Thermodynamics of liquid nickel-palladium alloys by computer-aided knudsen cell mass spectrometry

Journal of Alloys and Compounds, 196 (1993) 53-57 JALCOM 558

53

Thermodynamics of liquid nickel-palladium alloys by computer-aided Knudsen cell mass spectrometry H. Bittermann, K. K o p e c k y a n d J. T o m i s k a Institut fiir Physikalische Chemic der Universitiit Wien, Wiihringerstrafle 42, A-1090 Wien (Austria) (Received October 25, 1992)

Abstract Thermodynamic investigations on liquid binary Ni-Pd alloys have been performed by means of computer-aided Knudsen cell mass spectrometry. The enlarged "algebraic intensity ratio" (AIR) method ha~ been applied for the evaluation of the thermodynamic mixing functions. Two-parameter thermodynamically adapted power (TAP) series are used for the algebraic representation of the thermodynamic excess properties. Liquid Ni-Pd alloys are characterized by exothermic molar heats of mixing H E, slightly negative molar excess entropies S E and negative molar excess Gibbs energies G E. At 1850 K the minimum H E value is - 6 0 9 0 J m o l - ' (54.3 at.% Pd), the minimum S E value is - 0 . 2 4 J m o l - ' K - ' (59 at.% Pd) and the minimum G E value is - 5 6 6 0 J mo1-1 (53.7 at.% Pd). At 1850 K the thermodynamic activities of both components, Pd and Ni, show slight negative deviations from ideality over the entire range of composition.

1. Introduction The interest in Ni-Pd alloys has increased considerably since metallic glasses with the composition Ni41Pd41Pa8 were found. Generally, the technical interest in Pd alloys is connected with the fact that palladium is in many properties similar to platinum. Of course, Pt is still a bit more noble and shows a higher melting point than Pd, but Pd is considerably lighter and cheaper than Pt and therefore Pd will often be used instead of Pt. The objective of the present work is the determination of the thermodynamic mixing effects of liquid binary Ni-Pd alloys by means of computer-aided Knudsen cell mass spectrometry [1].

2. Mass spectrometric investigations In Knudsen cell mass spectrometry the effusion of a vaporized sample out of an isothermal vessel called a "Knudsen cell" is applied for the determination of the molar excess functions zE(z -- Gibbs energy G, heat of mixing H, entropy S; z-~ integral function Z, partial function Zj) of alloy systems [1-3]. Usually, Knudsen cells are manufactured as (cylindrical) crucibles with a small knife-edge-shaped orifice (0.5-1.5 mm in diameter) in the lid. This Knudsen cell is employed as a "gas source" and the effusing molecular beam is directed into the ionization chamber of the connected

0925-8388/93/$6.00

high temperature mass spectrometer (el. refs. 3 and 4). Detecting the ionized vapour beam by means of an electron multiplier then yields the ion current intensities J~ of the constituent species j of the vaporized sample (in this study j - Pd, Ni), which are proportional to the corresponding partial vapour pressures. Within the temperature ranges in which the logarithms of the partial pressures of the components j may be assumed to be proportional to T - 1, the measured ion current intensities Jj can be fitted by means of ln[J~(T, xj)T] = d~(xj) + d~(xj) T

(1)

where T (K) is the temperature, xj is the mole fraction of component j and dJo(Xj) and d~(xj) are best-fit parameters.

2.1. Measuring technique and data evaluation Thermodynamic evaluation makes use of the following relation between the ion current intensity Jj of a characteristic isotope k (in this study k - ' ° 6 p d , 5SNi) and the molar excess chemical potential/x E ("partial excess Gibbs energy GE'') of the investigated component j (in this study j - P d , Ni): #E(T, x~) = RT{In[Jj(T, x~)T] - In x~}- C, - Cj(T)

(2)

where R, C, and Cj(T) are the gas constant, an instrumental geometric constant and an isotope-specific constant [1, 2] respectively. The value of the geometric © 1993- Elsevier Sequoia. All rights reserved

