S. K. Halder

An x‐ray diffraction study of lattice imperfections in cold‐worked silver‐gallium (α‐phase) alloys

X‐ray diffraction profiles from four compositions of α‐phase Ag‐Ga alloys containing 3.55, 9.45, 13.05, and 15.90 at.% of solute gallium have been recorded in a Geiger‐counter x‐ray diffractometer for both the cold‐worked and fully annealed states of the samples, and a detailed analysis of the line shifts, line asymmetry, and Fourier line shapes has been performed considering recent improvements made in such studies. The line‐shift analysis from 111, 200, 220, and 311 reflections has shown the prominent effect of net stacking‐fault density α=α′−α″ (α′ and α″ being intrinsic and extrinsic fault densities, respectively) over the residual stresses and this has also been observed from the shifts in the lattice parameter values (Δahkl). The logarithmic dependence of α with the solute concentration X has been examined using the semiempirical expressions of the forms logα=logα0+K ‖ΔZ‖ X and logα=logα0+Kα[C/(1+C)]. Combining the results of all the methods of analysis, the individual stacking‐fault densities α′, α...

An X-Ray Line Broadening Analysis in the Vacuum-Evaporated Silver Films

An X-ray integral breadth analysis has been made for the 111, 200, 220, 311 and 222 diffraction profiles recorded on a Geiger counter X-ray diffractometer from the vacuum-evaporated thin films of silver in the range of thickness 580 to 2125 A. The analysis based on the methods of single and multiple order of reflection has yielded values for the effective particle sizes and non-uniform micro-strains in the films from a consideration of Gaussian, Cauchy and intermediate parabolic form of distribution, the Gaussian distribution being more favourable. The effective particle size values are found to be small and the strains quite appreciable and these effects which are the manifestations of lattice imperfections present in the films decrease very slowly with increasing film thickness. The dislocation density ρ calculated for the [111] direction from the particle size and strain values for the films above 1000 A thick is of the order of 10 11 cm/cm 3 comparable to that observed for the heavily deformed bulk ma...

An x‐ray diffraction study of lattice imperfection in cold‐worked FCC alloys. IV. Copper‐germanium (alpha‐phase)

X‐ray diffraction profiles from four compositions of α‐phase Cu‐Ga alloys with solute gallium at 3.40, 6.90, 10.85, and 15.00 at.% were recorded in a Geiger counter x‐ray diffractometer for both cold‐worked and annealed states of the samples. Detailed studies on the recorded profiles considering recent development in the analyses of line shift, line asymmetry, and Fourier line shape have been made in order to evaluate the microstructural parameters. Considerable influence of net stacking‐fault density α (=α′−α″) over the lattice parameter change and long‐range residual stresses in causing the changes in peak positions has been observed when the concentration of solute gallium is increased in the alloy system. An increased presence of intrinsic fault (density α′) over the extrinsic fault (density α″) has been found, while the twin fault (density β) is totally absent in the deformed structure analogous to the silver gallium (I) system. The logarithmic dependence of α with solute concentration X has been sat...

An x‐ray diffraction study on the microstructures of cold‐worked fcc Cu‐Ni‐Zn alloys

The state of cold work in the ternary Cu‐Ni‐Zn alloy system (fcc) has been investigated by x‐ray diffraction from a detailed analysis of the peak shift, peak asymmetry, and peak broadening. Cold working in the system produces an appreciable amount of intrinsic stacking faults which play the most important role in peak broadening as well as in shifting the positions of the diffraction profiles. For the observed peak shift, the other contributing factors (namely, lattice‐parameter change and long‐range residual stresses) are relatively small. Asymmetry in the profiles is due to the presence of a very small amount of extrinsic stacking fault, and deformation twins have been found to be totally absent. The estimations of domain size, rms strains, and the dislocation density in the alloys have been made from the peak‐broadening analysis, and the stacking‐fault energy for pure copper has also been evaluated and has been found to be comparable. The presence of the transitional solute Ni from 1 to 15 wt% has a ve...

