65 Pd Pd JAC 1998

LJournal of Alloys and Compounds 269 (1998) 123–132

Thermodynamics of the Pb–Pd systema a b c c c ,*V. Vassiliev , G.F. Voronin , G. Borzone , M. Mathon , M. Gambino , J.P. Bros

a Úniversite Lomonossov, Laboratoire de Thermodynamique chimique, Moscow, Russiab ` Ùniversita di Genova, Dipartimento di Chimica e Chimica Industriale, Via Dodecaneso, 31, 16146 Genova, Italy

c Úniversite de Provence, IUSTI, CNRS-UMR 6595, Rue Enrico Fermi 5, 13453 Marseille Cedex 13, France

Received 6 October 1997; received in revised form 2 January 1998

Abstract

In the ranges 590,T /K,1170 and 0.10,x ,0.75, the thermodynamic properties of the palladium–lead system were obtained fromPd

electromotive force measurements (E5f(T,x ) using the reversible concentration cell:Pd

2 21 1W,Pb(pure) /Pb in liquid electrolyte /Pb Pd ,W .x 12x

8Activities of lead in the liquid and solid [Pb1Pd] alloys derived from the measured cell potentials allowed the molar partial (D G ,mix Pb,xs ,xs ,xs8 8 8 8 8D H and D S ) and integral (D G , D H and D S ) excess thermodynamic functions to be calculated in the one-mix Pb mix Pb mix m mix m mix m

and two-phase regions (reference state, pure liquid Pd and Pb). The integral molar excess Gibbs energy of formation of the liquid alloyhas been described by the following relation:

i,xs n21D G8 5 x(1 2 x)[O A (1 2 2x) ] with x 5 x and A 5 h 2 Ts .mix m i51 i Pd i i i

The best description of this excess function was obtained with the following values:

h 5 2 16 564; h 5 13 270; h 5 2 8979; h 5 2984;1 2 3 4

and s 5 1.8554; s 5 2 0.7850; s 5 s 5 0.1 2 3 4

Assuming that all of the intermediate phases are stoichiometric, the excess functions of formation have been calculated. These data are asfollows:

Phase 2D G8(700 K) 2D H8f f

kJ /mol kJ /mol

Pb Pd 30.3360.1 33.3160.32

PbPd 42.4360.2 42.760.6Pb Pd 48.3160.3 47.361.29 13

(g)-Pb Pd 49.9660.4 48.6623 5

PbPd 55.7660.5 55.2643

The validity of this assumption will be discussed. Moreover, the liquidus and solidus lines of the equilibrium phase diagram, as well asthe range of stoichiometry of the definite compounds, have been specified. 1998 Elsevier Science S.A.

Keywords: Pb–Pd system; Potentiometric measurements; Activity of lead; Gibbs energy and enthalpy of formation; Phase diagram

1. Introduction

Thermochemical information for alloys formed by a* Group VIII-A transition metal and an element of GroupĆorresponding author. Universite de Provence, IUSTI, CNRS-UMR

6595, Rue Enrico Fermi 5, 13453 Marseille Cedex 13, France. III-B and IV-B are not broad enough to allow knowledge

0925-8388/98/$19.00 1998 Elsevier Science S.A. All rights reserved.PII S0925-8388( 98 )00120-0

124 V. Vassiliev et al. / Journal of Alloys and Compounds 269 (1998) 123 –132

of the nature of the metallic bonds in these systems to be 99.999 wt.% from Alfa-Ventron) have been already de-improved. Moreover, verification of the predicted values scribed [18,19].using Miedema’s semi-empirical model [1] is prevented by Emf (electromotive force) values were measured atthis lack of data. In recent years, by high temperature constant temperature with a digital voltameter (Keitley,

14calorimetry, we have studied a number of [Group VIII-A input impedance .10 ohms) with a resolution better thantransition1Group III-B] binary alloys [2–6] and have 10 mV. The reversibility of the cell was checked byshown the importance of the transfer of electrons from measuring the emf values of the same alloy during heatinggallium or indium towards the transition metals [7,8]. and cooling runs. An emf value was accepted when the