H. Bittermann et al. / Thermodynamics of liquid Ni-Pd alloys

54

factor CI in eqn. (2) depends strongly on the actual position of the Knudsen cell with respect to the ion source [4]. With binary alloy systems such as the Ni(1)--Pd(l) system investigated here, this problem can be overcome conveniently by determining the thermodynamic mixing functions z E from the differences in the molar excess chemical potentials of the two alloy components Pd and Ni (lZEd--/~ENi). As can be easily verified from eqn. (2), the difference /ZpEd--~ is independent of the geometric constant CI if one assumes identical experimental conditions for the measurements of the ion current intensities of both alloy components [1, 51. Substituting eqn. (1) in eqn. (2) and forming the required difference ( j - P d , Ni) yields (xN~= 1--Xpd) ~Pd - -

do+¥

~Ni

with COG0( T ) . * = C p d ( T) -- C N i ( T )

(3b)

d,:=d~d-d~ ~ (i=O, 1)

(3c)

A regression formula which is suitable for an algebraic best fit of the binary experimental data (right-hand side of eqn. (3a)) is obtained finally by algebraic representation of the difference/~Ed --/ZE~ on the left-hand side of eqn. (3a). Profitable expressions for this purpose are derived from the thermodynamically adapted power (TAP) series representation of the binary molar excess functions zZ: N

Z E-- (1 --Xpd)

E CZX~d rim1

(4a)

N

/~pEd= (1 --Xpd)2 E n'-r'nzXpd n-1

(4b)

n--1 N

Cf,Xpd(1 -- n + nxrd)

(4c)

(N is the number of TAP parameters CZ). The Weierstrass approximation theorem guarantees that these approximations can be done with arbitrarily high accuracy [6]. Use of the TAP series eqns. (4b) and (4c) ( Z E - G E) in eqn. (3) leads to the relation

N

= C~o(T) + • CC.xT.~~[n - (1 + n)Xpd] n--1

(5)

The technique is then to adjust the TAP parameters Cff.(T) as well as the isotope-specific constant CoCo(T) by means of a suitable least-squares computer procedure [7] to fit as closely as possible the experimental values

RT{do + d l / T - In[(1 --Xpa)/Xpd]} of all investigated alloy samples at constant temperature T. In accordance with eqn. (1) the temperature dependence of the TAP parameters C0(T) and the isotopespecific constant C0C(T) is given by Ccn(T)=CH-TC s

(n=0, 1, 2, ..., N)

(6)

The parameters Cff and Cs emerge as temperatureindependent constants and can be used to compute the molar heat of mixing H E and the molar excess entropy SE by means of the corresponding eqn. (4) ( z - H , S) [1].

2.2. Experimental procedure The alloy samples were prepared by arc melting weighed amounts of the metals (Ni: 99.998%, Koch-Light Ltd., UK; Pd: 99.998%, Johnson-Matthey, UK) and then annealed in closed quartz tubes for several days. Micrographic examination proved the homogeneity of the samples. The measuring device was a computer-aided Knudsen cell mass spectrometer reconstructed at the Institut ffir Physikalische Chemie der Universit/it Wien: a modified model RMU-6M instrument (single-focusing 90° magnetic sector field (r = 200 mm), Hitachi, Japan) equipped with a special ion source assembly [4], a computercontrolled high temperature Knudsen cell unit with improved temperature measurement [1] and a digital data acquisition system. Detailed specifications and ratings of the experimental set-up are given elsewhere [1, 3, 41. Cell liners for the Knudsen effusion studies were made from A1203. The diameters of the effusion orifices were 0.75 and 1 mm. The temperature range covered in these investigations was about 60-180 K. To prevent sample crystallization, the lower temperature limit was varied in r~lation to the composition of the sample. The electron current used was 40/zA and the ionization energy 16 eV.

3. Results

The mass spectrometric investigations were performed in 14 runs for five different alloy concentrations (Table 1). In each run the ion current intensities JPd and JNi have been measured at about seven different temperatures 10 times each, giving a total of more than 70 values each. The deviation of the experimental data from the computed regression lines (eqn. (1)) was in no case higher than 3%. Figure 1 gives the corresponding data of a sample containing 80.03 at.% Pd (run 13 of Table 1). The constants do and dl summarized in Table 1 are computed according to eqn. (3c) from the corresponding d/Pd(Xpd)and dNi(XNi)values of eqn. (1).