An X-ray line profile analysis in vacuum-evaporated silver films

An X-ray Fourier line profile analysis from multiple-order and single-order reflections has been performed considering 111, 200, 220, 311 and 222 reflections recorded in a counter X-ray diffractometer from eight vapour-deposited thin films in the range of thickness 58-212 nm. Detailed analysis of line shift, line asymmetry and Fourier line shapes measurements have been found to yield large concentrations of growth twin stacking faults only in the thin film range with a total absence of intrinsic and extrinsic ones for the entire range. Measurements of the domain size, dislocation density, RMS strains and orientation factors were made, and their dependence on the film thickness investigated.

An X-ray diffraction profile study in silver films vapour-deposited on a rotating substrate with the axial centre at 44 degrees to the vapour direction

A detailed X-ray diffraction profile analysis on silver films (thickness approximately 32-248 nm), vapour-deposited on a rotating substrate with the axial centre at 44 degrees to the vapour direction, shows the presence of small coherent domain sizes ( approximately 76-305 AA), appreciable microstrains, small lattice parameter change ( approximately 3.5-2.0*10-3 for films <100 nm thick), residual compressive stress, ( sigma approximately 0.05-0.003*10-10 N m-2), appreciable growth or twin stacking fault concentration ( beta approximately 115-25*10-3) and large dislocation density ( approximately 8-1*1011 cm-2). The effects decrease with increasing film thickness and are comparable or slightly reduced in magnitude relative to the case for normal vapour incidence. The films, which were initially random, develop (111) orientation at higher thickness.

An X-ray determination of the thermal expansion of α-phase Ag–Ga alloys at high temperatures

The lattice parameters of four Ag-Ga alloys in the solid-solution range have been determined by X-ray methods in the temperature interval of 26-522°C using a Unicam 19 cm high-temperature powder camera. In all the cases the lattice parameters have been found to increase in a non-linear manner in the measured range of temperature and the relationship has been expressed in analytical form from the least-squares fitting of data. The linear thermal expansion coefficients have, however, been found to decrease with increasing temperature.

An X-ray determination of the thermal expansion of silver and copper-base alloys at higher temperatures. III. Ag–Ge and Cu–Ge

X-ray measurements of the lattice spacings in three Ag-Ge alloys in the temperature interval 30-595°C and in two Cu-Ge alloys in the temperature interval 25-611°C, in the solid-solution range, have been made with a Unicam 19 cm high-temperature camera. The measured lattice spacings have been found to increase non-linearly with temperature, this non-linearity being slightly enhanced for Cu-9.25 at.% Ge alloy. The dependence of the measured lattice spacings on temperature has been expressed in an analytical form (polynomial of second degree) from least-squares fitting of the data. The thermal expansion coefficient, α, for the alloys considered, in general, has been found to decrease linearly with increasing temperature (from ∼25 to ∼17 × 10-6°C-1), except for the greater germanium concentration (9.25 at.%) in copper solvent where the tendency is reversed.

An X-ray determination of the thermal expansion of silver and copper-base alloys at high temperature. II. Cu–Ga

X-ray measurements of the lattice parameters have been made in four Cu-Ga alloys in the solid-solution range using a Unicam 19 cm high-temperature camera in the temperature interval of 30-514 °C. The measured lattice parameters have been found to increase non-linearly with the temperature and this variation has been expressed in an analytical form from least-squares fitting. The linear thermal expansion coefficients have been found to decrease with increasing temperature in these alloys with a tendency to attain a nearly constant value at higher solute concentrations, and the decrease is rather slow compared to that observed earlier with Ag-Ga alloys over the same range of temperature.

Voigt profile analysis for particle size and strain determinations in cold-worked FCC alloys from a single reflection

The diffraction profiles for several cold-worked copper- and silver-base alloys have been analysed as Voigt profiles using the Voigt-profile data of Van de Hulst and Reesinck. The analysis has shown that the cold-worked profiles and the instrumental profiles also approximate to the Voigt nature. With this consideration the two Voigt parameters (Cauchy and gaussian) for the true diffraction profiles have been determined in a simple manner for the 111 and 200 reflections of the alloys concerned. The values of the effective particle sizes and strains derived from these parameters agree fairly well with the average values of those obtained from the multiple-order reflection methods for Voigt profiles, namely the Fourier and the Schoening. The present method thus appears to be helpful for the analysis of a single Voigt profile.