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Influence of aluminium and copper, as well as of relative difference of ionic volumes, on the activity of Pb in {(1 − x1 − x2)Ni + x1Pb + x2(Al or Cu)} for x1, x2 ⪡ 1
M-2171 J (‘hem.
Thermo&numics
1988, 20, 665-674
Influence of aluminium and copper, as well as of relative difference of ionic volumes, on the activity of Pb in {(I -x,-xJNi + x,Pb + x,(Al or Cu)} for x,, x* << 1 TADEUSZ POMIANEK Technical University, 35-959 Rzesziw, MI. W.Pola 2. Poland i Received 18 May 1987: in$nalform
28 October 1987)
The activity of Pb in ((1-x,-x,)Ni + .x,Pb + x,(Al or G)}(l) for x1, x2 << 1 has been determined by equilibrium vacuum saturation with metal vapour at the temperature 1753 K. The interaction parameters eflbdetermined experimentally have been interpreted in terms of the relative difference of ionic volumes. This idea and several experimental values of E& make it possible to propose an equation describing the activity of Pb in any ((l-x,-yz)Ni + .x,Pb + x~M}(I).
1. Introduction Lead shows a very negative influence on the mechanical properties of heat-resistant nickel alloys at elevated temperatures, because it is insoluble in the alloy matrix. Therefore the largest permissible mass fraction of lead is limited to 5 x 10-h.“’ The solubility of lead in the alloy matrix is dependent on its thermodynamical properties formed by the particular alloy components. To estimate which metals increase and which reduce the destructive influence of Pb on the mechanical properties, the activity of Pb in numerous ((1 -x1 -x,)Ni + .x,Pb + x*~}(l) mixtures has been determined. The influence of tin and silver,(2’ silicon, cobalt, and cerium,‘3’ and boron and chromium,(4) on the activity of Pb in [(l -x,-x,)Ni + x,Pb + x~M)(~) for x1, x2 CC1 at 1753 K has already been established. This paper presents measurements of the activity of Pb in (( 1-x, -x,)Ni + x,Pb + xz(Al or Cu)} for x1, x1 << 1.
2. Experimental All studied alloys are characterized by a big difference between the vapour pressures of their elements and the vapour pressure of lead: pPb = 19.8 kPa at 1753 K,“’ while 0021-9614/88/060665+ IO %02.00/O
(‘ 1988 Academic Press Limited
T. POMIANEK
666
for aluminium, the most volatile component, pA, = 60 Pa.(5) It has been shown in a critical review of methods of determination of thermodynamic properties,(6’ that at temperatures of 1700 K or greater it is very difficult to carry out reliable measurements of the activity of a volatile metal. Therefore a relative method of equilibrium vacuum saturation, already described in detailt6* 7’ has been applied in this study. For the determination of the activity of Pb in {(l -x1 -x,)Ni + x,Pb + x,~}(l). the method depends on saturating the mixture studied and the reference mixture, i.e. ((1 -x)Cu + xPb)(l), with vapour. Both mixtures were placed inside a closed crucible under a reduced pressure of argon (see figure 1) until equilibrium had been reached. The activity of Pb in all the mixtures inside the closed system is the same in the equilibrium state. If the activity of Pb in the {( 1 -x)Cu + xPb}(l) reference mixture is known it is possible to calculate the activity of Pb in ((1 -x1-x,)Ni + x,Pb + .x*~}(l): fPb(Ni,Pb.
ht) =
x Pb(Cu.
Pb)
f Pb(Cu.
/u
Pb) . Pb(Ni.
Pb. M)*
(1)
mole fractions of Pb in xPb(Cu, Pb) and -vPb(Ni, Pb. M) denote the equilibrium {( 1 -x)Cu + xPb} and ((1 -x1 -x,)Ni + x,Pb + x*M}, and respectively, fPbcCu, Pb, and fpbcNi, Pb,Mj are the corresponding activity coefficients of Pb. Alloys were prepared from nickel cathodes of purity 99.98 mass per cent, copper MOOB grade (oxygen free) rolls (99.99 mass per cent), aluminium wire: 99.999 mass per cent, and lead: 99.99 mass per cent. Graphite elements were made of EK 412 type graphite (ash residue < 0.1 mass per cent) supplied by Ringsdorf Co. (F.R.G.). Alundum crucibles and covers were manufactured by the Institute of Refractories in Gliwice (Poland), while the aluminium sheaths for the thermocouple were supplied by Morgan Co. (U.K.). Both the alundum and graphite elements were preliminarily annealed in a vacuum furnace at a temperature greater than 1800 K and at an argon pressure (argon purity: 99.98 moles per cent) of about 0.01 Pa. The alundum cricible was sealed with (alumina (Degussa, F.R.G.) + orthophosphoric acid}. An alundum crucible was the main part of the apparatus (see figure 1). This crucible was placed inside the graphite container, which was inserted into the induction coil of the VSG 02 vacuum furnace manufactured by Balzers. A modified apparatus was also used. In this, instead of graphite block 2. four alundum crucibles were placed inside the crucible 1. The two alloys to be studied {(l-x,-x,)Ni + x,Pb + x,(AI or Cu))(l) and ((I-x)Cu + xPbj(1) reference mixture were placed in three alundum crucibles. In the fourth alundum crucible the {( 1 - x)Cu + xPb}(l) mixture with the alundum sheath of the thermocouple inserted were placed for temperature control only. The temperature was measured with a Pt-to-(Pt + 10 mass per cent of Rh) thermocouple with estimated accuracy +8 K. The pressure in the furnace was measured with a manometer (0 to lo5 Pa) and with a vacuum meter in the range 1.33 x lo2 to 1.33 x lob3 Pa. The procedure was described in detail in reference 2. Alloys ((1 -x,)Ni + X~M} of appropriate composition were prepared by melting the carefully weighed masses of the pure components in an alundum crucible in a where
ACTIVITY
OF Pb IN ((1 -x,
--x,)Ni+.x,Pb+xJAl
OR Cu)](l)
667
FIGURE 1. Apparatus for the equilibrium vacuum saturation with metal vapour. I. Alundum crucible; 2, graphite block; 3, graphite heater; 4, alundum crucible containing {( 1 -xi -u,)Ni + xi Pb + x2M}; 5. grooves containing ((1 -x)Cu + xPbJ; 6, alundum sheath of thermocouple; 7. Pt-to-(Pt + 10 mass per cent of Rh) thermocouple; 8. alundum cover: 9. graphite cover: 10. sealing bond.
