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Thermochimica Acta 544 (2012) 57– 62
Contents lists available at SciVerse ScienceDirect
Thermochimica Acta
jo ur n al homepage: www.elsev ier .com/ locate / tca
olid solubility of germanium in silver
amed Kazemi, Ludger Weber ∗
aboratory of Mechanical Metallurgy, Ecole Polytechnique Fédérale de Lausanne, EPFL, CH-1015 Lausanne, Switzerland
r t i c l e i n f o
rticle history:eceived 8 May 2012eceived in revised form 14 June 2012ccepted 16 June 2012vailable online 26 June 2012
eywords:erminal solubility
a b s t r a c t
The solid solubility of germanium in silver has been measured in the temperature range of 520 K to 913 Kvia measurements of density and of electrical conductivity of two near-eutectic Ag–Ge alloys. The atomicfraction of germanium in solid solution varied between 0.014 and 0.089 over the mentioned range of tem-perature and an extrapolated maximum solubility of 0.093 at the eutectic temperature of 924 K is found.For samples with spheroidized Ge-particles before the equilibrium heat treatments at low temperaturefor 24 or 48 h, thermodynamic equilibrium was supposedly not achieved at temperatures below 723 K.Much longer heat treatments (tens of days) on the significantly finer as-cast microstructure allowed
ilver–germanium alloyslectrical resistivitypecific gravity
to reach equilibrium probably down to 600 K. Independently of whether thermodynamic equilibriumwas reached or not the electrical conductivity and the density measurements yielded good agreementtypically within a few tenth of percent of atomic Ge-concentration in solid solution in �-Ag for a giventemperature. The results are close to, yet consistently slightly lower than, the values given by Owen andRowland on which the current assessment of the solvus in the Ag–Ge binary is based. More recent resultsby Filipponi and co-workers are clearly not in agreement with the data presented here.
. Introduction
Phase diagrams, an essential working tool for many aspects oflloy design, have been established for the majority of binary metal-ic alloy systems in the 50s, 60s, and 70s of the last century. Apartrom melting points and information on intermetallic phases, ter-
inal solid solubility, whose temperature dependence is given byhe solvus line, is of particular technical importance with regard to,.g. solid solution hardening, potential for precipitation hardening,r heat treatments to obtain improved electrical and thermal con-uctivity. A major campaign of (re-)assessment of these diagramsas been conducted in the late 1980s under the auspices of themerican Society of Materials (ASM). Despite the neat drawingsiven in this handbook of reference edited by Massalski [1], manyines in these diagrams are not as well established as it may looknd partial reassessment of lines with scarce database or stronglyiverging results may be necessary.
The binary system Ag–Ge is a point in case. There is generalgreement that the system is characterized as a simple eutecticithout intermediate phases with the eutectic point at 24.5 at.%
f Ge at a temperature of 924 K and with negligible solubility of
g in Ge. While the liquidus lines have been measured by severalesearch groups with good agreement, data on the solid solubilityf Ge in �-Ag is scarce. The current assessments of the solvus line∗ Corresponding author.E-mail address: [email protected] (L. Weber).
040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.tca.2012.06.018
© 2012 Elsevier B.V. All rights reserved.
[2–4] are based on work by Owen and Rowlands [5] who derivedthe solid solubility via changes in the lattice parameter as a functionof the annealing temperature in the range between 543 and 848 K.They estimated the maximum solubility at the eutectic tempera-ture by extrapolation of their data to 9.6 at.%. Earlier work by Briggset al. [6] based on metallographic analysis had led to the conclusionthat the maximum solubility at 913 K was below 8.8 at.% and theyestimated the maximum solubility of Ge in �-Ag between 6 and7 at.%. Nowotny and Bachmayer [7] estimated the maximum sol-ubility to 8.1 at.% at 923 K based on metallographic investigations.In a much more recent investigation Filipponi et al. [8] used in situ(i.e. at temperature) X-ray diffraction to extract the solubility ofGe in �-Ag from the difference of the lattice parameter of �-Ag inan Ag–Ge powder mixture to that of pure Ag-powder. To convertthe difference in lattice parameter into a Ge-concentration theyused the calibration factor determined by Owen and Rowlands [5]at ambient temperature. They determined a maximum solid sol-ubility of 23 at.% at 912 K which is even far beyond the levels of(metastable) solid solubility obtained in rapidly quenched Ag–Gealloys given as ≈13.5 at.% by two independent groups [9,10].
