monotonic increasing with t i n concentration except for the high t i n concentration range where the accuracy of the calcula-
Vol.
21, No.
2
DIFFUSIVITY
OF Sn IN Pb
iSS
tion from the Boltzmann-Matano analysis is expected to be low. As can be see the d i f f u s i v i t y for 0% which is of the order of 3 x 10-9 mm 2/s has qood agreement with the l i t e r a t u r e value of t i n in pure lead, 3.3 x 10-9 mm 2/s. Fig. 4
Fig. 5
10.'3
T = 250° C
1.8 ].6 1.4 CZ~
o LU 614
"~=~1.2 5
~E
@ 0
ORUN #2
o" o
I
l.O
" RUN # I
I
l
o.8
I
I
I
4 6 8 I0 2 Csn CONCENTRATION ( a l . % )
I
2 4 6 8 I0 TIN CONCENTRATION( at.% ) Chemical d i f f u s i v i t y of t i n in lead-tin alloys
Thermodynamic factor of t i n in lead-tin alloys
Combining the knowledge of both tracer d i f f u s i v i t y D (see Fig. 2) and chemical d i f f u s i v i t y Dch of t i n in Pb-Sn a l l o y , one can obtain the thermodynamic factor. From Fig. 5 the thermodynamic factor of t h i s system at 250°C as a function of t i n concentration has a value of about 1.5 at 5% Sn and 1,6 at 8.4% Sn. The value of thermodynamic factor at 12% Sn concentration was obtained from the experimental data of tracer d i f f u s i v i t y in Fig. 2 and an estimated value of chemical d i f f u s i v i t y from Fig. 4. The open c i r c l e in Fig. 5 indicates this is an estimated value. The experimental error, resulting from the misalignment in sectioning, errors in temperature measurement, weiqhinq, counting etc., was controlled within 10%. As mentioned in the Introduction, t h i s determination of the thermodynamic factor would be of interest for a possible investigation of electromigration of t i n in lead. SUMMARY This result of a modest increase of Dch with t i n concentration shows that the thermodynamic potential ~ = [ I + (dln~/dlnc)] ~here y is the a c t i v i t y coefficient) is greater than one. As a result the t i n atoms do not distribute themselves comoletely randomly but tend to keep somewhat separate as the concentration increases. Acknowledgements We thank Dr. Paul Ho of the IBM Research & Develooment Laboratories at Yorktown Heights, NY for suggesting this research topic.
156
DIFFUSIVITY OF Sn IN Pb
Vol.
21, No. 2
References I. 2. 3. 4.
H. B. Huntington, C. K. Hu and S. Mei, Atomic transport of d i l u t e imourities in lead-tin alloys, "Diffusion in Solids: Recent Development," edited by G. A, Dayananda and G. E. Murch (1985). H. B. Huntington and C. K. Hu, Atom movement in lead and lead-tin alloys, Mat. sci. Vol. I , 29 (1984). C. K. Hu and H. B. Huntington, Phys. Rev. B 26, 2782 (1982). Paul G. Shewman, "Diffusion in Solids", McGraw-Hill, NY (1967).
Vol. 21, pp. 153-156, 1987 Printed in the U.S.A.
Pergamon Journals, Ltd. All rights reserved
EXPERIMENTAL MEASUREMENTOF CHEMICAL DIFFUSIVITY OF TIN IN LEAD S. Mei, H. B. Huntington, C. K. Hu* and M. J. McBride**
Physics Department of Rensselaer Polytechnic Institute Troy, New York 12181 (Received October 6, 1986) (Revised November i0, 1986)
Introduction Lead solders, p a r t i c u l a r l y l e a d - t i n solders, are materials of considerable technological i n t e r e s t . From the standooint of atom movement studies of bulk soecimens only a few measurements [ i ] [2] [3] have been made. I t is known that t i n diffuses more r a o i d l y than lead in these a l l o y s . Because of the considerable use of these solders, i t seemed worthwhile to explore the behavior of the chemical d i f f u s i v i t y of t i n and also i t s thermodynamic f a c t or . The thermodynamic factor enters as a correction in the i n t e r o r e t a t i o n of the e f f e c t i v e charge numher Z* a as determined by the steady state technique measuring e l e c t r o m i g r a t i o n . Sample PreParation Two sample disks, 3 mm in thickness and 5 mm in diameter were Dreoared f i r s t , one of them pure Pb (Cominco 99.999%) and the other Pb + i0 at.% Sn a l l o y containinQ uniformly distributed 113Sn tracer. The press used is displayed in Fig. 1. Before being mounted between the Fig. 1
Helium
Press fo r preparation of d i f f u s i o n - c o u p l e ( I ) specimens, (2) pistons pressing pistons, the sample surfaces were etched in etching s o l u t i o n (2 Darts of acetic acid, 3 parts of hydrogen peroxide and 2 Darts of d i s t i l l e d water by volume), rinsed with d i s t i l l e d water and acetone. In order to protect the sample surfaces from being oxidized, the sample * IBM Thomas J. Watson Research and Development, Yorktown Heiqhts, New York ** General E l e c t r i c Company at Syracuse, New York
153 0036-9748/87 $3.00 + .00 Copyright (c) 1987 Pergamon Journals Ltd.
154
DIFFUSIVITY OF Sn IN Pb
Vol.
21, No.
