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The PdPb system: excess functions of formation and liquidus line in the range O <XPd < 0.60 and 600 <T < 1200 K
Journal of Alloys and Compounds, 215 (1994) 141-149 JALCOM 1191
141
The Pd-Pb system: excess functions of formation and liquidus line in the range 0
Muriel Mathon,
Mich~le Gambino
and Jean Pierre Bros*
IUSTI-CNRS UA 1168, Universitd de Provence, Centre de Saint JdrOme, F-13397 Marseille Cedex 20 (France)
(Received November 4, 1993; in final form February 21, 1994)
Abstract
Using a galvanic cell with liquid electrolyte, the activity of lead in the Pd-Pb system has been investigated in the molar fraction range 0.10
1. Introduction
Previous studies of the thermodynamic properties of the palladium-based liquid binary alloys P d - G a and Pd-In [1--4] have shown the importance of the redistribution of electrons between the palladium and associated polyvalent metal when the alloys are formed. The purpose of the present work is to improve the knowledge of the thermodynamics of the Pd-Pb system. Because of the large difference between the vapour pressures of palladium and lead (at 1000 K PPb = 1.63 Pa and ppd----'8.21X10 -9 Pa and at 1200 K p p b = 6 4 . 4 Pa andppd = 1.42 × 10-5 Pa [5]), a precise determination of the enthalpy of formation of the Pb-Pd liquid alloy in the entire range of composition by direct drop calorimetry is difficult at high temperature. Consequently, we chose to determine first the activity of lead by the potentiometric technique in the following composition and temperature range: 0.10
of the enthalpy of formation were carried out at three temperatures (952, 1108 and 1170 K). Like many Pd-M (with M an element from columns 13 and 14 of the periodic table) binary alloys, the Pd-Pb equilibrium phase diagram presents several compounds. The equilibrium diagram was published by Hansen and Anderko [6], Hultgren et al. [7] and then Moffatt [8]. The diagram shown in Fig. 1 was redrawn from ref. 8. Using thermal analysis, X-ray diffraction and micrography, Ruer [9], Marcotte [10] and Schubert and coworkers [11-13] studied the phase diagram and found that it exhibited the following: (1) two definite compounds, Pb2Pd and PbPd3, melting at 747 and 1493 K respectively; (2) three compounds, PbPd, PbgPd13 and PbaPds, the peritectic temperatures of which are respectively 774, 884 and 1108 K. PbaPd5 presents three structures (a, /3 and 3') and a eutectoid transformation (696 K). The maximum width of this phase is about 0.61
0925-8388/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)01191-J
142
V. Vassiliev et al. / The Pd-Pb system
2100
L
I
I
I
i
r
i
i
i
Pb-Pd I1828 Tm,Pd
1800 1500 1200
900 -
i /77' 600, Tm,Pb
533
IQ-
2. Experimental details
~ I a.
300 0.50
Pd-Pb alloys (with xrd <0.50) at 950, 1000 and 1050 K. Moreover, the values of the molar enthalpy of formation, negative and strongly asymmetrical ( - 26 kJ mo1-1 with xpd =0.70), and the molar excess entropy have been calculated. The activity data obtained by Schwerdtfeger [15] and Sommer et al. [16] are listed in Table 1. Unfortunately, a comparison between these two series of data is difficult, since the temperature and molar fraction ranges investigated are different. Consequently, a new study of the Pd-Pb alloy was undertaken using the following techniques: potentiometry, calorimetry and differential scanning calorimetry. In the following some of the results obtained by potentiometry and calorimetry are reported.
XPd
Fig. 1. Equilibrium phase diagram redrawn from ref. 8.
and the limit of the palladium solid solution is not well known. The enthalpies of formation of liquid Pd-Pb alloys (with 0
2.1. Potentiometry The electromotive force (e.m.f.) method utilizing a galvanic cell with liquid electrolyte is widely used for thermodynamic measurements in metallurgy. For this study the electrolytic cell, operable between 600 and 1190 K, is represented schematically as
Pb(liq.)[Pb 2+ in liquid electrolytelPbl_xPdx(liq.) 2.1.1. Experimental cells To perform the measurements, the following two devices have been employed. Cell type I. This cell (diameter 50 mm; height 60 ram), made of Pyrex, is operable between 600 and 800 K. A complete description has been published in ref. 17 and only particular features are recalled here. Its bottom has five cavities used as crucibles in which the pure metal (reference electrode, Pb in this case) and the alloy (working electrode) are placed. The electrodes are connected to the voltmeter by tungsten wires. On top of the cell and in the same vertical axis as one of the cavities, five vertical narrow tubes are sealed. These tubes contain the tungsten wires and allow a gas-tight connection (flame sealed) between the wires and the cell. An annex vessel charged with electrolyte (ingot) is connected to the cell by a standard taper joint. Several precautions must be taken when filling the cell: (i) the device is maintained under vacuum (10 -3 Pa), then under purified argon; (ii) the mass of electrolyte is melted and immediately poured into the cell; (iii) the cell is ultimately sealed off under vacuum, then quickly transferred into the furnace. Cell type II. This cell, made of quartz and described by Hayer [18], is operable between 800 and 1200 K. The main parts of this device are as follows. (1) A large quartz tube (experimental cell) with a lateral connection towards the vacuum pump or the
0.507 0.367 0.23
0.455 0.32 0.19
0.553 0.42 0.27
0.894 0.7
apb(1050 K) /16]
0.37 0.18 0.044 (so1. + liq.)
0.54
aeb(l123 K) [15]
0.38 0.2 0.08 (sol. + liq.)
0.55
apb(l173 K) [15]
0.41 0.22 0.057 (sol. + liq.)
0.57
apb(1273 K) [15]
0.42 0.23 0.063 (sol. + liq.)
0.59
apb(1373 K) [15]
0.24 0.072 (sol. + liq.)
a~(1473 K) [15]
0.567 0.38 0.176
0.88 0.74
apb(1050 K)
0.388 0.185
0.665 ~
apb(l123 K)
Xpd
0.100 0.150 0.200 0,250 0.300 0.330 0.332 0.350 0.400 0.430 0.450 0.500 0.600
No.
1 2 3 4 5 6 7 8 9 10 11 12 13
598-1164 624-863 666-1080 678-863 690-1175 717-802 704-810 713-863 717-1175 760-863 797-810 880-1189 1120-1186
T (K)
0.31 __0.09 2.36 + 0.17 3.75 + 0.08 6.04 + 0.19 7.89 -I- 0.23 10.86 ____0.21 _ 11.44 + 0.24 11.62+1.25 15.324-0.11 17.12 + 0.47 18.01 + 1.60 32.56 + 0.45 91.64+1.1
a (mY)
3.359 4- 0.06 4.06 + 0.02 4.379 ___0.043 6.13+1.0
2.712+__0.013
0.507 ____0.012 _ 0.659 + 0.023 0.940 + 0.010 1.182 + 0.026 1.694 +___0.025 1.753 + 0.028 1.759 + 0.031 2.047+0.032
b X 102 (mV K ~) 4.29 7.22 11.28 15.00 22.92 24.95 24.91 27.38 38.62 43.96 50.62 77.45 162.7(4)
Em (mY) 785.6 737.8 800.7 758.4 887.2 752.8 765.3 770.1 858.2 799.1 803.1 1025.3 1159.7
Tm (K) 131 86 57 70 72 39 54 53 61 28 8 29 7
1
0.73 0.38 0.18 0.19 1.9 0.06 0.12 0.19 0.43 0.16 0.01 1.22 5.84
cro× 102
2187056 281500 766771 118494 1406330 21237 50003 71246 1081840 18873 128.9 272530 4103
E(Ti - Tin)2
4.87 + 0.02 8.29 + 0.04 12.21 ____0.02 _ 16.62 4- 0.04 23.14 + 0.03 26.64 + 0.05 27.27 + 0.04 30.044-0.04 39.73+0.002 47.35 4- 0.06 54.55 72.0 4- 0.7 146.8+2.0
E(900 K) (mV)
5.89 + 0.04 9.61 + 0.09 14.09 + 0.03 19.04 + 0.09 26.52 4- 0.06 30.14 4- 0.12 30.79 + 0.10 34.14+0.11 45.15+0.04 54.07 4- 0.18 62.67 80.7 + 0.7 159.1+0.5
E(1100 K) (mV)
TABLE 2. Potentiometric results: column 2, molar fraction of palladium; column 3, experimental temperature range; columns 4 and 5, calculated values of coefficients a and b; columns 6-10, average values and n u m b e r of experiments (l) required to apply the least-squares method; columns 11 and 12, e.m.f, values calculated at 900 and 1100 K
aMeasured at Xpd= 0.25.