H. Bittermann et al. / Thermodynamics of liquid Ni-Pd alloys 1820 7.8

TABLE 1. Constants do and dl of eqn. (3c), the relation between the ion current ratios ln(JpJJr~i) and the inverse sample temperature of the investigated liquid Ni-Pd alloys (Xpdis the mole fraction of palladium) Run

Xp~

do

dl

1 2 3 4 5 6 7 8 9 10 11 12 13 14

0.2005 0.2005 0.2005 0.3999 0.3999 0.3999 0.4998 0.4998 0.6015 0.6015 0.6015 0.8003 0.8003 0.8003

-4.111 -4.0735 -4.2884 -3.2194 -3.1398 -3.2376 -2.8191 -2.8198 -2.4847 -2.4247 --2.3816 - 1.5066 - 1.4870 - 1.5554

1114.5 851.4 1339.7 2368.8 1627.7 2098.1 2308.3 2825.2 3403.6 2995.8 3225.3 4582.2 4793.4 4399.7

4. Discussion

The enlarged "algebraic intensity ratio" ( A I R ) method also allows one to check the quality of the

Temperoturo T. K , ,

i

1680

,

7.2

~6.5 Z 2 59

(o)

5.3 5./*9

t

5.58

J

1820

i

5.67 lIT

8.9

Figure 2 shows the experimental RT{do + dll T--ln[(1--Xpd)/Xed]} data as a function of the mole fraction Xpd at the m e a n t e m p e r a t u r e T = 1850 K. As can be seen from Fig. 2, satisfactory best fit according to eqn. (5) was achieved using a two-parameter ( N = 2) T A P series for GE. Table 2 presents the values of the adjustable p a r a m e t e r s C z ( Z = H , S; n = 0 , 1, 2) determined by eqn. (6) from the t e m p e r a t u r e dependence of G E. T h e corresponding values of the molar heats of mixing H E, the molar excess entropies S E, the molar excess Gibbs energies G E and the thermodynamic activities ay of liquid N i - P d alloys at 1850 K are listed in Table 3. Liquid N i - P d alloys are characterized by exothermic molar heats of mixing H E (Fig. 3, Table 3), slightly negative molar excess entropies S E (Table 3) and negative m o l a r excess Gibbs energies G E (Fig. 4, Table 3). At 1850 K the m i n i m u m H E value is - 6 0 9 0 J tool-1 (54.3 at.% Pd), the minimum S E value is - 0 . 2 4 J mo1-1 K -1 (59 at.% Pd) and the minimum G E value is - 5660 J tool -1 (53.7 at.% Pd). It might be of interest that the minima of all three molar excess functions are found in this study at nearly the same alloy composition. Figure 5 gives a plot of the thermodynamic activities of liquid N i - P d alloys at 1850 K determined in this study. The thermodynamic activities of both components, Pd and Ni, show slightly negative deviations from ideality over the entire range of composition.

55

5.76 , K -1

Temperature ,

,

i

5,85 ×t0 -~

T,K

1691

~

8.4

_.E7.8 ¢-

7.3

\ t

6.8

5./*9

5.58

(b)

i 5.67 lIT,

i

L

5.76 K -1

5.8/*

x l O -4

Fig. 1. Plots of ln(JyT) as a function of T -1 for liquid Ni-Pd alloys with 80.03 at.% Pd (run 13 of Table 1): O, experimental points; O, corresponding points; - - , regression line (eqn. (1)) from 70 points. experimental results by determining the heats of mixing H E by means of the equation [1] E

E

I~

Hpd-- HNi + Co -

RO(do+ d l/T)

O(I/T)

(7)

In Fig. 6 are plotted the experimentally determined RO(do+dl/T)/O(1/T) values vs. the mole fraction xp~ as well as the "best-fit" curve according to eqn. (7) at the m e a n t e m p e r a t u r e T = 1850 K. Sufficient accuracy of the best-fit data is indicated by the small scattering of the experimental data (Fig. 6). An additional check is based on the relation between the calibration constant Con and the heats of vaporization of the pure c o m p o n e n t s j, H~,.y [1]: CoH = -- ( B y°. Pd - B y °, Ni)

(8)