Similarly, thermodynamic data of binary alloys of a difference between three or four measurements was lessGroup VIII-A transition metal with a Group IV-B element than 0.02 mV at constant temperature. Experimental tem-are scarce. In the present work, the purpose of this peratures were determined in the cell with a [Pt /Pt1Rh 10electrochemical investigation was to determine the thermo- wt.%] thermocouple with an accuracy of about 60.1 K.dynamic properties of the palladium–lead system in liquid, The Gibbs energy of compounds was obtained with aliquid1solid and solid regions. In opposition to the precision better than 2%.previously investigated systems containing gallium or It is of a great interest to measure the emf versusindium, because of the large vapor tension of lead, it was temperature [E5f(T )] of a reversible galvanic cell con-very difficult to obtain reliable calorimetric data at high taining alloys of different molar fractions; such a studytemperatures for the [Pb1Pd] system. Consequently, allows one:potentiometric investigations were been chosen to obtain (i) to measure the variation of the chemical potential

* *the excess functions of formation of this binary alloy (Dm 5m 2m 522FEj versus T and x , (m and mmPb Pb Pb i i

instead of the classical high temperature calorimetric are the chemical potential of i in the binary alloy and thedeterminations. Moreover, high temperature calorimetric chemical potential of the pure element i, respectively),determinations, already published [9], have been per- (ii) to obtain the equilibrium temperatures of the phaseformed to complete this thermodynamic study. diagram lines of the system,

There is not much information on the palladium–lead (iii) to calculate the Gibbs energy of formation ofsystem. The phase diagrams published by Hansen and definite compounds.Anderko [10], Hultgren et al. [11], Moffatt [12], Durussel Actually, in a one-phase region, variation of the chemi-and Feschotte [13] and Massalski [14] exhibit five inter- cal potential depends both on the temperature and themediate compounds: Pb Pd, PbPd (melting congruently at composition of the phase. Consequently, the break points2 3

747 and 1493 K, respectively), PbPd, Pb Pd and Pb Pd in the representation of Dm (or E) versus temperature9 13 3 5

(melting incongruently). Fig. 1a–b are from refs. [13,14]. correspond to equilibrium points of the phase diagram. OnIn a recent paper [9], all of the available thermodynamic the other hand, in a heterogeneous region (in a two-phase

data proposed by Schwerdtfeger [15], Sommer et al. [16] region, for example), at constant temperature, the chemicaland Michel et al. [17] have been gathered and compared potential is the same in each phase; in this case, a linearwith our potentiometric and calorimetric results. The main equation has been chosen to represent E5f(T ).point to note is the difference between the values of theintegral molar enthalpy of formation obtained either bydirect calorimetry or by potentiometry.

Using the potentiometric technique, the thermodynamic 3. Resultsstudy of this binary system has been pursued in (liquid)-,(solid–liquid)- and (solid) regions, between 590 and 1170 During this study, 1468 experimental values wereK. Information concerning the phase diagram is reported in determined in the ranges 590,T /K,1170 and 0.10,

this paper. Thermodynamic properties of the phases have x ,0.75. Twenty-four alloys (used as working electrodes)Pd

been also proposed. were synthesized: x 50.100, 0.150, 0.200, 0.250, 0.300,Pd

0.330, 0.350, 0.400, 0.430, 0.450, 0.498, 0.500, 0.502,0.504, 0.515, 0.550, 0.580, 0.590, 0.600, 0.610, 0.620,0.630, 0.690, 0.748 (with x 60.005).Pd2. Experimental

In Fig. 2, a schematic plot of the measured emf valuesfor the Pb–Pd alloys studied is presented. Some general

The following reversible concentration cell:features are:

2 21 1 (a) Two series of the straight lines are separated byW,Pb(pure) /Pb in liquid electrolyte /Pb Pd ,Wx 12xcurves. The lengths of the straight lines correspond to thetemperature range investigated.was used.

(b) Each curve (L) belongs to a liquid1solid domainThe preparation of cells (in Pyrex or quartz), of elec-(liquidus line).trolytes (RbCl1LiCl, KCl1LiCl, KCl1LiCl1BaCl )2

(c) For a composition of a given alloy, prolongation ofand of alloys (Pb, 99.99 wt.% from Koch-Light and Pd,

V. Vassiliev et al. / Journal of Alloys and Compounds 269 (1998) 123 –132 125

Fig. 1. (a) Equilibrium phase diagram of the Pb–Pd system from ref. [13]. (b) Equilibrium phase diagram of the Pb–Pd system from ref. [14].

the E5f(T ) beyond the curves (L) corresponds to the Moreover, this figure exhibits some interesting trends:results obtained in the supercooled state. (1) On the right side, at high temperature, the series of

(d) The break points on the solid domain [on the left of straight lines corresponds to the variation of the chemicalthe curves (L)] indicate a phase transformation. potential (Dm ) in the following liquid alloys (x 50.100,Pb Pd


Fig. 2. General trend of the experimental emf results.

