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Effect of indium on lead self-diffusion
Acta metall. Vol. 35,No. 7,pp. 1649-1651, 1987 Printed in Great Britain. All rights reserved
OOOl-6160187 $3.00+O.OO
Copyright 0 1987Pergamon Journals Ltd
EFFECT OF INDIUM ON LEAD SELF-DIFFUSION L. CHERIET and H. B. HUNTINGTON Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12181, U.S.A. (Received
10 October
1986)
Abstract-Diffusion measurements of the tracer z’“Pb in PbIn alloys over the temperature range 468-558 K have been carried out using the standard radiotracer and serial sectioning techniques. A considerable enhancement of Pb self-diffusion was observed due to the alloying with indium. This enhancement exceeded by a large factor the minimum value predicted as a requirement for diffusion by vacancies. R&nn&La 468-558 K a augmentation augmentation diffusion par
diffusion du traceur “‘Pb dans bs alliages PB-In dans un intervalle de temperature et6 etudiee en utilisant les techniques standard de radiotraceur et sectionnement. Une considerable de l’autodiffusion du plomb a Ctb observee dti a son alliage avcc l’indium. Cette a d&passe d’un grand facteur la valeur minimale predite comme etant une condition de lacunes.
wurde im Tem~ratur~reich Z~~f~an~Die Diffusion des Tracers z’OPb in Pain-~~e~ngen von 468 bis 558 mit der Standard-Tracermethode und der Serienschnitt-T~hnik gemessen. Die Selbstdiffusion des Pb war durch die Legierung mit In betrachtlich beschleunigt. Diese Beschleunigung iiberstieg den Minimalwert, der fur die Diffusion iiber Leerstellen gefordert wird, urn einen hohen Faktor.
INTRODUCTION
EXPERIMENTAL
Because of their extensive practical use, dilute and concentrated alloys have been the object of considerable study in regard to their diffusion mobility. This is particularly true of concentrated lead alloys, predominantly used as solders. Here we report on the effect of indium alloying on the self-diffusion of lead. The effect of Cd impurities on Pb self-diffusion was first investigated by Miller [l]. He found that Pb self-diffusion enhancement is associated with a correlated motion of vacancies and interstitial Cd ions. Studies of the diffusion of nickel, silver, gold and copper in lead-indium alloys have been carried out by Mei [2] and Shi [3]. Diffusion measurements of the tracer ‘03Pb in Pb-In alloys over the temperature range 397-459 K have been reported by Gupta and Oberschmidt [4]. Their studies involved penetration distances of the order of a few micrometers for lattice diffusion and 60-100 grn for grain boundary diffusion. For the case of lattice diffusion, an RF sputtering technique was used. The present investigation, which is somewhat a continuation to the Gupta and Oberschmidt work, is on the diffusion of the tracer *‘*Pb in Pb-In alloys of concentration 7-30%. The temperature in our case varies from 468 to 558 K. The experiments were performed using the standard radiotracer and serial sectioning techniques. We have also studied the diffusion of In in Pb at 516 K which is needed for our attempt to understand the mechanism responsible for atomic motion.
Pure Pb and Pb-In alloy specimens of cylindrical form (about 0.5 cm in diameter) were obtained from the 99.999% pure Pb and 99.9999% pure In supplied from Materials Research Corporation and Aldrich Chemical Company respectively. Each sample was first mounted on a microtome and slices of 1 pm thickness were removed from the cross-sectional surface to be plated. The samples were then etchpolished with an acetic acid-hydrogen peroxide solution to remove flow layers. The electroplating baths contained radioactive “*Pb or ri4In in a slightly acid solution. Both Pb and In isotopes were purchased from New England Nuclear. The electroplating was done at 40 mA for a time varying from 20 s to several minutes depending on the strength of the plating solution. Immediately after the plating process, the samples were reduced in diameter to prevent any lateral contamination and were vacuum sealed in Pyrex capsules. In this process, the capsules were evacuated and flushed with helium repeatedly to get rid of any oxygen content. A Nichrome wound furnace was used to perform the diffusion runs. The sealed capsules were put into the furnace next to the regulator sensor and to the junction of a Chromel-Alumel thermocouple used for temperature measurements. The reference junction was immersed in ice water. The temperature of the furnace was controlled to within 0.5 K. The warm up times were not taken into account since they were negligible compared to the diffusion anneal times. To avoid
1649
1650
CHERIET
and HUNTINGTON:
EFFECT OF In ON Pb SELF-DIFFUSION
surface diffusion effects, the specimens were again reduced in diameter after their removal from the furnace. Each sample was then mounted on a microtome, the plated surface being set parallel to the blade, and 5 pm slices were cut and put into bottles. The activity of each bottle was counted on a Baird Atomic Spectrometer. The overall activity was usually over 50,00Ocounts/min. The weighing was performed on a Mettler Balance of 0.2mg precision.