A common feature of all contributions cited above, with theexception of the work by Filipponi et al. [8], is that the assessmentwas based on alloys whose compositions were very close to the pre-sumed solvus concentration. This entails the difficulty that either
existing second phases need to be dissolved and the solute atomsneed to be homogeneously redistributed throughout the matrix, orthe excess of solute atoms needs to precipitate for the system toreach equilibrium. Dissolution of second phases and redistribution
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f solute atoms may take very long times especially if the character-stic distance between second phases is large and the temperature isow. On the other hand, at marginal oversaturation, the thermody-amic driving force to form precipitates is small and concomitantlyhe kinetics of precipitation is very slow especially at low tempera-ures. Even if the nucleation barrier is overcome, the slow diffusion
ay lead to very fine precipitates. Due to the small radius of curva-ure of the precipitate’s surface, equilibrium solubility in the matrix
ay then be overestimated.Apart from the question on whether thermodynamic equi-
ibrium has been reached or not, microscopic techniques faceifficulties when observing minute amounts of second phases,hile the indirect methods, i.e. those based on a change in phys-
cal property, are subjected to uncertainties due to the calibrationrocedure and/or due to the underlying assumptions.
In view of the significantly differing experimental data on theolvus line on the silver-rich side of the Ag–Ge binary presentedbove, we propose here to determine the solid solubility of Ge in-Ag by experimental techniques unexploited so far for this sys-
em, i.e. measurement of electrical conductivity and specific massf two near eutectic Ag–Ge alloys as a function of annealing tem-erature. While electrical conductivity has frequently been usedo determine solid solubility in other systems, e.g. [11–13], were not aware of any assessment using density measurements tohat end so far. Density can be used to measure solid solubility ifhe molar volume of the solute is significantly different in solidolution than in the second phase. It further has the beauty thatt does not necessitate a calibration (as is required for the meth-ds based on electrical conductivity or the lattice parameter, albeithe change of the latter with concentration in solid solution enterss a second order effect). In order to overcome the difficulty ofchieving equilibrium throughout the matrix, we work here withlloys of near eutectic composition for which the diffusion length iseduced to the order of the characteristic length scale of the eutecticicrostructure at the expense of a somewhat less straight-forward
ata extraction from measurement.
. Theory
.1. Electrical conductivity of eutectic Ag–Ge
The electrical conductivity of a near-eutectic alloy of Ag–Ges affected both by the presence of semiconducting germaniumarticles embedded in the electrically conductive matrix and ger-anium in solid solution in the silver lattice. The first effect can be
ccounted for by the composite factor � which relates the effectiveesistivity of the Ag–Ge solid solution to the macroscopic resistivity,c, of the Ag–Ge/Ge composite. Secondly, the presence of germa-ium in solid solution increases the electrical resistivity of silver.he composite resistivity can be expressed as [11]
c = �(�0 + ˛AgGexGe(Ag) + ˇAg
Gex2Ge(Ag)) (1)
with xGe(Ag) the concentration of Germanium in �-Ag. �0 ishe thermal contribution to electrical resistivity of the �-Ag phasend ˛Ag
GexGe(Ag) + ˇAgGex2
Ge(Ag) is the contribution due to solid solu-ion parameterized to second order necessary due to the large solidolubility of Ge in Ag at high temperatures. Indeed, for extendedolid solubility the commonly used linear effect of alloying ele-ents in solid solution would typically overestimate the increase
n electrical resistance, cf. e.g. [14]. �0 is given in reference [15] as.62 �� cm at 296 K and ˛Ag
Ge and ˇAgGe can be extracted from the
ork of Köster and Rave [14] to yield 517 �� cm and −826 �� cm,espectively. The composite factor � depends in all generality onhe volume fraction, size, and shape of the Ge-particles [16]. Forpheroidised Ge-particles with diameters much larger than the
ica Acta 544 (2012) 57– 62
electron mean free path of Ag, � is solely a function of volumefraction of Ge-particles, Vp, and is well approximated by
� = (1 − Vp)−n. (2)
with n having been determined for spherodized Si particles inAl to be 1.67 [17]. For plate-like particles with high aspect ratio, nchanges rapidly with aspect ratio and the aspect ratio itself is verydifficult to quantify, leading to large uncertainty in n and, thus, in� [17]. Therefore, the electrical conductivity measurements wereonly used in alloys with equiaxed second phases.