0.150, 0.200, 0.250, 0.300, 0.330, 0.350, 0.400, 0.430, x 50.63, one-phase region (located in the lower part ofPd

0.500, 0.600). Experimental results and analytical relations the g-phase),have been already published [see Table 2 in ref. [9]]. S corresponds to the two-phase region (g-phase18

(2) On the left side, (at low temperature) are reported PbPd ) with x 50.67 and 0.748.3 Pd

eight linear variations [E5f(T )] corresponding to the Results obtained with x 50.58 and x 50.59 (labelledPd Pd

experimental results obtained with solid alloys. In order to with an asterisk) have not been reported in Fig. 2, but thefully understand this paper, the regions of the phase coefficients of the linear equations are listed in Table 1.diagram have been symbolized by letters (Fig. 2) as (3) Five curves, symbolized by (L ,...L ), are located2 6

follows: between the two groups of linear representations.9S corresponds to the results obtained in the one-phase L corresponds to the coexistence of two phases (liq11 2

region Pb Pd (x 50.33), Pb Pd); results were obtained with x 50.150, 0.200,2 Pd 2 Pd

S corresponds to the two-phase region (Pb Pd1PbPd) 0.250, 0.300 and 0.330;2 2

with x 50.35, 0.40, 0.43, 0.45, 0.49, 0.498, L corresponds to the coexistence of two phasesPd 3

S corresponds to the two-phase region (PbPd1 (Pb Pd1liq.) with x 50.350;3 2 Pd

Pb Pd ) with x 50.498, 0.502, 0.504, 0.515, 0.55, L corresponds to the coexistence of two phases (liq19 13 Pd 4

9S corresponds to the one-phase region Pb Pd with PbPd); results were obtained with x 50.400, 0.430 and3 9 13 Pd

x 50.58 (*), 0.498;Pd

99S corresponds to the one-phase region Pb Pd with L corresponds to the coexistence of two phases (liq13 9 13 5

x 50.59(*), Pb Pd ); results were obtained with x 50.450, 0.500Pd 9 13 Pd

S corresponds to the two-phase region (Pb Pd 1 and 0.510;4 9 13

Pb Pd ) with x 50.595, 0.61 and 0.62, L corresponds to the coexistence of two phases (g-3 5 Pd 6

S corresponds to the two-phase region (Pb Pd 1 phase1PbPd ) with x 50.600.5 3 5 3 Pd2PbPd ) with x 50.63, 0.69 and 0.748, Using the following relation T / 8C5A 1A x1A x 13 Pd 0 1 2

3 4S corresponds to the two-phase region (Pb Pd 1g- A x 1A x with x5x , Table 2 allows us to know the6 9 13 3 4 Pd

phase) with x 50.61 and 0.62, equation of the different parts of the liquidus line (L , L ,Pd 2 4

9S corresponds to the one-phase region Pb Pd with L , L ).7 3 5 5 6


Table 1Potentiometric results obtained in the solid1liquid region

2 2 2 2¯ ¯ ¯Symbol Temperature range (K) a (mV) b.10 l T(K) E (mV) s8 10 o(T 2 T )i21(mV K )

9s 594–719 27.10 13.68 34 661.6 17.20 1.0 574931

s 594–717 81.18 27.04 142 646.9 35.65 2.1 1781782

s 600–774 107.46 28.10 70 703.0 50.50 9.1 2022373

9s 723–774 88.63 25.35 13 743.8 48.83 2.5 35183

99s 595–750 101.08 26.83 31 657.0 56.19 2.3 749033

s 620–702 85.43 11.11 70 656.0 92.71 9.7 397204

s 644–744 122.18 20.35 27 711.2 119.65 5.6 118555

s 703–775 148.55 27.81 49 737.2 90.97 7.5 179516

9s 753–775 134.81 22.01 5 764.0 119.48 0.5 2847

s 748–928 61.31 17.86 79 821.1 125.82 4.3 1780288

Column 1, name of the experimental series; column 2, experimental temperature range; columns 3 and 4, calculated values of coefficients a and b of the¯E5a1bT relation; in column 5, l corresponds to the number of experiments performed; in columns 6 and 7 are listed the mean values T 5 oT /l andi

2¯ ¯E 5 oE /l; o(T 2 T ) values (column 7) are required to calculate the standard deviation, s8(column 8).i i

4. Discussion Moreover, the emf values obtained for the x 50.330Pd

alloy, between 447 and 4528C, deviate slightly from theAll the results allow us (i) to obtain some equilibrium liquidus line: This proves the existence of a solid solution

points of the phase diagram, (ii) to calculate the thermo- based on the intermetallic compound (Pd), and the ABCDdynamic properties of this binary system. In the following,a comparison with the phase diagrams already publishedhas been proposed.