Table 1. Diffusion constants
Solute Pb Pb Pb Pb Pb Pb Pb In
Solvent
T(K)
PL7%In Pb-7%In Pbl2%In PblZ%In Pb12%In Pb20%In Pb30%In Pb
wn*/s) 8.1 x 10-15 2.7 x lo-l4 4.0 x lo-‘5 1.8 x IO-I4 5.6 x IO-l4 3.0 x IO_‘4 5.8 x lo-l4 1.3 x IO_‘5
516 558 468 516 558 516 516 516
Table 2. Estimated D from eouation (21 RESULTS
AND DISCUSSIONS
The diffusion constants for all runs have been determined using the thin film solution to Fick’s law [5] C = [C,/(nDt)“2]exp(-x2/4Dt)
In c/&615)m513 (40/t)“2
(2)
where D and D' represent the lattice and GB diffusion respectively, K is the segregation factor, 6 is the GB width, c is the tracer concentration and y the penetration depth of the tracer. The values of the diffusion constants calculated from the slopes of the penetration profiles and those estimated using equa-
1
.
T(K)
PL7%In Pl+2%In PL+l2%In Pb-ZO%In Pb30%In
516 468 516 516 516
D(m2/s) 8.0 x 3.2 x 1.7 x 2.8 x 5.7 x
1oV lo-” lo-” 10~‘” lo-‘4
(1)
where C, is the quantity of solute plated on the surface of the sample, x the penetration depth of the solute and t the diffusion anneal time. Most of the penetration profiles presented some curvatures away from the surface as can be seen in Fig. 1 which shows a typical penetration profile at 516K. Since the diffusion along grain boundaries is usually faster than through the lattice, we believe that the curvatures are due, at least partially, to the contributions from the grain boundaries. Accordingly, we have roughly estimated the net diffusion through the lattice using Suzuoka-Whipple type of solution [4] K6D’ =0.661(--a
Solvent
tion (2) are shown in Tables 1 and 2 respectively and are in good agreement. The diffusion runs at 516 K don’t seem to be seriously affected by the contributions from the grain boundaries. For the low temperature run, however, the estimated value of D is about 20% lower than the one calculated from equation (1) indicating a relatively considerable GB effect. The diffusivity of Pb in P&In alloys containing 7 and 12 at.%In is shown as a function of temperature in Fig. 2. The solid line represents the Arrhenius plot for pure Pb [l] and if we compare it with the Arrhenius plots for PbIn alloys, we simply find that the activation energy Q decreases with the increase of In impurities. This effect may be due to the decrease in the energy needed for a lead atom to jump into a vacancy in the presence of an indium impurity, but it is also most likely that the presence of indium increases the number of vacancies. The frequency factor D, also decreases with the addition of In as
. . 0 A
T=243’C G.B. Correction
7% In 12%In PURE Pb 7%In 12%In
‘\ ‘\ ‘\
1.
\
\ ‘\
-::.::.-_
I
1
IO
I
IS
30
20 X2( 104CrnZ)
Fig.
1. Penetration
profile for the Pt+20%In.
20
of
Pb
in Fig. 2. Arrhenius
plots.
’
‘\
‘1
I
19
I/T (Xl&‘) diffusion
‘9
A.,
21
‘\
CHERIET
and HUNTINGTON:
EFFECT OF In ON Pb SELF-DIFFUSION
The calculated enhancement
Table 3. Activation energies and frequency factors Solvent
DnW/s)
Pb-12%In Pb-7%In Pure Pb[l]
5.1 x 10-s 7.2 x lo-* 0.995 x lo-’
CXJ/mol) 6.40 x 10’ 6.91 x 10’ 1.073 x 10’
expected. The values of Q and 4, calculated using a least square fit analysis, are shown in Table 3. Figure 3 shows the enhancement of Pb self-diffusion. The errors in D were estimated from the variations in the slopes of the straight lines believed to represent best the lattice diffusion. The data points in Fig. 3 were least square fitted to a parabola according to the equation [6] D(x) = D(O)(l + b,!x + b,,x’).
