APT · Short-range order
Short-range order in atom probe tomography: why it is hard to see
Short-range order means atoms prefer certain neighbours (A next to B more than chance); see how much of it a model atom probe, which maps atoms one by one in 3D, still finds.
Why does atom probe lose short-range order?
As in He et al. (2024), the model misses some atoms (detection efficiency is the share caught) and shifts the rest at random.
Try it: raise sideways noise from 0.1 to 0.25 nm: the coral dot drops into the grey band.
How do you tell real order from chance?
Keep the measured positions, shuffle which atom is A or B (random labelling), and measure again: that is what chance gives.
Try it: pick 864 atoms and set sideways noise to 0.2 nm in picture 1: α falls inside the range. With 10976 atoms, it stays outside.
Why is order easier to see in depth than sideways?
Atom probe places atoms better in depth than sideways (Gault et al. 2010), so atomic planes survive in depth.
Try it: set sideways noise to 0: the sideways peaks return. Press "0.25 / 0.077 nm": the depth peaks fade too.
What to take away
Missing atoms dilute
Measured order falls toward zero as atoms go missing (He et al. 2024). Here the 12 counted neighbours then reach farther out.
Sideways blur hurts most
It changes measured order more than depth noise does (He et al. 2024).
Always shuffle
Compare with shuffled copies; more atoms narrow the band.
Look along depth
Planes survive in depth; Gault et al. (2022) expect depth analyses to be more robust.
More detail: the model, the order parameter and its limits
The order parameter
He et al. (2024) define α = (PAB − XB) / XB. PAB is the chance of finding a B atom among the k nearest neighbours of an A atom, and XB is the B fraction of the whole dataset. α = 0 for a random alloy; in their convention α > 0 means A and B are found together more than by chance and α < 0 means they avoid each other. This page always counts the k = 12 nearest detected atoms, the value He et al. used to build their ordered models. With atoms missing, those 12 reach past the first shell, and that is why missing atoms lower α here. For their 57% data He et al. counted 7 neighbours (0.57 × 12); in this model that keeps more of the order (+0.045 instead of +0.030 at the defaults). He et al. call this a modified form of the Warren-Cowley parameter. The Warren-Cowley form on our short-range order page, α = 1 − PAB/XB, gives the same number with the opposite sign.
The crystal
An fcc lattice with a = 0.36 nm, as in He et al., but much smaller (864 to 10976 sites, with periodic edges) and with two elements at 50:50 instead of their three. Order is set by reverse Monte Carlo, as in their work: swap an A and a B atom, keep the swap if it brings α (k = 12) closer to the target. Targets of ±0.1 are the limits of the range they simulated.
The model atom probe
Each atom is kept with a chance equal to the detection efficiency, then shifted by Gaussian noise with zero mean: σxy in each of x and y, σz in depth (He et al. 2024). Slider ranges: efficiency 10 to 100% and depth noise 0 to 0.1 nm (their ranges); the default depth noise of 0.024 nm is the lowest value they measured with spatial distribution maps near the (111) pole (0.024 to 0.077 nm); lateral noise up to 1 nm, the upper bound for lateral resolution in pure metals quoted by Gault et al. (2010). The random band is the lowest to highest α of the shuffled copies of this small crystal, so it is much wider than the |α| ≤ 0.00022 He et al. found with about 4 million sites, 100 runs and a 95% level. A random value lands outside the range of n shuffles about 2 times in n + 1.
Spatial distribution maps
A spatial distribution map (Geiser et al. 2007) is a histogram of the offsets between pairs of atoms. Here: offsets along depth for pairs less than 0.5 nm apart sideways, and offsets sideways for pairs less than 0.5 nm apart in the other two directions. "Plane contrast" is the strength of the repeat at the plane spacing a/2 = 0.18 nm of this lattice seen along a cube axis: about 1 for sharp planes, 0 for none. He et al. looked along (111) instead, so their numbers do not carry over directly. Real reconstructions add trajectory aberrations and other effects that this noise model leaves out; Larson et al. (2013) note that near-field effects still keep the full lattice from being imaged.
On this site: Short-range order · APT reconstruction and resolution · APT data analysis · Correlative APT and TEM · 4D-STEM diffuse scattering
Questions people ask
Can atom probe tomography measure short-range order?
He et al. (2024) report an approach to measure it, using simulations to work out how much detection efficiency and spatial noise shrink the value. Gault et al. (2022) caution that lateral (sideways) neighbour relationships are typically not kept by field evaporation and reconstruction, and that analyses along the depth are expected to be more robust.
How does detection efficiency affect short-range order in APT?
