- Email: [email protected]
Heat of solidification of lead-bismuth eutectic alloy
Scripta METALLURGICA
Vol. 5, pp. 895-900, 1971 Printed in the United States
Pergamon Press,
Inc
KEAT OF SOLIDIFICATION OF LEAD-BISMUTH EUTECTIC ALLOY
S.N.Tiwari,H.P.Singh,S.L.Malhotra
and S.Misra
Department of Metallurgical Engineering, Institute of Technology, Banaras HinSu University, Varanasi, India
(Received August 21, 1971)
A knowledge of latent heats of solidification of alloys has an impoztant role in predicting the progress of solidification.
This is an
essential information for man2 industrial applications such as design of gating, rlsering, by solidification.
continuous casting and production of composite materials In recent years, attempts have been made (1-3) to
predict the progress of solidification by solving the unsteady-heatconduction equations by numerical techniques.
In all such solutions for
alloys, the value of the latent heat of solidification has been substituted as an additive value of the laten~ heats of the constituents.
It has been
observed (4) that the values so calculated for eutectic alloys are often much different from those determined experimentally.
In thls paper the
latent heat of solidlficatlon of the eutectic alloy in the system Pb-BI has been calculated using published thermodynamic data and the same has been compared with e~perimentally determined value.
Some auxiliary
thermodynamic data for this system were also obtained. The eutectic reaction in the system Pb-Bi (5) occurring at 56.3 at.% bismuth and 398°K, following the lever rule, may be represented as: ~5)
T(X~b ~ 0 . 4 3 7 ) ~ 0 . 7 5 3
¢
('s)
+ o.24~p
.. (1)
In this reaction, L is the liquid alloy, ~(S)is the intermediate phase and ~s) is the primary solid solution of lead in bismuth and may be treated as pure bismuth because of negligible solid solubility.
The latent heat of
solidification of the eutectlc alloy may be calculated in the following manner: The heat conten~ of the liquid eutectic alloy at the eutectlc 895
896
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
Vol. 5, No. I0
t e m p e r a t u r e may be e x p r e s s e d ass H1 = Xpb. Hipb+XBi. HIBi+ A H I
(ii )
where, Xpb and XBi are the atomic fractions of Pb and Bi respectively in the liquid phase, HIpb and HIBi are the heat contents of liquid Pb and Bi and AHlis the heat of formation of the eutectic liquid alloy.
The h e a t c o n t e n t of t h e e q u i l i b r i u m m i x t u r e of s o l i d p h a s e s ~ and a t t h e e u t e c t i c t e m p e r a t u r e may be g i v e n ass Hs - 0.753 HE ( s ) + 0.247 Hp ( s ) or /
= 0.753 (XpboHSpb+~i.HSBi+~He(S))+0,247
HSBi . . ( i i i )
I
where, Xpb and XBi a r e t h e a t o m i c f r a c t i o n s o f Pb and Bi i n R - p h a s e r e s p e c t i v e l y , HSpb and HsBi a r e t h e h e a t c o n t e n t s o f s o l i d Pb and Bi and He ( s ) i s t h e h e a t of f o r m a t i o n o f ~ - p h a s e . Therefore, the latent
heat of f u s i o n of t h e e u t e c t i c a l l o y a t t h e
eutectic temperature is:
~HfBi_Pb - (HI-H a)
., (iv)
= ~ X p b o H i p b ÷ ~ i . H i B l * ~E~ ) - ~0°247 HSBI +Oo753(X;b.HSpb÷~i.HSBi÷ ~ H ~ ( S ) ) ~
substltuti
X b=0.437,
..
(V)
H:pb-1706.5 cal/g.
atom; HIBi=3090o8 c a l / g . a t o m ! HSpb=640.7 c a l / g . a t o m ! HSBi=631.1 e a l / g . a t o m , from the data compiled by HultKren et al. (67 at 398eK, and values of ~(s) _ I 5 oal/go atom a n d ~ H l T 0 0 = - -'~- 257 cal/g.atom from reference (7) AH400OK-7 in equation (v), the latent heat of solidification of the eutectic alloy has been calculated to be -1055~I00 cal/g.atom. The heat content values used in the above calculations are relative to the standard state at 298.15eK.
tion in a have were
To verify the above theoretical prediction, experimental determinaof the latent heat of solidification of the eutectic alloy was made liquid alloy solution calorimeter, the technique and details of which been described elsewhere (8). Lead and bismuth, each of 99°99% purity, used in the investigation. About 500 g. of Pb-Bi euteotio alloy
Vol. 5~ No. i0
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
897
solvent was made by melting stoichlometric proportions of lead and bismuth in an evacuated glass capsule.