vacuum furnace at a pressure of about 0.01 Pa. The prepared ((1 -x,)Ni + .x~M) alloys were placed in crucible 4, copper was placed in grooves 5 in graphite block 2, and lead was placed either in grooves 5 or in crucible 4 (see figure 1). Weighing was assumed to be the most precise method of determination of the alloy composition, as all the alloy components had vapour pressures at least 100 times smaller than that of lead. The accuracy of the weighing method was proved by the small content of copper in ((1 -x1 - x,)Ni + x, Pb + x,Al}(l) alloys (0.055 to 0.074 mass per cent) and that of nickel (0.0025 to 0.0080 mass per cent) and of aluminium (0.0068 to 0.0072 mass per cent) in ((1 -x)Cu + xPb}(l) alloys. The small oxygen content in the alloys studied (<0.0057 mass per cent) (determined with LECO RO 16) testified that the vacuum furnace was leak-proof. The quantities determined experimentally i.e. argon pressure and equilibration time are meant to guarantee the attainment of equilibrium between Pb(g) and the reference and test mixtures. In preliminary tests all mixtures in the crucible were Cu and Pb alloys (see table 1). The argon pressure was specially chosen to make it higher than the vapour pressure of lead and also to limit the evaporation process to that of lead only but at a sufficient rate and with a properly sealed crucible. These requirements were fulfilled at argon pressure 13.3 and 17.3 kPa. The escape of Pb(g) from the crucible varied in these cases from 12 to 25 per cent without upsetting the equilibrium state. An equilibrium state was attained even at a loss of lead vapour of 76.3 per cent (see run no. 9 in table 1; due to lack of crucible
668
T. POMIANEK
TABLE 1, The results of preliminary experiments. The inthrence of argon pressure p, on the time I, necessary for equilibrium between {(I -x)Cu+xPb}(l) mixtures and Pb(g) at 1753 K. Fractional losses [(Pb) of Pb(g) were due to the lack of tightness of the measuring crucible
Run
t, min
1 2 3 4 5 6 7 8 9
22 15 25 20 35 35 25 30 22
10 11 12
30 35 40
/& kPa
13.3 13.3 13.3 13.3 13.3 17.3 17.3 17.3 13.3
x alundum crucible
5.66 18.11 37.28 29.31 22.04 Il.38 22.73 8.95 16.68
Modified
apparatus
13.3 13.3 17.3
12.81 28.42 25.73
I
Y grooves in graphite block II
5.69 17.02 36.28 29.40 23.25 12.10 22.99 8.77 16.57
5.70 16.93 37.98 30.60 24.35 12.25 23.53 9.42 16.82
13.04 29.05 26.34
12.03 27.93 27.15
Placing
of lead
lO’l( Pb)
III ~ 38.66 31.90 24.81 12.59 23.88 9.61
alundum crucible alundum crucible grooves grooves alundum crucible alundum crucible grooves grooves alundum crucible
12.15 28.28 25.90
14.0 12.1 17.0 15.6 25.1 15.0 17.7 18.8 76.3
21.2 25.9 17.4
sealing). Thus the rate of reaching equilibrium was considerably higher than that of lead evaporation due to the lack of crucible sealing. It was also shown in preliminary tests that the placing of the charge of lead had no influence on the apparent equilibrium state (see table 1). It was established in preliminary runs that the time necessary to reach equilibrium was 25 min at 13.3 kPa or 30 min at 17.3 kPa. For the modified apparatus, these times were 30 and 40 min respectively; a longer experimental time resulted from a decreased evaporation area of the reference mixture.
3. Results The influence of Al and Cu on the activity of Pb in ((1 -x1 -x,)Ni + xi Pb + x,(Al or Cu)}(l) at 1753 K was determined by the equilibrium vacuum-saturation method. To make sure that equilibrium had been attained, the time was long compared with that established in preliminary runs. For added aluminium considerably increasing the activity of Pb, an argon pressure of 17.3 kPa and time of 35 min were applied, while for added copper, which decreased fPb in the alloys, the argon pressure was 13.3 kPa and the time 30 min. The times 45 and 40 min, respectively, were applied in tests with the modified apparatus. The experimental activity coefficients Jr,, of Pb in {( 1 -x1 -x,)Ni + x1 Pb + x,(Al or Cu)j(l) alloys were calculated from equation (l), basing on fPb values in ((1 -x)Cu + xPb)(l) determined from the dependence proposed by Wypartowicz, Zabdyr, and Fitzner:‘g’ lnf,, = (3360(K/T)-0.6}(1 -x)*.l. (2) The results are presented in table 2 and in figures 2 and 3.
ACTIVITY
OF Pb IN {(I-x,
-x,)Ni+x,Pb+r,(Al
OR Cu)}(l)
TABLE 2. Experimental values of In& in {(l-x, --x,)Ni + x,Pb + x,AI}(l) Y, Pb + .uzCu)(l) at 1753 K and equilibrium compositions of tested mixtures (( 1 -x)Cu + xPb)(l) .Y *
;I
I (1 -Y,
I” 2 .3 4 .i 6 I” 8 Y II)” I I0 I?
0.0109 0.0224 0.0292 0.0392 0.0046 0.0144 0.0270 0.0397 0.0115 0.0185 0.0326
0.0306 0.03 17 0.0315 0.0323 0.0430 0.0428 0.0430 0.0429 0.0569 0.0566 0.0585 0.0572
(1 -I, 13 I 31
I5 16” 17 IX IO” 20” 21 22 23” 24 ” Experiment
0.0108 0.0224 0.0353 0.0372 0.0155 0.0260 0.0363 0.0402 0.0136 0.0252 0.0374 0.0424 carried
0.0319 0.0319 0.0326 0.0319 0.0473 0.0470 0.0464 0.0468 0.0642 0.0643 0.0655 0.0655
- x,)Ni
0.0471 0.1175 0.1444 0.2040 0.0194 0.0662 0.1359 0.2471 0.0567 0.1128 0.1771 0.1995
-
out in the modified
I
and ((I -xl -x,)Ni + and reference mixture
In fPh II
111
Pb + r,Al
0.1203 0.1428 0.2034 0.0207 0.0658 0.2358 0.0586
0. I 142 0.1575 0.2160 0.0 196 0.0665
0.2089
0.2060
x,)Ni
0.0334 0.0722 0.121 I 0.1203 0.0421 0.0770 0.1113 0.1203 0.0328 0.0723 0.1164 0.1327
+x,
III
669
0.0589
2.655 2.671 2.548 2.464 2.700 2.663 2.584 2.554 2.763 2.833 2.687 2.636
2.687 2.541 2.462 2.765 2.657 2.530 2.792 2.662
3.650 2.605 2.495 7.712 2.666
2.795
7.654
+ x, Pb + .xzCu
0.0321
0.0322
0. I228
0.1271
0.0466 0.0835
0.0468 0.0806
0.0382 0.0728
0.0370 0.0747
0.1329
0. I329
2.359 2.296 2.238 2.181 2.199 2.198 2.148 2.103 2.108 2.178 2.150 2.118
2.323 2.248
’ 337 -.. -
2.289 2.262 -
2.294 3 ‘34 -.-.
