Self- and Interdiffusion in Ternary Cu-Fe-Ni Alloys

Diffusion of Cu, Fe, and Ni radiotracers has been measured in Cu–Fe–Ni alloys of different compositions at 1271 K. The measured penetration profiles reveal grain boundary-induced part along with the volume diffusion one. Correction on grain boundary diffusion was taken into account when determining the volume diffusivities of the components. When the Cu content in the alloys increases, the diffusivities increase by order of magnitude. This behaviour correlates well with decreasing of the melting temperature of corresponding alloys, as the Cu content increases. Modelling of interdiffusion in the Cu–Fe–Ni system based on Danielewski-Holly model of interdiffusion is presented. In this model (extended Darken method for multi-component systems) a postulate that the total mass flow is a sum of the diffusion and the drift flows was applied for the description of interdiffusion in the closed system. Nernst-Planck’s flux formula assuming a chemical potential gradient as a driving force for the mass transport was used for computing the diffusion flux in non-ideal multi-component systems. In computations of the diffusion profiles the measured tracer diffusion coefficients of Cu, Fe and Ni as well as the literature data on thermodynamic activities for the Cu–Fe–Ni system were used. The calculated interdiffusion concentration profiles (diffusion paths) reveal satisfactory agreement with the experimental results. Introduction Advanced materials are very often multi-component and have complex structure (gradient materials, coatings, etc.) and from thermodynamic point of view are non-ideal. Interdiffusion and interfacial reactions play important role during processing of many functional materials and limit their long term exploitation. Understanding of these processes has fundamental practical importance. There are different approaches to reach this goal. These are Onsager phenomenology [1] and Darken method [2], they differ in form of the constitutive flux formula. Up to now they were not unified and the fundamental question is whether the computed diffusivities or interdiffusion coefficients represent real material constants [3]. Situation is even more difficult because the proof of the uniqueness of the inverse Darken problem does not exist [4]. We selected relatively simple Cu-Fe-Ni system to study the interdiffusion in non-ideal alloys showing limited solubility. This system has advantage because its thermodynamic and kinetic data are fairly well known. This paper has two goals: first to measure the tracer diffusivities of all components as a function of the ternary alloy composition, second the theoretical examination of the extended Darken method (Danielewski-Holly model) for a ternary system. Experimental measurements Sample preparation and radiotracer measurements Copper, iron and nickel (99.99 pct purity) were used as starting materials. The ternary alloys (Table 1) were melted in induction furnace in argon atmosphere. Such obtained ingots were homogenized at 1273 K for 250 hour in argon ( 2 6 10 O p atm − < ). Subsequently, the alloys of different composition were reannealed at the temperature 50 C below their melting temperature for 4 hours for recrystalization. The grain size of polycrystalline alloys was measured to vary from 30 (Cu-richest alloy) to about 300 μm. Alloys in the form of the cylindrical ingots of 8 mm in diameter were cut into slices of 3 mm thick by spark erosion. One face of the specimen was polished to optical quality by standard metallographical procedure. The samples were encapsulated into Cu–Fe–Ni containers (made of nearly the same alloy which was under study), wrapped in Ta foil, and sealed in silica tubes under purified Ar atmosphere. The use of the containers guarantees that the chemical composition of the specimen was not changed during thermal treatment. The samples were subsequently annealed at 1373 K for 24 h in order to remove the mechanical stresses, which could be built up during cutting and polishing procedures and which could affect the diffusion behaviour. After the pre-annealing the blanc surface was slightly chemically polished with Syton colloidal silica slurry to remove the effects of thermal etching. Table 1. Alloy compositions in wt. % Alloy Fe Ni Cu #1 12 68 20 #2 25 50 25 #3 10 45 45 #4 28 37 35 #5 45 40 15 #6 6 24 70 #7 75 20 5 #8 10 80 10 Penetration profile measurements The radiotracer Cu (half-life 12.7 hours) was produced by neutron irradiation of a cupper chip at the research reactor in Geesthacht, Germany. The nuclear reaction was used. Its initial specific activity was about 500 MBq/mg. Due to short life-time of the isotope it was delivered to the lab in Munster in few hours after irradiation. The activated chip was dissolved in nitric acid and then diluted with double-distilled water. 63 64 29 29 Cu(n, ) Cu γ The radiotracer Fe (half-life 45 days) was also produced by neutron irradiation of iron powder at the research reactor in Geesthacht according to the nuclear reaction . The activated isotope material was dissolved in 30% HCl and then further diluted with double-distilled water. 58 59 26 26 Fe(n, ) Fe γ The radiotracer Ni (half-life 100 years) was purchased in form of a HCl solution and dissolved with double-distilled water. Each radiotracer (Cu, Fe, or Ni) was dropped as a dilute acid solution on the polished face of the samples. The samples were again encapsulated into containers, which were then wrapped into Ta foil, to avoid any undesirable contamination. The specimens were sealed in silica tubes under purified Ar atmosphere and subjected to the diffusion anneals at T = 1271 K. The temperatures were measured and controlled with Ni–NiCr thermocouples with an accuracy of about ±1 K. After the diffusion anneal the samples were reduced in diameter (at least 1 to 2 mm) by grinding on a lathe to remove the effect of lateral and surface diffusion. The penetration profiles were determined by the precision grinding sectioning technique using special abrasive mylar foils. The radioactivity of each section was determined with high efficiency using a Packard TRI CARB 2500 TR liquid scintillation counter. The penetration profiles present the plots of the normalized activity of each sections (the activity divided by the weight of the section) against the penetration depth x. The latter was calculated from the weight loss of the sample with known geometry after each sectioning step. The uncertainties of individual points on the penetration profiles, stemming from the counting procedure and the errors of the depth determination, were estimated to be typically less than 10 %. 0 5 10 15 20 25 Ni Fe Cu42.8Fe10.8Ni46.4