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Register a new userA tunable multi-color rainbow filter for improved stress and dislocation density field mapping in polycrystals using x-ray Laue microdiffraction
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White beam x-ray Laue microdiffraction allows fast mapping of crystal orientation and strain fields in polycrystals, with a submicron spatial resolution in two dimensions. In the well crystallized parts of the grains, the analysis of Laue spot positions provides the local deviatoric strain tensor. The hydrostatic part of the strain tensor may also be obtained, at the cost of a longer measuring time, by measuring the energy profiles of the Laue spots using a variable-energy monochromatic beam. A new Rainbow method is presented, which allows measuring the energy profiles of the Laue spots while remaining in the white-beam mode. It offers mostly the same information as the latter monochromatic method, but with two advantages : i) the simultaneous measurement of the energy profiles and the Laue pattern; ii) the rapid access to energy profiles of a larger number of spots, for equivalent scans on the angle of the optical element. The method proceeds in the opposite way compared to a monochromator-based method, by simultaneously removing several sharp energy bands from the incident beam, instead of selecting a single one. It uses a diamond single crystal placed upstream of the sample. Each Laue diffraction by diamond lattice planes attenuates the corresponding energy in the incident spectrum. By rotating the crystal, the filtered-out energies can be varied in a controlled manner, allowing one to determine the extinction energies of several Laue spots of the studied sample. The energies filtered-out by the diamond crystal are obtained by measuring its Laue pattern with an other 2D detector, at each rotation step. This article demonstrates the feasibility of the method, and its validation through the measurement of a known lattice parameter.
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We propose a novel data-driven approach for analyzing synchrotron Laue X-ray microdiffraction scans based on machine learning algorithms. The basic architecture and major components of the method are formulated mathematically. We demonstrate it through typical examples including polycrystalline BaTiO$_3$, multiphase transforming alloys and finely twinned martensite. The computational pipeline is implemented for beamline 12.3.2 at the Advanced Light Source, Lawrence Berkeley National Lab. The conventional analytical pathway for X-ray diffraction scans is based on a slow pattern by pattern crystal indexing process. This work provides a new way for analyzing X-ray diffraction 2D patterns, independent of the indexing process, and motivates further studies of X-ray diffraction patterns from the machine learning prospective for the development of suitable feature extraction, clustering and labeling algorithms.
Micro-Laue diffraction and simultaneous rainbow-filtered micro-diffraction were used to measure accurately the full strain tensor and the lattice orientation distribution at the sub-micron scale in highly strained, suspended Ge micro-devices. A numerical approach to obtain the full strain tensor from the deviatoric strain measurement alone is also demonstrated and used for faster full strain mapping. We performed the measurements in a series of micro-devices under either uniaxial or biaxial stress and found an excellent agreement with numerical simulations. This shows the superior potential of Laue micro-diffraction for the investigation of highly strained micro-devices.
In an interesting recent paper [1] (A. Acharya, Stress of a spatially uniform dislocation density field, J. Elasticity 137 (2019), 151--155), Acharya proved that the stress produced by a spatially uniform dislocation density field in a body comprising a nonlinear elastic material may fail to vanish under no loads. The class of counterexamples constructed in [1] is essentially $2$-dimensional: it works with the subgroup $mathcal{O}(2) oplus langle{bf Id}rangle subset mathcal{O}(3)$. The objective of this note is to extend Acharyas result in [1] to $mathcal{O}(3)$, subject to an additional structural assumption and less regularity requirements.
The application of harmonic expansions to estimate intra-grain stress distributions from grain-averaged stress data is presented that extends the capabilities of the open source code, MechMonics. The method is based on using an optimization algorithm to determine the harmonic expansion weights that reduce the violation of equilibrium while maintaining prescribed grain-averages. The method is demonstrated using synthetic data generated for uniaxial extension of a virtual polycrystal with the mechMet code.
Plastic deformation mediated by collective dislocation dynamics is investigated in the two-dimensional phase-field crystal model of sheared single crystals. We find that intermittent fluctuations in the dislocation population number accompany bursts in the plastic strain-rate fluctuations. Dislocation number fluctuations exhibit a power-law spectral density $1/f^2$ at high frequencies $f$. The probability distribution of number fluctuations becomes bimodal at low driving rates corresponding to a scenario where low density of defects alternate at irregular times with high population of defects. We propose a simple stochastic model of dislocation reaction kinetics that is able to capture these statistical properties of the dislocation density fluctuations as a function of shear rate.
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