TEM · Diffuse scattering
Diffuse scattering in electron diffraction and 4D-STEM
Electrons sent through a crystal scatter into bright dots (Bragg spots); see when a camera can record the faint glow between them (diffuse scattering), map it, and what may cause it.
Dose and detectorVirtual dark fieldWhere it comes fromQuestionsReferences
How many electrons does it take to see diffuse scattering?
In one electron diffraction study (Nb0.84CoSb, Poppe et al. 2024) Bragg spots were 1000 times stronger than the diffuse glow; one frame must record both.
Try it: switch to 12 bit and press Fill the detector: the best signal ÷ noise falls from 8.0 to 2.0.
What does a virtual dark-field image of diffuse scattering show?
In 4D-STEM the beam steps across the sample, saving a pattern at each step; adding pixels inside a drawn circle (virtual aperture) maps where that signal comes from.
Try it: set Low dose and the patches turn to speckle; add 4 × 4 steps and they return.
What causes diffuse intensity, and is it short-range order?
Papers name several causes and disagree on which dominates in fcc (face-centred cubic) alloys like CrCoNi.
Try it: pick a cause to ring its papers, or a paper to read it.
What to take away
Counting noise
Counting n electrons scatters by √n. Signal ÷ noise (SNR) 5, the Rose criterion, needs 25 electrons, more on a background.
Detector range
One frame must hold bright spots and faint glow. The EMPAD reaches 1,000,000 : 1, but about 28,000 electrons in a 1 ms frame.
An open question
Papers read diffuse features in fcc alloys as short-range order or other effects.
More detail: the models and their limits
Plain words used here
Bragg spots: the sharp bright dots in the electron diffraction pattern of a crystal. Diffuse scattering: weaker, spread-out intensity between or around those spots. Signal to noise ratio (SNR): how far a signal stands above the random scatter in the counts. Dynamic range: the brightest count a pixel can hold divided by the faintest it can still see. Virtual dark field: a map made by adding, at every beam position, only the pixels inside a chosen part of the pattern (Ophus 2019). fcc: face-centred cubic, the crystal type of nickel, aluminium and CrCoNi (Coury et al. 2023; Zhang et al. 2020).
Counting noise
Electron arrivals are counted as a Poisson process. For a mean of λ counts the standard deviation is √λ (NIST handbook), so the signal to noise ratio of a feature with full contrast is SNR = √n (Du and Jacobsen 2018). They quote SNR = 5 as the Rose criterion for acceptable image quality, which needs n = SNR² = 25 counts. Their general form compares a feature pixel with a background pixel: signal n|If − Ib|, noise √n √(If + Ib). For S diffuse counts on B background counts this is S ÷ √(S + 2B), so 25 is the minimum, reached only with no background. Poppe et al. (2024) note diffuse data need careful background subtraction.
The detector model
The page draws a recorded count as min(Poisson(λ), C) and draws no background. For the bit options C = 2n (256, 4,096, 65,536) and the page assumes one level per electron, its own best case: an integrating camera spends many levels on each electron, and a direct-conversion CCD saturates on the charge of only a few electrons per pixel (Tate et al. 2016). The EMPAD options use electron limits from Tate et al. (2016) for 100 keV electrons: a full well of 3.7 × 106 per pixel per frame, but 2.8 × 104 in a 1 ms frame, set by the in-pixel charge removal rate. Its 1,000,000 : 1 range is that full well over a single-electron noise floor. Fill the detector sets the Bragg peak D so that D + 3√D = C, three standard deviations of counting noise below the limit (a choice of this page). The diffuse pixel then holds r × D electrons, so the best single-frame SNR is √(r D), just under √(r C).
The virtual dark field
A virtual detector adds (or subtracts) a chosen set of pixels in the pattern at each probe position (Ophus 2019). The page builds its schematic scan from a Bragg template plus a diffuse template at 1/1000 of the Bragg peak, switched on only inside drawn patches. Binning adds the counts of k × k positions. Patch signal ÷ noise uses the Du and Jacobsen form S ÷ √(S + 2B), with B the counts away from the patches. Hsiao et al. (2022) note that the sensitivity of their scanning nanodiffraction rises because the exposure is multiplied by the number of scan points.
What the page leaves out
No inelastic background, no dynamical diffraction, no real crystal, no camera read noise. With a background in the aperture, a larger radius also collects more background noise, so the gains shown are an upper limit. Zhang et al. (2020) and Hsiao et al. (2022) used energy filters with 5 eV and 10 eV slits to remove inelastic background before looking at the diffuse signal.
Questions people ask
What is diffuse scattering in electron diffraction?
It is intensity that falls between or around the sharp Bragg spots of a crystal. Walsh et al. (2024) list thermal and static displacement scattering, planar defects, surface terminations and dynamical effects as sources, and earlier papers read some of it as chemical short-range order.
Does a diffuse spot prove short-range order?
That is debated. Walsh et al. (2023) argue that extra reflections in concentrated alloys do not necessitate short-range order. Coury et al. (2023) give a framework to tell which diffuse intensities could indicate it, and other groups report SRO from diffraction together with imaging and chemical mapping.