Assuming zero solubility of Ag in Ge, the volume fraction of Ge-particles can be expressed in terms of concentration of Ge in solidsolution in �-Ag and of the overall Ge-content in the alloy, xGe as
Vp = (xGe − xGe(Ag))vGe
(xGe − xGe(Ag))vGe + (1 − xGe)vAg(Ge)(3)
where vAg(Ge) and vGe are the molar volume of silver solid solu-tion and pure germanium, respectively. It is worth noting that themolar volume of the silver solid solution depends also slightly onxGe(Ag). According to the lattice parameter study of Owen and Row-lands [5], this dependence can be expressed as
vAg(Ge) = vAg(1 + 0.02xGe(Ag)) (4)
with vAg the molar volume of pure silver.
2.2. Density of near-eutectic Ag–Ge alloys
Since the molar volume of germanium in solid solution in �-Ag islower than in pure Ge the transfer of germanium in solid solution topure Ge will lead to a decrease in density of the alloy. As mentionedabove, cf. Eq. (4), the change of lattice parameter of the host matrixhas also a small effect on the molar volume of the �-Ag(Ge) solidsolution. The density of the alloy, �, can be expressed as
� = VpmGe
vGe+ (1 − Vp)
mGexGe(Ag) + mAg(1 − xGe(Ag))vAg(1 + 0.02xGe(Ag))
(5)
where mGe and mAg are the molar mass of germanium and silver,respectively. Combining Eqs. (3) and (5) leads to an explicit relationbetween xGe(Ag) and � as
xGe(Ag) = �(vAg − xGe(vAg − vGe)) + xGe(mAg − mGe) − mAg
�(vGe − 0.02vAg(1 − xGe)) + xGe(mAg − mGe) − mAg. (6)
While vAg, vGe, mAg, and mGe have little ambiguity and can betaken from the handbooks, the overall content of Ge in the alloy inmole-fraction, xGe, is the only non-trivial input parameter whichmay be obtained from the weighed-in quantities of Ag and Ge orfrom chemical analysis of the alloy after melting.
3. Experimental procedures
Two ingots of near-eutectic Ag–Ge alloy have been cast in cop-per moulds, the first ingot containing 333.00 g of silver (with 99.99%purity provided by Argor Heraeus SA, Mendrisio Switzerland) and66.00 g of germanium of 99.9+% (provided by Alpha Aesar) andthe second ingot containing 100.05 silver and 22.08 g germaniumcorresponding to atomic fractions of germanium of respectively22.75 at.% (alloy 1) and 24.70 at.% (alloy 2). The casting has beendone under 200 mbar of Argon in an induction furnace. Beforemelting, the atmosphere has been purged three times with argon(varying pressure between 10−5 and 200 mbar). Two cylindricalingots of about 30 mm of diameter for alloy 1 and 20 mm diameter
for alloy 2 have been produced.Heat treatments have been carried out in a resistance mufflefurnace with a closed steel tube inserted in which the samples wereheld. The temperature was measured at a few mm distance from
ochimica Acta 544 (2012) 57– 62 59
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he sample. The steel tube allowed carrying out the heat treatmentnder primary vacuum including argon purging. The time betweenraking the vacuum and transfer of the sample in the water quenchath was typically 3–5 s. Alloy 1 has been subjected to an initial heatreatment of 3 h at 900 K to spheroidise the Ge-particles, while alloy
was left in the as-cast state. Alloy 1 has been sectioned to discs ofpproximately 1 mm thickness and 30 mm diameter.
Further heat treatment where conducted on a pack of 9 discsf alloy 1. Starting from 913 K after one hour the specimen for13 K was taken out. For the second specimen the temperature waseduced to 873 K and the next specimen was taken out and this pro-ess continued according to the specific time each specimen had totay in the furnace at a certain temperature. The duration of thennealing and the annealing temperature is given in Table 1.
The heat treatments of alloy 2 from the as-cast state were con-ucted on a cylindrical sample (diameter 20 mm, height 10.3 mm)tarting at much lower temperature, i.e. 615 K, to keep theicrostructure as fine as possible. The temperature of the subse-
uent heat treatments was first reduced in steps of roughly 50 K to minimum of 472 K and then increased again at steps of roughly0 K to a maximum temperature of 876 K. Thus the characteristic
ength scale could be kept at much lower values for the treatmentst lower temperature. The heat treatment temperature and dura-ion are given also in Table 1. For both alloys the heat treatmentsre given in chronological order.
