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REVIEW 2 major objections 7 minor 25 references

Connecting Diffuse Scattering to Atomic-Site-Resolved Occupancy and Displacement Fields through Fourier Filtering

T0 review · 2 major / 7 minor · reviewed 2026-07-14 · grok-4.5

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Pith's one-line read Fourier filtering of a calculated scattering amplitude recovers the atomic occupancies and displacements that produce selected diffuse-scattering features.

desk verdict Solid, usable methods paper that turns known large-box models into site-resolved maps of which atoms produce which diffuse features; scoped carefully and backed by code. read the letter →

arxiv 2607.10440 v1 pith:3C34BBGA submitted 2026-07-11 cond-mat.mtrl-sci

Maksim Eremenko , Victor Krayzman , Matthew G. Tucker , Igor Levin This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords diffusescatteringFourierfilteringlocalstructureatomicdisplacementschemicalshort-rangeorderReverseMonteCarloperovskitesMOSAIC
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Diffuse scattering encodes local chemical order and atomic displacements, but even a large atomic model that reproduces the pattern often leaves unclear which sites and motifs generate which features. This paper introduces MOSAIC, a framework that starts from a known configuration, computes its complex scattering amplitude, masks chosen reciprocal-space regions, and inverse-transforms those regions back onto the atomic sites. Linear estimators then return site-resolved occupancy contrast and picometer-scale displacement vectors for the selected features. Because every stage is linear, fields from disjoint masks add exactly, so overlapping signals can be separated and recombined as a consistency check. The method applies to reverse Monte Carlo models, molecular-dynamics snapshots, and two-dimensional electron-microscopy projections, giving a practical way to interrogate large disordered structures.

What carries the argument

MOSAIC: a phase-preserving Fourier-filtering pipeline that isolates diffuse features in the calculated scattering amplitude and maps them, via site-centered inverse transforms and a linear M-decoder trained on the same configuration, onto occupancy scalars and displacement vectors at each atomic site.

What would settle it

On a controlled perovskite model with known octahedral rotations and breathing distortions, apply complementary cylindrical and spherical masks; if the decoded rotation and breathing fields do not sum to the full-rod reconstruction within residual scale of the known displacements (~0.1 Å), the linear additivity claim fails.

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Extended reading notes

Core claim

When an atomistic configuration is available and a phase-bearing scattering amplitude can be calculated, Fourier filtering that amplitude over selected reciprocal-space regions, followed by site-centered inverse transforms and a linear decoder, recovers the atomic-site-resolved occupancy and displacement fields responsible for those features, with exact additivity across disjoint masks.

Load-bearing premise

The method assumes displacements stay small enough that a first-order linear map from filtered amplitude patches to site displacements remains accurate; larger shifts make the decoder underestimate magnitudes.

Editorial extensions

If this is right

  • Specific diffuse rods, peaks, or surfaces can be attributed to particular chemical orderings or distortion modes even when those signals overlap in reciprocal space.
  • Large reverse Monte Carlo and molecular-dynamics configurations become interpretable site by site for chosen scattering signatures.
  • Two-dimensional STEM projections can be filtered to reveal polar textures or chemical order that uncorrelated noise otherwise conceals.
  • Complementary masks can be summed to reconstruct the full field, giving a built-in consistency check on the recovered displacements.
  • The same operators can be adapted to 4D-STEM scans and to tracking displacement fields of selected vibrational modes along molecular-dynamics trajectories.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the input must already be a phase-bearing configuration, the method complements rather than replaces intensity-only approaches such as three-dimensional difference pair-distribution-function analysis.
  • Replacing the linear decoder with a compact nonlinear network could improve accuracy for large displacements, but would forfeit exact additivity across masks—an explicit trade-off the paper notes but does not explore.
  • Slice-wise application to experimental 4D-STEM data might yield real-space order-parameter maps without first building a full atomistic reverse Monte Carlo model.
  • The additivity property suggests a practical way to partition experimental reciprocal-space volumes into chemically versus displacively dominated contributions once a reliable average structure is known.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 7 minor