2.244 2.184 2.119
2.215 2.206
2.272
2.119
apparatus.
The activity of Pb was determined equation’lO’ could be applied:
in dilute
solutions
In .fPb = In .f; + E;~x, + J&X,.
and so the Wagner (3)
where ,f$ is the activity coefficient of Pb in {( 1 -x,)Ni + x,Pb)- at x, + 0, ER = (a widW,,+, is the interaction parameter for Pb on Pb in {( I- s,)Ni + x,Pb} at x1-+0, E;,, = (alnf,,/ax M) x,+0,xr+0 is the interaction parameter for M on Pb in ((1 -x1 -x,)Ni+x,Pb+x,M) at xX -+O and x, + 0. Values of the activity of Pb in ((1 -x,)Ni+x,Pb}(l) in the temperature range 1703 to 1783 K were also determined by the equilibrium vacuum-saturation method.@’ In this case the Wagner equation takes the form at 1753 K: In f& = 2.498 - 5.94~~.
(4)
The parameters of equation (3) were not established in the traditional way. The 1n.f;: was taken equal to 2.498 and was the most reliable value as it had been
670
T. POMIANEK
2.5OT-. ‘. 2.40-
. .
‘\ ‘. ‘.
2.30-
.
L 0 FIGURE
Xl - -
--?{(I
I 0.01
I 0.02
1 0.03
2. Activity coefficient ,f,,, of Pb in {(I -x1 -xZ)Ni temperature 1753 K. A. (x2) = 0.0317; 0, -x,)Ni + .x,Pb).
‘.
. .
I’. 0.04
+ x,Pb + xzAl}(I) plotted against (x2) = 0.0429; 0. (x2) = 0.0572;
determined at three different temperatures. The E:! and E&, interaction parameters were calculated by the least-squares method based on experimental values for particular ternary mixtures. Equal influence of Pb and of M on the activity of Pb in (( 1 -x1 -x,)Ni + x,Pb + x,~}(l) was obtained when applying this method. The
FIGURE 3. Activity coefficient f&, of Pb in ((I-x-x,)Ni at temperature 1753 K. A. (x2) = 0.0321; -Xl - - -, ((1 -x,)Ni + x,Pb}.
+ x,Pb + x,Cu](l) plotted against 0,(.x,) = 0.0470; 0. (x2) = 0.0650;
ACTIVITY OF
Pb IN
((I-x,
--u,)Ni+u,Pb+.u,(Al
OR Cu))tl)
671
correlation between experimental points and lines calculated by the described method (equation 3) can be observed in figures 2 and 3. As had already been pointed out.‘7. 9, there were some discrepancies of experimental values for the {( 1 - x)Cu + xPb}(l) ref erence mixture. It was essential to show their influence on the value of I:&,. Therefore the experimental fPb values for ((I --x1 -x,)Ni + x,Pb + x~M}(~) were calculated again taking into account the activity coefficient of Pb in ((1 -x)Cu + xPbl(1) proposed by Esdaile and McAdam:” ” lg./Lb =(l-~)~[2634.5(K/~)--1.1293-(2375(K/T)-1.5675f.w].
(5)
The $!,, values calculated by equations (2) and (5) are compared in table 3. Very small differences of &, show, that the ,f,, values in {( 1 -x1 -.uz)Ni + X, Pb + .lz~)(l) could differ in both cases, while E$, values depend very slightly on discrepant thermodynamic values for the reference mixture. A very small error in J$,, determination (table 3) should be pointed out, in view of such high temperatures and the kind of values. Besides, very similar values of a:: determined for :(I --x1-xz)Ni + x,Pb + x,~}(l) (table 3) and for ((1 -x,)Ni + x,PbJ(l) (equation 4) show that the procedure applied was reliable. 4. Discussion When only metallic mixtures with a majority of metallic bonds are considered then, according to their nature, such mixtures may be regarded as ionic systems without valence electrons. The latter can be treated as free electrons, because their mean free path is long. (12) It has been pointed out by Onderka and Fitzner(13) that the nearlyfree-electron model (NFE) can be applied to many liquid metallic mixtures. as values calculated by the NFE model are consistent with experimental values of the Hall constant and the electric conductivity of many liquid metals.(14’ The observation above gives reason for the assumption that it is incorrect to take the atomic radius TAHLE 3. Experimentally determined interaction parameters c$ and &Fb in [(I-r,-x-,)Ni + x,Pb + YAMS factor R. and relative difference of ionic volumes dp- N. For at I753 K as well as metal ionic radii rM, correlation I:):: and t:,,: h fPh calculated (I), from Wypartowicz et u/.,“’ and (2), from Esdaile and McAdam”” R
((I ((I ((I [(I :(I ((1
~.~,-.~,)Ni+.u,Pb+u,B -1, -x,)Ni+x,Pb+x,Si -u,-x,)Ni+x,Pb+x,Al -~(,-\-,)Ni+u,Pb+x,Cr - \-, -u,)Ni+\-,Pb+.x,Co
-.~-,-x,)Ni+.u,Pb+x,Sn {(I -.x1-x,)Ni+x,Pb+x,Cu [(I - rl -xZ)Ni+x,Pb+x,Ce I(1 -Y, -x,)Ni+u,Pb+x,Ag
-6.6kO.7 -6.3kO.5 -5.OkO.5 - 5.5 * 0.3 -5.2kO.4 -5.OkO.3 -4.OkO.3 -5.4kO.4 - 7.7 f I .o
11.3* 1.2 8.3kO.6 6.1 *0.6 5.4kO.3 3.1kO.2 1.5&0.1 - 3.6kO.3 -~ 14.1+ 1.1 -13.7* 1.9
0.96 0.99 0.95 0.99 0.97 0.97 0.96 0.96 0.95
12.5* 1.5 9.2kO.8 6.5kO.7 6.2kO.5 3.4kO.3 1.7kO.l -3.5kO.3 - 14.1+ 1.3 - 12.5k2.3
4 3
-
4 3 2 3 2
Ni’ + Pb’+ B”+ Si’+ Al-‘+ Cr”’ co2 + Sn4+ Cu’ + Ce”+
A$+
0.072 0.120 0.020 0.041 0.050 0.063 0.072 0.071 0.096 0.111 0.126
1.29 I .98 1.85 1.73 I .49 1.79 1.31 0.65 0.23 -0.15
T.POMIANEK
672
or molar volume as a geometrical factor for the mixture because in reality ions occupy lattice points. Therefore it was suggested (‘I that the ionic radius should be regarded as a geometrical factor for metallic mixtures. This conception proved to be justified. A method for the prediction of thermodynamic properties of binary and ternary metallic mixtures was worked out’2) on the basis of relative differences of ionic volumes and electron density as well as of electronegativity. It was shown,‘” for all 13 analysed families of binary mixtures of a constant component A and a variable component M, that thermodynamic properties of mixtures depended on the relative difference d:-” of ionic volumes between A and M ions. Furthermore. distinct linear dependence of E: values on d”-“, the relative difference of ionic volumes between metals N and M, for seven families of (( 1 -x1 -.Y~)A + .Y~N + X~M) with only the component M as variable, was established too.“’ The relative difference of ionic volumes in ternaries was defined by dr-”