0.88 0.66
0.864 0.6
0.10 0.20 0.26 0.30 0.40 0.50 0.60 0.70
apb(1000 K) [16]
a~(950 K) [16]
Xpa
TABLE 1. Activities of lead obtained by Sommer et al. [16] at 950, 1000 and 1050 K and by Schwerdtfeger [15] at 1123, 1173, 1273, 1373 and 1473 K are listed in columns 2-9. Our results at 1050 and 1123 K are given in columns 10 and 11
g~
144
V. Vassiliev et al. / The Pd-Pb system
purified argon tank. A special gas-tight cap (brass) allows electrode wires and thermocouple wires to be connected to the voltmeter. (2) A special device (quartz) maintaining four small cylindrical crucibles (quartz) in the lower part of the experimental cell. In this case two references and two working electrodes are used. The level of liquid electrolyte is up to the aperture of the crucibles. The design of the furnace used for the two cells was intended to eliminate thermal gradients and to ensure accuracy in measurements of electromotive forces and temperatures. The furnace has two resistors and the experimental cell is surrounded by a thick metallic cylinder. The temperature of the furnace was controlled ( + 1 K) with an electronic device monitored by an Ni/ Cr thermocouple. 2.1.2. Preparation of alloys Alloys were prepared from high purity metals (99.999 wt.% Pd plates from Alfa-Ventron and 99.99 wt.% Pb ingots from Koch-Light, London) by direct combination (approximately 1 g samples). Stoichiometric amounts of the metals (weighed to + 10- 5 g) were melted under vacuum (10 -4 Pa) in sealed silica capsules by heating to 1100 K. After the liquid state was reached, the alloys were cooled progressively until 800 K, then homogenized by annealing for approximately 1 week at this temperature. The following alloys have been prepared: Xvd=0.60, 0.50, 0.45, 0.43, 0.40, 0.332, 0.33, 0.30, 0.25, 0.20, 0.15 and 0.10. The composition of the alloys was accurate to + 0.001 at.%. During the preparation the weight loss due to the evaporation of lead was negligible; so the nominal composition was maintained.
2.1.3. Preparation of electrolytes RbC1 + LiC1, KC1 + LiC1 and KC1 + LiC1 + BaC12 eutectic mixtures with 0.05 wt.% PbC12 were employed in this study as electrolytes. The coordinates of these eutectic points given by Janz et al.'s critical compilation [19] are respectively Teus=587 K with Xubcl=0.415, Tfos=625 K with xKa=0.42 and Tfus=593 K with xKa = 0.40 and XLIO= 0.54. The dehydration of LiC1 was carried out as follows. LiCI was dried under vacuum for 48 h at room temperature, then heated under vacuum to 473 K for 1 week. After this operation the other dried salts were added. The mixture of salts, melted in a quartz vessel, was further dried under an HC1 gas flow. The electrolyte obtained was perfectly transparent and sealed off in Pyrex tubes under vacuum. E.m.f. values were measured at constant temperature using a digital voltmeter (Keithley electrometer with a resolution better than 10 /xV) with a large input impedance (greater than 1014 12). An e.m.f, value was accepted when the difference between three or four measurements was less than _+0.01 mV at constant
temperature. The reversibility of these determinations was checked by measuring e.m.f, values of the same alloy during heating and cooling runs. At high temperature (800-1200 K), with quartz cells, e.m.f, measurements were reproducible over 1 week. However, at low temperature, with Pyrex cells, good results were obtained for 2 or 3 weeks. The lower reproducibility at high temperature was probably due to reactions between materials and crucibles. Experimental temperatures were determined with a Pt/Pt-10 wt.% Rh thermocouple located in the potentiometric cell. 2.2. Calorimetry Two types of calorimeters were used to determine the enthalpies of formation of the Pd-Pb liquid alloys [20-22]. These measurements were performed by the direct drop method [23], i.e. by a series of direct additions of palladium to the liquid bath formed by lead or Pd-Pb alloy. A small flow of purified argon was maintained in the cell during the experiments. The calorimeters were calibrated by additions of a-alumina crystals (NIST*). To refer all our results to the liquid state, enthalpy contents of palladium (the added metal) were taken from ref. 24 assuming a constant Cp for the supercooled liquid phase. Experimental uncertainties depend on the type of calorimeter and the investigated temperature range. The main sources of error were caused by the vaporization of lead and heat transfer processes during the dropping of palladium and a-alumina crystals. Consequently, errors were estimated to vary between 3% and 6%. The experimental temperature was determined with an uncertainty of about + 2 K. Measurements at 1170 K were performed with a very high temperature microcalorimeter equipped with an automated thermostatted sample charger. This apparatus has been described elsewhere [20]. The alloying process was carried out in a thin-walled graphite (high purity graphite from Carbone-Lorraine, France) crucible (inside diameter 6.5 ram, height 50 mm) located in a long alumina crucible. This alumina tube, extending to the cold region of the calorimeter furnace, prevents the thermocouples of the detector from any contact with metal vapours. Measurements of the enthalpy of mixing were carried out in the molar fraction range 0.022
V. Vassiliev et al. / The Pd-Pb system
one. This allowed us to determine the partial molar enthalpies of palladium in the lead-rich molar fraction range. At the end of each series the difference between the total weight of charged metals and the final weight of the alloy after experiments was less than 1 mg. Thus the evaporation of lead is negligible and the error is about 0.3% in the molar fraction.
145
hGxs(pb) = AG(Pb) - AGid(Vb) =RT In "/Pb AS xs(pb) = AS(Pb) - AS'd(Pb) = AS(Pb) + R in Xpb The values of the partial molar enthalpy obtained by calorimetry (column 3) and potentiometry (column 2) exhibit the same variation with the palladium molar fraction, but the agreement between these two series of data is reasonably good taking into account the diversity of the two experimental methods.
3. Results
3.1. Potentiometry All the experimental results (E~ in mill±volts and 7",in kelvins) were treated by the least-squares method to obtain the coefficients a and b of the linear equation E = a +bT. For each alloy the average values of electromotive forces and temperatures ( E m and Tin), required to calculate the standard deviation Cro,are listed as well as the numbers of experiments and the values of the electromotive force calculated at 900 and 1100 K. All these data are given in Table 2. The partial molar functions of formation of liquid alloys corresponding to the reaction 6Pb(liq.) + Pbl _,Pd,(liq.)
