Strain Measurement in Single Crystals by 4D-ED
Abstract
A new method is presented to measure strain over a large area of a single crystal. The 4D-ED data are collected by recording a 2D diffraction pattern at each position in the 2D area of the TEM lamella scanned by the electron beam of STEM. Data processing is completed with a new computer program (available free of charge) that runs under the Windows operating system. Previously published similar methods are either commercial or need special hardware (electron holography) or are based on HRTEM, which involves limitations with respect to the size of the field of view. All these limitations are overcome by our approach. The presence of defects results in small local changes in orientation that change the subset of experimentally available diffraction spots in the individual patterns. Our method is based on a new principle, namely fitting a lattice to (a subset of) measured diffraction spots to improve the precision of the measurement. Although a spot to be measured may be missing in some of the patterns even the missing spot can be precisely measured by the lattice determined from the available spots. Application is exemplified by heavily boron-doped silicon with intended usage as a low-temperature superconductor in qubits.
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BibTeX
@article{labar2026strain,
title = {{Strain Measurement in Single Crystals by 4D-ED}},
author = {János L. Lábár and Béla Pécz and Aiken Van Waveren and Géraldine Hallais and Léonard Desvignes and Francesca Chiodi},
journal = {Nanomaterials},
year = {2026},
month = oct,
doi = {10.3390/nano13061007},
url = {https://hal.science/hal-05792044v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Strain Measurement in Single Crystals by 4D-ED
AU - János L. Lábár
AU - Béla Pécz
AU - Aiken Van Waveren
AU - Géraldine Hallais
AU - Léonard Desvignes
AU - Francesca Chiodi
PY - 2026
DA - 2026/10/11
JO - Nanomaterials
DO - 10.3390/nano13061007
UR - https://hal.science/hal-05792044v1
AB - A new method is presented to measure strain over a large area of a single crystal. The 4D-ED data are collected by recording a 2D diffraction pattern at each position in the 2D area of the TEM lamella scanned by the electron beam of STEM. Data processing is completed with a new computer program (available free of charge) that runs under the Windows operating system. Previously published similar methods are either commercial or need special hardware (electron holography) or are based on HRTEM, which involves limitations with respect to the size of the field of view. All these limitations are overcome by our approach. The presence of defects results in small local changes in orientation that change the subset of experimentally available diffraction spots in the individual patterns. Our method is based on a new principle, namely fitting a lattice to (a subset of) measured diffraction spots to improve the precision of the measurement. Although a spot to be measured may be missing in some of the patterns even the missing spot can be precisely measured by the lattice determined from the available spots. Application is exemplified by heavily boron-doped silicon with intended usage as a low-temperature superconductor in qubits.
SN - 2079-4991
SN - 2079-4991
ER -