{"id":"79812bb0-0747-4dc3-b3c0-277440f5a8ed","arxiv_id":"2608.11466","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Replacing XPCS-style intensity normalizations with a time- and azimuthal-averaged normalization removes artifacts in nanobeam electron correlation microscopy and correctly measures local relaxation and crystal formation.","lead":"This paper shows that standard X-ray-style analysis methods introduce errors when applied to nanoscale electron diffraction data, and proposes a corrected normalization that measures local atomic relaxation more accurately. The corrected method was tested on computer-simulated liquids and on an experimental metallic glass nanowire, where it reveals stable crystal domains that earlier analysis missed.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The stationarity/isotropy assumption behind the time-azimuthal normalization is only validated on equilibrium MD; the experimental crystallization violates it, and the ad hoc Δφ=30° and τ>1600 s masking are untested.","rationale":"Good-faith reading: the paper makes a specific, testable methodological claim—replacing the XPCS-style normalization denominators with a time- and azimuthal-averaged intensity removes the negative-tail and elevated-baseline artifacts and recovers self-ISF-compatible dynamics. The MD simulation is the right benchmark: it is an equilibrium isotropic supercooled liquid, exactly the regime where the assumption \\bar{I}(kr)=⟨{I}tw⟩kφ is correct, and the results are convincing (g2 matches self-ISF; \\tilde{g}_2 shows the predicted negative tail; \\tilde{c}_2 shows the predicted baseline). The experimental application, however, is a different test: the sample crystallizes during the measurement, violating the time-invariance premise. The paper's own text flags this ('assuming no major structural changes happen during the experiment') and then uses two parameters (Δφ=30°, τ>1600 s) to cope with the violation. No sensitivity analysis is given, and no non-stationary MD validation is provided. Thus the weakest link is not the math or the code—it is the unverified step from a stationary benchmark to a non-stationary experimental setting with free parameters. The concrete test directly probes that step: if the results are stable over a range of Δφ and thresholds, and if an early-time normalization gives the same liquid dynamics, the concern is resolved; if not, the quantitative claims for the experiment need to be softened. This matches the reader's weakest_assumption and rationale, so the CONDITIONAL verdict is appropriate and unchanged.","tokens_in":20728,"tokens_out":9426,"duration_ms":81988,"concrete_test":"Using the deposited code and data (Figshare DOI 10.6084/m9.figshare.33198822), recompute the experimental g2/c2 and the resulting τ, β, and crystal masks for Δφ = 10°, 20°, 45°, and 90° and for crystal thresholds of 800, 1200, 2000, and 3200 s. Additionally, recompute \\bar{I}(kr) from only the first 50 frames (≈320 s, before the reported crystallization events at 640 and 960 s) and compare the liquid τ/β with the full-time normalization. If the liquid relaxation time shifts by more than the stated uncertainty (97±3 s) or the crystal mask changes by more than a few percent, the non-stationarity and parameter choices are load-bearing; if the results are stable, the concern is mitigated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim that time- and azimuthal-averaged normalization (g2/c2) yields accurate relaxation parameters and correctly identifies immobile crystals rests on the assumption that the expected scattering intensity is time-invariant and depends only on |k| (Section 2.3.5). This assumption is validated only against the equilibrium CuZr MD trajectory, where it holds by construction. The Pt57.5Cu14.7Ni5.3P22.5 experiment, however, includes in situ crystallization: for a probe position that crystallizes partway through the run, the normalization denominator \\bar{I}(kr) is a time average over two distinct structures, so δI is systematically biased before and after the transition. The paper acknowledges the stationarity requirement ('assuming no major structural changes happen during the experiment', Section 2.3.5) but then handles the violation with hand-chosen parameters: a 60° moving azimuthal window (Δφ=30°) to mitigate ellipticity and a crystal mask defined by τ>1600 s (the full experiment duration). No sensitivity analysis is presented for either choice, and the MD benchmark does not include a non-stationary scenario. Consequently, the 13% overestimation of τ in the MD test (395.0 vs 349.4 ps) is not the main issue; the open question is whether the experimental liquid dynamics (τ=97±3 s, β=0.384) and the crystal/domain assignments would survive reasonable variations of Δφ and the threshold, and whether the normalization bias from crystallization contaminates even the masked liquid average.