Erratum: Anodes sliced with ions

Abstract

nature materials | VOL 5 | AUGUST 2006 | www.nature.com/naturematerials the platinum wire. Triangulation (a method that allows fi nding a position by combining three others) between the positions of the incident beam, the platinum wire and the shading of the diff racted image allows the identifi cation of the portion of specimen that produces the diff raction signal. In addition, the diff raction spots provide the local lattice spacing and lattice-spacing distribution. Th e spatial resolution is still far from what TEM provides routinely, but it is close to what can be achieved today [1][2][3][4][5]6 .Th e fundamentals of plastic deformation of crystals containing a dislocation cell structure were developed more than twenty years ago and are described in the so-called composite model 7 . Th e basic idea is that the cell-wall regions of high dislocation density are harder than the cell-interior regions of low dislocation density. Under the action of an externally applied stress, both cell walls and cell interiors are assumed to deform compatibly. Th e deformation induces internal stresses of the same sign as the external stress in the cell walls, and of opposite sign (or 'back') in the cell interiors. 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.Th e merit of the work by Levine and co-workers 5 lies in the fact that, in their X-ray-diff raction experiments, the diff racted signals are highly spatially resolved and in a one-to-one correlation with welldefi ned regions of submicrometre size in the cell interiors of the crystal. Th us, the authors could conclude from the shift s of the X-ray-diff raction profi les obtained from small local regions, that long-range internal back-stresses prevailed in the cell interiors of their specimens that had been deformed in tension or in compression. Moreover, the internal stresses could be assigned unambiguously to one particular cell-interior region from which the diff racted intensity came. Another interesting new feature of these fi ndings is that the magnitude of the internal back-stresses varied markedly from one cell interior to the next, indicating a signifi cant fl uctuation. Th is observation provides further direct evidence that fl uctuations are an inherent fea...