Summary. The manuscript introduces MOSAIC, a model-conditioned computational framework that attributes selected diffuse-scattering features to atomic-site-resolved occupancy and displacement fields when an atomistic configuration is available and a phase-bearing scattering amplitude can be calculated. Starting from the Butler–Welberry decomposition of the total amplitude into average and diffuse parts, the method applies phase-preserving reciprocal-space masks, evaluates restricted inverse Fourier transforms at atomic sites (via type-3 NUFFTs in a Map–Reduce pipeline), and recovers chemical contrast (Chemical Mode) and site displacements (Displacement Mode via a linear M-decoder). Exact additivity across disjoint masks is established by construction. Synthetic benchmarks separate coexisting Li/Fe short-range order from L11 nanodomains in a γ-LiFeO2 model and disentangle octahedral rotations from breathing distortions in a ReO3-type framework; applications to published RMC models of PMN and PMN–PT illustrate chemical SRO maps and polar textures. Open-source code is provided.

Significance. If the results hold as presented, MOSAIC fills a practical gap between large-box structural models (RMC, MD, MC) or STEM-derived projections and the interpretation of which real-space motifs generate particular diffuse features. The strictly linear, phase-preserving pipeline with demonstrated additivity, the Chemical/Displacement Mode separation, and the scalable NUFFT Map–Reduce implementation are genuine methodological contributions. Open code, synthetic recovery of known motifs, and application to established PMN/PMN–PT RMC configurations strengthen credibility and usability. The work is carefully scoped as attribution within a supplied model rather than structure solution from intensity alone, which is appropriate and useful for the diffuse-scattering and local-structure communities.

major comments (2)
  1. Section 2.3 and the Displacement Mode validation in §4.2: the M-decoder is trained on paired (r_s, u_true_s) samples drawn from the same configuration under analysis, then held fixed across masks. The manuscript acknowledges this and correctly frames the method as model-conditioned attribution, but the main-text language of “recovering” picometer-scale displacements can still be read as independent estimation. Please state explicitly in §2.3 what is being tested (linearity and mask additivity of a fixed decoder; topology and approximate magnitudes of attributed fields) versus what is not (cross-configuration generalization or structure solution from intensity). This is a framing clarification, not a change to the method.
  2. Section 4.2 (and claim of picometer-scale recovery in the Methods overview): quantitative reconstruction residuals for the ReO3-type benchmark are deferred to Supplementary Fig. S5, while the main text only states that the additivity residual is “negligible compared with the characteristic displacement scale (≈0.1 Å).” For a methods paper whose central quantitative claim is site-resolved displacement recovery, the main text should report at least summary error metrics (e.g., RMSE or |u_all − u_true| distribution for full, rod, and sphere masks) so readers can assess accuracy without the supplement.
minor comments (7)
  1. Eq. (15) and §2.3: the first-order expansion and the statement that large displacements cause magnitude underestimation while preserving topology are appropriate; a brief numerical example of the displacement magnitude at which the linear decoder’s error becomes appreciable (for the ReO3 or PMN cases) would help users judge applicability.
  2. Section 4.1 (LiFeO2 chemical benchmark): the intensity threshold used to display clusters in Fig. 4(d,e) is a free parameter. Please state the threshold criterion (or that it is for visualization only) so the reconstruction is reproducible.
  3. Section 5.2 / Fig. 7: the projected-column example uses the Fourier representation of the measured displacement field rather than a full kinematic scattering amplitude; this is noted in the text but could be flagged more prominently in the figure caption to avoid confusion with the 3D amplitude pipeline.
  4. Figure 5: the residual panel (j) and complementary reconstruction (k) are important for the additivity claim; ensuring consistent color scales and a short quantitative residual statement in the caption would improve readability.
  5. Implementation (§3): the Map–Reduce / NUFFT architecture is well motivated; a short note on typical wall-clock cost or memory for the million-atom / 10^7–10^8 Q-point regime would help practitioners.
  6. Minor typographical/formatting: “Here, weconsiderascenariowhere…” (start of §2) appears to have missing spaces; similar run-together words appear elsewhere in the provided text and should be cleaned in production.
  7. References: the prior MOSAIC-related applications [6–8] are appropriately cited; if space allows, a one-sentence contrast with 3D-ΔPDF peak interpretation would further situate the method for readers coming from that literature.

