Dislocation structure and twinning are much more complicated in Zr, Ti and Mg, and its alloys than in fcc materials because: (i) there are three different possible Burgers-vector types instead of one [1,2], (ii) at least 11 different slip systems can operate in principle [1,2], (iii) 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 [3,4], and (iv) some slip systems may not be activated because of the large variation of the critical resolved shear stress from one slip system to another [5]. It will be shown that the standard method to evaluate the effect twinning and faulting in fcc crystals on X-ray line broadening [6,7] cannot be applied for twinning on the above slip systems in hexagonal crystals. The reason for this is that, unlike in fcc materials where twinning and faulting occures on the close packed planes with the repetition of three normal to these planes, in hcp crystals, especially for the planes listed above, the crystal cannot be built up by a similar simple repetition in the normal direction. Therefore, the method developed earlier for fcc crystals [8] has been extended for hcp materials. The scattered intensity from twinned hexagonal crystals has been calculated in reciprocal space by using the DIFFaX [9] free software. A periodic behaviour of scattering has been observed which is used to simplify the numerical procedure in determining twinning together with dislocation densities and crystallite size in hcp-s. It is shown that in hot worked commercial purity Ti {10.2} tensile twins are by far more frequent than other twins. In tensile deformed Mg we found {10.1} compressive twinning whose frequency decreases with the temperature of deformation. In compression deformed Zr {10.2} tensile twinning is observed where twinning frequency decreases with deformation.

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1. Twinning together with dislocations and crystallite size in hexagonal materials determined by X-ray line profile analysis