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a new intensity normalization scheme for nanobeam electron correlation microscopy (NBED-ECM), replacing XPCS-style time-averaged and k-averaged normalizations with a time- and azimuthal-averaged reference I(kr) derived from the first diffraction ring. The authors argue that this removes artificial negative tails (from time-averaged normalization) and elevated baselines (from k-averaged normalization), yielding intensity autocorrelation functions g2 and c2 whose KWW relaxation times and stretching exponents match the self-intermediate scattering function (self-ISF) computed from MD trajectories. The method is validated on an equilibrium CuZr supercooled liquid simulation, where global relaxation parameters agree with the self-ISF benchmark (τ=395.0±0.9 ps vs 349.4±0.5 ps, β≈0.65), and is then applied to time-resolved 4D STEM data of a Pt57.5Cu14.7Ni5.3P22.5 nanowire, where it identifies stable crystalline domains that previous normalization schemes misclassified as relaxing. The paper also re-evaluates prior ECM results and discusses pitfalls of short observation windows and background-shift fitting.","tokens_in":21001,"tokens_out":3589,"duration_ms":32946,"significance":"If the claims hold, this is a valuable methodological contribution to ECM practice. The MD benchmark is an independent, parameter-free check: the self-ISF is computed from atomic positions, not fitted to the ECM result, and the normalization is derived from physical assumptions about isotropy and stationarity rather than tuned to the benchmark. The paper also makes code and data publicly available on Figshare, and it provides a concrete physical explanation (via a weighted k-averaged g2 plus ring-intensity variance) for the elevated baseline of {~c2}_tw. The identification of a systematic bias in previous tilted-DF and NBED-ECM studies is potentially important for the field. The main weakness is that the experimental portion rests on an assumption of stationarity that is explicitly violated by the in situ crystallization studied, and the sensitivity of the results to hand-chosen parameters is not examined.","major_comments":[{"comment":"The normalization denominator I(kr)=<{I(kr,kφ,tw)}_tw>_{kφ} assumes the expected scattering intensity is time-invariant and depends only on |k|, as the paper states in Section 2.3.5 ('assuming no major structural changes happen during the experiment'). The experimental dataset, however, contains in situ crystallization, so for probe positions that crystallize partway through the run the time average mixes two distinct structures and the normalized fluctuations δI are systematically biased before and after the transition. This is not a minor caveat: the paper's experimental claims—the liquid relaxation time τ=97±3 s, the stretching exponent β=0.384, and the crystal-domain maps in Figures 6 and 8—are all computed with this time-averaged reference. The authors should either validate the method on a synthetic non-stationary dataset with a known crystallization time, or provide a quantitative analysis of how the time-azimuthal normalization behaves across a crystallization event, e.g., by recomputing the results with a sliding-window time average for I.","section":"Section 2.3.5 and Section 3.4"},{"comment":"The azimuthal moving-window half-angle is set to Δφ=30° (a 60° window) with the statement that this 'works well' for the experimental data, but no sensitivity analysis or quantitative criterion is given. Because this parameter directly controls the normalization denominator for the experimental data, the reported relaxation parameters and the crystal/liquid classification may depend on it. The authors should demonstrate that the results are stable over a reasonable range of Δφ (for example 15° to 60°) or provide a principled method for selecting it, such as minimizing the residual ellipticity in the polar-transformed patterns.","section":"Section 2.3.5, experimental subsection"},{"comment":"Crystal-like domains are defined by τ>1600 s, equal to the entire experiment duration. Domains 2 and 3, which crystallize during the experiment, are not flagged by the time-averaged τ map (their time-averaged τ is shorter than 1600 s) and are detected only in the momentary τm maps of Figure 8. However, those τm maps are computed from c2 whose normalization denominator still includes both the pre- and post-crystallization intensity, so the detection is not