In He et al.'s simulations all SRO values fell toward zero almost linearly as more atoms went missing. Their models still showed a deviation from random with more than half of the data missing.
What is the detection efficiency of an atom probe?
It is the fraction of ions that are detected. Moody et al. (2014) give about 0.37 to 0.57 for most commercial instruments. Martin et al. (2017) compared a LEAP 3000 at 37% with a LEAP 5000 at a maker-estimated 52%. Gault et al. (2021) report that current detection efficiency reaches 80%.
What is random labelling in atom probe analysis?
A copy of the reconstruction keeps every atom position but swaps the mass-to-charge labels at random, giving a randomly distributed set of atoms (Gault et al. 2022). The same analysis run on the copy shows what chance alone produces.
Can the true short-range order be recovered?
He et al. (2024) divide the true by the measured SRO in simulations to get a correction factor, then apply it to measured values. This needs values for the spatial resolution and detection efficiency. At 0.25 nm spatial noise they could not tell apart true values below 0.0048.
What is lattice rectification?
Moody et al. (2014) use the crystal structure kept in the data to move each atom back to its most likely lattice site, then fill empty sites to make an atomically complete model. They note earlier estimates that upwards of 85% of rectified atoms in a pure Al subvolume return to their correct sites.
References
Show the 10 references
- D. J. Larson, T. J. Prosa, R. M. Ulfig, B. P. Geiser and T. F. Kelly, Local Electrode Atom Probe Tomography: A User's Guide, Springer, New York (2013): chapter 3, design and instrumentation; chapter 5, data processing and reconstruction; chapter 6, selected analysis topics. doi:10.1007/978-1-4614-8721-0
- B. P. Geiser, T. F. Kelly, D. J. Larson, J. Schneir and J. P. Roberts, Spatial distribution maps for atom probe tomography, Microscopy and Microanalysis 13, 437 to 447 (2007). doi:10.1017/S1431927607070948
- M. He, W. J. Davids, A. J. Breen and S. P. Ringer, Quantifying short-range order using atom probe tomography, Nature Materials 23, 1200 to 1207 (2024). doi:10.1038/s41563-024-01912-1
- B. Gault, B. Klaes, F. F. Morgado, C. Freysoldt, Y. Li, F. De Geuser, L. T. Stephenson and F. Vurpillot, Reflections on the spatial performance of atom probe tomography in the analysis of atomic neighborhoods, Microscopy and Microanalysis 28, 1116 to 1126 (2022). doi:10.1017/S1431927621012952
- D. J. Larson, B. Gault, B. P. Geiser, F. De Geuser and F. Vurpillot, Atom probe tomography spatial reconstruction: status and directions, Current Opinion in Solid State and Materials Science 17, 236 to 247 (2013). doi:10.1016/j.cossms.2013.09.002
- B. Gault, A. Chiaramonti, O. Cojocaru-Mirédin, P. Stender, R. Dubosq, C. Freysoldt, S. K. Makineni, T. Li, M. Moody and J. M. Cairney, Atom probe tomography, Nature Reviews Methods Primers (2021). doi:10.1038/s43586-021-00047-w
- B. Gault, M. P. Moody, F. De Geuser, A. La Fontaine, L. T. Stephenson, D. Haley and S. P. Ringer, Spatial resolution in atom probe tomography, Microscopy and Microanalysis 16, 99 to 110 (2010). doi:10.1017/S1431927609991267
- F. De Geuser and B. Gault, Metrology of small particles and solute clusters by atom probe tomography, Acta Materialia 188, 406 to 415 (2020). doi:10.1016/j.actamat.2020.02.023
- M. P. Moody, A. V. Ceguerra, A. J. Breen, X. Y. Cui, B. Gault, L. T. Stephenson, R. K. W. Marceau, R. C. Powles and S. P. Ringer, Atomically resolved tomography to directly inform simulations for structure-property relationships, Nature Communications 5, 5501 (2014). doi:10.1038/ncomms6501
- T. L. Martin, A. J. London, B. Jenkins, S. E. Hopkin, J. O. Douglas, P. D. Styman, P. A. J. Bagot and M. P. Moody, Comparing the consistency of atom probe tomography measurements of small-scale segregation and clustering between the LEAP 3000 and LEAP 5000 instruments, Microscopy and Microanalysis 23, 227 to 237 (2017). doi:10.1017/S1431927617000356
BibTeX
@misc{tripathy2026aptsro,
author = {Tripathy, Manisha},
title = {Short-Range Order in Atom Probe Tomography},
year = {2026},
howpublished = {\url{https://untetheredatom.com/apt/apt-short-range-order-detection}},
note = {Interactive web tool}
}