Why use an energy filter for diffuse scattering?
To remove electrons that lost energy in the specimen, which add a background. Zhang et al. (2020) used a 5 eV slit on the zero-loss peak to enhance the signal to noise ratio of the diffuse contrast. Hsiao et al. (2022) used a 10 eV slit.
What is a virtual dark-field image in 4D-STEM?
4D-STEM records a 2D diffraction pattern at each point of a 2D probe grid. A virtual detector adds the pixels in a chosen part of each pattern, so one dataset gives many images afterwards (Ophus 2019).
Why does detector dynamic range matter?
Tate et al. (2016) note that a direct-conversion CCD saturates on the charge from only a few electrons per pixel. Their pixel array detector (EMPAD) reached a 1,000,000 : 1 range in one frame, so it could image the direct beam while keeping single-electron sensitivity.
Which diffuse positions are discussed for fcc alloys?
Coury et al. (2023) discuss 1/3{422} positions in ⟨111⟩ patterns and 1/2{311} positions in ⟨112⟩ patterns, and show similar features in CdTe, pure Ni and pure Al. Chen et al. (2021) report superlattice reflections at 1/2{311} positions along a [112] zone axis in VCoNi.
Related pages
4D-STEM basics · Short-range order · SRO in atom probe data · Correlative APT-TEM · The Ewald sphere · Forbidden reflections
References
Show the 11 references
- R. Zhang, S. Zhao, J. Ding, Y. Chong, T. Jia, C. Ophus, M. Asta, R. O. Ritchie and A. M. Minor, Short-range order and its impact on the CrCoNi medium-entropy alloy, Nature 581, 283 to 287 (2020). doi:10.1038/s41586-020-2275-z
- X. Chen, Q. Wang, Z. Cheng, M. Zhu, H. Zhou, P. Jiang, L. Zhou, Q. Xue, F. Yuan, J. Zhu, X. Wu and E. Ma, Direct observation of chemical short-range order in a medium-entropy alloy, Nature 592, 712 to 716 (2021). doi:10.1038/s41586-021-03428-z
- H.-W. Hsiao, R. Feng, H. Ni, K. An, J. D. Poplawsky, P. K. Liaw and J.-M. Zuo, Data-driven electron-diffraction approach reveals local short-range ordering in CrCoNi with ordering effects, Nature Communications 13, 6651 (2022). doi:10.1038/s41467-022-34335-0
- F. Walsh, M. Zhang, R. O. Ritchie, A. M. Minor and M. Asta, Extra electron reflections in concentrated alloys do not necessitate short-range order, Nature Materials 22, 926 to 929 (2023). doi:10.1038/s41563-023-01570-9
- F. G. Coury, C. Miller, R. Field and M. Kaufman, On the origin of diffuse intensities in fcc electron diffraction patterns, Nature 622, 742 to 747 (2023). doi:10.1038/s41586-023-06530-6
- F. Walsh, M. Zhang, R. O. Ritchie, M. Asta and A. M. Minor, Multiple origins of extra electron diffractions in fcc metals, Science Advances 10, eadn9673 (2024). doi:10.1126/sciadv.adn9673
- M. Tate, P. Purohit, D. Chamberlain, K. Nguyen, R. Hovden, C. Chang, P. Deb, E. Turgut, J. Heron, D. Schlom, D. Ralph, G. Fuchs, K. Shanks, H. Philipp, D. Muller and S. Gruner, High dynamic range pixel array detector for scanning transmission electron microscopy, Microscopy and Microanalysis 22, 237 to 249 (2016). doi:10.1017/S1431927615015664
- C. Ophus, Four-dimensional scanning transmission electron microscopy (4D-STEM): from scanning nanodiffraction to ptychography and beyond, Microscopy and Microanalysis 25, 563 to 582 (2019). doi:10.1017/S1431927619000497
- R. Poppe, N. Roth, R. B. Neder, L. Palatinus, B. B. Iversen and J. Hadermann, Refining short-range order parameters from the three-dimensional diffuse scattering in single-crystal electron diffraction data, IUCrJ 11, 82 to 91 (2024). doi:10.1107/S2052252523010254
- M. Du and C. Jacobsen, Relative merits and limiting factors for x-ray and electron microscopy of thick, hydrated organic materials, Ultramicroscopy 184, 293 to 309 (2018). doi:10.1016/j.ultramic.2017.10.003 (Poisson statistics, SNR = √n, Rose criterion SNR = 5)
- NIST/SEMATECH e-Handbook of Statistical Methods, section 1.3.6.6.19, Poisson distribution (mean λ, standard deviation √λ); Teledyne Vision Solutions, Bit depth, full well, and dynamic range (8, 12 and 16 bit = 256, 4,096 and 65,536 grey levels).
BibTeX
@misc{tripathy2026diffusescattering,
author = {Tripathy, Manisha},
title = {Diffuse Scattering in 4D-STEM Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/4d-stem-diffuse-scattering}},
note = {Interactive web tool}
}