=
2[(r(N”+)13-Cr(#w+))3]/[{r(N”+)j3+
fr(Mn’+)i3],
(6)
where r(~'+) and r(MW+) denote the ionic radii of metals N and M, and u and w the numbers of valence electrons of metals N and M transferred to the electron cloud. Another regularity was discovered. .u) the interaction parameter c: > 0 if the ionic radius of the solvent r(A”‘) > r(M”‘+) the ionic radius of the metal M, and the opposite relation: E: < 0 if r(A"+) < r(M”+). This regularity appeared to be true in 56 cases of 66 analysed experimental F: values. Both described regularities can be summarized in the form: E; = B(d” M- d” +),
(7)
where B is a constant. The interpretation of E& for (( 1 -x1 -x,)Ni + x,Pb + x,M) with M = Al or Cu, as well as for M = Sn, Ag,(2’ Si, Co, Ce,‘3’ B, or Cr,(4) according to equation (7) as a linear formation of the relative difference of ionic volumes is shown in figure 4. The degree of ionization of the alloying additives was assumed to be equal to the main number of valence electrons, while the ionic radii were taken from reference 15 (see table 3 and figure 4). The interval of dPbwNivalues has been shown in figure 4, because the ionic radius of Ni 2+ determined by different methods varies from 0.069 to 0.078 nm.” ‘) An almost linear dependence of .$b on dPbwMwas obtained. The following form of equation (7) was calculated by least squares (correlation coefficient: R = 0.98): &ib = 11.22(dPbpM- 1.29) + 2.88 ) 1.1,
(8)
where 1.29 = drbeNi if r(Ni2+) = 0.072 nm and r(Pb”) = 0.12 nm. Both proposed regularities were, in general. fulfilled. However, sgb = 1.2 to 3.6 (instead of cib = 0) at r(Ni’+) = r(MW+) (eFb = 2.88 at r(Ni2+) = 0.072 nm) but, taking into account the experimental errors Of &&, and ionic-radii determination, the results are satisfactory. The relation presented in figure 4 can be interpreted as follows. If we introduce metal M with ionic radius r(M’“+) < r(Ni2’), into ((1 -x,)Ni + x,Pb}(l) alloy, the result is a more closely packed structure and consequently there is a decrease of
ACTIVITY
OF Pb IN {(l-.tl
-.r,)Ni+.u,Pb+x,(Al
OR Cu)}(l)
FIGURE 4. Experimental values of E& for ((1 -r,-x,)Ni + .y,Pb + TIM) plotted against relative difference of ionic volumes dpb-M. ++, dPhmNi.
673
at temperature 1753 K
solubility
of the large Pb ‘+ ions, while in the opposite case of a metal M with r(MW+) > r(Ni*+) the alloy structure is looser and increases the solubility of Pb. So it is proposed to reduce the destructive influence of Pb on the mechanical properties of Ni alloys by alloying additives of ionic radii much bigger than that of Ni. The existence of such a strong relation between $, and drbeM can be applied to draw &, dependence in any ((1 -x1 -x,)Ni + x,Pb + x,~j(l) at 1753 K. Taking into account the Wagner equation (3), the fPb dependence for {( 1 -x,)Ni + v,Pb}(l) given by equations (4) and (7). one obtains: lnf,,
= 2.498-5.94x,
+ \‘l 1.22(drbeM- 1.29)+2.881x2.
(9)
One difficulty, however, arises when using the suggested concept for E: prediction in I( 1 -x1 --x~)A + X,N + x~M}. This problem concerns the determination of the correct degree of ionization of the alloy components. The number of valence electrons is not a satisfactory factor for metals (e.g. Pb, Bi, Au, Sb) which can transfer different numbers of electrons to the common cloud. Some solution of this problem has already been proposed in reference 2. There is still no final answer, if all metals (including transition metals) fulfil the relations proposed. These doubts can be solved on the basis of more E: experimental results, enabling the prediction of activity coefficients in numerous ternary alloys. That would require two C: values in a family of mixtures (( 1 -x1 -x~)A + X~N + xzM) and an experimental value of /i\i only for {(l-X1)A + X,N).
i-. POMIANEK
674
The author thanks the Institute of Non-Ferrous Metals (Gliwice. Poland) for its financial support of the work reported here. He also wishes to express his gratitude to Professors W. Ptak, J. Sqdzimir, and J. Terpilowski, and Associate Professors K. Fitzner and J. Botor, for their helpful analysis and discussion. REFERENCES R. T.; Wallace, W. Inr. Mer. Rev. 1976, 21. I. Pomianek, T. Zes:yty Naukowe Politechniki Rzexowkiej 1986, 32. I. Pomianek, T.: Rychlewski, M. ZN AGH Me/. Odlew. 1987, 109, 39. Pomianek, T. Trans. Jpn Insi. Met. 1988, 29. 3. Kubaschewski, 0.; Alcock, C. B. Mefallurgical Thermochemi.str~. Pergamon Press: Oxford. 1979. Pomianek. T.; Rychlewski, M. Z. Merallkd. 1986, 77. 112. Pomianek. T.; Golonka, J. Met. Technol. 1979, 6. 433. Pomianek. T. Z. Metallkd. 1986, 77. 388. Wypartowicz. J.; Zabdyr, L.; Fitzner. K. Arch. Hum. 1979, 24. 473. Wagner, K. Thermo&namics c~fAlloys. Addison-Wesley: Reading, Mass. 1952. Esdaile, J. D.; McAdam, J. C. H. Proc. Ausf. Ins. Min. Me/a/l. 1971, 239, 71. Mott, N. F.; Davis, E. A. Electrons in Non-Crystalline Materials. Clarendon Press: Oxford. 1979. Onderka, B.; Fitzner, K. Arch. Hum. 1985, 30. 443. Ziman, J. M. Phil. Mag. l%l, 6, 1013. Chojnacki. J. Element?, Kryralogrqfii Chemicznej i Fi:yc=nei. PWN: Warszawa. 1973.