The electrical conductivity was measured using an Eddy-currentased Sigmatest 2.069 device (Foerster Instruments Inc., USA).n order to minimize the effect of limited sample thickness, therequency was set to 960 kHz. For each temperature and each con-ition at least 6 measurements have been recorded and the valuesiven are the average of all measurements. Standard deviation ofhe 6 measurements was typically 0.2% of the absolute value.
The density of the specimens was measured using a high preci-ion balance (precision 10 �g) and applying Archimedes’ principley measuring the weight of the sample in air and when suspended
n water. First the sample was measured in air. The buoyancy forcen air of 0.0012 g/cm3 was also taken into account for the den-ity calculation. For the weight measurement when submerged inater the sample was placed in the beaker containing the water
nd the balance was zeroed. The sample was then transferred into bucket that was suspended by a 0.05 mm nickel wire on the frameonnected to the load cell. Hence, possible errors due to changes inhe water level induced by submerging the sample could be elimi-ated. The water temperature was measured to 0.1 K close and theorresponding density of water was taken from tables providedn the manual of the microbalance. For each specimen the density
easurements have been carried out at least 8 times of which anverage value was calculated. Overall, the repeatability of the den-ity measurements derived from the standard deviation from the 8easurements in a given condition was typically better than 0.01%
f the absolute value.
. Results
The as-cast microstructure of the alloys was that of an irregularutectic, shown in Fig. 1a. After the speroidisation treatment theicrostructure of alloy 1 consists of rather equiaxed Ge-particles
mbedded in a matrix of silver–germanium solid solution, cf.ig. 1b. The typical length scale of the microstructure was deter-ined on ten binary images of the microstructure using the ImageJ
oftware. The matrix was skeletonized and the average maximum
istance, �, was determined as= S
2Ls(7)
Fig. 1. Light microscopy pictures of (a) microstructure of the as-cast alloy 2; (b)microstructure of the spheroidised alloy 1 after 3 h treatment at 900 K.
with S the area of the matrix and Ls the length of the skele-ton line. The thus determined characteristic length scale was0.98 ± 0.15 �m in alloy 1 and 0.31 ± 0.03 �m in alloy 2.
The result of electrical conductivity measurements on alloy 1is presented in Fig. 2 as a function of the annealing temperature.It can be seen that the conductivity of the alloy is by more than afactor of 10 smaller than that of pure silver (61.7 MS/m). Further-more, by increasing the annealing temperature the conductivity isconsiderably decreased. Standard deviations of the 6–8 measure-ments taken led to error bars that are typically smaller than thedata points shown.
The result of density measurements for both alloys is presentedin Fig. 3. While both alloys show a similar general trend, they dif-fer significantly in absolute value. For each individual alloy it canbe seen that by increasing the annealing temperature the densityincreases. The error bars derived from the variations in the mea-surement are in most cases comprised in the data point.
5. Discussion
The microstructures shown in Fig. 1a and 1b indicate that bothalloys are sufficiently close to the eutectic composition that they donot contain significant amounts of primary phases. The microstruc-
ture of alloy 1 shows nicely equiaxed Ge-particles.The evolution of density as a function of annealing treat-ment temperature is quite significant, changing by close to 2%of the nominal value over the whole range of heat treatment
60 H. Kazemi, L. Weber / Thermochimica Acta 544 (2012) 57– 62
Table 1Time and temperature of the sequence of heat treatments conducted on discs of alloy 1 and on the cylindrical sample of alloy 2 in chronological order. The ratio, ϕ, definedby Eq. (7) is given as well.
Alloy 1
Annealing temperature (K) 913 873 823 773 723 673 619 577 520Duration (h) 1 2 1 10 10 24 24 48 48ϕ 7.57 6.75 2.52 3.87 1.70 1.03 0.31 0.15 0.03
Alloy 2
Annealing temperature (K) 615 568 520 472
Duration (h) 216 264 264 280
ϕ 2.76 0.89 0.2 0.03
Fig. 2. Evolution of electrical conductivity of alloy 1 as a function of annealingtemperature (the small error bars being comprised in the data points).
Fig. 3. The evolution of specific mass as a function of the annealing temperature forboth alloy 1 and 2. The difference between the two alloys stems from the differencein overall Ge-content (cf. Section 3).