The addition alloy sample of the eutectic
composition was prepared in the above manner by cooling slowly the homogenized melt in the furnace to room temperature.
The ingot of the
sample was then hammered and rolled at room temperature into thin strips and then annealed for 5 hours at 373eK.
The equilibrium eutectic
structure was verified metallographlcally. Solid samples of the eutectic alloy mixture, lead and bismuth were added sequentially from 373OK to the calorimeter solvent bath at 408OK and the variation of the temperature of the solvent with time during dlssolution, in each case, was noted.
In a typical run, five samples, each of
the eutectic mixture, lead and bismuth were added.
The elemental samples
were added in proportion of the eutectic stoichiometry so as not to alter the bath composition. bility of the results.
Runs were repeated twice to check the reproduciThe calorimeter was calibrated by adding pure
copper from 273OK and the published value (6) of its heat content was used in the calculation. The heat of dissolution in each case was determined by substracting the sensible heat changes of the additions in the temperature interval from 373 to 408@K from the measured heat effect on dissolution.
The latent heat
of solidification of the eutectic alloy Is the heat of dissolution of the corresponding solid alloy mixture in the solvent of the same composition. The samples of lead and eutectic mixture dissolved in less than 3 minutes thus ensuring the accuracy in the calculated values of their respective heats of dissolution.
Bismuth required an excessively long dissolution
time of the order of 40 minutes.
This prolonged time may be responsible
for the error associated with its heat of dissolution.
From the measured
values of the heats of dissolution, various thermodynamic ~uantities were computed and are given in Table I, along with available data from other sources.
The latent heat of solidification of the eutectic alloy at 408OK was determined to be -1185+15 cal/g, atom and is more exothermic than the theoretical value by about 130 calories.
By taking into account the
Kirchoff's law correction for the heat of solidification at the eutectic temperature (398eK) instead of at 408OK, the value comes to -1165+ 15 cal/ g.atom.
The rest of the difference in the values (110 calories) may be
898
HEAT OF SOLIDIFICATION OF Pb~Bi EUTECTIC ALLOY
Vol. 5, No. I0
In part attributed to the error limits in the experimental values, and largely to the data available for temperatures other than the eutectlc temperature for use in the theoretical calculation, resulting in large error limits for the latter. However, our experimental value compares reasonably well with the value determined by Rao (9) subsequently using the quantitative thermal analysis technique.
TABLE
1
Thermodynamic Data for Pb-Bi Alloys in cal/g.atom Thermal Effects
This Investigatlon
Theoretical Values
• HfBl_Pb
1185+_15
1055_+100
AHBI(s)
1975+25
-
&~Pb(s)
575_+15
-
n BiCl )
90+ 0
-
-200
(6)
-4 0+20
-
-400
(6)
-470_+40
-
-257
(7)i-295(11);-475(10)
n
b(1 )
nHBi_Pb(1) AH f
615+25
The p a r t i a l
Other Experimentally Determined Values
1103+_15 (9)
-
790-+50 (12)
molar heat of solution
-
of liquid
lead in eutectic
Pb-Bi alloy determined in this investigation is in satisfactory agreement with that reported by Hultgren et a_~l. (6) at 700oK, in view of the large temperature difference between the two determinations. The corresponding values for liquid bismuth show a large deviation. This discrepancy in part may be due to the temperature dependence of the heat of solution of bls~uth in liquid eutectlc alloy and the uncertainty in the transfer of heat to the bath during the prolonged time for dissolution as already mentioned. The d i f f e r e n c e
in the value of the heat of mixing or the heat
of
f o r m a t i o n o f l i q u i d e u t e o t i c a l l o y f r o m t h o s e o f Roy e_~t a l . ( 7 ) , Kawakaml (10) and Strlokler et al. (11) may be mainly due to different
techniques of measurement. The data from liquid alloy solution calorimetry is believed to be more accurate. The heat of fusion of ~-phase was calculated using Predel's formula (12) and is found to be 175 oalorles more
Vol. 5, No. I0
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
endothermlc than our experimental value.