, Pb, _~,P@(liq.)
have been calculated from the relations AG°m(Pb) = - z F E ,
M-/°m(Pb) = -zFa,
AS°m(Pb) =zFB in which 6 is sufficiently small to keep the molar fraction of alloy constant ( x + a = x ' ) , z is the number of transferred electrons (z = 2) and F = 96484.6 C. The values of excess functions listed in Table 3 were deduced from the equations
3.2. Calorimetry The experimental integral molar enthalpies of formation of liquid alloys obtained at 952, 1108 and 1170 K are given in Table 4. At 1170 K the coordinates of the extremum are Xvd = 0.66 with A m i x H ° m = - - 38 + 2 kJ mo1-1, to be compared with Michel et al.'s [14] results of m m i x H ° m = - 3 7 + 2 kJ mo1-1 with xp~=0.66+0.01. Figure 2 allows a comparison between all the calorimetric results. The data are in good agreement, but the dependence on the temperature is not so marked. The molar enthalpies referred to liquid lead and supercooled liquid palladium are negative, comparable with the Pd-In system value (Xpd=0.60 with A m i x H ° m = - 3 1 kJ mo1-1) [2, 3], but less negative than those obtained for the Pd-Ga system (xpd=0.60 with A m i x H ° m = - - 7 0 . 4 kJ mol-1) [1]. The interatomic bonds seem to be of the same order of magnitude in the Pd-Pb and Pd-In liquid alloys, but the shift of the extremum towards the palladium-rich side indicates a more asymmetrical type of interaction. The limiting partial molar enthalpy of liquid palladium in liquid lead was obtained by extrapolation to 1170 K: AH°rnPd(liq.) in ~ liquid Pb) = - 78 _+3 kJ tool- 1 The values of the ~:function (AmixH°m/Xp~(1 -xpd) = sc) were calculated at 1170 K. Extrapolation to xed=l
T A B L E 3. Excess m o l a r partial e n t h a l p i e s , e n t r o p i e s a n d free e n e r g i e s of lead calculated at 1100 K f r o m p o t e n t i o m e t r i c m e a s u r e m e n t s ( c o l u m n s 3, 5 a n d 6). M o l a r partial e n t h a l p i e s o b t a i n e d by direct c a l o r i m e t r y are given in c o l u m n 4. S c h w e r d t f e g e r ' s results (z3G°XSm(Pb)) [15] a r e listed in c o l u m n 7 NO.
1 2 3 4 5 6 7 8 9 10 11 12
Xpd
0.10 0.15 0.20 0.25 0.26 0.30 0.33 0.332 0.35 0.40 0.43 0.50 0.60
-- ~ n ° m ( P b )
- M-/°m(Pb)
- ma°XSm(Pb )
- ma°XSm(Pb )
- ma°XSm(Pb )
(J mol - I ) (e.m.f)
(J mo1-1) (cal.)
(J K -1 mol - l )
(J mo1-1)
(J mo1-1)
271 + 8 443 + 12 589 ± 18 765+23 2005 1100 ± 35 1460 + 45 1490 ± 45 1799 _+55 3140 _+ 100 4396 ± 140 9233 + 270 23095 ± 700
+ 0.10 - 0.08 - 0.05 -0.11
60 + 0.20 455 + 35 724 ± 15 1166±40 1523 _ 2096 ± 2208 + 2242 + 2956 ± 3304 ± 6283 ± 17684 +
45 40 45 50 20 90 90 2200
+_0.03 + 0.04 ± 0.03 ±0.05
173 + 10 368 ± 20 695 ± 10 1043 ± 2 0 1670 + 200
+ + + + + + + +
0.30_+ 0.05 0.05 ± 0.05 0.04 :tz 0.06 0.37 ± 0.06 0.98 ___0.03 1.81 ± 0.12 2.69 ± 0.08 4.21 _+ 1.9
1856 + 2153 ± 2252 ± 2648 ± 4041 ± 5293 ± 9234 ± 22320 ±
10 10 20 20 10 20 10 100
3960 +_300 8790 _+300 20570 ± 300
I1.. Vassiliev et al. / The P d - P b system
146
T A B L E 4. E x p e r i m e n t a l r e s u l t s o b t a i n e d a t 9 5 2 , 1 1 0 8 a n d 1 1 7 0 K. The molar integral enthalpies of formation of Pd-Pb alloys are referred to liquid lead and supercooled liquid palladium (Ar, ixH°m). F o u r a n d t h r e e s e r i e s o f m e a s u r e m e n t s w e r e p e r f o r m e d at 952 and 1170 K respectively
0
0.2
0.4 x(Pd) 0.6
I
I
0.8
I
1
I
,-- -10
n0
T=952
K
Xvd
T=1170
Amixn°=
o
E.
K
Xpd
Amixn°m (kJ mol -I)
(kJ mol -z) 0.008 0.018 0.028 0.038 0.048
-
0.54 1.23 1.91 2.58 3.25
0.022 0.054 0.093 0.136 0.177
- 1.62 - 3.97 - 6.88 - 10.15 - 13.00
0.058 0.069 0.079
- 3.93 - 4.60 - 5.24
0.217 0.255 0.291
- 15.49 - 17.86 - 20.26
0.008 0.016
- 0.54 - 1.11
0.327 0.350
- 22.71 -24.16
0.025 0.033 0.042 0.051
----
0.041 0.108 0.161 0.219
- 3.26 -- 8 . 5 3 -- 1 2 . 2 4 - 16.50
1.64 2.20 2.75 3.33
0.008 0.016 0.025 0.034 0.042 0.053 0.062 0.073
- 0.53 -- 1 . 0 9 -- 1.68 -- 2 . 2 6 -- 2 . 8 4 -- 3.51 -4.16 - 4.82
0.271 0.332 0.371 0.402 0.440 0.464 0.491 0.525
- 20.03 - 23.90 -- 2 6 . 3 7 - 28.36 -- 3 0 . 5 3 -- 3 1 . 7 9 --33.19 -- 3 4 . 8 2
0.007 0.017 0.028
- 0.50 - 1.17 - 1.98
0.546 0.566 0.586
-- 3 5 . 5 1 -- 3 6 . 1 4 -- 3 6 . 6 6
0.040 0.053 0.066
- 2.82 - 3.28 - 4.19
0.021 0.049 0.079 0.117
- 1.64 - 3.71 - 5.98 -8.48
0.155 0.199
-11.13 - 14.17
0.242 0.283 0.323 0.354 0.374
-
T= 1108 K Xpd
Amixn°m (kJ mol -I)
0.003 0.015 0.028 0.042 0.055
-
0.22 1.05 1.91 2.86 3.77
17.18 20.05 22.63 24.69 25.83
allows us to obtain the limiting enthalpy with very low accuracy indeed: AH°m(Pb(liq.) in ooliquid P d ) = - 2 7 2 kJ mo1-1. The AH°m(Pd(liq.) in ooliquid Pb) value calculated by Miedema and Niessen [25] is not very different from the experimental one ( - 6 2 kJ mo1-1 instead of - 7 8 kJ mol-1). On the other hand, the
"-
E
._x E <3
-20
-30
-40 F i g . 2. E n t h a l p y o f f o r m a t i o n o f l i q u i d P d - P b a l l o y s vs. p a l l a d i u m m o l a r f r a c t i o n : t-l, t h i s w o r k a t 1 1 7 0 K , - - , smoothed curve. T h e c u r v e s ( a ) , ( b ) a n d (c) c o r r e s p o n d t o t h e e x p e r i m e n t a l temperatures 1240, 1154 and 922 K respectively published in ref. 14.
5
0.2 I
0.4 I
x(Pd)
0.6 I
0
X 0 S. -5
[]
• []
,,-j
[]
•
~, -lO ,,,Q
E -15 <3
-20 -25 F i g . 3. M o l a r p a r t i a l e n t h a l p y o f l e a d ( r e f e r r e d t o t h e l i q u i d s t a t e ) v s . p a l l a d i u m m o l a r f r a c t i o n : O , f r o m p o t e n t i o m e t r y ; IS], from calorimetry at 1170 K; --, smoothed curve corresponding to the average between potentiometric and calorimetric data.
difference between the experimental ( - 38 kJ tool -~) and calculated ( - 18 kJ mol -~) values of the extremum of
mmlxH°m =f(Xpd ) is very
large.
It is note worthy that for many Pd-M alloys (with M=A1, Ga, In, Sn, etc.) the A m i x a ° m values proposed by Miedema and Niessen [25] are less exothermic than the experimental data [1-4].