I. Holt,
2. 3. 4. 5. 6. 7. 8. 9. IO. I I. 12. 13. 14. 15.
Thermo&numics
1988, 20, 665-674
Influence of aluminium and copper, as well as of relative difference of ionic volumes, on the activity of Pb in {(I -x,-xJNi + x,Pb + x,(Al or Cu)} for x,, x* << 1 TADEUSZ POMIANEK Technical University, 35-959 Rzesziw, MI. W.Pola 2. Poland i Received 18 May 1987: in$nalform
28 October 1987)
The activity of Pb in ((1-x,-x,)Ni + .x,Pb + x,(Al or G)}(l) for x1, x2 << 1 has been determined by equilibrium vacuum saturation with metal vapour at the temperature 1753 K. The interaction parameters eflbdetermined experimentally have been interpreted in terms of the relative difference of ionic volumes. This idea and several experimental values of E& make it possible to propose an equation describing the activity of Pb in any ((l-x,-yz)Ni + .x,Pb + x~M}(I).
1. Introduction Lead shows a very negative influence on the mechanical properties of heat-resistant nickel alloys at elevated temperatures, because it is insoluble in the alloy matrix. Therefore the largest permissible mass fraction of lead is limited to 5 x 10-h.“’ The solubility of lead in the alloy matrix is dependent on its thermodynamical properties formed by the particular alloy components. To estimate which metals increase and which reduce the destructive influence of Pb on the mechanical properties, the activity of Pb in numerous ((1 -x1 -x,)Ni + .x,Pb + x*~}(l) mixtures has been determined. The influence of tin and silver,(2’ silicon, cobalt, and cerium,‘3’ and boron and chromium,(4) on the activity of Pb in [(l -x,-x,)Ni + x,Pb + x~M)(~) for x1, x2 CC1 at 1753 K has already been established. This paper presents measurements of the activity of Pb in (( 1-x, -x,)Ni + x,Pb + xz(Al or Cu)} for x1, x1 << 1.
2. Experimental All studied alloys are characterized by a big difference between the vapour pressures of their elements and the vapour pressure of lead: pPb = 19.8 kPa at 1753 K,“’ while 0021-9614/88/060665+ IO %02.00/O
(‘ 1988 Academic Press Limited
T. POMIANEK
666
for aluminium, the most volatile component, pA, = 60 Pa.(5) It has been shown in a critical review of methods of determination of thermodynamic properties,(6’ that at temperatures of 1700 K or greater it is very difficult to carry out reliable measurements of the activity of a volatile metal. Therefore a relative method of equilibrium vacuum saturation, already described in detailt6* 7’ has been applied in this study. For the determination of the activity of Pb in {(l -x1 -x,)Ni + x,Pb + x,~}(l). the method depends on saturating the mixture studied and the reference mixture, i.e. ((1 -x)Cu + xPb)(l), with vapour. Both mixtures were placed inside a closed crucible under a reduced pressure of argon (see figure 1) until equilibrium had been reached. The activity of Pb in all the mixtures inside the closed system is the same in the equilibrium state. If the activity of Pb in the {( 1 -x)Cu + xPb}(l) reference mixture is known it is possible to calculate the activity of Pb in ((1 -x1-x,)Ni + x,Pb + .x*~}(l): fPb(Ni,Pb.
ht) =
x Pb(Cu.
Pb)
f Pb(Cu.
/u
Pb) . Pb(Ni.
Pb. M)*
(1)
mole fractions of Pb in xPb(Cu, Pb) and -vPb(Ni, Pb. M) denote the equilibrium {( 1 -x)Cu + xPb} and ((1 -x1 -x,)Ni + x,Pb + x*M}, and respectively, fPbcCu, Pb, and fpbcNi, Pb,Mj are the corresponding activity coefficients of Pb. Alloys were prepared from nickel cathodes of purity 99.98 mass per cent, copper MOOB grade (oxygen free) rolls (99.99 mass per cent), aluminium wire: 99.999 mass per cent, and lead: 99.99 mass per cent. Graphite elements were made of EK 412 type graphite (ash residue < 0.1 mass per cent) supplied by Ringsdorf Co. (F.R.G.). Alundum crucibles and covers were manufactured by the Institute of Refractories in Gliwice (Poland), while the aluminium sheaths for the thermocouple were supplied by Morgan Co. (U.K.). Both the alundum and graphite elements were preliminarily annealed in a vacuum furnace at a temperature greater than 1800 K and at an argon pressure (argon purity: 99.98 moles per cent) of about 0.01 Pa. The alundum cricible was sealed with (alumina (Degussa, F.R.G.) + orthophosphoric acid}. An alundum crucible was the main part of the apparatus (see figure 1). This crucible was placed inside the graphite container, which was inserted into the induction coil of the VSG 02 vacuum furnace manufactured by Balzers. A modified apparatus was also used. In this, instead of graphite block 2. four alundum crucibles were placed inside the crucible 1. The two alloys to be studied {(l-x,-x,)Ni + x,Pb + x,(AI or Cu))(l) and ((I-x)Cu + xPbj(1) reference mixture were placed in three alundum crucibles. In the fourth alundum crucible the {( 1 - x)Cu + xPb}(l) mixture with the alundum sheath of the thermocouple inserted were placed for temperature control only. The temperature was measured with a Pt-to-(Pt + 10 mass per cent of Rh) thermocouple with estimated accuracy +8 K. The pressure in the furnace was measured with a manometer (0 to lo5 Pa) and with a vacuum meter in the range 1.33 x lo2 to 1.33 x lob3 Pa. The procedure was described in detail in reference 2. Alloys ((1 -x,)Ni + X~M} of appropriate composition were prepared by melting the carefully weighed masses of the pure components in an alundum crucible in a where
ACTIVITY
OF Pb IN ((1 -x,
--x,)Ni+.x,Pb+xJAl
OR Cu)](l)
667
FIGURE 1. Apparatus for the equilibrium vacuum saturation with metal vapour. I. Alundum crucible; 2, graphite block; 3, graphite heater; 4, alundum crucible containing {( 1 -xi -u,)Ni + xi Pb + x2M}; 5. grooves containing ((1 -x)Cu + xPbJ; 6, alundum sheath of thermocouple; 7. Pt-to-(Pt + 10 mass per cent of Rh) thermocouple; 8. alundum cover: 9. graphite cover: 10. sealing bond.
