Stacking faults and twin boundaries in fcc crystals determined by x-ray diffraction profile analysis

A systematic procedure is developed to evaluate the density of planar defects together with dislocations and crystallite or subgrain size by x-ray line profile analysis in fcc crystals. Powder diffraction patterns are numerically calculated by using the DIFFAX software for intrinsic and extrinsic stacking faults, and twin boundaries for the first 15 Bragg reflections up to 20% fault density. It is found that the Bragg reflections consist of five subreflection types categorized by specific selection rules for the hkl indices in accordance with the theory of Warren [Prog. Met. Phys. 8, 147 (1959)]. It is shown that the profiles of the subreflections are Lorentzian-type functions. About 15 000 subreflections are evaluated for their full widths of half maxima and their positions relative to the exact Bragg angle. These values are parametrized as a function of the density and type of planar faults. A whole profile fitting procedure, previously worked out for determining the dislocation structure and crystallite size distributions, is extended for planar fault by including these data into the software. The method is applied to evaluate twin densities in nanocrystalline and submicron grain-size copper specimens. It is found that twinning becomes substantial under a critical crystallite or subgrain size of about 40 nm, in accordance with other observations.