566 623 673 719 774 826 876432 240 500 72 36 36 2
1.07 3.53 15.2 13.8 24.2 51.1 22.7
temperatures. This is to be compared to a typical standard devia-tion of the density measurement on the order of 1 × 10−4 indicatingthat the density measurement should be able to give rather preciseinformation about the Ge-content in solid solution.
Using the development presented in section 2, the atomic frac-tion of germanium in solid solution can be calculated based on theelectrical conductivity (alloy 1) and the density (alloy 1 and 2) usingEqs. (1)–(3) and (6), respectively. The results are presented in Fig. 4.The input parameters used for the electrical conductivity are thosegiven by Bass [15] and Köster and Rave [14] and for the density con-version tabulated values for density of the pure elements and molarmass have been used to calculate vAg and vGe. The overall atomicconcentration of germanium was calculated based on the weighedin quantities of elements, cf. section 3. The maximum solubilitymeasured at 913 K is 8.7 at.% and 9.03 at.% for density and electri-cal conductivity, respectively. As can be seen for alloy 1, both theconductivity and the density reach very similar results, albeit notwithin the limits of uncertainty associated with each measurement.We note that the values derived from electrical conductivity mea-surement are quite strongly dependent on the parameters used inthe calibration curve, cf. Eq. (1) especially the term ˇAg
Ge. The corre-spondence between the two methods is nevertheless remarkablefor two measurements of completely different nature and strength-
ens the confidence in either of the two methods. It is also a strongindication that the sample does not contain any porosity since theresults deduced from density would be very strongly affected byFig. 4. Germanium concentrations in �-Ag derived from electrical conductivity anddensity measurements for spheroidised (alloy 1) and as-cast (alloy 2) microstruc-tures.
ochimica Acta 544 (2012) 57– 62 61
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Fig. 5. Solvus data derived by electrical conductivity and density of alloys 1 and2 for the range of temperature where equilibrium has supposedly been reached(i.e. ϕ ≥ 1.5) compared to assessments as well as individual data points from theliterature. The solvus line assessed in this work is shifted to lower solid solubility
H. Kazemi, L. Weber / Therm
orosity (about 4 at.% Ge in solid solution per vol.% of porosity)hile for the electrical conductivity porosity would only affect the
eometry factor ̌ and thus would have a minor effect on the resultabout 0.6 at.% Ge in solid solution per vol.% of porosity). Further-
ore, the effect would be of opposite sign, i.e. porosity would leado an underestimation of Ge in solid solution based on density,hile for conductivity porosity would lead to an overestimation
f Ge in solid solution.Comparing the solvus measurement based on density of alloy
and 2 we first note that, despite the apparent difference in den-ity evolution in alloys 1 and 2 shown in Fig. 3, the Ge-content inolid solution is in good agreement for the two alloys at least atigh heat treatment temperatures, while for lower temperatureshe experiments on alloy 2 lead to significantly lower Ge-contents.he agreement at high temperatures indicates that the difference inig. 3 is largely due to the difference in overall Ge-content. The dif-erence at lower temperatures can be rationalized by the shorterharacteristic length scale in alloy 2, where the low temperatureeat treatments have been conducted on the as-cast microstructurend for significantly longer times. To quantify this we compare theiffusion length x ≈ √
Dt to the characteristic length-scale of theicrostructure, �. Diffusion data of Ge in Ag are taken from the
iterature [18,19]. For every heat treatment the ratio ϕ given by
=√
Dt
�(8)
can be determined. A value of ϕ smaller than 1 would suggesthat equilibrium has not been reached during the annealing treat-
ent. The values of ϕ are given for the heat treatments appliedo alloys 1 and 2 in Table 1. It is seen that for the range of heatreatment temperatures for which ϕ ≥ 1.5 for both alloys the con-entrations of Ge in solid solution in Ag deduced by Eq. (6) areeasonably consistent with each other. Starting from 673 K andelow, ϕ becomes smaller than 1 for alloy 1 while for alloy 2, ϕemains (well) above 1 down to an annealing temperature of 623 K.he difference at the low end of temperatures is thus rational-zed by the fact that due to the microstructure and the longer heatreatment times, alloy 2 has been brought closer to equilibriumompared to the samples from alloy 1.