independent of the very artifact the method is designed to remove. Please report how the crystal-domain maps change with the τ threshold (e.g., 800 s, 1600 s, 3200 s) and clarify whether the momentary c2 for a crystallizing probe position is reliable when the reference I(kr) is a mixture of two structures.","section":"Section 3.4, crystal masking"}],"minor_comments":[{"comment":"The abstract contains a grammatical error: 'Other previous ECM research is reevaluated in light of these observation' should be 'these observations'.","section":"Abstract"},{"comment":"The sentence 'the absolute values from both functions are with 0.55 and 0.75' should read 'are between 0.55 and 0.75' or similar.","section":"Section 3.2"},{"comment":"The text states 'with R2 = 0.70 for the linear regression of τm from c2 vs from the self-ISF', but this R2 value is not shown in any figure; consider reporting it in the caption of Figure 5 or stating explicitly where it is computed.","section":"Section 4.1"},{"comment":"The phrase 'ther-dependence is omitted hereafter for brevity' is missing a space; it should read 'the r-dependence'.","section":"Section 2.3.5"},{"comment":"The caption says 'All X-ray ranges were shifted to center the CuZr X-ray intensity profile peak', but the shift is not defined in the text; please state the shift convention clearly.","section":"Figure 12"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for a materials science methods journal and the central methodological contribution is sound as demonstrated by the MD benchmark. My main concern is the experimental validation: the normalization's stationarity assumption is violated by the in situ crystallization, and the analysis relies on hand-chosen parameters (Δφ=30°, τ>1600 s) without sensitivity tests. These issues are fixable within the manuscript's scope, which is why I recommend major revision rather than rejection. I do not see any citation-pattern problems; the self-citations refer to the prior data and methods that the paper builds upon."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version. This paper identifies a genuine and non-obvious problem: when you import XPCS normalization into nanobeam electron correlation microscopy, time-averaging the intensity forces an artificial negative tail into g2, and k-averaging injects a constant baseline into c2 because the structure factor varies across the diffraction ring. The proposed fix—normalizing by the time- and azimuthal-averaged intensity of the first ring—removes both artifacts in the MD test: the relaxation time is 395 ps vs 349 ps from the self-ISF (about 13% high), the stretching exponent matches within 0.02, and the behavior is stable across time-series lengths. That is a real contribution, and it is backed by a benchmark that was not fitted to the method. The code and data are deposited. The re-evaluation of earlier ECM work is careful and appropriately hedged. Credit is due.\n\nNow the soft spots, in proportion. The stationarity and isotropy assumption in Section 2.3.5 is validated only on equilibrium MD, where it holds by construction. The Pt-based nanowire experiment includes in situ crystallization, so for positions that crystallize mid-run the normalization denominator averages over two distinct structures. The paper knows this and masks crystals with tau > 1600 s and uses Delta phi = 30 degrees, but neither choice gets a sensitivity analysis. That matters because the crystallization is precisely where the new method is supposed to outperform the old ones. I don't think the stress-test's concern is fatal—the crystal assignments are corroborated by direct diffraction patterns (Fig. 9), so the demonstration is not circular—but it is a genuine gap. The 'artifact-free' framing in the abstract and conclusion is stronger than what is shown; 'artifact-reduced under stated assumptions' would be accurate. The hand-chosen KWW exclusions and smoothing kernel are minor by comparison.\n\nWho is this for? The ECM and 4D-STEM method-development community, and anyone using correlation functions on small scattering volumes. It does not reorganize glass physics, but it corrects a measurement bias in a technique that is growing. I would send it to peer review. A serious referee should ask for sensitivity analysis on Delta phi and the crystal threshold, or at least an explicit statement of when the stationarity assumption fails, and should push the authors to soften the universal claim.","headline":"The paper identifies a genuine normalization artifact in NBED-ECM and offers a fix that checks out against MD self-ISF; the experimental nonstationarity handling needs work before the 'artifact-free' claim will