4.1. Equilibrium phase diagram

(a) The observation in Fig. 3 (it is an enlarged part ofFig. 2) leads us to the following remarks. The E5f(T ) dataobtained with the Pb Pd and Pb Pd samples are67 33 70 30

symbolized by the black (n) and white (n) triangles,respectively. The curve ABCD (L on Fig. 3) corresponds2

to the [liq.1Pb Pd] region (with 0.15,x ,0.33). The2 Pd

points C and D belong to the liquidus line [449618C withx 50.30, and 452618C with x 50.33].Pd Pd

The Pb Pd alloy results (black n) exhibit four67 33

distinct parts corresponding to: The single solid phase(320,T / 8C,447) (EB), the single liquid phase (DM), thesupercooled liquid phase (ND) and the solid–liquid regionlimit (BD). B is a point of the solidus line. The liquidusline (L ) obtained by emf measurements is in agreement Fig. 3. Emf (mV)5f[T (8C)] obtained with Pb Pd (m) and Pb Pd2 67 33 70 30

with the liquidus line already published. (n) in liquid and solid states.

Table 2Coefficients of the equations of the different parts of the liquidus line of the Pb–Pd system

Domains A A A A A 2s ,x ,0 1 2 3 4 o Pd

Pb Pd1liq.2 205.2 5444.4 224969.1 58934.9 256903.1 62K 0.117–0.3732

Pb Pd1liq.3 205.2 5444.4 224969.1 58934.9 256903.1 62K2

PbPd1liq.4 247.0 1591.1 2865.0 61.5K 0.373–0.434Pb Pd 1liq.5 2250.0 2906.5 1268.0 61K 0.434–0.4999 13

g-Pb Pd 1liq. 6 2254.0 2282.8 62K 0.499–0.5973 5

2 3 4T (8C)5A 1A x1A x 1A x 1A x with x5x . To calculate these coefficients, (a) 133 experimental points have been used from the domains0 1 2 3 4 Pd

(Pb Pd1liq. 2) and (Pb Pd1liq.3), (b) 62 experimental points have been used from the domain (PbPd1liq. 4), (c) 55 experimental points have been used2 2

from the domain (Pb Pd 1liq. 5), (d) 13 experimental points have been used from the domain (Pb Pd 1liq. 6).9 13 3 6


line corresponds to the equilibrium between the (Pb ) tained with alloys that were not in thermodynamic equilib-22´

phase and liquid (L ). rium.2

The points (white n) of the line N9CF were obtained For the x 50.498 alloy, the large differences betweenPd

with the Pb Pd alloy: N9C and CF correspond to the the emf values (ef and dc lines) show the great sensitivity0.70 0.30

supercooled state and the liquid state, respectively. of the potentiometric technique: The large variation of theThe Pb Pd alloy does not melt congruently; the con- emf values allows one to detect microheterogeneities in the2

gruent composition is located between x 50.33 and experimental alloy.Pd

0.334. A slightly unbalanced composition can involve the(b) Emf measurements were performed in the two-phase following reaction:

regions [Pb Pd1PbPd] and [PbPd 1Pb Pd ]. For each2 9 13d PbPd 1 d Pb Pd 1 d Pb Pd → (d 2 d )PbPd1 0.992 2 9 13 3 2 1 3 0.992alloy belonging to these regions, the chemical potential of

lead is constant for a given temperature (Fig. 4); therefore, 1 (d 1 d )Pb Pd with d . d 4 d2 3 9 13 1 2 3

the emf values obtained with the alloys x 50.334, 0.400Pd

and 0.450 are located on the same line, S (white triangles, The presence of a small quantity of the Pb Pd phase2 2n). In an identical manner, the results obtained with the induces the following electrochemical reaction:alloys x 50.502, 0.504 and 0.515 are on the line SPd 3

21 2Pb 1 2e 1 PbPd → Pb Pd(black triangles, n). The large difference between S and 0.992 22