4. D i s c u s s i o n
In agreement with the equilibrium phase diagram, the deviation of the activity apb from Raoult's law is negative. Table 1 allows a comparison of the activity of lead. At 1050 K, with Xpd< 0.30, our values (column 10) are in agreement with those of Sommer et al. [16] (column 5). On the other hand, at 1123 K, around the equimolar fraction, our results (column 11) are in good
V. Vassiliev et al. / The Pd-Pb system 22
>
21
to
20
I
I
J
I
I
I
TABLE 5. Temperature and palladium molar fraction of experimental points of the liquidus
I
e
xea
19
1817-
16• 15 680
'
, L , • 700
.
.
. •
720
. , 740
.
. '
, 760
•
xPdT, 780
147
0:30 ' 800
T/K
Fig. 4. E =f(T). Along the segments A O and OB the Pd0.3oPb0.70 alloy is supercooled and liquid respectively. The line OC corresponds to the equilibrium l i q . o l i q . + P b 2 P d ( s o l . ) .
agreement with those of Schwerdtfeger [15]. New investigations on the palladium-rich side are essential to propose a correct description of the apb =f(Xpb) function. The values of the partial molar excess functions of lead (AG°m(Pb), AS°m(Pb) and zSd-/°m(Pb)) calculated at 1100 K from potentiometric results have been listed in Table 3. Schwerdtfeger's values [15] of the excess partial molar free energy at 1100 K (column 7, Table 4) are tess negative than our values (column 6, Table 4) but not very different. Unfortunately, the comparison is very difficult, since high temperature results are scarce and exhibit a large dispersion. Moreover, the extrapolation of partial molar excess functions on the palladium-rich side is very tricky, so a description of the partial functions over the entire molar fraction range will be unreliable. Consequently, a description of the molar integral function of formation from these results is very difficult. Partial molar enthalpies of lead obtained by potentiometric measurements and calculated from calorimetric results have been reported in Fig. 3. The discrepancies between these two series of data depend on the experimental temperature and the molar fraction of the alloys. Nevertheless, by using the following polynomial relation to describe the molar partial enthalpy of lead (in joules per mole),
0.0000 0.0382 0.0475 0.0568 0.0750 0.1000 0.1103 0.1106 0.1290 0.1361 0.1448 0.1500 0.1775 0.2000 0.2098 0.2172 0.2500 0.2553 0.2709 0.2918 0.2995 0.3000 0.3269 0.3300 0.3340 0.3370 0.3500 0.3548 0.3606 0.4000 0.4010 0.4242 0.4300 0.4500 0.4543 0.4580 0.4833 0.5000 0.5112 0.5320 0.5382 0.5643 0.5844 0.6000 0.6020 0.6138 0.6410 0.6420
T (K) [91 600
T (K) [101
T (K) (this work)
T (K) [14]
600 574
567 560 537 573 617 581 654
632 629
672 674 691 703 702 710 722 725 737 722 727 725 727 747 725 733 723 743 765
750 768 797
797 821 856 875 869 922 968 1052 1093 1115 1154 1165 1240 1278
~/°m(Pb) =Alxea + A a X p d 2 + A 3 x r,d3 -]-A4Xpd4 -{-AsXpcl5 (with A1 = 1680.6, a 2 = 4.4248 X 104,A3 = - 5.3166 × 10s, 1.6289 × 106 and As = - 1.6573 x 106 in the molar fraction range 0
A 4=
- 2 6 kJ mo1-1 with Xp~=0.70 for the extremum and - 7 6 kJ mol-1 for the limiting molar partial enthalpy of liquid palladium in liquid lead. This last datum is in good agreement with our result: zSd/°m(Pd(liq.) in liquid Pb) = - 78 + 3 kJ mol- 1. Obviously, to propose a complete description of the thermodynamic excess functions of this binary system, more experimental data in the palladium-rich region are needed.
V. Vassiliev et al. I The Pd-Pb system
148
definite compound Pb2Pd. Figure 5 allows a comparison between these different results.
1400
0
/
1200
/
5. Conclusions
/o
On one hand, from potentiometric measurements performed in the molar fraction range 0.10
I
Liquid
/
1000 /
/
I"
J
io
w'~ I .
. . . .
act ¢i
800
I,,,,
600
Y',~. d: __:.~"
400 Pb2Pd+PbPd
Pb+Pb2Pd
200
' 0
I 0.2
'
I 0.4
I x(Pd)
0.6
Fig. 5. Experimental points of the Pd-Pb liquidus line in the molar fraction range 0
Moreover, the study of the variation in the chemical potential AG°m(Pb) v s . temperature - or in the electromotive force E v s . temperature - has given some information concerning the equilibrium phase diagram. Indeed, the graphical representation o r E =f(T) exhibits a break point when a phase transition occurs. For example, for the alloy Xpd= 0.30 the experimental data are reported in Fig. 4. Along the linear segments AO and OB the state of the alloy is supercooled and liquid respectively and the line OC corresponds to the equilibrium liq. ,~,liq. +Pbl_xPdx(sol.). Thus the temperature of the point O and the molar fraction of the alloy are the coordinates of a point of the liquidus line. Data so obtained are given in Table 5 (column 4) for the molar fraction range 0.10
References 1 D. E1 Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans. B, 23 (1992) 39. 2 D. El Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans., B in press. 3 D. E1 Allam, Thdse, Universit6 d'Aix-Marseille I, 1989. 4 R. Haddad, Th~se, Universit6 d'Aix-Marseille I, 1993. 5 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, ASM, Metals Park, OH, 1973. 6 H. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1965. 7 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, OH, 1973. 8 W.G. Moffatt, The Handbook of Binary Phase Alloys, Genium, Schenectady, NY, 1987. 9 R. Ruer, Anorg. Chem., 52 (1970) 345. 10 V.C. Marcotte, Metall. Trans. B, 8 (1977) 185. 11 M. Ellner, T. Godecke and K. Schubert, Z. Metallkd., 64 (1973) 566. 12 H.W. Mayer, M. Eliner and K. Schubert, J. Less-Common Met., 71 (1980) 29. 13 H.W. Mayer and K. Schubert, J. Less-Common Met., 72 (1980) 1. 14 M.L. Michel, H. Bros and R. Castanet, Z. Metallkd., 3 (1993) 174. 15 K. Schwerdtfeger, Trans. Metall. Soc. AIME, 236 (1966) 32. 16 F. Sommer, Y.H. Suh and B. Predel, Z. Metallkd., 69 (1978) 401.
V. Vassiliev et al. / The Pd-Pb system 17 V. Vassiliev, M. Bikov, M. Gambino and J.P. Bros, Z. MetaUkd., 84 (1993) 461. 18 E. Hayer, personal communication, 1988. 19 G.J. Janz, J.R. Downey, C.B. Allen and R.P.T. Tomkins, Physical Properties Data Compilations Relevant to Energy Storage. L Molten Salts: Eutectic Data, NSRDS-NBS-61, US Government Printing Office, Washington, DC, 1978. 20 J.P. Bros, 3". Less-Common Met., 154 (1989) 9. 21 M. Gaune-Escard, Thdse de Doctorat d'Etat Sci. Phys., Marseille, 1972.
149
22 Y. Adda, J.M. Dupouy, J. Philibert and Y. Qu6r6, Techniques du Laboratoire de Science des Matdriaux, INSTN-CEA Saclay, Gif-sur-Yvette, 1993, p. 64. 23 O. Kubaschewsky and C.B. Alcock, Metallurgical Thermochemistry, Pergamon, Oxford, 5th edn., 1979. 24 I. Barin and O. Knacke, ThermochemicalProperties of Inorganic Substances, Springer, Berlin, 1973. 25 F.R. de Boer, R. Boom, W.C. Mattens, A.R. Miedema and A.K. Niessen, Cohesion in Metals, North-Holland, Amsterdam, 1988.
