X-ray diffraction profiles from deformed metals

Abstract

Pure diffraction profiles have been obtained for several reflections from cold worked and partially annealed samples of spectroscopically pure aluminium and copper and four alloys containing aluminium and copper. Intensity distributions were determined with the help of crystal monochromated copper Kα radiations and a Geiger counter spectrometer manually operated and provided with scalars and dekatron counters. The observed line profiles were corrected for Kα2 overlap, thermal diffuse scattering, Lorentz and polarization factors, absorption and background error. A method has been developed for correcting for the background level from multiple measurements of the integral breadths of the line profiles at several assumed background levels. From the corrected line profiles, pure diffraction line profiles were recovered by the method due to Stokes. The R(x) test described by Mitra when applied to these pure diffraction profiles showed that none of them belonged to either Cauchy or Gauss type. Since many experimental R(x) curves were found to terminate at about x = 2, another function, the R'(x) function, has been developed. This function assumes the theoretical curves also to be truncated at the same ranges as the experimental curves. R'(x) tests also showed that the pure diffraction profile was neither of Cauchy nor of Gaussian type. The parameter γ = μ4/μ22, μ4 and μ2 being fourth and second central moments respectively of the profiles, has been evaluated for all the curves, and comparison with standard statistical tests showed that most of the curves belonged to Pearson types VII and IV while some might also be Gaussian. The results indicate that the intensity distribution curves can be expressed in terms of a maximum number of four unknown parameters and hence determination of the first four moments only is expected to lead to the proper expression for the line profile.