56

H. Bittermann et aL / Thermodynamics of liquid Ni-Pd alloys 33

11

5

~

0

I

I

I

I

i

a 0.4

i 0.6

i 0.8

22

0 "o

X i

11 ~',

"~-11 X

"IS zm

•

~ -3.2

E

0

"-22

0

0

~-

T

0

z

O

-4.8 -11

,- -33 l

I

I

I

0.2

0.4

0.6

0.8

-6.4

-22

0

0.2

Xpd

Fig. 2. RT{do+dl/T-ln[(1-xpd)/Xpd] } as a function of the mole fraction Xrd at 1850 K: (9, experimental values; - - , regression curve (eqn. (5)). TABLE 2, TAP parameters Cz and calibration constants Cz of liquid Ni-Pd alloys (C~,=C~-TC~,) n

C~, (J m o l - ' )

~

2 1 0

-20120 -8135 23493

-0.550 -0.723 23.59

Xpd

Fig. 3. Molar heats of mixing HE of liquid Ni-Pd alloys: - - , this study (1850 K); - - - , Meschter [13].

I

I

I

I

i 0.2

L 0.4

i 0.6

0.8

(J tool-' K - ' ) -1.5 0

E

5-3.(

TABLE 3. Molar heats of mixing HE, molar excess entropies S E, molar excess Gibbs energies G E and thermodynamic activities ai of liquid Ni-Pd alloys at 1850 K (Cffvalues in J m o l - l : C~o= - 2 0 153, C~= - 1 9 101, C~2= -6797) Xrd

0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00

H E

SE

G E

(J tool-I)

(J mol -I K -I)

(J mol -I)

0 - 1883.8 -3479.2 -4737.3 - 5609.3 - 6046.4 - 5999.8 -5420.6 -4260.2 - 2469.6

0 - 0.05598 -0.11108 -0.16098 - 0.20134 - 0.22780 - 0.23605 -0.22173 -0.18050 - 0.10804

0 - 1780.3 -3273.7 -4439.5 - 5236.8 - 5625.0 - 5563.1 -5010.4 -3926.2 - 2269.7

0

0

aNi

0

apd

-4.!

-6.0 0

1.00 0.892 0.769 0.636 0.499 0.367 0.248 0.150 0.076 0.028 0

0 0.034 0.081 0.143 0.225 0.328 0.452 0.592 0.740 0.882 1.00

A c o m p a r i s o n shows g o o d a g r e e m e n t b e t w e e n t h e c o m p u t e d v a l u e o f Co~ (23 493 J m o l - 1 , listed in T a b l e 2) a n d t h e n e g a t i v e d i f f e r e n c e in t h e h e a t s o f v a p o r i z a t i o n o f P d a n d Ni (49 150 J m o 1 - 1 ) c o m p u t e d f r o m t h e d a t a given by H u l t g r e n et al. [8] at 1850 K ( H °, p~ = 348 400 J m o l - 1, HvO N~= 397 550 J m o l - 1). O i s h i et al. [9] d e t e r m i n e d by m e a n s o f a q u a d r u p o l e m a s s s p e c t r o m e t e r large e x o t h e r m i c h e a t s o f mixing

t

Xpd

Fig. 4. Molar excess Gibbs energies G ~ of liquid Ni-Pd alloys at 1850 K from this study.

( m i n i m u m v a l u e - 2 0 000 J m o l - a at 50 a t . % P d ) . T h e c a l o r i m e t r i c investigations o f T i m o f e e v et al. [10] as well as t h e e.m,f, m e a s u r e m e n t s o f V a t o l i n a n d K o z l o v [11] y i e l d e d positive h e a t s o f mixing. E n d o t h e r m i c h e a t s o f mixing, however, a p p e a r n o t to b e c o n s i s t e n t with t h e f o r m o f t h e p h a s e d i a g r a m , b e c a u s e they w o u l d i m p l y a miscibility gap. V a t o l i n et al. [12] r e p o r t e d that t h e mixing b e h a v i o u r o f liquid N i - P d alloys s h o u l d b e close to i d e a l with r e s p e c t to t h e results o f an X - r a y s t u d y o f s h o r t - r a n g e o r d e r in the liquid state. M e s c h t e r [13] c o m p u t e d e x o t h e r m i c h e a t s o f mixing by m e a n s o f t h e p h a s e d i a g r a m d a t a , t h e H E v a l u e s o f solid alloys f r o m ref. 14 a n d a s s u m i n g vanishing m o l a r excess entropy. T h e c o m p u t e d d a t a o f M e s c h t e r [13] a g r e e well with t h e results ~)f this investigation (Fig. 3).