141
The Pd-Pb system: excess functions of formation and liquidus line in the range 0
Muriel Mathon,
Mich~le Gambino
and Jean Pierre Bros*
IUSTI-CNRS UA 1168, Universitd de Provence, Centre de Saint JdrOme, F-13397 Marseille Cedex 20 (France)
(Received November 4, 1993; in final form February 21, 1994)
Abstract
Using a galvanic cell with liquid electrolyte, the activity of lead in the Pd-Pb system has been investigated in the molar fraction range 0.10
1. Introduction
Previous studies of the thermodynamic properties of the palladium-based liquid binary alloys P d - G a and Pd-In [1--4] have shown the importance of the redistribution of electrons between the palladium and associated polyvalent metal when the alloys are formed. The purpose of the present work is to improve the knowledge of the thermodynamics of the Pd-Pb system. Because of the large difference between the vapour pressures of palladium and lead (at 1000 K PPb = 1.63 Pa and ppd----'8.21X10 -9 Pa and at 1200 K p p b = 6 4 . 4 Pa andppd = 1.42 × 10-5 Pa [5]), a precise determination of the enthalpy of formation of the Pb-Pd liquid alloy in the entire range of composition by direct drop calorimetry is difficult at high temperature. Consequently, we chose to determine first the activity of lead by the potentiometric technique in the following composition and temperature range: 0.10
of the enthalpy of formation were carried out at three temperatures (952, 1108 and 1170 K). Like many Pd-M (with M an element from columns 13 and 14 of the periodic table) binary alloys, the Pd-Pb equilibrium phase diagram presents several compounds. The equilibrium diagram was published by Hansen and Anderko [6], Hultgren et al. [7] and then Moffatt [8]. The diagram shown in Fig. 1 was redrawn from ref. 8. Using thermal analysis, X-ray diffraction and micrography, Ruer [9], Marcotte [10] and Schubert and coworkers [11-13] studied the phase diagram and found that it exhibited the following: (1) two definite compounds, Pb2Pd and PbPd3, melting at 747 and 1493 K respectively; (2) three compounds, PbPd, PbgPd13 and PbaPds, the peritectic temperatures of which are respectively 774, 884 and 1108 K. PbaPd5 presents three structures (a, /3 and 3') and a eutectoid transformation (696 K). The maximum width of this phase is about 0.61
0925-8388/94/$07.00 © 1994 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)01191-J
142
V. Vassiliev et al. / The Pd-Pb system
2100
L
I
I
I
i
r
i
i
i
Pb-Pd I1828 Tm,Pd
1800 1500 1200
900 -
i /77' 600, Tm,Pb
533
IQ-
2. Experimental details
~ I a.
300 0.50
Pd-Pb alloys (with xrd <0.50) at 950, 1000 and 1050 K. Moreover, the values of the molar enthalpy of formation, negative and strongly asymmetrical ( - 26 kJ mo1-1 with xpd =0.70), and the molar excess entropy have been calculated. The activity data obtained by Schwerdtfeger [15] and Sommer et al. [16] are listed in Table 1. Unfortunately, a comparison between these two series of data is difficult, since the temperature and molar fraction ranges investigated are different. Consequently, a new study of the Pd-Pb alloy was undertaken using the following techniques: potentiometry, calorimetry and differential scanning calorimetry. In the following some of the results obtained by potentiometry and calorimetry are reported.
XPd
Fig. 1. Equilibrium phase diagram redrawn from ref. 8.
and the limit of the palladium solid solution is not well known. The enthalpies of formation of liquid Pd-Pb alloys (with 0
2.1. Potentiometry The electromotive force (e.m.f.) method utilizing a galvanic cell with liquid electrolyte is widely used for thermodynamic measurements in metallurgy. For this study the electrolytic cell, operable between 600 and 1190 K, is represented schematically as
Pb(liq.)[Pb 2+ in liquid electrolytelPbl_xPdx(liq.) 2.1.1. Experimental cells To perform the measurements, the following two devices have been employed. Cell type I. This cell (diameter 50 mm; height 60 ram), made of Pyrex, is operable between 600 and 800 K. A complete description has been published in ref. 17 and only particular features are recalled here. Its bottom has five cavities used as crucibles in which the pure metal (reference electrode, Pb in this case) and the alloy (working electrode) are placed. The electrodes are connected to the voltmeter by tungsten wires. On top of the cell and in the same vertical axis as one of the cavities, five vertical narrow tubes are sealed. These tubes contain the tungsten wires and allow a gas-tight connection (flame sealed) between the wires and the cell. An annex vessel charged with electrolyte (ingot) is connected to the cell by a standard taper joint. Several precautions must be taken when filling the cell: (i) the device is maintained under vacuum (10 -3 Pa), then under purified argon; (ii) the mass of electrolyte is melted and immediately poured into the cell; (iii) the cell is ultimately sealed off under vacuum, then quickly transferred into the furnace. Cell type II. This cell, made of quartz and described by Hayer [18], is operable between 800 and 1200 K. The main parts of this device are as follows. (1) A large quartz tube (experimental cell) with a lateral connection towards the vacuum pump or the
0.507 0.367 0.23
0.455 0.32 0.19
0.553 0.42 0.27
0.894 0.7
apb(1050 K) /16]
0.37 0.18 0.044 (so1. + liq.)
0.54
aeb(l123 K) [15]
0.38 0.2 0.08 (sol. + liq.)
0.55
apb(l173 K) [15]
0.41 0.22 0.057 (sol. + liq.)
0.57
apb(1273 K) [15]
0.42 0.23 0.063 (sol. + liq.)
0.59
apb(1373 K) [15]
0.24 0.072 (sol. + liq.)
a~(1473 K) [15]
0.567 0.38 0.176
0.88 0.74
apb(1050 K)
0.388 0.185
0.665 ~
apb(l123 K)
Xpd
0.100 0.150 0.200 0,250 0.300 0.330 0.332 0.350 0.400 0.430 0.450 0.500 0.600
No.
1 2 3 4 5 6 7 8 9 10 11 12 13
598-1164 624-863 666-1080 678-863 690-1175 717-802 704-810 713-863 717-1175 760-863 797-810 880-1189 1120-1186
T (K)
0.31 __0.09 2.36 + 0.17 3.75 + 0.08 6.04 + 0.19 7.89 -I- 0.23 10.86 ____0.21 _ 11.44 + 0.24 11.62+1.25 15.324-0.11 17.12 + 0.47 18.01 + 1.60 32.56 + 0.45 91.64+1.1
a (mY)
3.359 4- 0.06 4.06 + 0.02 4.379 ___0.043 6.13+1.0
2.712+__0.013
0.507 ____0.012 _ 0.659 + 0.023 0.940 + 0.010 1.182 + 0.026 1.694 +___0.025 1.753 + 0.028 1.759 + 0.031 2.047+0.032
b X 102 (mV K ~) 4.29 7.22 11.28 15.00 22.92 24.95 24.91 27.38 38.62 43.96 50.62 77.45 162.7(4)
Em (mY) 785.6 737.8 800.7 758.4 887.2 752.8 765.3 770.1 858.2 799.1 803.1 1025.3 1159.7
Tm (K) 131 86 57 70 72 39 54 53 61 28 8 29 7
1
0.73 0.38 0.18 0.19 1.9 0.06 0.12 0.19 0.43 0.16 0.01 1.22 5.84
cro× 102
2187056 281500 766771 118494 1406330 21237 50003 71246 1081840 18873 128.9 272530 4103
E(Ti - Tin)2
4.87 + 0.02 8.29 + 0.04 12.21 ____0.02 _ 16.62 4- 0.04 23.14 + 0.03 26.64 + 0.05 27.27 + 0.04 30.044-0.04 39.73+0.002 47.35 4- 0.06 54.55 72.0 4- 0.7 146.8+2.0
E(900 K) (mV)
5.89 + 0.04 9.61 + 0.09 14.09 + 0.03 19.04 + 0.09 26.52 4- 0.06 30.14 4- 0.12 30.79 + 0.10 34.14+0.11 45.15+0.04 54.07 4- 0.18 62.67 80.7 + 0.7 159.1+0.5
E(1100 K) (mV)
TABLE 2. Potentiometric results: column 2, molar fraction of palladium; column 3, experimental temperature range; columns 4 and 5, calculated values of coefficients a and b; columns 6-10, average values and n u m b e r of experiments (l) required to apply the least-squares method; columns 11 and 12, e.m.f, values calculated at 900 and 1100 K
aMeasured at Xpd= 0.25.