. Tz243.C G B Correction & I’
(3)
1651
factors are
b,, = 64.5
(4)
b,* = 285.3
(5)
These values are consistant with the range of results found by Gupta and Oberschmidt. In accordance to Miller, the minimum enhancement factor for the vacancy mechanism is given by [l] bmin= - 18 + 1.9448 Dz(O)/D1(0)
(6)
where D*(O) and D,(O) represent the impurity and self-diffusion in the pure solvent, respectively. The minimum enhancement factor was found to be b,,, = 2.2
(7)
which is substantially smaller than the linear enhancement factor b,, suggesting that a simple vacancy mechanism is most probably operative. The end result of this research is then to explore the lead self-diffusion enhancement from adding indium as an alloying agent and to demonstrate the likelihood of the vacancy mechanism in this self-diffusion process. Acknowledgemenrs4ne of the authors, L.C., is grateful for the support from the “Ministtre de l’enseignement sup&ieur et de la recherche scientifique, Algeria.” REFERENCES
at. % In
Fig. 3. Enhancement plot.
J. W. Miller, Whys. Rev. 181, 1095 (1969). S. N. Mei, Ph.D thesis, Rensselaer Polytechnic Institute, Troy, New York (1985). J. Shi, Ph.D thesis, Rensselaer Polytechnic Institute, Troy, New York (1986). J. Gupta and J. Oberschmidt, &‘&ion in Soli&: Recent Developments (edited by A. S. Nowick and J. J. Burton) pp. 121-140. Academic Press, New York (1975). 5. P. G. Shewman, Diffusion in Solids, p. 7. McGraw-Hill, New York (1963). 6. W. K. Warburton and D. Turnbull, Diffusion in Solids: Recent Developments (edited by A. S. Nowick and J. J. Burton) p. 179. Academic Press, New York (1975).
OOOl-6160187 $3.00+O.OO
Copyright 0 1987Pergamon Journals Ltd
EFFECT OF INDIUM ON LEAD SELF-DIFFUSION L. CHERIET and H. B. HUNTINGTON Department of Physics, Rensselaer Polytechnic Institute, Troy, NY 12181, U.S.A. (Received
10 October
1986)
Abstract-Diffusion measurements of the tracer z’“Pb in PbIn alloys over the temperature range 468-558 K have been carried out using the standard radiotracer and serial sectioning techniques. A considerable enhancement of Pb self-diffusion was observed due to the alloying with indium. This enhancement exceeded by a large factor the minimum value predicted as a requirement for diffusion by vacancies. R&nn&La 468-558 K a augmentation augmentation diffusion par
diffusion du traceur “‘Pb dans bs alliages PB-In dans un intervalle de temperature et6 etudiee en utilisant les techniques standard de radiotraceur et sectionnement. Une considerable de l’autodiffusion du plomb a Ctb observee dti a son alliage avcc l’indium. Cette a d&passe d’un grand facteur la valeur minimale predite comme etant une condition de lacunes.
wurde im Tem~ratur~reich Z~~f~an~Die Diffusion des Tracers z’OPb in Pain-~~e~ngen von 468 bis 558 mit der Standard-Tracermethode und der Serienschnitt-T~hnik gemessen. Die Selbstdiffusion des Pb war durch die Legierung mit In betrachtlich beschleunigt. Diese Beschleunigung iiberstieg den Minimalwert, der fur die Diffusion iiber Leerstellen gefordert wird, urn einen hohen Faktor.
