## 5 Conclusions  
The present capabilities of the RCI experimental setup we developed, which is located at the ESRF, allowed us to show that a long-range distortion and interaction takes place  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Distance \(D\) (\(\upmu\)m)** & **Calculated \(\alpha\) (\(\upmu\)rad)** & **Experimental \(|\alpha|\) (\(\upmu\)rad)** \\ \hline
50 & 10 & 10 \\
105 & 4.7 & 3.8 \\
140 & 3.6 & 4.4 \\
200 & 2.5 & 3.3 \\
240 & 2.1 & 2.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Reported \(\alpha\) values for different distance D, as measured in Figure 3 and as calculated by the formula in the text.  
Figure 7: The dashed curve corresponds to \(|\alpha|\) proportional to \(1/D\), with the point \(D=50\)\(\upmu\)m, \(\alpha=10\)\(\upmu\)radians being, by construction, on the curve. The circles are the measured modulus of \(\alpha\) for five pairs of dislocations with opposite Burgers vectors that we can observe in Figure 3.  
between non-mobile parallel dislocations located a distance \(D\) (nearly horizontal in the image) and exhibits opposite Burgers vectors in a 4H-SiC crystal. This distortion is observable for a range of macroscopic distances (\(D\)-50-250 \(\upmu\)m).  
Our phenomenological model rests on a distortion coupling the non-mobile dislocations and allowing a reduction in the total energy. The main physical idea is that the region displaying an average angle \(\alpha\) with respect to the matrix and lying between the dislocations with opposite Burgers vectors  
1. permits the reduction in the extension of the distortion field associated with the dislocations, and consequently the energy of the dislocation pair,
2. introduces an extra energy associated with subgrain boundary-like areas.  
For each distance \(D\) between the dislocations, there is an angle \(\alpha\) that minimises the energy of the whole configuration.  
The simple model resulting from the above considerations has only one parameter: the average angle \(\alpha\). It leads to a dependence of this average angle \(\alpha\)-\(1/D\), which is in fair agreement with the experimental results. This mechanism should modify the attractive force and thus potentially the dislocation dynamics.  
This original experiment mainly provides the angular distortion of the reflecting planes along the diffraction vector (vertical for all the presented images) and, as such, opens the way to further diffraction experiments aimed at measuring the complete two-dimensional distortion and at visualising in this way the long-range interactions between dislocations that are not located in nearly the same horizontal plane of the image. This should provide a more complete view of the distortion and lead to further comparisons with more sophisticated theoretical calculations.  
Conceptualization: A.D., T.N.T.C. and J.B.; methodology: T.N.T.C. and C.D.; software: T.N.T.C.; validation: T.N.T.C., C.D. and A.D.; formal analysis: D.C., J.B. and C.D.; investigation: T.N.T.C.; resources: T.N.T.C.; data curation: T.N.T.C.; writing--original draft preparation: J.B.; writing--review and editing: C.D. and J.B. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the French National Research Agency (ANR) under the \"Investissements d'avenir\" programs: ANR-10-AIRT-0005 (IRT-NANOELEC).  
Not applicable.  
The data supporting the reported results are stored at the ESRF.  
The authors declare no conflict of interest.