B.L Averbach

X-ray measurements of dislocation density in deformed Copper and Aluminum single crystals☆

Abstract Measurements of double crystal rocking curve broadening were used to estimate the dislocation density in annealed and plastically strained single crystals of copper and aluminum. The deformation was carried out at room temperature. By using several characteristic radiations, the total diffraction broadening was resolved into components which depended separately on average lattice tilting, localized bending, dislocation strain and subgrain size. Dislocation densities of about 108/cm2 and subgrain sizes of about 10−4 cm were obtained for the annealed crystals; these values changed relatively little with shear strains up to 10−3 in the easy glide region. In the strain-hardening range, however, the dislocation densities increased rapidly, reaching a magnitude of 1010–1011/cm2 with plastic shear strains in the range 0.3–0.5. The corresponding subgrain sizes decreased to approximately 10−5 cm, and this was interpreted as indicating the formation of essentially randomized dislocation arrays at large strains. For severely strained crystals, evidence was also found for a small number of piled-up arrays with 4–6 dislocations in each pile-up.

Diffusion of nickel into iron

The diffusion of nickel into iron was measured in the temperature range 600 to 1050 deg C. Radioactive Ni/sup 6//sup 3/ was used as the tracer element; the surface-decrease and the tracer element; the surface-decrease and the residualactivity sectioning methods were employed. The diffusivity below the Curie temperature was observed to be lower than that expected from an extrapolation of the diffusion data for paramagnetic alpha-iro-n. The diffusion coefficients may be expressed as follows (in cm/sup 2//sec): gamma-iron, D = 0.77 exp (-67,000/RT); paramagnetic alpha-iron above 800 deg C, D = 1.3 exp (-56,000/ RT); and ferromagnetic alpha-iron below 680 deg C, D = 1.4 exp (-58,700/RT). The anomalous decrease in the diffusion coefficient starts at about 800 deg C, somewhat above the Curie temperature, and is thought to be associated with the effect of short range magnatic order on the formation energy of vacancies. (auth)

Self and interdiffusion in aluminum-zinc alloys☆

Abstract The self-diffusion rates of radioactive Zn65 and the interdiffusion rates have been determined in f.c.c. aluminum-zinc alloys. The self-diffusivity of zinc D Zn ∗ increases as the zinc content is increased, while the thermodynamic driving force decreases with increasing zinc content until a minimum is reached at about 38 at. % Zn, just above the miscibility gap. As a result of these two opposing trends, the inter-diffusion coefficient D changes only slightly with variation in composition. The values of D follow the relationship: D = X Al D Zn ∗ (1 + d ln ƒ Zn dl ln X Zn ) , where XAl and XZn are the respective atomic fractions, and ƒ Zn is the thermodynamic activity coefficient of zinc. The lack of an observable contribution of D Al ∗ to the interdiffusion coefficient indicates that the self-diffusivity of aluminum is considerably smaller than that of zinc over the ranges of temperature and composition studied.

Self-diffusion and interdiffusion in gold-nickel alloys

Abstract Measurements are described on the self-diffusion and interdiffusiori coefficients in gold-nickel alloys as a function of composition and temperature. These data are combined with the thermodynamic properties of the gold-nickel system to test the validity of the Darken equation: D = (X 1 D 2 ∗ + X 2 D 1 ∗ ) ( 1 + d ln ƒ 1 d ln X 1 ). This relationship is found to hold within the experimental accuracy of the measurements, and the results may be considered to demonstrate the concept that the chemical potential gradient is the driving force for the chemical diffusion process. The influence of the thermodynamic factor ( 1 + d ln ƒ 1 d ln X 1 ) on the activation, energy for interdiffusion is also shown.

Formation of modulated structures in copper-nickel-iron alloys☆

Abstract By means of X-ray diffraction, the formation of modulated structures with periodic variations in composition due to a simple interchange of atoms has been studied in copper-nickel-iron alloys as a function of composition, temperature and time. The results are compared with two models suggested for this type of “exchange transformation”. The reaction characteristics seem to favor a kinetic model rather than the Guinier model. The activation energies for the transformation, evaluated at the first detectable stage and for a later stage, show that both these stages are diffusion-controlled inside as well as outside the spinodal. This indicates that the spinodal is of no real significance with regard to the nucleation process. The variation with temperature and composition of the first wavelength to form in the modulated structure is in agreement with the kinetic model.