INTRODUCTION
EXPERIMENTAL
Because of their extensive practical use, dilute and concentrated alloys have been the object of considerable study in regard to their diffusion mobility. This is particularly true of concentrated lead alloys, predominantly used as solders. Here we report on the effect of indium alloying on the self-diffusion of lead. The effect of Cd impurities on Pb self-diffusion was first investigated by Miller [l]. He found that Pb self-diffusion enhancement is associated with a correlated motion of vacancies and interstitial Cd ions. Studies of the diffusion of nickel, silver, gold and copper in lead-indium alloys have been carried out by Mei [2] and Shi [3]. Diffusion measurements of the tracer ‘03Pb in Pb-In alloys over the temperature range 397-459 K have been reported by Gupta and Oberschmidt [4]. Their studies involved penetration distances of the order of a few micrometers for lattice diffusion and 60-100 grn for grain boundary diffusion. For the case of lattice diffusion, an RF sputtering technique was used. The present investigation, which is somewhat a continuation to the Gupta and Oberschmidt work, is on the diffusion of the tracer *‘*Pb in Pb-In alloys of concentration 7-30%. The temperature in our case varies from 468 to 558 K. The experiments were performed using the standard radiotracer and serial sectioning techniques. We have also studied the diffusion of In in Pb at 516 K which is needed for our attempt to understand the mechanism responsible for atomic motion.
Pure Pb and Pb-In alloy specimens of cylindrical form (about 0.5 cm in diameter) were obtained from the 99.999% pure Pb and 99.9999% pure In supplied from Materials Research Corporation and Aldrich Chemical Company respectively. Each sample was first mounted on a microtome and slices of 1 pm thickness were removed from the cross-sectional surface to be plated. The samples were then etchpolished with an acetic acid-hydrogen peroxide solution to remove flow layers. The electroplating baths contained radioactive “*Pb or ri4In in a slightly acid solution. Both Pb and In isotopes were purchased from New England Nuclear. The electroplating was done at 40 mA for a time varying from 20 s to several minutes depending on the strength of the plating solution. Immediately after the plating process, the samples were reduced in diameter to prevent any lateral contamination and were vacuum sealed in Pyrex capsules. In this process, the capsules were evacuated and flushed with helium repeatedly to get rid of any oxygen content. A Nichrome wound furnace was used to perform the diffusion runs. The sealed capsules were put into the furnace next to the regulator sensor and to the junction of a Chromel-Alumel thermocouple used for temperature measurements. The reference junction was immersed in ice water. The temperature of the furnace was controlled to within 0.5 K. The warm up times were not taken into account since they were negligible compared to the diffusion anneal times. To avoid
1649
1650
CHERIET
and HUNTINGTON:
EFFECT OF In ON Pb SELF-DIFFUSION
surface diffusion effects, the specimens were again reduced in diameter after their removal from the furnace. Each sample was then mounted on a microtome, the plated surface being set parallel to the blade, and 5 pm slices were cut and put into bottles. The activity of each bottle was counted on a Baird Atomic Spectrometer. The overall activity was usually over 50,00Ocounts/min. The weighing was performed on a Mettler Balance of 0.2mg precision.
Table 1. Diffusion constants
Solute Pb Pb Pb Pb Pb Pb Pb In
Solvent
T(K)
PL7%In Pb-7%In Pbl2%In PblZ%In Pb12%In Pb20%In Pb30%In Pb
wn*/s) 8.1 x 10-15 2.7 x lo-l4 4.0 x lo-‘5 1.8 x IO-I4 5.6 x IO-l4 3.0 x IO_‘4 5.8 x lo-l4 1.3 x IO_‘5
516 558 468 516 558 516 516 516
Table 2. Estimated D from eouation (21 RESULTS
AND DISCUSSIONS
The diffusion constants for all runs have been determined using the thin film solution to Fick’s law [5] C = [C,/(nDt)“2]exp(-x2/4Dt)
In c/&615)m513 (40/t)“2
(2)
where D and D' represent the lattice and GB diffusion respectively, K is the segregation factor, 6 is the GB width, c is the tracer concentration and y the penetration depth of the tracer. The values of the diffusion constants calculated from the slopes of the penetration profiles and those estimated using equa-
1
.