H. Bittermann et al. / Thermodynamics of liquid Ni-Pd alloys 1.0

I

I

I

57

5 also shows good agreement between the Pd activities determined mass spectrometrically by Oishi et al. [9] at 1833 K and the data of this work at 1850 K. Hultgren et al. [8] compiled from the results of the e.m.f, measurements by Timofeev et al. [10] at 1873 K slightly positive molar excess Gibbs energies G E. However, these data cannot be used for successful calculations of the phase diagram.

I

0.8

06 O

>

~ O.Z, .<

5. Conclusions 0.2

Ni

0.2

0.4

0.6

0.8

Pd

Xpd

Fig. 5. Thermodynamic activities aj of liquid Ni-Pd alloys: - - , this study (1850 K); - - - , Oishi et al. [9] (1833 K), mass spectrometric data; ©, e.m.f, data, • . . . . , Timofeev et al. [10] (1873

K).

The mass spectrometric investigations of this work yielded molar excess properties of liquid Ni-Pd alloys which can be expressed by means of two-parameter TAP series, eqns. (4). The G ~ values of this investigation can be used successfully for calculations of the binary phase diagram [15]. Acknowledgment

60

,I

,

I

I

-~48

36

Grateful acknowledgment is made for the financial support given by the "Fonds zur F6rderung der Wissenschaftlichen Forschung in Osterreich" (FWF).

2l.

References "

36

0

0

1 2 ~ "Im "Izrn

~'~

-~C0 H

o

0

"

0 x-

0

"-E 12

-12-

o/

rr

0

0

i 0.2

I 0.4

t 0.6

I 0.8

-24

Xpd

Fig. 6. Ra(do+dl/T)/O(1/T) (eqn. (7)) as a function of the mole fraction xpd at 1850 K: ©, experimental values; - - , repression curve (eqn. (7)).

Both the mass spectrometric as well as the additional e.m.f, measurements of Oishi et al. [9] yielded at 1833 K Ni activities in good agreement with the results of this study (Fig. 5). The Ni activities obtained by Timofeev et al. [10] at 1873 K from e.m.f, measurements exhibit slightly positive deviations from ideality (Fig. 5). Figure

1 J. Tomiska, K. Kopecky and A. Neckel, Ber. Bunsenges. Phys. Chem., 94 (1990) 47. 2 J. Tomiska, Calphad, 4 (1980) 63. 3 J. Tomiska, Z. Metallkd., 76 (1985) 532. 4 J. Tomiska, J. Phys. E.: ScL Instrum., 17 (1990) 1165. 5 A. Neckel and S. Wagner, Monatsh. Chem., 100 (1969) 664. 6 J. Tomiska, Thermochim. Acta, 151 (1988) 145. 7 J. Tomiska, Calphad, 9 (1985) 15. 8 R. Hultgren, L. Orr and K. K. Kelley, Supplement to Selected Thermodynamic Properties of Metals and Alloys, University of California, Berkeley, CA, 1969, Supplement 1973. 9 T. Oishi, S. Nishi and K. Ono, Trans. Jpn. Inst. Met., 27 (1986) 288. 10 A. I. Timofeev, N. A. Vatolin, O. A. Esin and E. L. Dubinin, Tr. Sverdlovsk. Met. Inst., 20 (1969) 120. 11 N. A. Vatolin and Yu. S. Kozlov, Russ. Metall., 1 (1977) 67. 12 N. A. Vatolin, Yu. S. Kozlov and E. A. Pastukhov, Izv. Akad. Nauk USSR, Met., 5 (1977) 226. 13 P. J. Meschter, Chemical Metallurgy - A Tribute to Carl Wagner, TMS/AIME, Warrendale, PA, 1981, p. 252. 14 L. R. Bidwell and R. Speiser, Acta Metall., 13 (1965) 61. 15 K. Kopecky, M. S. Belegratis, A. Neckel and J. Tomiska, Ber. Bunsenges. Phys. Chem., 96 (1992) 1658.