Section I: Basic and Applied Research The Solidus Line of the Cu–Bi Phase Diagram L.–S. Chang, B.B. Straumal*, E. Rabkin, W. Gust, and F. Sommer Max-Planck-Institut für Metallforschung Institut für Metallkunde der Universität Seestrasse 75, D–70174 Stuttgart, Germany (Submitted 18 September 1996; in revised form 8 November 1996) The solid solubility of Bi in Cu single crystals has been experimentally determined. It is shown that the solidus line is a retrograde curve without a monotectic transition. The solid and liquid phases are successfully described with simple thermodynamic models. The experimentally measured maxi- mum solubility of 0.0207 at.% Bi at 975°C correlates well with that from the model (0.0193 at.% Bi at 968°C). A linear temperature dependence of the interchange energies is suggested and the values of the optimized coefficients are in accordance with those estimated from the thermal expansion co- efficients. The calculated thermodynamic functions are in good agreement with the assessed experi- mental data. Introduction for measurement of very dilute alloys. Other experiments were performed by Voce and Hallowes [47Voc] using me- chanical testing. These results suggested that the solidus line Studies of the Cu-Bi binary phase diagram began more than is a retrograde curve either with or without a continuous a century ago. On the basis of numerous investigations, par- maximum. The continuity on the maximum depends on the ticularly the intensive studies in the first decade of this cen- occurrence of a monotectic transition proposed by Vasil’ev tury [05Hio, 07Jer, 07Por] and in the 1950s and 1960s [81Vas] in a mathematical treatment of these data. This work [52Kle , 57Tay, 61Oel, 62Nat], the liquidus line was collec- estimated the maximum solubility as 0.016 at.% Bi at 850 tively established. On the other hand, relatively little atten- °C. Although this solubility curve, which was constructed by tion was given to the determination of the solid solubilities, two parabolic lines, was adopted in some research on the Cu- which generally are not considered in calculations of the Bi system in recent years, a degenerate monotectic transition thermodynamic properties of the liquid phase. Most of the experimental data on the solubility of Bi in solid Cu are not *On leave from the Institute of Solid Physics, Russian Academy of convincing because they were determined by optical micros- Sciences, Chernogolovka, Moscow District, 142432 Russia. copy [07Jer, 27Han, 46Rau, 57Bas] which is not well suited Table 1 Details of Experimental Conditions Specimen thickness, Annealing temperature, Annealing time, Diffusion penetration length, No. mm °C ks mm 1.............................................. 0.65 1040 32.8 0.80 2.............................................. 0.5 1020 25.2 0.61 3.............................................. 0.4 1000 21.0 0.49 4.............................................. 0.3 975 10.8 0.30 5.............................................. 0.3 950 15.7 0.30 6.............................................. 0.3 925 22.8 0.30 7.............................................. 3.0 900 1210 1.80 8.............................................. 0.3 875 50.4 0.30 9.............................................. 1.2 850 605 0.84 10............................................ 0.3 825 119 0.30 11............................................ 0.6 800 605 0.54 12............................................ 0.3 775 518 0.39 13............................................ 0.9 750 2590 0.68 14............................................ 0.3 725 864 0.30 15............................................ 0.3 700 864 0.23 16............................................ 0.3 650 2590 0.21 17............................................ 0.1 600 1210 0.07 128 Journal of Phase Equilibria Vol. 18 No. 2 1997 Basic and Applied Research: Section I was never experimentally observed in the past. This uncer- Thermodynamic Modeling tainty can now be clarified as a result of advances in analyz- ing very dilute compositions. In the present work, the Solid Phase solubility of Bi in solid Cu was determined in the tempera- The Cu-Bi solid solution is described by the regular solution ture range from 600 to 1040°C. A recently proposed thermody- model. This is a satisfactory assumption as the mutual solubil- namic model of the liquid phase with a demixing tendency ity of Cu and Bi is so small that foreign atoms are statistically [92Sin] was used to reconstruct the Cu-Bi phase diagram distributed in the matrix. Regular solutions were considered over the entire composition range. for the face-centered cubic (fcc) and rhombohedral (rhomb) Experimental Procedure structure of the Cu-rich and Bi-rich solid solutions, respec- tively. The activities of Cu and Bi in the different crystal struc- The vapor transfer method was used to obtain Cu saturated tures can be expressed in the form: with Bi. Pure Cu single crystal cylinders were produced by the Bridgman method and cut into thin disks with various thick- S 2 Ω S S S nesses (0.1 to 3 mm). These disks were etched in an aqueous ln a = ln x + (X ) Cu Cu Bi RT solution of 50% HNO3 to remove the oxidized film. Each disk (Eq 1) S 2 Ω was then sealed separately in a silica tube with a Bi vapor S = S + S ln a Bi ln x Bi (X Cu ) source. In contrast to the pure Bi source used by Li and Zhang RT [95Li], Cu–Bi alloys were prepared as Bi vapor sources. The compositions of these alloys were Cu–4.5 at.