899
This difference may be attributed
to the different temperatures for which A H s and ~ H f values are available for calculation using Predel's formula. The authors are grateful to Dr. T.R.Anantharaman, Professor and Head of the Department of Metallurgy, Banaras Hindu University, for providing necessary facilities and his keen interest in this investigation. One of the authors (H.P.S.) is grateful to the C.S.I.R., New Delhi, for the award of a Senior Research Fellowship. REFERENCES I.
R.H.Tien and V.Koump, Trans.Met.Soc.AI~E,242,1283(1968).
2.
V.Koump,R.H.Tien and T.F.Perzak, Trans.Met. Soc.AIME, 242,1589(1968).
3.
H.D.Bordy and M.C.Flemlngs, Trans.Met.Soc.AIME,23.6,615(1966).
4.
S.L.Malhotra, Ph.D.Thesls, p.86, London University (1969).
5.
M.Hansen and K.Anderko, Constitution of Binary Alloys,p.324, ZcGraw-Hill, New York (1958).
6.
R.Hult&ren, R.L.Orr, 2.D.Anderson and K.K.Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, p.50 and 206, John Wiley, New York (1963).
7.
P.Roy, R.L. Orr and R.Hultgren, J.Phys.Chem.,64,1034(1960).
8.
S.Misra, H.P.Singh and P.U.Nayak, Indian J.Technol.,_6,254(1968).
9.
S.V.Rao, Private Communication, Department of Metallurgy, Banaras Hindu University, Varanasi, India (1971).
10.
I~.Kawakami, Sci.Repts.Tohoku Imp.Unlv.,19,521(1930).
11.
H.S.Strickler and H.Seltz, J.Am. Chem. Soc.,58,2084(1936).
12.
B.Predel and D.Rothecker, Acta Met.,15, 135(1967).
Vol. 5, pp. 895-900, 1971 Printed in the United States
Pergamon Press,
Inc
KEAT OF SOLIDIFICATION OF LEAD-BISMUTH EUTECTIC ALLOY
S.N.Tiwari,H.P.Singh,S.L.Malhotra
and S.Misra
Department of Metallurgical Engineering, Institute of Technology, Banaras HinSu University, Varanasi, India
(Received August 21, 1971)
A knowledge of latent heats of solidification of alloys has an impoztant role in predicting the progress of solidification.
This is an
essential information for man2 industrial applications such as design of gating, rlsering, by solidification.
continuous casting and production of composite materials In recent years, attempts have been made (1-3) to
predict the progress of solidification by solving the unsteady-heatconduction equations by numerical techniques.
In all such solutions for
alloys, the value of the latent heat of solidification has been substituted as an additive value of the laten~ heats of the constituents.
It has been
observed (4) that the values so calculated for eutectic alloys are often much different from those determined experimentally.
In thls paper the
latent heat of solidlficatlon of the eutectic alloy in the system Pb-BI has been calculated using published thermodynamic data and the same has been compared with e~perimentally determined value.
Some auxiliary
thermodynamic data for this system were also obtained. The eutectic reaction in the system Pb-Bi (5) occurring at 56.3 at.% bismuth and 398°K, following the lever rule, may be represented as: ~5)
T(X~b ~ 0 . 4 3 7 ) ~ 0 . 7 5 3
¢
('s)
+ o.24~p
.. (1)
In this reaction, L is the liquid alloy, ~(S)is the intermediate phase and ~s) is the primary solid solution of lead in bismuth and may be treated as pure bismuth because of negligible solid solubility.
The latent heat of
solidification of the eutectlc alloy may be calculated in the following manner: The heat conten~ of the liquid eutectic alloy at the eutectlc 895
896
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
Vol. 5, No. I0
t e m p e r a t u r e may be e x p r e s s e d ass H1 = Xpb. Hipb+XBi. HIBi+ A H I
(ii )
where, Xpb and XBi are the atomic fractions of Pb and Bi respectively in the liquid phase, HIpb and HIBi are the heat contents of liquid Pb and Bi and AHlis the heat of formation of the eutectic liquid alloy.