S proves that these alloys belong of two different3

heterogenous regions of the phase diagram. As soon as the Pb Pd phase completely disappears, by2However, the x 50.498 alloy exhibits a strange be- annealing, the E5f(T ) values to the series S are obtained,Pd 3

haviour (Fig. 4): corresponding to the chemical modification:ab corresponds to the non-linear variation of the chemi-

21 2Pb 1 2e 1 Pb Pd → PbPdcal potential of lead in the liquid state, 9 13 0.992

bc corresponds to the liquidus line,cd (S line) corresponds to the variation of the chemical The variation in the stoichiometry between the phases2

potential of lead in the two-phase [PbPd1Pb Pd] region. PbPd and PbPd only reaches 0.2 at.%. Taking into2 0.992

Over sixteen days, the emf values obtained with the first account the experimental uncertainties, this variation hasalloy (x 50.498; black triangles, n) were identical to no influence on the calculation of the molar integralPd

those of the other alloys (white triangles, n) (0.334,x , thermodynamic functions; this point will be discussedPd

0.450) of the series S (cd on Fig. 4). After that, the emf further.2

values increase (de on Fig. 4) and seven days after, they (c) With the two x 50.580 and x 50.590 alloysPd Pd

reached the values (ef on Fig. 4) of the series S (0.502, belonging to the two-phase region (PbPd1Pb Pd ) of the3 9 13

99 9x ,0.550), corresponding to the two-phase [PbPd1 phase diagram, the results [lines S and S ; equations arePd 3 3

Pb Pd ] region. Obviously, these results have been ob- given in Table 1] are higher than those obtained with the9 13

x 50.502 and x 50.550 alloys [lines S and S ]. So,Pd Pd 2 3

9 99the intersections of S with S and S (corresponding to3 3 3

the equality of the chemical potentials) allow one todeduce the limits of the Pb Pd phase [calculated coordi-9 13

nates from Table 1: x 50.58 with T54118C (684 K) andPd

x 50.59 with T52308C (503 K)]. These results allow aPd

narrow non-stoichiometric range of the Pb Pd compound9 13

to be proposed.(d) The graphical representation E5f(T ), obtained in

the temperature range 620–775 K, with the x 50.610 andPd

x 50.620 alloys (series S and S ) clearly exhibits aPd 4 6

break at 703 K (4308C).For other Pd-rich series (S with x 50.690 and 0.7485 Pd

and S with x 50.670 and 0.748), a break is also8 Pd

observable at 4708C (743 K). Moreover, a slight differencein the slope is noticeable with the x 50.630 samplePd

9(series S and S ) at 4308C (703 K).5 7

In the temperature- and molar fraction ranges investi-gated, no other thermal effect has been found with alloyssurrounding the g-Pb Pd phase. So, taking into account3 5

the published phase diagrams, our potentiometric resultsFig. 4. Emf (mV)5f[T (8C)] obtained with Pb Pd (m, black) and50.2 49.8

Pb Pd (n) in liquid and solid states (S and S ). can be interpreted as follows (Fig. 5), supposing that:66.6 33.4 2 3


Using the least squares method, the numerical values ofh and s have been calculated; with n55, the besti i

description of the excess molar Gibbs free energy:

i,xs n218D G 5 x(1 2 x)[O A (1 2 2x) ]mix m i51 i

with x 5 x and A 5 h 2 Ts (3)Pd i i i

has been obtained with the following values: h 521

16 564; h 513 270; h 528979; h 52984, and s 52 3 4 1

1.8554; s 520.7850 and s 5s 50.2 3 4,xs8Using Eq. (3), the values of D G at 700 K,mix m

,xs ,xs8 8D H and D S versus x5x have been calcu-mix m mix m Pd

lated, at 700 K, and are reported in Fig. 6.In Table 3 are listed the partial molar enthalpies of lead

(i) deduced from the experimental variations of thechemical potential of lead versus T (column 2), (ii)calculated by using Eq. (2) (column 3), (iii) calculated(column 4) with an other polynomial in [9]. Up to x 5Pd

,xs80.60, the Dm values have been obtained by extrapola-Pb

tion. These calculated and experimental results are com-parable. The values of the thermodynamic functions offormation of the liquid phase are listed in Table 4. TheFig. 5. The proposed shape of the equilibrium phase diagram between