Circularity Check

1 steps flagged · score 2.0 of 10

Mild same-config M-decoder calibration is self-consistency, not a load-bearing circular derivation; method is scoped as model-conditioned attribution with independent synthetic checks.

  1. fitted input called prediction [Section 2.3, Eq. (16) and following paragraph]
    "In the analysis presented here, M was calibrated separately for each configuration using paired samples{(rs,u true s)} derived from that same configuration, and was then held fixed when using different reciprocal-space masks. Thus, the additivity tests reported below probe the linearity of the masked-field decomposition and the stability of the fixed decoder, rather than cross-configuration generalization."

    M is a linear map fitted so that site patches rs of the inverse-transformed field recover the known true displacements u_true of that same configuration. Full-field ûs ≈ u_true is therefore the training residual (a fit), not an independent prediction. Partial-mask attributions inherit this same-config calibration. The paper acknowledges the scope; synthetic mode-separation tests still provide external checks, so the circularity is limited and not load-bearing for the attribution claim.

full rationale

MOSAIC is explicitly model-conditioned: it attributes selected diffuse features inside a supplied atomistic configuration (or 2D projection) for which a phase-bearing amplitude can be calculated, and does not claim structure solution from intensity alone. The Chemical Mode follows directly from the Butler–Welberry decomposition with umn set to zero. Displacement Mode uses a first-order expansion and a linear M-decoder; M is trained on paired (rs, u_true) samples from the same configuration, so full-field recovery of displacements is essentially a fit residual rather than an external prediction. The paper states this limitation and uses the fixed decoder mainly to test mask additivity and feature attribution. That is a minor fitted-input self-consistency, not a circular derivation of the central claim. Synthetic benchmarks (γ-LiFeO2 SRO vs L11; ReO3 rotations vs breathing) supply independent ground-truth checks of mode separation and complementary-mask residuals; PMN applications inherit RMC models but do not close a definitional loop. Self-citations [6–8] are prior applications/background, not uniqueness theorems or load-bearing premises. No self-definitional identity, uniqueness import, ansatz smuggling, or renaming of a known result was found. Score 2 reflects one acknowledged same-config calibration step that does not force the main attribution claim.

Assumptions & free parameters 3 free parameters · 4 assumptions · 2 invented entities

The central claim rests on standard kinematic diffraction, a first-order displacement expansion, linearity of the Fourier operators, and the practical assumption that a sufficiently accurate atomistic configuration (RMC, MD, or STEM projection) is already available. Free parameters are mainly mask geometry and decoder training choices; the invented entities are the software framework and the linear decoder itself.

free parameters (3)
  • reciprocal-space mask radii and shapes (r1, r2, spherical/cylindrical windows)
    Chosen by the user to isolate features of interest; different choices alter which real-space correlations are recovered.
  • M-decoder linear map (and optional class-conditional maps)
    Trained once per configuration on paired local patches and known displacements; coefficients are fitted rather than derived from first principles.
  • intensity threshold for displaying chemical clusters
    Used in visualization of L11 nanoregions; affects which atoms are shown as ordered.
assumptions (4)
  • domain assumption Kinematic single-scattering approximation for the total complex amplitude
    Stated at the opening of Section 2.1; multiple scattering is neglected.
  • domain assumption First-order expansion of the displacement contribution to the diffuse amplitude (Eq. 15)
    Underpins the linear M-decoder; validity limited to small displacements (Section 2.3).
  • standard math Linearity and exact additivity of masked inverse transforms across disjoint reciprocal-space windows
    Follows directly from the definition of the inverse Fourier transform and the feature-independent normalization (Eqs. 6-7, 18).
  • domain assumption An atomistic configuration (or 2D projection) that already reproduces the diffuse scattering is available
    The method does not reconstruct structure from intensity-only data; it interrogates a supplied model (Abstract and Introduction).
invented entities (2)
  • MOSAIC framework / software package independent evidence
    purpose: Implements the full pipeline of amplitude calculation, masking, restricted inverse NUFFT, chemical and displacement modes, and Map-Reduce scaling.
    New software artifact released with the paper; independent evidence is the public GitHub repository.
  • M-decoder (linear site-centered displacement estimator)
    purpose: Maps local patches of the filtered real-space field back to atomic displacement vectors while preserving linearity across masks.
    Data-driven linear operator introduced in Section 2.3; trained per configuration rather than derived analytically for general cases.