The h e a t c o n t e n t of t h e e q u i l i b r i u m m i x t u r e of s o l i d p h a s e s ~ and a t t h e e u t e c t i c t e m p e r a t u r e may be g i v e n ass Hs - 0.753 HE ( s ) + 0.247 Hp ( s ) or /
= 0.753 (XpboHSpb+~i.HSBi+~He(S))+0,247
HSBi . . ( i i i )
I
where, Xpb and XBi a r e t h e a t o m i c f r a c t i o n s o f Pb and Bi i n R - p h a s e r e s p e c t i v e l y , HSpb and HsBi a r e t h e h e a t c o n t e n t s o f s o l i d Pb and Bi and He ( s ) i s t h e h e a t of f o r m a t i o n o f ~ - p h a s e . Therefore, the latent
heat of f u s i o n of t h e e u t e c t i c a l l o y a t t h e
eutectic temperature is:
~HfBi_Pb - (HI-H a)
., (iv)
= ~ X p b o H i p b ÷ ~ i . H i B l * ~E~ ) - ~0°247 HSBI +Oo753(X;b.HSpb÷~i.HSBi÷ ~ H ~ ( S ) ) ~
substltuti
X b=0.437,
..
(V)
H:pb-1706.5 cal/g.
atom; HIBi=3090o8 c a l / g . a t o m ! HSpb=640.7 c a l / g . a t o m ! HSBi=631.1 e a l / g . a t o m , from the data compiled by HultKren et al. (67 at 398eK, and values of ~(s) _ I 5 oal/go atom a n d ~ H l T 0 0 = - -'~- 257 cal/g.atom from reference (7) AH400OK-7 in equation (v), the latent heat of solidification of the eutectic alloy has been calculated to be -1055~I00 cal/g.atom. The heat content values used in the above calculations are relative to the standard state at 298.15eK.
tion in a have were
To verify the above theoretical prediction, experimental determinaof the latent heat of solidification of the eutectic alloy was made liquid alloy solution calorimeter, the technique and details of which been described elsewhere (8). Lead and bismuth, each of 99°99% purity, used in the investigation. About 500 g. of Pb-Bi euteotio alloy
Vol. 5~ No. i0
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
897
solvent was made by melting stoichlometric proportions of lead and bismuth in an evacuated glass capsule.
The addition alloy sample of the eutectic
composition was prepared in the above manner by cooling slowly the homogenized melt in the furnace to room temperature.
The ingot of the
sample was then hammered and rolled at room temperature into thin strips and then annealed for 5 hours at 373eK.
The equilibrium eutectic
structure was verified metallographlcally. Solid samples of the eutectic alloy mixture, lead and bismuth were added sequentially from 373OK to the calorimeter solvent bath at 408OK and the variation of the temperature of the solvent with time during dlssolution, in each case, was noted.
In a typical run, five samples, each of
the eutectic mixture, lead and bismuth were added.
The elemental samples
were added in proportion of the eutectic stoichiometry so as not to alter the bath composition. bility of the results.
Runs were repeated twice to check the reproduciThe calorimeter was calibrated by adding pure
copper from 273OK and the published value (6) of its heat content was used in the calculation. The heat of dissolution in each case was determined by substracting the sensible heat changes of the additions in the temperature interval from 373 to 408@K from the measured heat effect on dissolution.
The latent heat
of solidification of the eutectic alloy Is the heat of dissolution of the corresponding solid alloy mixture in the solvent of the same composition. The samples of lead and eutectic mixture dissolved in less than 3 minutes thus ensuring the accuracy in the calculated values of their respective heats of dissolution.
Bismuth required an excessively long dissolution
time of the order of 40 minutes.
This prolonged time may be responsible
for the error associated with its heat of dissolution.
From the measured
values of the heats of dissolution, various thermodynamic ~uantities were computed and are given in Table I, along with available data from other sources.
The latent heat of solidification of the eutectic alloy at 408OK was determined to be -1185+15 cal/g, atom and is more exothermic than the theoretical value by about 130 calories.