0.88 0.66
0.864 0.6
0.10 0.20 0.26 0.30 0.40 0.50 0.60 0.70
apb(1000 K) [16]
a~(950 K) [16]
Xpa
TABLE 1. Activities of lead obtained by Sommer et al. [16] at 950, 1000 and 1050 K and by Schwerdtfeger [15] at 1123, 1173, 1273, 1373 and 1473 K are listed in columns 2-9. Our results at 1050 and 1123 K are given in columns 10 and 11
g~
144
V. Vassiliev et al. / The Pd-Pb system
purified argon tank. A special gas-tight cap (brass) allows electrode wires and thermocouple wires to be connected to the voltmeter. (2) A special device (quartz) maintaining four small cylindrical crucibles (quartz) in the lower part of the experimental cell. In this case two references and two working electrodes are used. The level of liquid electrolyte is up to the aperture of the crucibles. The design of the furnace used for the two cells was intended to eliminate thermal gradients and to ensure accuracy in measurements of electromotive forces and temperatures. The furnace has two resistors and the experimental cell is surrounded by a thick metallic cylinder. The temperature of the furnace was controlled ( + 1 K) with an electronic device monitored by an Ni/ Cr thermocouple. 2.1.2. Preparation of alloys Alloys were prepared from high purity metals (99.999 wt.% Pd plates from Alfa-Ventron and 99.99 wt.% Pb ingots from Koch-Light, London) by direct combination (approximately 1 g samples). Stoichiometric amounts of the metals (weighed to + 10- 5 g) were melted under vacuum (10 -4 Pa) in sealed silica capsules by heating to 1100 K. After the liquid state was reached, the alloys were cooled progressively until 800 K, then homogenized by annealing for approximately 1 week at this temperature. The following alloys have been prepared: Xvd=0.60, 0.50, 0.45, 0.43, 0.40, 0.332, 0.33, 0.30, 0.25, 0.20, 0.15 and 0.10. The composition of the alloys was accurate to + 0.001 at.%. During the preparation the weight loss due to the evaporation of lead was negligible; so the nominal composition was maintained.
2.1.3. Preparation of electrolytes RbC1 + LiC1, KC1 + LiC1 and KC1 + LiC1 + BaC12 eutectic mixtures with 0.05 wt.% PbC12 were employed in this study as electrolytes. The coordinates of these eutectic points given by Janz et al.'s critical compilation [19] are respectively Teus=587 K with Xubcl=0.415, Tfos=625 K with xKa=0.42 and Tfus=593 K with xKa = 0.40 and XLIO= 0.54. The dehydration of LiC1 was carried out as follows. LiCI was dried under vacuum for 48 h at room temperature, then heated under vacuum to 473 K for 1 week. After this operation the other dried salts were added. The mixture of salts, melted in a quartz vessel, was further dried under an HC1 gas flow. The electrolyte obtained was perfectly transparent and sealed off in Pyrex tubes under vacuum. E.m.f. values were measured at constant temperature using a digital voltmeter (Keithley electrometer with a resolution better than 10 /xV) with a large input impedance (greater than 1014 12). An e.m.f, value was accepted when the difference between three or four measurements was less than _+0.01 mV at constant
temperature. The reversibility of these determinations was checked by measuring e.m.f, values of the same alloy during heating and cooling runs. At high temperature (800-1200 K), with quartz cells, e.m.f, measurements were reproducible over 1 week. However, at low temperature, with Pyrex cells, good results were obtained for 2 or 3 weeks. The lower reproducibility at high temperature was probably due to reactions between materials and crucibles. Experimental temperatures were determined with a Pt/Pt-10 wt.% Rh thermocouple located in the potentiometric cell. 2.2. Calorimetry Two types of calorimeters were used to determine the enthalpies of formation of the Pd-Pb liquid alloys [20-22]. These measurements were performed by the direct drop method [23], i.e. by a series of direct additions of palladium to the liquid bath formed by lead or Pd-Pb alloy. A small flow of purified argon was maintained in the cell during the experiments. The calorimeters were calibrated by additions of a-alumina crystals (NIST*). To refer all our results to the liquid state, enthalpy contents of palladium (the added metal) were taken from ref. 24 assuming a constant Cp for the supercooled liquid phase. Experimental uncertainties depend on the type of calorimeter and the investigated temperature range. The main sources of error were caused by the vaporization of lead and heat transfer processes during the dropping of palladium and a-alumina crystals. Consequently, errors were estimated to vary between 3% and 6%. The experimental temperature was determined with an uncertainty of about + 2 K. Measurements at 1170 K were performed with a very high temperature microcalorimeter equipped with an automated thermostatted sample charger. This apparatus has been described elsewhere [20]. The alloying process was carried out in a thin-walled graphite (high purity graphite from Carbone-Lorraine, France) crucible (inside diameter 6.5 ram, height 50 mm) located in a long alumina crucible. This alumina tube, extending to the cold region of the calorimeter furnace, prevents the thermocouples of the detector from any contact with metal vapours. Measurements of the enthalpy of mixing were carried out in the molar fraction range 0.022
V. Vassiliev et al. / The Pd-Pb system
one. This allowed us to determine the partial molar enthalpies of palladium in the lead-rich molar fraction range. At the end of each series the difference between the total weight of charged metals and the final weight of the alloy after experiments was less than 1 mg. Thus the evaporation of lead is negligible and the error is about 0.3% in the molar fraction.
145
hGxs(pb) = AG(Pb) - AGid(Vb) =RT In "/Pb AS xs(pb) = AS(Pb) - AS'd(Pb) = AS(Pb) + R in Xpb The values of the partial molar enthalpy obtained by calorimetry (column 3) and potentiometry (column 2) exhibit the same variation with the palladium molar fraction, but the agreement between these two series of data is reasonably good taking into account the diversity of the two experimental methods.
3. Results
3.1. Potentiometry All the experimental results (E~ in mill±volts and 7",in kelvins) were treated by the least-squares method to obtain the coefficients a and b of the linear equation E = a +bT. For each alloy the average values of electromotive forces and temperatures ( E m and Tin), required to calculate the standard deviation Cro,are listed as well as the numbers of experiments and the values of the electromotive force calculated at 900 and 1100 K. All these data are given in Table 2. The partial molar functions of formation of liquid alloys corresponding to the reaction 6Pb(liq.) + Pbl _,Pd,(liq.)