The structure of lithium-magnesium solid solutions—I: Measurements on the Bragg reflections

Abstract Lattice parameters have been measured at 20°C and −183°C for seven BCC Li-Mg alloys. There is a strong negative deviation from Vegards law and a minimum in the parameter-composition curve at 65 atomic per cent Li. Two measurements have been made on martensitic FCC Li-Mg alloys at −183°C, and a negative deviation from Vegards law is also indicated for these alloys. In the HCP solid solutions of Li in Mg. both the a and c axes decrease with increasing Li content, while the c a ratio decreases from 1.6235 for pure Mg to 1.608 at 18.4 atomic per cent Li (the α α + β phase boundary). The presence of local static displacements of the atoms from the sites of the average lattice has been demonstrated from measurements of the Bragg intensities at 295°K and 90°K. These intensity measurements have also been used to derive values of the Debye characteristic temperature for five BCC alloys.

X-ray measurements of local atomic arrangements in aluminum-zinc and in aluminum-silver solid solutions

Abstract The X-ray diffuse scattering from Al-Zn solid solutions has been measured at equilibrium above the solubility temperature. Observations were made for compositions ranging from 5 to 50 atomic per cent zinc at 400°C, and at 300 and 500°C for a 10 atomic per cent zinc alloy. The diffuse scattering exhibits a strong small-angle component, and this has been interpreted in terms of Zn and Al-rich clusters. The excess of like neighbors does not appear to extend beyond the first shell of atoms, and the average nearest neighbor excess has been measured. The diffuse scattering from an Al-10 atomic per cent Ag solid solution at 540°C has also been measured, and a similar clustering has been observed. The quasi-chemical theory is used to compare the X-ray results with the measured thermodynamic data and an apparent agreement is obtained.

Grain-boundary energies in gold-copper alloys☆

Abstract The ratio of grain-boundary to surface energy has been determined as a function of composition in the gold-copper system. From interferometric measurements of the boundary groove angles in specimens thermally etched at 850°C, the following average grain-boundary to surface-energy ratios were obtained: 0.25, 0.28, 0.34, 0.42, 0.37, and 0.36 at 0, 20, 40, 60, 80, and 100 at. % copper, respectively. Existing data for the surface energies yield 370, 320, 310, 390, 430 and 590 erg cm −2 , respectively, for the absolute grain-boundary energies. A calculation is included of the boundary adsorption corresponding to this energy variation, and an estimate is made of the minimum number of atoms required at the grain boundary to accommodate the calculated absorption.

Local atomic arrangements in gold-nickel alloys

Abstract The local atomic arrangements in gold-nickel alloys are determined as a function of composition by observations of diffuse X-ray scattering. Measurements are made at − 190°C on alloys quenched from above the solubility gap, there being experimental evidence to show that the high temperature atomic configurations can be retained on quenching. The X-ray data reveal that these alloys exhibit a preference for unlike neighbors above the solubility temperature and have short range order analogous to that in copper-gold alloys. The sizes of the atoms in the solid solutions are also measured from the diffuse scattering. The gold atom in solution is smaller than in the pure metal, but larger than the average atomic dimension calculated from the lattice parameter of the solution. Correspondingly, the nickel atom in solution is larger than in the pure metal, but smaller than the average atomic dimension of the solution. Moreover, the size of each atom varies with the composition of the solution.

X-ray and calorimetric investigations of cold working and annealing of a gold-silver alloy

Abstract Calorimetric and X-ray diffraction line-broadening measurements were carried out on samples of a 75Au–25Ag (weight per cent) alloy deformed by filing and annealed at various temperatures up to 500°C. Stored energy, hardness, subgrain size, local strain, and short-range order determinations were made. It appears that most of the stored energy is associated with the presence of subboundaries; a small fraction of the energy is attributable to a reduction in the short-range order and a negligible amount is stored in the local elastic distortions. The recovery process involves a substantial reduction of the local strains and a small increase in the subgrain size in this alloy. Recrystallization appears to involve a removal of the low-angle boundaries and the complete elimination of the local strains.