By taking into account the
Kirchoff's law correction for the heat of solidification at the eutectic temperature (398eK) instead of at 408OK, the value comes to -1165+ 15 cal/ g.atom.
The rest of the difference in the values (110 calories) may be
898
HEAT OF SOLIDIFICATION OF Pb~Bi EUTECTIC ALLOY
Vol. 5, No. I0
In part attributed to the error limits in the experimental values, and largely to the data available for temperatures other than the eutectlc temperature for use in the theoretical calculation, resulting in large error limits for the latter. However, our experimental value compares reasonably well with the value determined by Rao (9) subsequently using the quantitative thermal analysis technique.
TABLE
1
Thermodynamic Data for Pb-Bi Alloys in cal/g.atom Thermal Effects
This Investigatlon
Theoretical Values
• HfBl_Pb
1185+_15
1055_+100
AHBI(s)
1975+25
-
&~Pb(s)
575_+15
-
n BiCl )
90+ 0
-
-200
(6)
-4 0+20
-
-400
(6)
-470_+40
-
-257
(7)i-295(11);-475(10)
n
b(1 )
nHBi_Pb(1) AH f
615+25
The p a r t i a l
Other Experimentally Determined Values
1103+_15 (9)
-
790-+50 (12)
molar heat of solution
-
of liquid
lead in eutectic
Pb-Bi alloy determined in this investigation is in satisfactory agreement with that reported by Hultgren et a_~l. (6) at 700oK, in view of the large temperature difference between the two determinations. The corresponding values for liquid bismuth show a large deviation. This discrepancy in part may be due to the temperature dependence of the heat of solution of bls~uth in liquid eutectlc alloy and the uncertainty in the transfer of heat to the bath during the prolonged time for dissolution as already mentioned. The d i f f e r e n c e
in the value of the heat of mixing or the heat
of
f o r m a t i o n o f l i q u i d e u t e o t i c a l l o y f r o m t h o s e o f Roy e_~t a l . ( 7 ) , Kawakaml (10) and Strlokler et al. (11) may be mainly due to different
techniques of measurement. The data from liquid alloy solution calorimetry is believed to be more accurate. The heat of fusion of ~-phase was calculated using Predel's formula (12) and is found to be 175 oalorles more
Vol. 5, No. I0
HEAT OF SOLIDIFICATION OF Pb-Bi EUTECTIC ALLOY
endothermlc than our experimental value.
899
This difference may be attributed
to the different temperatures for which A H s and ~ H f values are available for calculation using Predel's formula. The authors are grateful to Dr. T.R.Anantharaman, Professor and Head of the Department of Metallurgy, Banaras Hindu University, for providing necessary facilities and his keen interest in this investigation. One of the authors (H.P.S.) is grateful to the C.S.I.R., New Delhi, for the award of a Senior Research Fellowship. REFERENCES I.
R.H.Tien and V.Koump, Trans.Met.Soc.AI~E,242,1283(1968).
2.
V.Koump,R.H.Tien and T.F.Perzak, Trans.Met. Soc.AIME, 242,1589(1968).
3.
H.D.Bordy and M.C.Flemlngs, Trans.Met.Soc.AIME,23.6,615(1966).
4.
S.L.Malhotra, Ph.D.Thesls, p.86, London University (1969).
5.
M.Hansen and K.Anderko, Constitution of Binary Alloys,p.324, ZcGraw-Hill, New York (1958).
6.
R.Hult&ren, R.L.Orr, 2.D.Anderson and K.K.Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, p.50 and 206, John Wiley, New York (1963).
7.
P.Roy, R.L. Orr and R.Hultgren, J.Phys.Chem.,64,1034(1960).
8.
S.Misra, H.P.Singh and P.U.Nayak, Indian J.Technol.,_6,254(1968).
9.
S.V.Rao, Private Communication, Department of Metallurgy, Banaras Hindu University, Varanasi, India (1971).
10.
I~.Kawakami, Sci.Repts.Tohoku Imp.Unlv.,19,521(1930).
11.
H.S.Strickler and H.Seltz, J.Am. Chem. Soc.,58,2084(1936).
12.
B.Predel and D.Rothecker, Acta Met.,15, 135(1967).