2
was then quickly transferred into a helium atmosphere in the chamber of the tool while a thin layer of acetone s t i l l covered the whole sample surfaces. This procedure was important in preventing the formation of any surface oxide, which forms in a few seconds on exposing lead to a i r and causes a discontinuity in the diffusion p r o f i l e . After being carefully aligned to each other and dried under the protection of the helium gas, the specimens were pressed together and kept under high uniaxial pressure for 10 hours at room temperature. The two disks were then sintered t i g h t l y together in one sample disk. At the end of diffusion anneal, the tracer concentration p r o f i l e was obtained using the standard sequential-sectioning technique. The Boltzmann-Matano analysis [4] was emDloyed to determine the chemical d i f f u s i v ' i t y as a function of composition of Sn in Pb. Experimental Results Contrary to the fast diffusers which diffuse in lead by a type of i n t e r s t i t i a l mechanism, the diffusion of tiq in lead, where a vacancy mechanism dominates the process, is very slow (of the order of !) -9 mm2/sec at 250°C). The addition of t i n enhances the diffusion of t i n in lead. This impurity d i f f u s i o n enhancement is displayed in Fig. 2. The measurement of Dch of Sn in Pb-Sn alloy provided a result consistent with that observation. Fig. 2
Fiq. 3
10"13
10 m a f a ~ [nterfacl
8 6
C) LU U)
l~ 4
RUN # 1 Sn in Pb'Sn
0
~E
M 5 ~ S~ a 8 . 4 ~ Sn
rh
• 12~
2
Sn
1
2 X ( 1 0 -4
10-is
, 1.7
I
I/T
, J 1.8 ( 10 -3 K " )
M)
119
Tracer diffusion of t i n in lead-tin alloys
Concentration p r o f i l e of chemical diffusion of t i n in lead-tin alloy
In Fig. 3 one sees a typical run with a welded specimen. One can notice that the concentration p r o f i l e dropped down faster at lower t i n composition. Fiq. 4 depicts the Dch value calculated using the Boltzmann-Matano method as a function of t i n composition. The diffusion concentration p r o f i l e in Fig. 3 shows that no discontinuity resulted from the interface oxidation. Consequently, the helium gas protection in the sample preparation seems to be a successful technique. The Dch of t i n in Pb-Sn alloys at 250°C is monotonic increasing with t i n concentration except for the high t i n concentration range where the accuracy of the calcula-
Vol.
21, No.
2
DIFFUSIVITY
OF Sn IN Pb
iSS
tion from the Boltzmann-Matano analysis is expected to be low. As can be see the d i f f u s i v i t y for 0% which is of the order of 3 x 10-9 mm 2/s has qood agreement with the l i t e r a t u r e value of t i n in pure lead, 3.3 x 10-9 mm 2/s. Fig. 4
Fig. 5
10.'3
T = 250° C
1.8 ].6 1.4 CZ~
o LU 614
"~=~1.2 5
~E
@ 0
ORUN #2
o" o
I
l.O
" RUN # I
I
l
o.8
I
I
I
4 6 8 I0 2 Csn CONCENTRATION ( a l . % )
I
2 4 6 8 I0 TIN CONCENTRATION( at.% ) Chemical d i f f u s i v i t y of t i n in lead-tin alloys
Thermodynamic factor of t i n in lead-tin alloys
Combining the knowledge of both tracer d i f f u s i v i t y D (see Fig. 2) and chemical d i f f u s i v i t y Dch of t i n in Pb-Sn a l l o y , one can obtain the thermodynamic factor. From Fig. 5 the thermodynamic factor of t h i s system at 250°C as a function of t i n concentration has a value of about 1.5 at 5% Sn and 1,6 at 8.4% Sn. The value of thermodynamic factor at 12% Sn concentration was obtained from the experimental data of tracer d i f f u s i v i t y in Fig. 2 and an estimated value of chemical d i f f u s i v i t y from Fig. 4. The open c i r c l e in Fig. 5 indicates this is an estimated value. The experimental error, resulting from the misalignment in sectioning, errors in temperature measurement, weiqhinq, counting etc., was controlled within 10%. As mentioned in the Introduction, t h i s determination of the thermodynamic factor would be of interest for a possible investigation of electromigration of t i n in lead. SUMMARY This result of a modest increase of Dch with t i n concentration shows that the thermodynamic potential ~ = [ I + (dln~/dlnc)] ~here y is the a c t i v i t y coefficient) is greater than one. As a result the t i n atoms do not distribute themselves comoletely randomly but tend to keep somewhat separate as the concentration increases. Acknowledgements We thank Dr. Paul Ho of the IBM Research & Develooment Laboratories at Yorktown Heights, NY for suggesting this research topic.
156
DIFFUSIVITY OF Sn IN Pb
Vol.
21, No. 2
References I. 2. 3. 4.
H. B. Huntington, C. K. Hu and S. Mei, Atomic transport of d i l u t e imourities in lead-tin alloys, "Diffusion in Solids: Recent Development," edited by G. A, Dayananda and G. E. Murch (1985). H. B. Huntington and C. K. Hu, Atom movement in lead and lead-tin alloys, Mat. sci. Vol. I , 29 (1984). C. K. Hu and H. B. Huntington, Phys. Rev. B 26, 2782 (1982). Paul G. Shewman, "Diffusion in Solids", McGraw-Hill, NY (1967).