Line Profiles Caused by Planar Faults

Abstract

The planar faults in crystalline materials yield characteristic broadening of X-ray line profiles. The diffraction peak shape caused by intrinsic and extrinsic stacking faults and twin boundaries formed on close packed {111} planes in face centered cubic (fcc) crystals are calculated. The Bragg reflections consist of subreflections that can be categorized by specific selection rules for the hkl indices. The breadth and the position of the subreflections relative to the exact Bragg angle depend on their indices. For instance, if the sum of indices of a subreflection is a multiple of three, neither the position nor the breadth of this peak is influenced by planar faults. Other subreflections are broadened and shifted simultaneously due to intrinsic and extrinsic stacking faults. For both fcc and hexagonal close packed (hcp) crystals each subreflection caused by twin boundaries is a sum of symmetric and antisymmetric Lorentzian functions. The latter profile component is caused by the interference between the radiations scattered from the parent and twinned lamellae in the crystal. The antisymmetric Lorentzian function yields a shift of the subprofile center. For fcc materials this displacement of peak position is marginal since twin boundaries are formed on close packed {111} planes; however in hcp crystals, where twinning usually occurs on pyramidal planes, this effect should be taken into account in the line profile evaluation. The effect of anti-phase boundaries on line profiles of superstructure reflections for Cu3Au is also discussed in this chapter.