% Bi for tempera- where a S and X S are the activity and mole fraction of the ele- tures lower than 850°C and Cu–0.3 at.% Bi for the higher tem- ment Cu or Bi in the solid solution, R is the gas constant, T is S peratures. Alloys of these compositions are in the (Cu) + the absolute temperature, and Ω is the interchange energy be- liquid two-phase region at the annealing temperature so that tween Cu and Bi atoms in the solid phase. the formation of a liquid phase in the Cu single crystal could not occur during annealing. A pure liquid Bi source, even in a Liquid Phase small amount, can produce a liquid phase on a Cu target. Sev- It is impossible to fit the experimentally observed strong in- enteen different temperatures between 600 and 1040°C were crease of the solubility of Bi in the temperature range from 600 chosen. At temperatures lower than 600°C the diffusion rate of to 800°C with the regular solution model for the liquid phase. Bi in (Cu) is too slow to yield equilibrium in a reasonable time. Otherwise, the asymmetry of the metastable miscibility gap in It is expected that at lower temperatures the Bi solubility in Cu the liquid phase calculated by Chakrabarti and Laughlin (a few ppm) is much smaller than that at higher temperatures. [84Cha] and Taskinen and Niemelä [81Tas] showed that the Because the purity of the Cu single crystals was not better than classical regular model and its improvements cannot be used 99.999 wt.%, it was inappropriate to perform experiments at to represent satisfactorily the Cu–Bi phase diagram. The self– temperatures lower than 600°C. The silica tubes were posi- as-sociate model developed recently by Singh and Sommer tioned in the furnace such that the Cu crystals were kept at the [92Sin] represents a relevant tool for the description of a liquid desired temperature while the temperature of the Cu–Bi alloy phase exhibiting an asymmetric miscibility gap. Singh and was about 5°C lower in the temperature range 600 to 1000°C Sommer emphasized that such an asymmetric demixing be- and about 5°C higher in the temperature range 1000 to 1040 havior occurs mainly in systems exhibiting a large difference °C. The annealing times for a complete vapor transfer were in atomic volumes and a small difference in electronegativi- chosen by estimating the time, at which the diffusion penetra- ties. This is expected in the Cu–Bi system because of the large tion depth of Bi in solid Cu, 2 Dt , considerably exceeds the ratio of the atomic volumes and the small difference in the thickness of the sample. In the calculation of the penetration electronegativities of the Cu and Bi atoms. depth, D is the volume diffusion coefficient of Bi in solid Cu [90Meh] and t is the annealing time. Details of the experimen- It is supposed that Cu and Bi have the tendency to self–aggre- tal conditions are given in Table 1. gate and form atomic clusters in the liquid alloy. It can be ex- pressed as follows: After long annealing the specimens were etched again to re- move the liquid film or liquid particles which may have con- iCu ↔ Cu densed from the Bi vapor during water quenching. Finally, the i ↔ solute contents in the Cu-Bi single crystals were measured by jBi Bij atomic absorption spectroscopy (AAS). A Perkin–Elmer (model 5000) spectrometer was used with a relative accuracy where i and j are the numbers of atoms in the Cu and Bi clus- -9 of 10 g/g. Because only a small amount of the specimen mass ters. The thermodynamic functions were derived from the was needed for the measurement (≈10 mg), it was possible to quasi–lattice statistical mechanical theory [92Sin]. The expres- analyze thin disks (0.1 mm) and thus decrease the time re- sions of the Gibbs energy, enthalpy and entropy of mixing are: quired for complete saturation with Bi at low temperatures. For the analysis, the specimens were cut into three or four pieces ∆ G = RT[ X L ln X L + X L ln X L − X L ln n + ln η] mix Cu Cu Bi Bi Cu (Eq 2) and the Bi concentration in each piece was determined inde- + X L X L ηW pendently. Cu Bi Journal of Phase Equilibria Vol.