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Bragg coherent X-ray diffractive imaging is a cutting-edge method for recovering three-dimensional crystal structure with nanoscale resolution. Phase retrieval provides an atomic displacement parallel to the Bragg peak reciprocal lattice vector. The derivative of the displacement along the same vector provides the normal strain field, which typically serves as a proxy for any structural changes. In this communication it is found that the other component of the displacement gradient, perpendicular to the reciprocal lattice vector, provides additional information from the experimental data collected from nanocrystals with mobile dislocations. Demonstration on published experimental data show how the perpendicular component of the displacement gradient adds to existing analysis, enabling an estimate for the external stresses, pinpointing the location of surface dislocations, and predicting the dislocation motion in in situ experiments.
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This content will become publicly available on June 1, 2026
A shape derivative algorithm for reconstructing elastic dislocations in geophysics
Not AvailableWe consider the inverse problem of determining an elastic dislocation that models a seismic fault in the quasi-static regime of aseismic, creeping faults, from displacement measurements made at the surface of Earth. We derive both a distributed and a boundary shape derivative that encodes the change in a misfit functional between the measured and the computed surface displacement under infinitesimal movements of the dislocation and infinitesimal changes in the slip vector, which gives the displacement jump across the dislocation. We employ the shape derivative in an iterative reconstruction algorithm. We present some numerical test of the reconstruction algorithm in a simplified 2D setting.
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- PAR ID:
- 10648650
- Publisher / Repository:
- Springer
- Date Published:
- Journal Name:
- Research in the Mathematical Sciences
- Volume:
- 12
- Issue:
- 2
- ISSN:
- 2522-0144
- Subject(s) / Keyword(s):
- Elastic dislocation Slip Inverse problem Shape derivative Iterative reconstruction Elastostatics Discontinuous Galerkin Seismic fault
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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