The effect of twinning and faulting on X-ray line broadening is worked out theoretically to a large extent for the close packed planes in fcc crystals [1-6]. Profiles of faulted or twinned crystals consist of sub-profiles which satisfy specific conditions for the hkl indices. Especially in fcc crystals, these conditions are that: (i) planar faults affect line profiles if, and only if: h+k+l≠3m, and that (ii) for a particular {hkl} reflection both, the FWHM and the shifts of sub-profiles are strictly proportional to |h+k+l| [1], where m is an arbitrary integer [3]. The profile function of a specific sub-profile corresponding to twins or stacking faults can be shown to be the sum of a symmetrical and an antisymmetrical Lorentzian function [5,6]. In fcc crystal faulting or twinning occures on the close packed {111} planes which repeat periodically in the directions normal to the planes. In hexagonal materials, especially in titanium, zirconium, magnezium ant their alloys the dislocation structure and twinning are much more complicated than in fcc metals: (a) there are three different possible Burgers-vector types instead of one [7,8], (b) at least 11 different slip systems can operate in principle [7,8], (c) there are a variety of twinning systems, e.g., {10.1}<10.-2> and {11.2}<11.-3> compressive twins and {10.2}<10.-1> and {11.1}<-1-1.6> tensile twins [9], and (d) some slip systems may not be activated because of the large variation of the critical resolved shear stress from one slip system to another [9]. In hexagonals the crystal cannot be built up by a similar simple repetition in the normal directions to these planes. In a previous paper a numerical method was developed to give the breadths and shifts of sub-profiles as a function of fault or twin densities [10]. This procedure is extended for hexagonal crystals. The outline of the theoretical basis and a few specific applications will be presented here.

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1. Twinning in coarse grain and nanocrystalline Zr, Ti and Mg determined together with dislocations and crystallite size by X-ray line profile analysis