,xsextremum of D G8 at 700 K and of D H8 are locatedx 50.50 and x 50.60. mix mixPd Pd

at about x 50.70. It should be noted that calorimetric andPd

potentiometric determinations of the enthalpy of formationof the [Pb–Pd] liquid system are in quite good agreement(i) The g-phase (NiAs structure) probably shows a

21 21(238 kJ mol at x 50.66 and 242.8 kJ mol atpolymorphic congruent transformation at 4888C (761 K), Pd

x 50.7, respectively). On the other hand, the result(ii) two eutectoid points are located on both sides of the Pd21proposed by de Boer et al. [1] is different (218 kJ moldefinite incongruent compound (Pb Pd ), the two eutec-3 5

at x 50.5).toids [4308C (703 K)] and [4708C (743 K)] are at roughly Pd

x 50.620 and x 50.637, respectively. Nevertheless,Pd Pd

complementary experiments will be necessary to support 4.2.2. Results obtained in the (solid1 liquid) and (solid)this proposal. regions

To calculate the thermodynamic functions of the solidphases, the following assumption has been accepted: All of4.2. Thermodynamicsthe intermediate phases of this binary system are consid-ered to be stoichiometric. When the non-stoichiometricFrom these experimental results, the molar enthalpies,range is small, this assumption brings an uncertainty ofentropies and free energies of formation of compoundsabout 1% in the determination of the Gibbs free energy ofhave been calculated:formation of the phase. The calculation of the Gibbsenergy of formation of a solid definite compound from the4.2.1. Results obtained in the liquid phasethermodynamic properties of the liquid alloy and from theAll of the experimental results (695) obtained withequilibrium phase diagram has been extensively explainedliquid alloys allowed us to calculate the chemical potential

8 by Voronine [20,21] and applied on sodium–antimony,of lead [Dm /R5223.2096 E (mV)] or the excessPb,xs8 8 sodium–bismuth,...binary systems. Moreover, Voroninechemical potential [Dm /R5Dm /R1T ln (12x )].Pb Pb Pd

analyzed the relation between the uncertainty in theFrom the Redlich-Kister polynomial form:determination of the D G /R value and the width of non-,xs f8DG liq. /R 5 x(1 2 x)[A (T ) 1 A (T )(1 2 2x)1 2 stoichiometry (Dx). For example, in this case, the uncer-

21 A (T )(1 2 2x) 1 ... 1 A (T )(1 tainty on the molar Gibbs energy of formation of the3 n

g-Pb Pd (with Dx of about 4%) does not exceed 1%.n21 3 52 2x) ]j (1)Obviously, the error in the determination of the other

the following relation can be used to express the excess functions (D H8 and D S8) will be more important.f fchemical potential: In this work, emf measurements E(T,x) performed with

liquid alloys in equilibrium with the corresponding solid,xs 2 i228Dm Pb,liq. /R 5O[x (2i(1 2 x) 2 1)(1 2 2x) ]A (2)i phases allow one to calculate the coordinates of thein which A 5 h 2Ts . liquidus points. For measurements performed in the rangei i i


Fig. 6. D G , 700 K ( ), D H 8 (d) and D S 8 ( ) versus x . Calorimetric results (s) from ref. [9]. Molar Gibbs energy of formation of solidmix m mix m mix m Pd

compounds (j).

Table 3Experimental and calculated (with equations 2 and 4 from ref. [9]) values of the molar partial enthalpy of lead in the liquid state

x 2DH 8 2DH 8 2DH 8 x 2DH 8 2DH 8 2DH 8Pd Pb Pb Pb Pd Pb Pb Pb

kJ /mol kJ /mol kJ /mol kJ /mol kJ /mol kJ /mol(exp.) (eq. 2) (eq. 4) (exp.) (eq. 2) (eq.4)

0.10 0.0660.02 0.15 0.11 0.55 10.93 10.340.15 0.4560.04 0.38 0.34 0.60 17.6862.2 17.44 17.690.20 0.7260.02 0.68 0.73 0.65 27.4 30.00.25 1.1660.04 1,04 1.20 0.70 42.2 49.50.30 1.5260.05 1.48 1.70 0.75 63.5 790.35 2.2460.05 2.05 2.22 0.80 93 1220.40 2.9560.02 2.93 2.89 0.85 133 1830.45 (3.560.3) 4.38 4.03 0.90 187 2660.50 6.2860.09 6.85 6.21 0.95 257 377

