X-ray line-broadening study of the dislocation cell structure in deformed [001]-orientated copper single crystals

Erratum: Anodes sliced with ions

“…Th is observation provides further direct evidence that fl uctuations are an inherent feature in deformed microstructures, in line with earlier work of others [9][10][11] . Finally, Levine and co-workers could also show that the average diff raction profi les, obtained from larger volumes of the same crystal, exhibit characteristic asymmetrically broadened line profi les, similar to the earlier observations 7,8 . All these facts confi rm that the principles of the composite model are correct.…”

“…Th e X-rays probe the lattice strains due to dislocations and, at the same time, the superimposed external and internal stresses. Th e results of early TEM observations and X-ray diff raction experiments on deformed single crystals of copper were consistent with the composite model 7,8 , and revealed the presence of long-range internal stresses within the cell structure of the crystals, as shown schematically in Fig. 1.…”

“…In particular, it could be shown that the X-ray-diff raction line profi les exhibited a characteristic asymmetric line broadening. It can be shown that this is a direct consequence of the presence of long-range internal stresses 7,8 . Nevertheless, some questions remained open, partly related to the fact that the results obtained in these earlier X-ray studies were not spatially resolved but represented average values from larger regions.…”

The effect of cooling rates on the microstructure and mechanical properties of thermo-mechanically processed Ti–Al–Mo–V–Cr–Fe alloys

“…Other factors such as dislocation density, slip activity [32], and the presence of stacking faults can also affect the shape and/or position of diffraction peaks [27]. Warren [39], Randle and Engler [40] developed the XRDLPA approach for the analysis of the microstructure, which was later followed by others [28,[41][42][43][44][45] with some modifications making it possible to determine the crystallite size and microstrain in materials reliably. Similarly to [16,23], the modified Rietveld [46] method has been used in order to characterise microstructures in this investigation.…”

“…For materials containing two or more phases, it generally is more convenient to use XRD as the peaks of the constituent phases appear distinctly in the profile. Several XRDLPA investigations have been performed on steels [22][23][24][25][26], Cu [27][28][29] and Zr [30][31] alloys. In contrast, a fewer number of investigations using the XRDLPA have been performed on Ti alloys [32][33][34].…”