, Pb, _~,P@(liq.)
have been calculated from the relations AG°m(Pb) = - z F E ,
M-/°m(Pb) = -zFa,
AS°m(Pb) =zFB in which 6 is sufficiently small to keep the molar fraction of alloy constant ( x + a = x ' ) , z is the number of transferred electrons (z = 2) and F = 96484.6 C. The values of excess functions listed in Table 3 were deduced from the equations
3.2. Calorimetry The experimental integral molar enthalpies of formation of liquid alloys obtained at 952, 1108 and 1170 K are given in Table 4. At 1170 K the coordinates of the extremum are Xvd = 0.66 with A m i x H ° m = - - 38 + 2 kJ mo1-1, to be compared with Michel et al.'s [14] results of m m i x H ° m = - 3 7 + 2 kJ mo1-1 with xp~=0.66+0.01. Figure 2 allows a comparison between all the calorimetric results. The data are in good agreement, but the dependence on the temperature is not so marked. The molar enthalpies referred to liquid lead and supercooled liquid palladium are negative, comparable with the Pd-In system value (Xpd=0.60 with A m i x H ° m = - 3 1 kJ mo1-1) [2, 3], but less negative than those obtained for the Pd-Ga system (xpd=0.60 with A m i x H ° m = - - 7 0 . 4 kJ mol-1) [1]. The interatomic bonds seem to be of the same order of magnitude in the Pd-Pb and Pd-In liquid alloys, but the shift of the extremum towards the palladium-rich side indicates a more asymmetrical type of interaction. The limiting partial molar enthalpy of liquid palladium in liquid lead was obtained by extrapolation to 1170 K: AH°rnPd(liq.) in ~ liquid Pb) = - 78 _+3 kJ tool- 1 The values of the ~:function (AmixH°m/Xp~(1 -xpd) = sc) were calculated at 1170 K. Extrapolation to xed=l
T A B L E 3. Excess m o l a r partial e n t h a l p i e s , e n t r o p i e s a n d free e n e r g i e s of lead calculated at 1100 K f r o m p o t e n t i o m e t r i c m e a s u r e m e n t s ( c o l u m n s 3, 5 a n d 6). M o l a r partial e n t h a l p i e s o b t a i n e d by direct c a l o r i m e t r y are given in c o l u m n 4. S c h w e r d t f e g e r ' s results (z3G°XSm(Pb)) [15] a r e listed in c o l u m n 7 NO.
1 2 3 4 5 6 7 8 9 10 11 12
Xpd
0.10 0.15 0.20 0.25 0.26 0.30 0.33 0.332 0.35 0.40 0.43 0.50 0.60
-- ~ n ° m ( P b )
- M-/°m(Pb)
- ma°XSm(Pb )
- ma°XSm(Pb )
- ma°XSm(Pb )
(J mol - I ) (e.m.f)
(J mo1-1) (cal.)
(J K -1 mol - l )
(J mo1-1)
(J mo1-1)
271 + 8 443 + 12 589 ± 18 765+23 2005 1100 ± 35 1460 + 45 1490 ± 45 1799 _+55 3140 _+ 100 4396 ± 140 9233 + 270 23095 ± 700
+ 0.10 - 0.08 - 0.05 -0.11
60 + 0.20 455 + 35 724 ± 15 1166±40 1523 _ 2096 ± 2208 + 2242 + 2956 ± 3304 ± 6283 ± 17684 +
45 40 45 50 20 90 90 2200
+_0.03 + 0.04 ± 0.03 ±0.05
173 + 10 368 ± 20 695 ± 10 1043 ± 2 0 1670 + 200
+ + + + + + + +
0.30_+ 0.05 0.05 ± 0.05 0.04 :tz 0.06 0.37 ± 0.06 0.98 ___0.03 1.81 ± 0.12 2.69 ± 0.08 4.21 _+ 1.9
1856 + 2153 ± 2252 ± 2648 ± 4041 ± 5293 ± 9234 ± 22320 ±
10 10 20 20 10 20 10 100
3960 +_300 8790 _+300 20570 ± 300
I1.. Vassiliev et al. / The P d - P b system
146
T A B L E 4. E x p e r i m e n t a l r e s u l t s o b t a i n e d a t 9 5 2 , 1 1 0 8 a n d 1 1 7 0 K. The molar integral enthalpies of formation of Pd-Pb alloys are referred to liquid lead and supercooled liquid palladium (Ar, ixH°m). F o u r a n d t h r e e s e r i e s o f m e a s u r e m e n t s w e r e p e r f o r m e d at 952 and 1170 K respectively
0
0.2
0.4 x(Pd) 0.6
I
I
0.8
I
1
I
,-- -10
n0
T=952
K
Xvd
T=1170
Amixn°=
o
E.
K
Xpd
Amixn°m (kJ mol -I)
(kJ mol -z) 0.008 0.018 0.028 0.038 0.048
-
0.54 1.23 1.91 2.58 3.25
0.022 0.054 0.093 0.136 0.177
- 1.62 - 3.97 - 6.88 - 10.15 - 13.00
0.058 0.069 0.079
- 3.93 - 4.60 - 5.24
0.217 0.255 0.291
- 15.49 - 17.86 - 20.26
0.008 0.016
- 0.54 - 1.11
0.327 0.350
- 22.71 -24.16
0.025 0.033 0.042 0.051
----
0.041 0.108 0.161 0.219
- 3.26 -- 8 . 5 3 -- 1 2 . 2 4 - 16.50
1.64 2.20 2.75 3.33
0.008 0.016 0.025 0.034 0.042 0.053 0.062 0.073
- 0.53 -- 1 . 0 9 -- 1.68 -- 2 . 2 6 -- 2 . 8 4 -- 3.51 -4.16 - 4.82
0.271 0.332 0.371 0.402 0.440 0.464 0.491 0.525
- 20.03 - 23.90 -- 2 6 . 3 7 - 28.36 -- 3 0 . 5 3 -- 3 1 . 7 9 --33.19 -- 3 4 . 8 2
0.007 0.017 0.028
- 0.50 - 1.17 - 1.98
0.546 0.566 0.586
-- 3 5 . 5 1 -- 3 6 . 1 4 -- 3 6 . 6 6
0.040 0.053 0.066
- 2.82 - 3.28 - 4.19
0.021 0.049 0.079 0.117
- 1.64 - 3.71 - 5.98 -8.48
0.155 0.199
-11.13 - 14.17
0.242 0.283 0.323 0.354 0.374
-
T= 1108 K Xpd
Amixn°m (kJ mol -I)
0.003 0.015 0.028 0.042 0.055
-
0.22 1.05 1.91 2.86 3.77
17.18 20.05 22.63 24.69 25.83
allows us to obtain the limiting enthalpy with very low accuracy indeed: AH°m(Pb(liq.) in ooliquid P d ) = - 2 7 2 kJ mo1-1. The AH°m(Pd(liq.) in ooliquid Pb) value calculated by Miedema and Niessen [25] is not very different from the experimental one ( - 6 2 kJ mo1-1 instead of - 7 8 kJ mol-1). On the other hand, the
"-
E
._x E <3
-20
-30
-40 F i g . 2. E n t h a l p y o f f o r m a t i o n o f l i q u i d P d - P b a l l o y s vs. p a l l a d i u m m o l a r f r a c t i o n : t-l, t h i s w o r k a t 1 1 7 0 K , - - , smoothed curve. T h e c u r v e s ( a ) , ( b ) a n d (c) c o r r e s p o n d t o t h e e x p e r i m e n t a l temperatures 1240, 1154 and 922 K respectively published in ref. 14.
5
0.2 I
0.4 I
x(Pd)
0.6 I
0
X 0 S. -5
[]
• []
,,-j
[]
•
~, -lO ,,,Q
E -15 <3
-20 -25 F i g . 3. M o l a r p a r t i a l e n t h a l p y o f l e a d ( r e f e r r e d t o t h e l i q u i d s t a t e ) v s . p a l l a d i u m m o l a r f r a c t i o n : O , f r o m p o t e n t i o m e t r y ; IS], from calorimetry at 1170 K; --, smoothed curve corresponding to the average between potentiometric and calorimetric data.
difference between the experimental ( - 38 kJ tool -~) and calculated ( - 18 kJ mol -~) values of the extremum of
mmlxH°m =f(Xpd ) is very
large.
It is note worthy that for many Pd-M alloys (with M=A1, Ga, In, Sn, etc.) the A m i x a ° m values proposed by Miedema and Niessen [25] are less exothermic than the experimental data [1-4].
4. D i s c u s s i o n
In agreement with the equilibrium phase diagram, the deviation of the activity apb from Raoult's law is negative. Table 1 allows a comparison of the activity of lead. At 1050 K, with Xpd< 0.30, our values (column 10) are in agreement with those of Sommer et al. [16] (column 5). On the other hand, at 1123 K, around the equimolar fraction, our results (column 11) are in good
V. Vassiliev et al. / The Pd-Pb system 22
>
21
to
20
I
I
J
I
I
I
TABLE 5. Temperature and palladium molar fraction of experimental points of the liquidus
I
e
xea
19
1817-
16• 15 680
'
, L , • 700
.
