A Systematic Evaluation of Strain Broadening from Stretched Aluminium Foils Using a Convolution-fitting Approach to Line Profile Analysis

A systematic investigation has been carried out to determine how the shape of X-ray line profiles from stretched aluminium foils is influenced by increasing levels of induced residual strain. Macroscopic residual strains from 4% to values close to the breaking point (220%) were induced by stretching annealed foils beyond the yield point into the plastic deformation region and then releasing the applied stress. X-ray data were collected using a Siemens D5000 diffractometer fitted with a fine focus Cu X-ray tube and a graphite post-monochromator set for CuKa. In this analysis we have synthesised and fitted the instrument and broadened line profiles using a fundamental parameters approach to profile analysis. Parameters defining the instrument profiles 1(20), such as the receiving slit width and the slit length, were obtained by fitting the profiles from annealed aluminium foils. The observed broadened profiles B(28) were then fitted as a convolution of a Voigt profile V(28) and the fitted instrument profile 1(28), B=I*V=I*L*G where V(29) is a convolution of a Lorentzian profile L(20) and a Gaussian profile G(28). Results are presented to show that size-strain broadening is modelled well by the Voigt function. For each specimen, the fitted widths of the Gaussian components tend to comply with a tan0 dependence. Surprisingly, the Lorentzian widths also tend to follow a tan9 dependence rather than a se& dependence as would be expected for pure size broadening. The mean rms microstrain &rn,s within each of the foils increases as the macroscopic residual strain E increases following a power law of the form &rms = K&n where n=1/3 fits. Some anisotropy in the rms strain with l&l was evident in the results.