vacuum furnace at a pressure of about 0.01 Pa. The prepared ((1 -x,)Ni + .x~M) alloys were placed in crucible 4, copper was placed in grooves 5 in graphite block 2, and lead was placed either in grooves 5 or in crucible 4 (see figure 1). Weighing was assumed to be the most precise method of determination of the alloy composition, as all the alloy components had vapour pressures at least 100 times smaller than that of lead. The accuracy of the weighing method was proved by the small content of copper in ((1 -x1 - x,)Ni + x, Pb + x,Al}(l) alloys (0.055 to 0.074 mass per cent) and that of nickel (0.0025 to 0.0080 mass per cent) and of aluminium (0.0068 to 0.0072 mass per cent) in ((1 -x)Cu + xPb}(l) alloys. The small oxygen content in the alloys studied (<0.0057 mass per cent) (determined with LECO RO 16) testified that the vacuum furnace was leak-proof. The quantities determined experimentally i.e. argon pressure and equilibration time are meant to guarantee the attainment of equilibrium between Pb(g) and the reference and test mixtures. In preliminary tests all mixtures in the crucible were Cu and Pb alloys (see table 1). The argon pressure was specially chosen to make it higher than the vapour pressure of lead and also to limit the evaporation process to that of lead only but at a sufficient rate and with a properly sealed crucible. These requirements were fulfilled at argon pressure 13.3 and 17.3 kPa. The escape of Pb(g) from the crucible varied in these cases from 12 to 25 per cent without upsetting the equilibrium state. An equilibrium state was attained even at a loss of lead vapour of 76.3 per cent (see run no. 9 in table 1; due to lack of crucible
668
T. POMIANEK
TABLE 1, The results of preliminary experiments. The inthrence of argon pressure p, on the time I, necessary for equilibrium between {(I -x)Cu+xPb}(l) mixtures and Pb(g) at 1753 K. Fractional losses [(Pb) of Pb(g) were due to the lack of tightness of the measuring crucible
Run
t, min
1 2 3 4 5 6 7 8 9
22 15 25 20 35 35 25 30 22
10 11 12
30 35 40
/& kPa
13.3 13.3 13.3 13.3 13.3 17.3 17.3 17.3 13.3
x alundum crucible
5.66 18.11 37.28 29.31 22.04 Il.38 22.73 8.95 16.68
Modified
apparatus
13.3 13.3 17.3
12.81 28.42 25.73
I
Y grooves in graphite block II
5.69 17.02 36.28 29.40 23.25 12.10 22.99 8.77 16.57
5.70 16.93 37.98 30.60 24.35 12.25 23.53 9.42 16.82
13.04 29.05 26.34
12.03 27.93 27.15
Placing
of lead
lO’l( Pb)
III ~ 38.66 31.90 24.81 12.59 23.88 9.61
alundum crucible alundum crucible grooves grooves alundum crucible alundum crucible grooves grooves alundum crucible
12.15 28.28 25.90
14.0 12.1 17.0 15.6 25.1 15.0 17.7 18.8 76.3
21.2 25.9 17.4
sealing). Thus the rate of reaching equilibrium was considerably higher than that of lead evaporation due to the lack of crucible sealing. It was also shown in preliminary tests that the placing of the charge of lead had no influence on the apparent equilibrium state (see table 1). It was established in preliminary runs that the time necessary to reach equilibrium was 25 min at 13.3 kPa or 30 min at 17.3 kPa. For the modified apparatus, these times were 30 and 40 min respectively; a longer experimental time resulted from a decreased evaporation area of the reference mixture.
3. Results The influence of Al and Cu on the activity of Pb in ((1 -x1 -x,)Ni + xi Pb + x,(Al or Cu)}(l) at 1753 K was determined by the equilibrium vacuum-saturation method. To make sure that equilibrium had been attained, the time was long compared with that established in preliminary runs. For added aluminium considerably increasing the activity of Pb, an argon pressure of 17.3 kPa and time of 35 min were applied, while for added copper, which decreased fPb in the alloys, the argon pressure was 13.3 kPa and the time 30 min. The times 45 and 40 min, respectively, were applied in tests with the modified apparatus. The experimental activity coefficients Jr,, of Pb in {( 1 -x1 -x,)Ni + x1 Pb + x,(Al or Cu)j(l) alloys were calculated from equation (l), basing on fPb values in ((1 -x)Cu + xPb)(l) determined from the dependence proposed by Wypartowicz, Zabdyr, and Fitzner:‘g’ lnf,, = (3360(K/T)-0.6}(1 -x)*.l. (2) The results are presented in table 2 and in figures 2 and 3.
ACTIVITY
OF Pb IN {(I-x,
-x,)Ni+x,Pb+r,(Al
OR Cu)}(l)
TABLE 2. Experimental values of In& in {(l-x, --x,)Ni + x,Pb + x,AI}(l) Y, Pb + .uzCu)(l) at 1753 K and equilibrium compositions of tested mixtures (( 1 -x)Cu + xPb)(l) .Y *
;I
I (1 -Y,
I” 2 .3 4 .i 6 I” 8 Y II)” I I0 I?
0.0109 0.0224 0.0292 0.0392 0.0046 0.0144 0.0270 0.0397 0.0115 0.0185 0.0326
0.0306 0.03 17 0.0315 0.0323 0.0430 0.0428 0.0430 0.0429 0.0569 0.0566 0.0585 0.0572
(1 -I, 13 I 31
I5 16” 17 IX IO” 20” 21 22 23” 24 ” Experiment
0.0108 0.0224 0.0353 0.0372 0.0155 0.0260 0.0363 0.0402 0.0136 0.0252 0.0374 0.0424 carried
0.0319 0.0319 0.0326 0.0319 0.0473 0.0470 0.0464 0.0468 0.0642 0.0643 0.0655 0.0655
- x,)Ni
0.0471 0.1175 0.1444 0.2040 0.0194 0.0662 0.1359 0.2471 0.0567 0.1128 0.1771 0.1995
-
out in the modified
I
and ((I -xl -x,)Ni + and reference mixture
In fPh II
111
Pb + r,Al
0.1203 0.1428 0.2034 0.0207 0.0658 0.2358 0.0586
0. I 142 0.1575 0.2160 0.0 196 0.0665
0.2089
0.2060
x,)Ni
0.0334 0.0722 0.121 I 0.1203 0.0421 0.0770 0.1113 0.1203 0.0328 0.0723 0.1164 0.1327
+x,
III
669
0.0589
2.655 2.671 2.548 2.464 2.700 2.663 2.584 2.554 2.763 2.833 2.687 2.636
2.687 2.541 2.462 2.765 2.657 2.530 2.792 2.662
3.650 2.605 2.495 7.712 2.666
2.795
7.654
+ x, Pb + .xzCu
0.0321
0.0322
0. I228
0.1271
0.0466 0.0835
0.0468 0.0806
0.0382 0.0728
0.0370 0.0747
0.1329
0. I329
2.359 2.296 2.238 2.181 2.199 2.198 2.148 2.103 2.108 2.178 2.150 2.118
2.323 2.248
’ 337 -.. -
2.289 2.262 -
2.294 3 ‘34 -.-.