T(K)
PL7%In Pl+2%In PL+l2%In Pb-ZO%In Pb30%In
516 468 516 516 516
D(m2/s) 8.0 x 3.2 x 1.7 x 2.8 x 5.7 x
1oV lo-” lo-” 10~‘” lo-‘4
(1)
where C, is the quantity of solute plated on the surface of the sample, x the penetration depth of the solute and t the diffusion anneal time. Most of the penetration profiles presented some curvatures away from the surface as can be seen in Fig. 1 which shows a typical penetration profile at 516K. Since the diffusion along grain boundaries is usually faster than through the lattice, we believe that the curvatures are due, at least partially, to the contributions from the grain boundaries. Accordingly, we have roughly estimated the net diffusion through the lattice using Suzuoka-Whipple type of solution [4] K6D’ =0.661(--a
Solvent
tion (2) are shown in Tables 1 and 2 respectively and are in good agreement. The diffusion runs at 516 K don’t seem to be seriously affected by the contributions from the grain boundaries. For the low temperature run, however, the estimated value of D is about 20% lower than the one calculated from equation (1) indicating a relatively considerable GB effect. The diffusivity of Pb in P&In alloys containing 7 and 12 at.%In is shown as a function of temperature in Fig. 2. The solid line represents the Arrhenius plot for pure Pb [l] and if we compare it with the Arrhenius plots for PbIn alloys, we simply find that the activation energy Q decreases with the increase of In impurities. This effect may be due to the decrease in the energy needed for a lead atom to jump into a vacancy in the presence of an indium impurity, but it is also most likely that the presence of indium increases the number of vacancies. The frequency factor D, also decreases with the addition of In as
. . 0 A
T=243’C G.B. Correction
7% In 12%In PURE Pb 7%In 12%In
‘\ ‘\ ‘\
1.
\
\ ‘\
-::.::.-_
I
1
IO
I
IS
30
20 X2( 104CrnZ)
Fig.
1. Penetration
profile for the Pt+20%In.
20
of
Pb
in Fig. 2. Arrhenius
plots.
’
‘\
‘1
I
19
I/T (Xl&‘) diffusion
‘9
A.,
21
‘\
CHERIET
and HUNTINGTON:
EFFECT OF In ON Pb SELF-DIFFUSION
The calculated enhancement
Table 3. Activation energies and frequency factors Solvent
DnW/s)
Pb-12%In Pb-7%In Pure Pb[l]
5.1 x 10-s 7.2 x lo-* 0.995 x lo-’
CXJ/mol) 6.40 x 10’ 6.91 x 10’ 1.073 x 10’
expected. The values of Q and 4, calculated using a least square fit analysis, are shown in Table 3. Figure 3 shows the enhancement of Pb self-diffusion. The errors in D were estimated from the variations in the slopes of the straight lines believed to represent best the lattice diffusion. The data points in Fig. 3 were least square fitted to a parabola according to the equation [6] D(x) = D(O)(l + b,!x + b,,x’).
. Tz243.C G B Correction & I’
(3)
1651
factors are
b,, = 64.5
(4)
b,* = 285.3
(5)
These values are consistant with the range of results found by Gupta and Oberschmidt. In accordance to Miller, the minimum enhancement factor for the vacancy mechanism is given by [l] bmin= - 18 + 1.9448 Dz(O)/D1(0)
(6)
where D*(O) and D,(O) represent the impurity and self-diffusion in the pure solvent, respectively. The minimum enhancement factor was found to be b,,, = 2.2
(7)
which is substantially smaller than the linear enhancement factor b,, suggesting that a simple vacancy mechanism is most probably operative. The end result of this research is then to explore the lead self-diffusion enhancement from adding indium as an alloying agent and to demonstrate the likelihood of the vacancy mechanism in this self-diffusion process. Acknowledgemenrs4ne of the authors, L.C., is grateful for the support from the “Ministtre de l’enseignement sup&ieur et de la recherche scientifique, Algeria.” REFERENCES
at. % In
Fig. 3. Enhancement plot.
J. W. Miller, Whys. Rev. 181, 1095 (1969). S. N. Mei, Ph.D thesis, Rensselaer Polytechnic Institute, Troy, New York (1985). J. Shi, Ph.D thesis, Rensselaer Polytechnic Institute, Troy, New York (1986). J. Gupta and J. Oberschmidt, &‘&ion in Soli&: Recent Developments (edited by A. S. Nowick and J. J. Burton) pp. 121-140. Academic Press, New York (1975). 5. P. G. Shewman, Diffusion in Solids, p. 7. McGraw-Hill, New York (1963). 6. W. K. Warburton and D. Turnbull, Diffusion in Solids: Recent Developments (edited by A. S. Nowick and J. J. Burton) p. 179. Academic Press, New York (1975).