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Cite this review

Pith. "Pith review of Connecting Diffuse Scattering to Atomic-Site-Resolved Occupancy and Displacement Fields through Fourier Filtering." pith.science (2026). https://pith.science/paper/3C34BBGA

@misc{pith2026260710440,
  author       = {Pith},
  title        = {Pith review of: Connecting Diffuse Scattering to Atomic-Site-Resolved Occupancy and Displacement Fields through Fourier Filtering},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3C34BBGA}},
  note         = {Machine review of arXiv:2607.10440}
}
read the original abstract

Local structural correlations are encoded in diffuse scattering, but identifying atomic motifs that produce specific diffuse features can be challenging. We introduce MOSAIC, a computational framework for this task when an atomistic configuration is available and a phase-bearing scattering amplitude can be calculated. Our approach relies on applying the Fourier filter to this amplitude over the reciprocal-space regions encompassing the scattering features of interest to obtain maps of atomic displacements and site occupancies responsible for those features. The method is effective in interrogating the nature and spatial distributions of interatomic correlations in large-scale structural models, such as obtained using Reverse Monte Carlo refinements from experimental data, molecular dynamics, or Monte Carlo simulations, or 2D structural projections derived from atomic-resolution electron microscopy images.

Figures

Figures reproduced from arXiv: 2607.10440 by the authors.

Figure 1
Figure 1. Conceptual illustration of MOSAIC. Starting from an atomistic configuration (left), [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Example of a real-space 2D representation of a local atomic displacement obtained by [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Schematic of the scalable Map–Reduce computational pipeline used in MOSAIC. [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Application of MOSAIC to a simulated γ-LiFeO2 structure with the coexisting Li/Fe short-range order and nanoscale L11 ordering. (a) Structural model containing 40×40×40 unit cells with cubic nanoregions exhibiting the L11-type Li/Fe superstructure, embedded in a matrix…
Figure 5
Figure 5. Figure 5: Disentangling overlapping diffuse-scattering signatures of rotational and breathing [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Chemical short-range order in PMN and PMN-PT is visualized via the001 planar [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Analysis of a 2D projection of a PMN supercell. (a) Pb-column displacement vectors [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]

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Reference graph

Works this paper leans on

25 extracted references

  1. [1]

    M. A. Krivoglaz.X-Ray and Neutron Diffraction in Nonideal Crystals. Springer, Berlin, 2012

    2012

  2. [2]

    Calculationofdiffusescatteringfromsimulateddisordered crystals: a comparison with optical transforms.J

    B.D.ButlerandT.R.Welberry. Calculationofdiffusescatteringfromsimulateddisordered crystals: a comparison with optical transforms.J. Appl. Crystallogr., 25:391–399, 1992

    1992

  3. [3]

    T. R. Welberry and B. D. Butler. Interpretation of diffuse X-ray scattering via models of disorder.J. Appl. Crystallogr., 27:205–231, 1994

    1994

  4. [4]

    R. L. McGreevy. Reverse Monte Carlo modelling.J. Phys.: Condens. Matter, 13:R877– R913, 2001

    2001

  5. [5]

    Weber and A

    T. Weber and A. Simonov. The three-dimensional pair distribution function analysis of disordered single crystals: basic concepts.Z. Kristallogr. Cryst. Mater., 227:238–247, 2012

    2012

  6. [6]

    Eremenko et al

    M. Eremenko et al. Local atomic order and hierarchical polar nanoregions in a classical relaxor ferroelectric.Nat. Commun., 10:2728, 2019

    2019

  7. [7]

    Eremenko et al

    M. Eremenko et al. Emergent topological polarization textures in relaxor ferroelectrics. Nat. Commun., 16:7531, 2025

    2025

  8. [8]