2.244 2.184 2.119
2.215 2.206
2.272
2.119
apparatus.
The activity of Pb was determined equation’lO’ could be applied:
in dilute
solutions
In .fPb = In .f; + E;~x, + J&X,.
and so the Wagner (3)
where ,f$ is the activity coefficient of Pb in {( 1 -x,)Ni + x,Pb)- at x, + 0, ER = (a widW,,+, is the interaction parameter for Pb on Pb in {( I- s,)Ni + x,Pb} at x1-+0, E;,, = (alnf,,/ax M) x,+0,xr+0 is the interaction parameter for M on Pb in ((1 -x1 -x,)Ni+x,Pb+x,M) at xX -+O and x, + 0. Values of the activity of Pb in ((1 -x,)Ni+x,Pb}(l) in the temperature range 1703 to 1783 K were also determined by the equilibrium vacuum-saturation method.@’ In this case the Wagner equation takes the form at 1753 K: In f& = 2.498 - 5.94~~.
(4)
The parameters of equation (3) were not established in the traditional way. The 1n.f;: was taken equal to 2.498 and was the most reliable value as it had been
670
T. POMIANEK
2.5OT-. ‘. 2.40-
. .
‘\ ‘. ‘.
2.30-
.
L 0 FIGURE
Xl - -
--?{(I
I 0.01
I 0.02
1 0.03
2. Activity coefficient ,f,,, of Pb in {(I -x1 -xZ)Ni temperature 1753 K. A. (x2) = 0.0317; 0, -x,)Ni + .x,Pb).
‘.
. .
I’. 0.04
+ x,Pb + xzAl}(I) plotted against (x2) = 0.0429; 0. (x2) = 0.0572;
determined at three different temperatures. The E:! and E&, interaction parameters were calculated by the least-squares method based on experimental values for particular ternary mixtures. Equal influence of Pb and of M on the activity of Pb in (( 1 -x1 -x,)Ni + x,Pb + x,~}(l) was obtained when applying this method. The
FIGURE 3. Activity coefficient f&, of Pb in ((I-x-x,)Ni at temperature 1753 K. A. (x2) = 0.0321; -Xl - - -, ((1 -x,)Ni + x,Pb}.
+ x,Pb + x,Cu](l) plotted against 0,(.x,) = 0.0470; 0. (x2) = 0.0650;
ACTIVITY OF
Pb IN
((I-x,
--u,)Ni+u,Pb+.u,(Al
OR Cu))tl)
671
correlation between experimental points and lines calculated by the described method (equation 3) can be observed in figures 2 and 3. As had already been pointed out.‘7. 9, there were some discrepancies of experimental values for the {( 1 - x)Cu + xPb}(l) ref erence mixture. It was essential to show their influence on the value of I:&,. Therefore the experimental fPb values for ((I --x1 -x,)Ni + x,Pb + x~M}(~) were calculated again taking into account the activity coefficient of Pb in ((1 -x)Cu + xPbl(1) proposed by Esdaile and McAdam:” ” lg./Lb =(l-~)~[2634.5(K/~)--1.1293-(2375(K/T)-1.5675f.w].
(5)
The $!,, values calculated by equations (2) and (5) are compared in table 3. Very small differences of &, show, that the ,f,, values in {( 1 -x1 -.uz)Ni + X, Pb + .lz~)(l) could differ in both cases, while E$, values depend very slightly on discrepant thermodynamic values for the reference mixture. A very small error in J$,, determination (table 3) should be pointed out, in view of such high temperatures and the kind of values. Besides, very similar values of a:: determined for :(I --x1-xz)Ni + x,Pb + x,~}(l) (table 3) and for ((1 -x,)Ni + x,PbJ(l) (equation 4) show that the procedure applied was reliable. 4. Discussion When only metallic mixtures with a majority of metallic bonds are considered then, according to their nature, such mixtures may be regarded as ionic systems without valence electrons. The latter can be treated as free electrons, because their mean free path is long. (12) It has been pointed out by Onderka and Fitzner(13) that the nearlyfree-electron model (NFE) can be applied to many liquid metallic mixtures. as values calculated by the NFE model are consistent with experimental values of the Hall constant and the electric conductivity of many liquid metals.(14’ The observation above gives reason for the assumption that it is incorrect to take the atomic radius TAHLE 3. Experimentally determined interaction parameters c$ and &Fb in [(I-r,-x-,)Ni + x,Pb + YAMS factor R. and relative difference of ionic volumes dp- N. For at I753 K as well as metal ionic radii rM, correlation I:):: and t:,,: h fPh calculated (I), from Wypartowicz et u/.,“’ and (2), from Esdaile and McAdam”” R
((I ((I ((I [(I :(I ((1
~.~,-.~,)Ni+.u,Pb+u,B -1, -x,)Ni+x,Pb+x,Si -u,-x,)Ni+x,Pb+x,Al -~(,-\-,)Ni+u,Pb+x,Cr - \-, -u,)Ni+\-,Pb+.x,Co
-.~-,-x,)Ni+.u,Pb+x,Sn {(I -.x1-x,)Ni+x,Pb+x,Cu [(I - rl -xZ)Ni+x,Pb+x,Ce I(1 -Y, -x,)Ni+u,Pb+x,Ag
-6.6kO.7 -6.3kO.5 -5.OkO.5 - 5.5 * 0.3 -5.2kO.4 -5.OkO.3 -4.OkO.3 -5.4kO.4 - 7.7 f I .o
11.3* 1.2 8.3kO.6 6.1 *0.6 5.4kO.3 3.1kO.2 1.5&0.1 - 3.6kO.3 -~ 14.1+ 1.1 -13.7* 1.9
0.96 0.99 0.95 0.99 0.97 0.97 0.96 0.96 0.95
12.5* 1.5 9.2kO.8 6.5kO.7 6.2kO.5 3.4kO.3 1.7kO.l -3.5kO.3 - 14.1+ 1.3 - 12.5k2.3
4 3
-
4 3 2 3 2
Ni’ + Pb’+ B”+ Si’+ Al-‘+ Cr”’ co2 + Sn4+ Cu’ + Ce”+
A$+
0.072 0.120 0.020 0.041 0.050 0.063 0.072 0.071 0.096 0.111 0.126
1.29 I .98 1.85 1.73 I .49 1.79 1.31 0.65 0.23 -0.15
T.POMIANEK
672
or molar volume as a geometrical factor for the mixture because in reality ions occupy lattice points. Therefore it was suggested (‘I that the ionic radius should be regarded as a geometrical factor for metallic mixtures. This conception proved to be justified. A method for the prediction of thermodynamic properties of binary and ternary metallic mixtures was worked out’2) on the basis of relative differences of ionic volumes and electron density as well as of electronegativity. It was shown,‘” for all 13 analysed families of binary mixtures of a constant component A and a variable component M, that thermodynamic properties of mixtures depended on the relative difference d:-” of ionic volumes between A and M ions. Furthermore. distinct linear dependence of E: values on d”-“, the relative difference of ionic volumes between metals N and M, for seven families of (( 1 -x1 -.Y~)A + .Y~N + X~M) with only the component M as variable, was established too.“’ The relative difference of ionic volumes in ternaries was defined by dr-”