Taking for the determination of the solvus line only samplesrom both alloys for which ϕ ≥ 1.5 we can compare our results tohose given in the literature [5–8] and to the assessments in [2–4],f. Fig. 5. It can be seen that, over the whole temperature rangessessed here, the measured solubility of Ge in Ag is slightly loweri.e. the solvus line is shifted to the left) than the assessed valuesnd also than the data reported by Owen and Rowlands [5]. Theifference is largest in the intermediate temperature range around30 K where the values obtained in this study are more than 1 at.%maller than previously assessed solubility. We first note that theolvus line deduced by Owen and Rowlands has an unnatural pos-tive curvature in the coordinates of a typical phase diagram. Aossible reason for this is that the characteristic diffusion lengtharied strongly for the annealing treatments of their samples andhat equilibrium was not reached in all heat treatments. We furtherote that Owens and Rowlands postulated for the data extraction
linear increase in the lattice parameter with Ge-concentration inhe matrix. However, in the series of samples they had used forhe calibration, the rate of increase in lattice parameter with Ge-oncentration was slightly steeper at high concentrations than atow concentrations. Therefore, they may have overestimated theolubility at high temperatures. If one were to correct their analysis
aking into account the non linear evolution of the lattice parameterith Ge-concentration one would arrive at an extrapolated value athe eutectic temperature of 9.2 at.% compared to 9.6 at.% deducedn the original work.
compared to previous assessments.
The data by Filipponi et al. [8] have been established by in situmeasurement of the lattice parameter at high temperature andsubtraction of the handbook value of pure Ag at that tempera-ture, followed by conversion of the difference into solid solutionGe-contents using the calibration parameter determined by Owenand Rowlands [5]. Such a procedure supposes that the coefficientof thermal expansion does not change with Ge in solid solution.While this may serve as an approximation of 1st order, it is highlylikely that the significant amount of solute atom does affect theaverage interatomic potential such that the coefficient of thermalexpansion of the solid solution differs slightly from the pure matrix.It then reduces to extract information from the difference of twolarge values where the uncertainty of each of the large values issmall compared to the large value itself, yet large compared totheir difference. Accordingly, the solvus line determined by theseauthors is far off from the ones determined by Owen and Rowlandsas well as those determined by metallographic means and thoseobtained in this work. Their values for Ge-solubility would even besignificantly larger than those determined by Klement [10] or morerecently by Ning and Zhou [9] on rapidly solidified Ag–Ge alloys. Theevidence given here points towards a systematic error due to over-simplifying assumptions in the evaluation of the data by Filipponiet al. [8].
The solid solubility of Ge in �-Ag determined in this work forthe conditions where thermodynamic equilibrium was supposedlyachieved, quantified by the parameter ϕ, can be described in termsof the Redlich–Kister formalism generally used for thermodynamicassessment of the Ag–Ge system using the following tentative val-ues:
0afccAg,Ge = −1000 J
0bfccAg,Ge = −9.917 J K−1
1 fcc
aAg,Ge = −7500 JAll other parameters are the same as those used in the assess-ment by Chevalier [2]. The uncertainty of the experimental data
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oints does not warrant higher precision in the Redlich–Kisterarameters given here. Extrapolating the assessed solvus curve tohe eutectic temperature of 924 K we find a maximum solubilityf 9.3 at.%. While this is only slightly lower than the value giveny Owen and Rowlands, the solubility at intermediate tempera-ures is significantly (>1 at.%) smaller than the values in the currentssessments.
. Conclusion
The solid solubility of germanium in silver has been assessedn the range of 473 to 913 K based on measurements of electricalonductivity and of density of two near eutectic Ag–Ge alloys. Theollowing conclusions can be drawn:
. In the Ag–Ge system, density and electrical conductivity mea-surements given consistent values for the Ge-content in solidsolution in �-Ag in the range of 520 to 913 K.
. The solid solution content of Ge in �-Ag increased in the tem-perature range from 473 to 913 K from 1.4 to 9.0 at.%.
. Equilibrium terminal solubility may only have been reached inthe range between 913 and 600 K due to slow diffusion at lowertemperatures. In this range the equilibrium concentration goesfrom 9.0 down to 2.0 at.% and is, for a given temperature typi-cally between 0.3 and 1.2 at.% below the values given in currentassessments.
. The maximum solubility is estimated to 9.3 at.% at the eutectictemperature of 924 K.
. Redlich–Kister parameters are given to account for the positionof the solvus curve assessed in this work.
cknowledgement
This work was financed by the core funding of EPFL.
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ica Acta 544 (2012) 57– 62
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