Evaluation of Clusters in a RPV Weld 381
Figure 8. Material irradiated to 2.0×1023n/m2, laser pulsed ana- lysis. a: Nearest neighbor distribution for Ni and Mn for first- and eighth-order nearest neighbors. b: Relative number of nonrandom clusters for first- and eighth-order dependent on Nmin. dmax is 0.5nm for N = 1 and 0.75nm for N = 8.
decreasing the possibility of identifying small clusters. For this material the small clusters are of interest and hence the use of higher orders seems to be disadvantageous.
Influence of Density Variations
The atom density within a data set varies, due to crystal- lographic effects (i.e., trajectories being altered at the edges of the atomic planes) (Stephenson et al., 2007; Gault et al., 2012). The MSM is affected by this effect as it is using distances to define clusters. Close to poles, the density is much lower than elsewhere, see Figure 9a. The expected density with a detection efficiency of 37% is 31 atoms/nm3 for bcc iron. Histograms of the density distributions for one laser analysis and one voltage analysis can be seen in Figure 9b. In general, the density distributions are wider when using laser pulsing. The distribution will also differ depending on which crystallographic directions are included within the field of view. A part of the contribution to low density in Figure 9b comes from the edges of the analyzed volume. There is a large spread in the density, up to around 60 atoms/nm3, in some cases up to 75 atoms/nm3 or more. In regions of low density, the cluster parameter dmax will
tend to be too small, and some small clusters might bemissed in these regions. In order to avoid this, Stephenson et al. (2007) excluded volumes of low density at poles and high- density volumes around these low-density volumes by the use of 100 NN distances. Clusters in high-density regions might be too large or too many due to dmax being too large,
that is random fluctuations in these regions being identified as clusters. Thus, also high-density volumes can be removed in order to improve the cluster analysis. In this paper, iso- density surfaces are used for their simplicity, with a voxel size of 2×2×2nm3 (and delocalization of 3×3×1.5nm3)in order to make the surfaces smooth. The effect of removing the regions can be seen in Figure 10. A full analysis is com- pared with an analysis where all volumes with a density smaller than 25 atoms/nm3 were removed and one where all volumes of density <25 and >55 atoms/nm3 were removed. The limits were put so that the volume remaining should still be large, in this case the number of ions used decreased by merely 15%. The NND in Figure 10a shows a small effect from removing the low-density regions. In Figure 10b the influence on the choice of Nmin is shown for a dmax of 0.50nm. Removing the volumes of high density makes it possible to choose a smaller Nmin and thereby detect smaller clusters without the risk of identifying random fluctuations in the matrix composition as clusters. With a level of toler- ance of 0.995, Nmin could be decreased from 16 to 13 owing to the removal of high-density regions.
DISCUSSION
The MSM method has been used in order to identify fine- scale clustering in irradiated RPV welds. The results of the method are strongly dependent on the choice of parameters, and the parameters need to be adjusted dependent on the features studied, which is important to consider when com- paring different analyses and different studies. Here, some approaches to the choice of parameters are studied. Using the relative number of nonrandom clusters (Fig. 5), with a
threshold value close to 1, is a relatively easy and fast way of finding a reasonable value for dmax. The elegant methods proposed by Stephenson et al. and Jägle et al. require some more advanced analysis of the data set, fitting CSR dis- tributions to the first-order NNDs that are not bimodal for small and diffuse clusters. The simplified version of the method proposed by Jägle et al. gave similar values for the parameters as the comparison with isoconcentration sur- faces and the usage of relative number of nonrandom clusters. A sensitivity analysis, investigating the impact on the
cluster number density to small changes in the parameters, was performed for the two irradiated materials. According to the analysis above, dmax was set to 0.50nm and Nmin to 18, that is with a low tolerance to random clusters (see Fig. 5). For the sensitivity analysis, dmax was varied by ±0.05nm and Nmin was varied by ±2. These variations are regarded as
moderate and represent reasonable parameters. For the high fluence material, the cluster number density was found to be 7.7 ×1023 clusters/m3 (with dmax = 0.50nm and Nmin = 18). The impact on the number density of changing the para- meters within the stated ranges was small. At most, the number density decreased by 7% or increased by 5%. However, the cluster number density of the low fluence
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