=
2[(r(N”+)13-Cr(#w+))3]/[{r(N”+)j3+
fr(Mn’+)i3],
(6)
where r(~'+) and r(MW+) denote the ionic radii of metals N and M, and u and w the numbers of valence electrons of metals N and M transferred to the electron cloud. Another regularity was discovered. .u) the interaction parameter c: > 0 if the ionic radius of the solvent r(A”‘) > r(M”‘+) the ionic radius of the metal M, and the opposite relation: E: < 0 if r(A"+) < r(M”+). This regularity appeared to be true in 56 cases of 66 analysed experimental F: values. Both described regularities can be summarized in the form: E; = B(d” M- d” +),
(7)
where B is a constant. The interpretation of E& for (( 1 -x1 -x,)Ni + x,Pb + x,M) with M = Al or Cu, as well as for M = Sn, Ag,(2’ Si, Co, Ce,‘3’ B, or Cr,(4) according to equation (7) as a linear formation of the relative difference of ionic volumes is shown in figure 4. The degree of ionization of the alloying additives was assumed to be equal to the main number of valence electrons, while the ionic radii were taken from reference 15 (see table 3 and figure 4). The interval of dPbwNivalues has been shown in figure 4, because the ionic radius of Ni 2+ determined by different methods varies from 0.069 to 0.078 nm.” ‘) An almost linear dependence of .$b on dPbwMwas obtained. The following form of equation (7) was calculated by least squares (correlation coefficient: R = 0.98): &ib = 11.22(dPbpM- 1.29) + 2.88 ) 1.1,
(8)
where 1.29 = drbeNi if r(Ni2+) = 0.072 nm and r(Pb”) = 0.12 nm. Both proposed regularities were, in general. fulfilled. However, sgb = 1.2 to 3.6 (instead of cib = 0) at r(Ni’+) = r(MW+) (eFb = 2.88 at r(Ni2+) = 0.072 nm) but, taking into account the experimental errors Of &&, and ionic-radii determination, the results are satisfactory. The relation presented in figure 4 can be interpreted as follows. If we introduce metal M with ionic radius r(M’“+) < r(Ni2’), into ((1 -x,)Ni + x,Pb}(l) alloy, the result is a more closely packed structure and consequently there is a decrease of
ACTIVITY
OF Pb IN {(l-.tl
-.r,)Ni+.u,Pb+x,(Al
OR Cu)}(l)
FIGURE 4. Experimental values of E& for ((1 -r,-x,)Ni + .y,Pb + TIM) plotted against relative difference of ionic volumes dpb-M. ++, dPhmNi.
673
at temperature 1753 K
solubility
of the large Pb ‘+ ions, while in the opposite case of a metal M with r(MW+) > r(Ni*+) the alloy structure is looser and increases the solubility of Pb. So it is proposed to reduce the destructive influence of Pb on the mechanical properties of Ni alloys by alloying additives of ionic radii much bigger than that of Ni. The existence of such a strong relation between $, and drbeM can be applied to draw &, dependence in any ((1 -x1 -x,)Ni + x,Pb + x,~j(l) at 1753 K. Taking into account the Wagner equation (3), the fPb dependence for {( 1 -x,)Ni + v,Pb}(l) given by equations (4) and (7). one obtains: lnf,,
= 2.498-5.94x,
+ \‘l 1.22(drbeM- 1.29)+2.881x2.
(9)
One difficulty, however, arises when using the suggested concept for E: prediction in I( 1 -x1 --x~)A + X,N + x~M}. This problem concerns the determination of the correct degree of ionization of the alloy components. The number of valence electrons is not a satisfactory factor for metals (e.g. Pb, Bi, Au, Sb) which can transfer different numbers of electrons to the common cloud. Some solution of this problem has already been proposed in reference 2. There is still no final answer, if all metals (including transition metals) fulfil the relations proposed. These doubts can be solved on the basis of more E: experimental results, enabling the prediction of activity coefficients in numerous ternary alloys. That would require two C: values in a family of mixtures (( 1 -x1 -x~)A + X~N + xzM) and an experimental value of /i\i only for {(l-X1)A + X,N).
i-. POMIANEK
674
The author thanks the Institute of Non-Ferrous Metals (Gliwice. Poland) for its financial support of the work reported here. He also wishes to express his gratitude to Professors W. Ptak, J. Sqdzimir, and J. Terpilowski, and Associate Professors K. Fitzner and J. Botor, for their helpful analysis and discussion. REFERENCES R. T.; Wallace, W. Inr. Mer. Rev. 1976, 21. I. Pomianek, T. Zes:yty Naukowe Politechniki Rzexowkiej 1986, 32. I. Pomianek, T.: Rychlewski, M. ZN AGH Me/. Odlew. 1987, 109, 39. Pomianek, T. Trans. Jpn Insi. Met. 1988, 29. 3. Kubaschewski, 0.; Alcock, C. B. Mefallurgical Thermochemi.str~. Pergamon Press: Oxford. 1979. Pomianek. T.; Rychlewski, M. Z. Merallkd. 1986, 77. 112. Pomianek. T.; Golonka, J. Met. Technol. 1979, 6. 433. Pomianek. T. Z. Metallkd. 1986, 77. 388. Wypartowicz. J.; Zabdyr, L.; Fitzner. K. Arch. Hum. 1979, 24. 473. Wagner, K. Thermo&namics c~fAlloys. Addison-Wesley: Reading, Mass. 1952. Esdaile, J. D.; McAdam, J. C. H. Proc. Ausf. Ins. Min. Me/a/l. 1971, 239, 71. Mott, N. F.; Davis, E. A. Electrons in Non-Crystalline Materials. Clarendon Press: Oxford. 1979. Onderka, B.; Fitzner, K. Arch. Hum. 1985, 30. 443. Ziman, J. M. Phil. Mag. l%l, 6, 1013. Chojnacki. J. Element?, Kryralogrqfii Chemicznej i Fi:yc=nei. PWN: Warszawa. 1973.
I. Holt,
2. 3. 4. 5. 6. 7. 8. 9. IO. I I. 12. 13. 14. 15.