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Figure 5
Two-point Pearson autocorrelations of the interfacial orientations within the specimen x–z plane. The spatial dimension measures 650 µm along each axis. The temperatures and times are as follows: (a) 1222.8 K (3020 s), (b) 1218.2 K (3300 s) and (c) 1213.5 K (3580 s). The Pearson correlation coefficient is undefined (white regions) when the [{\bf r}]-dependent standard deviations [Sun et al., 2017BB89, equations (28), (29)] of interfacial orientations are zero. More generally, correlations are only valid when the underlying distributions have finite second moments. White–black (i.e. solid–liquid) interfaces in the segmented images (inset) were those used to compute the two-point Pearson correlations (see also Fig. S3). The scale bar measures 100 µm in each inset. (d) Superimposed two-point Pearson correlations along the white line in (c), see text for details. Grey curves correspond to those time-steps (correlation maps not pictured) in between times (a), (b) and (c). The distinction between `short'- and `long'-range autocorrelations in (d) is clarified in Appendix A[link].

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ISSN: 2053-2733
Volume 75| Part 2| March 2019| Pages 281-296
https://doi.org/10.1107/S2053273318017114
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