.
. •
720
. , 740
.
. '
, 760
•
xPdT, 780
147
0:30 ' 800
T/K
Fig. 4. E =f(T). Along the segments A O and OB the Pd0.3oPb0.70 alloy is supercooled and liquid respectively. The line OC corresponds to the equilibrium l i q . o l i q . + P b 2 P d ( s o l . ) .
agreement with those of Schwerdtfeger [15]. New investigations on the palladium-rich side are essential to propose a correct description of the apb =f(Xpb) function. The values of the partial molar excess functions of lead (AG°m(Pb), AS°m(Pb) and zSd-/°m(Pb)) calculated at 1100 K from potentiometric results have been listed in Table 3. Schwerdtfeger's values [15] of the excess partial molar free energy at 1100 K (column 7, Table 4) are tess negative than our values (column 6, Table 4) but not very different. Unfortunately, the comparison is very difficult, since high temperature results are scarce and exhibit a large dispersion. Moreover, the extrapolation of partial molar excess functions on the palladium-rich side is very tricky, so a description of the partial functions over the entire molar fraction range will be unreliable. Consequently, a description of the molar integral function of formation from these results is very difficult. Partial molar enthalpies of lead obtained by potentiometric measurements and calculated from calorimetric results have been reported in Fig. 3. The discrepancies between these two series of data depend on the experimental temperature and the molar fraction of the alloys. Nevertheless, by using the following polynomial relation to describe the molar partial enthalpy of lead (in joules per mole),
0.0000 0.0382 0.0475 0.0568 0.0750 0.1000 0.1103 0.1106 0.1290 0.1361 0.1448 0.1500 0.1775 0.2000 0.2098 0.2172 0.2500 0.2553 0.2709 0.2918 0.2995 0.3000 0.3269 0.3300 0.3340 0.3370 0.3500 0.3548 0.3606 0.4000 0.4010 0.4242 0.4300 0.4500 0.4543 0.4580 0.4833 0.5000 0.5112 0.5320 0.5382 0.5643 0.5844 0.6000 0.6020 0.6138 0.6410 0.6420
T (K) [91 600
T (K) [101
T (K) (this work)
T (K) [14]
600 574
567 560 537 573 617 581 654
632 629
672 674 691 703 702 710 722 725 737 722 727 725 727 747 725 733 723 743 765
750 768 797
797 821 856 875 869 922 968 1052 1093 1115 1154 1165 1240 1278
~/°m(Pb) =Alxea + A a X p d 2 + A 3 x r,d3 -]-A4Xpd4 -{-AsXpcl5 (with A1 = 1680.6, a 2 = 4.4248 X 104,A3 = - 5.3166 × 10s, 1.6289 × 106 and As = - 1.6573 x 106 in the molar fraction range 0
A 4=
- 2 6 kJ mo1-1 with Xp~=0.70 for the extremum and - 7 6 kJ mol-1 for the limiting molar partial enthalpy of liquid palladium in liquid lead. This last datum is in good agreement with our result: zSd/°m(Pd(liq.) in liquid Pb) = - 78 + 3 kJ mol- 1. Obviously, to propose a complete description of the thermodynamic excess functions of this binary system, more experimental data in the palladium-rich region are needed.
V. Vassiliev et al. I The Pd-Pb system
148
definite compound Pb2Pd. Figure 5 allows a comparison between these different results.
1400
0
/
1200
/
5. Conclusions
/o
On one hand, from potentiometric measurements performed in the molar fraction range 0.10
I
Liquid
/
1000 /
/
I"
J
io
w'~ I .
. . . .
act ¢i
800
I,,,,
600
Y',~. d: __:.~"
400 Pb2Pd+PbPd
Pb+Pb2Pd
200
' 0
I 0.2
'
I 0.4
I x(Pd)
0.6
Fig. 5. Experimental points of the Pd-Pb liquidus line in the molar fraction range 0
Moreover, the study of the variation in the chemical potential AG°m(Pb) v s . temperature - or in the electromotive force E v s . temperature - has given some information concerning the equilibrium phase diagram. Indeed, the graphical representation o r E =f(T) exhibits a break point when a phase transition occurs. For example, for the alloy Xpd= 0.30 the experimental data are reported in Fig. 4. Along the linear segments AO and OB the state of the alloy is supercooled and liquid respectively and the line OC corresponds to the equilibrium liq. ,~,liq. +Pbl_xPdx(sol.). Thus the temperature of the point O and the molar fraction of the alloy are the coordinates of a point of the liquidus line. Data so obtained are given in Table 5 (column 4) for the molar fraction range 0.10
References 1 D. E1 Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans. B, 23 (1992) 39. 2 D. El Allam, M. Gaune-Escard, J.P. Bros and E. Hayer, Metall. Trans., B in press. 3 D. E1 Allam, Thdse, Universit6 d'Aix-Marseille I, 1989. 4 R. Haddad, Th~se, Universit6 d'Aix-Marseille I, 1993. 5 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.D. Wagman, Selected Values of the Thermodynamic Properties of the Elements, ASM, Metals Park, OH, 1973. 6 H. Hansen and K. Anderko, Constitution of Binary Alloys, McGraw-Hill, New York, 1965. 7 R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser and K.K. Kelley, Selected Values of the Thermodynamic Properties of Binary Alloys, ASM, Metals Park, OH, 1973. 8 W.G. Moffatt, The Handbook of Binary Phase Alloys, Genium, Schenectady, NY, 1987. 9 R. Ruer, Anorg. Chem., 52 (1970) 345. 10 V.C. Marcotte, Metall. Trans. B, 8 (1977) 185. 11 M. Ellner, T. Godecke and K. Schubert, Z. Metallkd., 64 (1973) 566. 12 H.W. Mayer, M. Eliner and K. Schubert, J. Less-Common Met., 71 (1980) 29. 13 H.W. Mayer and K. Schubert, J. Less-Common Met., 72 (1980) 1. 14 M.L. Michel, H. Bros and R. Castanet, Z. Metallkd., 3 (1993) 174. 15 K. Schwerdtfeger, Trans. Metall. Soc. AIME, 236 (1966) 32. 16 F. Sommer, Y.H. Suh and B. Predel, Z. Metallkd., 69 (1978) 401.
V. Vassiliev et al. / The Pd-Pb system 17 V. Vassiliev, M. Bikov, M. Gambino and J.P. Bros, Z. MetaUkd., 84 (1993) 461. 18 E. Hayer, personal communication, 1988. 19 G.J. Janz, J.R. Downey, C.B. Allen and R.P.T. Tomkins, Physical Properties Data Compilations Relevant to Energy Storage. L Molten Salts: Eutectic Data, NSRDS-NBS-61, US Government Printing Office, Washington, DC, 1978. 20 J.P. Bros, 3". Less-Common Met., 154 (1989) 9. 21 M. Gaune-Escard, Thdse de Doctorat d'Etat Sci. Phys., Marseille, 1972.
149
22 Y. Adda, J.M. Dupouy, J. Philibert and Y. Qu6r6, Techniques du Laboratoire de Science des Matdriaux, INSTN-CEA Saclay, Gif-sur-Yvette, 1993, p. 64. 23 O. Kubaschewsky and C.B. Alcock, Metallurgical Thermochemistry, Pergamon, Oxford, 5th edn., 1979. 24 I. Barin and O. Knacke, ThermochemicalProperties of Inorganic Substances, Springer, Berlin, 1973. 25 F.R. de Boer, R. Boom, W.C. Mattens, A.R. Miedema and A.K. Niessen, Cohesion in Metals, North-Holland, Amsterdam, 1988.