Table 4Values of the thermodynamic functions of formation of the Pd–Pb system

xs xsx 2 D G 8 2 D H 8 1 D S 8 x 2 D G 8 2 D H 8 1 D Sm8Pd mix m mix m mix m Pd mix m mix m mix

kJ /mol kJ /mol J /K/mol kJ /mol kJ /mol J /K/mol

0.1 7.61 6.96 0.92 0.65 44.85 42.08 3.950.2 14.65 13.36 1.84 0.7 45.43 42.78 3.790.3 21.96 20.08 2.69 0.75 44.44 41.99 3.500.4 29.65 27.28 3.39 0.8 41.47 39.31 3.090.5 37.13 34.43 3.86 0.9 27.72 26.42 1.850.6 43.07 40.25 4.02 0.95 15.90 15.19 1.01


,2F Table 58L –L , the chemical potential of lead (Dm ) in the2 6 PbMolar enthalpies and molar Gibbs energy (at 700 K) of formation of theheterogeneous region is given by the relation:definite compounds

,2F8Dm /R 5 2 23.2096 E /mV Phase 2D G8(700 K) 2D H8f fPbkJ /mol kJ /mol

2F(the two-phase region is marked by the symbol )Pb Pd 30.3360.1 33.3160.32For measurements performed in the (solid1liquid) PbPd 42.4360.2 42.760.6

region (reference states: liquid Pb and liquid Pd), the Pb Pd 48.3160.3 47.361.29 13

Pb Pd (g) 49.9660.4 48.662equilibrium conditions along the liquidus line are as 3 5

PbPd 55.7660.5 55.2643follows:

Dm8 5 Dm8 (Pb Pd ) (4) The mean data obtained using these four ways are listedPb in liq. Pb in sol. m n

in Table 5.Moreover, the temperatures of phase transitions haveDm8 5 Dm8 (Pb Pd ) (49)Pd in liq. Pd in sol. m n

been calculated from these thermodynamic data. For,2F instance, for the phase Pb Pd, at the melting temperature,8 2Dm8 5 Dm (Pb Pd ) (5)Pb in liq. Pb m n

the following equation can be written:,2F8Dm8 5 Dm (Pb Pd ) (59)Pd in liq. Pd m n 8D G8 5 D G (10)f (Pb Pd) f liq.2

where m and n are the stoichiometric coefficients of a and using the relations (8) and (1) to express the right andphase Pb Pd (such as Pb Pd, PbPd, Pb Pd , Pb Pd andm n 2 9 13 3 5 left part of relation (10), respectively, with the entropicPbPd ).3 term T [xLn x1(12x) Ln (12x)], the melting temperature

From the following equations: of the Pb Pd compound has been calculated: T 52 fus (Pb2Pd),2F 72562 K.8Dm (Pb Pd ) /R 5 2 23.2096.E (6)Pb m n

These calculated data are gathered in Table 6.,2F The coordinates of the eutectic point of the S range8 2Dm (Pb Pd ) /R 5 T ln xPb) m n liq

have been obtained by resolving the following equations:2

1 (1 2 x ) . O[(1 2 2i x ).(1liq liq ,2f (S )28 8Dm 5 DmPb in liq. Pbi222 2x ) ]A (T ) (7)liq i

,2f (S )28 8Dm 5 DmPd Pd,2F ,2F8 8D G8 /R 5 nDm /R 1 mDm /R (8)f (Pb Pd ) Pb Pdm nin which the left and right terms can be replaced, respec-

x and D G8 /R can be calculated. tively, by:liq f (Pb Pd )m n

Keeping the assumption of the simple stoichiometry of8 8 8Dm /R 5 DG /R 2 x[d(DG /R) /dx]the intermediate compounds, the integral molar functions Pb in liq. liq. liq.

of the other compounds (Pb Pd , Pb Pd and PbPd )9 13 3 5 3

8 8 8were calculated in the following ways: Dm /R 5 DG /R 2 (1 2 x)[d(DG /R) /dx]Pd liq. liq.

