Fig. 8
From: On the three-dimensional spatial correlations of curved dislocation systems
Quantities relevant to the certainty of the correlation calculations. For reference, the correlation functions are shown again in (a). The empirical mean of the coarse density product ρiρj normalized by the maximum value is shown in (b), and the standard error of the correlation calculation in (c). When the average density product (b) becomes small, this leads to a significantly increased standard error in the calculation, as it appears in the denominator of the correlation calculation of Eqs. (40-41). Notably, several regions of the separation space on the plane are seen to have standard error values comparable to the magnitude of the correlation, namely in the unconnected directions (the y-axis in the screw-screw case and the x-axis in the edge-edge case). All quantities shown are calculated for the coarsest calculation (L=162 nm)