    Krayzman, A

    V. Krayzman, A. Bosak, H. Y. Playford, B. Ravel, and I. Levin. Incommensurate modu- lation and competing ferroelectric/antiferroelectric modes in tetragonal tungsten bronzes. Chem. Mater., 34:9989–10002, 2022

    2022

Show all 25 references
  1. [9]

    Greengard and J.-Y

    L. Greengard and J.-Y. Lee. Accelerating the nonuniform fast fourier transform.SIAM Rev., 46:443–454, 2004

    2004

  2. [10]

    A. H. Barnett, J. Magland, and L. af Klinteberg. A parallel nonuniform fast fourier trans- form library based on an exponential-of-semicircle kernel.SIAM J. Sci. Comput., 41:C479– C504, 2019

    2019

  3. [11]

    Y.-h. Shih, G. Wright, J. Andén, J. Blaschke, and A. H. Barnett. cuFINUFFT: a load- balanced GPU library for general-purpose nonuniform FFTs. In2021 IEEE International Parallel and Distributed Processing Symposium Workshops, pages 688–697. IEEE, 2021

    2021

  4. [12]

    J. M. Cowley.Diffraction Physics. Elsevier, Amsterdam, 3 edition, 1995

    1995

  5. [13]

    T. R. Welberry.Diffuse X-Ray Scattering and Models of Disorder. Oxford University Press, Oxford, 2022. 18

    2022

  6. [14]

    Ji et al

    H. Ji et al. Hidden structural and chemical order controls lithium transport in cation- disordered oxides for rechargeable batteries.Nat. Commun., 10:592, 2019

    2019

  7. [15]

    Li et al

    L. Li et al. Atomic-scale probing of short-range order and its impact on electrochemical properties in cation-disordered oxide cathodes.Nat. Commun., 14:7448, 2023

    2023

  8. [16]

    Sauvage and E

    M. Sauvage and E. Parthé. Prediction of diffuse intensity surfaces in short-range-ordered ternary derivative structures based on SnS, NaCl, CsCl and other structures.Acta Crys- tallogr. A, 30:239–246, 1974

    1974

  9. [17]

    Eremenko, V

    M. Eremenko, V. Krayzman, A. Gagin, and I. Levin. Advancing reverse Monte Carlo structure refinements to the nanoscale.J. Appl. Crystallogr., 50:1561–1570, 2017

    2017

  10. [18]

    A. A. Bokov and Z.-G. Ye. Recent progress in relaxor ferroelectrics with perovskite struc- ture.J. Mater. Sci., 41:31–52, 2006

    2006

  11. [19]

    J. Hlinka. Do we need the ether of polar nanoregions?J. Adv. Dielectr., 2:1241006, 2012

    2012

  12. [20]

    T. Rojac. Piezoelectric response of disordered lead-based relaxor ferroelectrics.Commun. Mater., 4:12, 2023

    2023

  13. [21]

    R. A. Cowley, S. N. Gvasaliya, S. G. Lushnikov, B. Roessli, and G. M. Rotaru. Relaxing with relaxors: a review of relaxor ferroelectrics.Adv. Phys., 60:229–327, 2011

    2011

  14. [22]

    Paściak, T

    M. Paściak, T. R. Welberry, J. Kulda, M. Kempa, and J. Hlinka. Polar nanoregions and diffuse scattering in the relaxor ferroelectric PbMg1/3Nb2/3O3.Phys. Rev. B, 85:224109, 2012

    2012

  15. [23]

    M. J. Krogstad et al. The relation of local order to material properties in relaxor ferro- electrics.Nat. Mater., 17:718–724, 2018

    2018

  16. [24]

    M. J. Cabral, S. Zhang, E. C. Dickey, and J. M. LeBeau. Gradient chemical order in the relaxor Pb(Mg1/3Nb2/3)O3.Appl. Phys. Lett., 112:082901, 2018

    2018

  17. [25]

    I. M. Reaney, J. Petzelt, V. V. Voitsekhovskii, F. Chu, and N. Setter. B-site order and infrared reflectivity in A(B′B′′)O3 complex perovskite ceramics.J. Appl. Phys., 76:2086– 2092, 1994. 19

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