(I) (L 1 L ) → Pb Pd 1 S → PbPd 1 S → Pb Pd 12 3 2 2 3 9 13 and

S → Pb Pd (g ) 1 S → PbPd ,2f (S )24 3 5 5 8Dm 5 D G8(Pb Pd) 2 D G8(PbPd)Pb f 2 f

(II) L → PbPd 1 S → Pb Pd 1 S → Pb Pd (g ) 1 ,2f (S ) 2f (S )4 3 9 13 4 3 5 2 28Dm 5 D G8(PbPd) 2 DmPd f PbS → PbPd (9)5

From these equations, the following coordinates have(III) L → Pb Pd 1 S → Pb Pd (g ) 1 S → PbPd been found: T 5721 K and x 50.373, for the heteroge-5 9 13 4 3 5 5 eut. Pd

neous domain S . All of the calculated coordinates are in2

good agreement with those already published [13,14].(IV) L → Pb Pd (g ) 1 S → PbPd6 3 5 5

Table 6Calculated coordinates of some invariant points of the Pb–Pd phase diagram

Coordinates Pb1Pb Pd Pb Pd Pb Pd1PbPd Pb Pd Pb Pd2 2 2 9 13 3 5

eutectic congruent temp. eutectic peritectic peritectic

x 0.082 0.333 0.373 0.434 0.499Pd

T (K) 538 725 721 772.9 884.2


´[2] R. Haddad, Thesis, Universite de Provence, Marseille, 1993.5. Conclusion[3] D. El Allam, M. Gaune-Escard, E. Hayer, J.P. Bros, Metall. Trans. B

23 (1992) 39.From potentiometric measurements, (i) the molar en- ` ´[4] P. Anres, Thesis, Universite de Provence, Marseille, 1997.

thalpy and Gibbs energy of formation of the [Pb1Pd] `[5] P. Anres, M. Gaune-Escard, E. Hayer, J.P. Bros, J. Alloys Comp.solid and liquid phases have been calculated, (ii) in- 221 (1995) 143.

`[6] P. Anres, M. Gaune-Escard, J.P. Bros, J. Alloys Comp. 234 (1996)formation on the equilibrium phase diagram has been264.deduced. These results have been compared with the data

[7] E. Hayer, J.P. Bros, J. Alloys Comp. 220 (1995) 189.already published. It is noteworthy than the values of the[8] E. Hayer, M. Gaune-Escard, J.P. Bros, J. Non-crystalline Solids

enthalpy of formation of the liquid [Pb1Pd] alloy, de- 205,207 (1996) 312.duced from potentiometric measurements, are in good [9] V. Vassiliev, M. Mathon, M. Gambino, J.P. Bros, J. Alloys Comp.

215 (1994) 141.agreement with those directly obtained by calorimetry.[10] H. Hansen, K. Anderko, Constitution of Binary Alloys, McGraw-Moreover, the coordinates of several points of the equilib-

Hill, New York, 1965.rium phase diagram do not vary greatly from published[11] R. Hultgren, P.S. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley,

data. Unfortunately, these measurements do not allow the Selected Values of the Thermodynamic Properties of the Binarycomplete shape of the phase diagram around the com- Alloys, ASM, Metals Park, OH, 1973.pounds Pb Pd and Pb Pd to be given. [12] W.G. Moffatt, The Handbook of Binary Phase Diagrams, General9 13 3 5

Electric, Genium Publishing Co., Schenectady, NY, 1987.The next development of this research will be to propose[13] P. Durussel, P. Feschotte, Chimia 50 (1996) 606.a coherent set of thermodynamic properties of the [Pb1[14] T.B. Massalski (Ed.), Binary Alloy Phase Diagrams, second ed.,Pd] binary system taking into account: (i) the molar

ASM, Metal Park, OH, Vol. 3, 1990, p. 2999.enthalpies and Gibbs energies of formation of the solid and [15] K. Schwerdtfeger, Trans. Met. Soc. AIME 236 (1966) 32.liquid phases and (ii) the last modifications of the phase [16] F. Sommer, Y.H. Suh, B. Predel, Z. Metallk. 69 (1978) 401.

[17] M.L. Michel, H. Bros, R. Castanet, Z. Metallk. 3 (1993) 174.diagram.[18] V. Vassiliev, M. Bykov, M. Gambino, J.P. Bros, J. Chim. Phys 90

(1993) 463.[19] V. Vassiliev, M. Bykov, M. Gambino, J.P. Bros, Z. Metallkd 84(7)References (1993) 461.[20] G.F. Voronine, J. Chim. Phys. (in Russian) 48(9) (1979) 2195.

[1] F.R. de Boer, R. Boom, W.C.M. Matens, A.R. Miedema, A.K. [21] Dep. VINITI N2963-71, 11 pages, 1971.Niessen, Cohesion in Metals, North-Holland Company, Amsterdam,1989.

65 Pd Pd JAC 1998

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