hold.","tokens_in":21606,"tokens_out":2094,"would_cite":true,"duration_ms":20179,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Nanoscale electron correlation microscopy returns true relaxation dynamics when intensities are normalized by the time- and azimuthal-averaged first diffraction ring.","keywords":["electron correlation microscopy","4D scanning transmission electron microscopy","nanobeam electron diffraction","intensity normalization","supercooled liquids","heterogeneous dynamics","structural relaxation","intermediate scattering function"],"falsifier":"Re-run the molecular-dynamics validation on a simulated anisotropic or slowly crystallizing sample and compare $g_2$ and $c_2$ against the self-intermediate scattering function while sweeping the azimuthal averaging window ($\\pm10^\\circ$, $\\pm30^\\circ$, $\\pm60^\\circ$, $\\pm90^\\circ$) and the crystalline fraction. If the recovered relaxation time and stretching exponent stay within fitted uncertainty for all window widths and crystal fractions, the central claim survives; if the relaxation time drifts with the window width or with global structure-factor evolution, the time- and azimuthal-averaged reference still carries a residual, method-specific bias.","tokens_in":20475,"feed_emoji":"🔬","tokens_out":12994,"duration_ms":151236,"temperature":0.7,"pith_summary":"Electron correlation microscopy aims to map how atomic structure rearranges at the nanoscale by correlating intensity fluctuations in electron diffraction patterns over time. The paper argues that the two normalizations inherited from X-ray photon correlation spectroscopy, dividing by the time-averaged intensity or by the scattering-vector-averaged intensity, each introduce a systematic artifact: a forced negative tail, or an artificially high baseline. The remedy is to normalize intensity fluctuations by the time- and azimuthal-averaged intensity of the first diffraction ring, $\\bar I(k_r)\\approx\\langle\\{I(k_r,k_\\phi,t_w)\\}_{t_w}\\rangle_{k_\\phi}$. With that reference, the one-time and two-time correlation functions $g_2$ and $c_2$ reproduce the squared self-intermediate scattering function in a molecular-dynamics CuZr supercooled liquid, and in a Pt-based metallic glass nanowire they identify unchanging crystalline domains that earlier analyses misclassified as relaxing. The practical payoff is that relaxation times, stretching exponents, and maps of spatially and temporally heterogeneous dynamics become trustworthy with shorter experiments and without ad hoc background fitting.","feed_headline":"Ring-averaged normalization fixes nanoscale electron correlation artifacts","feed_subtitle":"Time- and angle-averaged intensity removes false correlations and recovers true relaxation times.","key_machinery":"The load-bearing object is the estimator of the expected scattering intensity. Instead of using each pixel's own time average or the instantaneous average over the full ring, the paper normalizes by the time- and azimuthal-averaged intensity of the first diffraction ring, $\\bar I(k_r)\\approx\\langle\\{I(k_r,k_\\phi,t_w)\\}_{t_w}\\rangle_{k_\\phi}$, computed within a $\\pm30^\\circ$ moving window along the azimuth to guard against residual ring ellipticity. This single denominator removes both artifacts: it is not constrained to have zero time mean, and it does not average over the radial range where the structure factor changes. It turns $g_2$ and $c_2$ into clean stretched-exponential decays that track the squared self-intermediate scattering function without an extra background parameter.","core_discovery":"The central claim is that the reference intensity used to define normalized fluctuations, $\\delta I=(I-\\bar I)/\\bar I$, determines whether electron correlation microscopy measures real dynamics. Estimating $\\bar I$ by the time average, $\\bar I(k)=\\{I(k,t_w)\\}_{t_w}$, consumes a degree of freedom and forces the autocorrelation negative at long delays; estimating it by the $k$-average, $\\bar I(t_w)=\\langle I(k,t_w)\\rangle_k$, is biased because the expected intensity varies across the first diffraction ring, adding a nearly constant positive background to the two-time correlation. The paper proposes $\\bar I(k_r)\\approx\\langle\\{I(k_r,k_\\phi,t_w)\\}_{t_w}\\rangle_{k_\\phi\\pm\\Delta\\phi}$, with a moving azimuthal window about 60 degrees wide to minimize ring ellipticity. In the molecular-dynamics benchmark this $g_2$ gives $\\langle\\tau\\rangle=395.0\\pm0.9$ ps and $\\langle\\beta\\rangle=0.653\\pm0.002$, close to the self-intermediate-scattering-function values of $349.4\\pm0.5$ ps and $0.670\\pm0.001$, while the time-averaged normalization gives $318\\pm5$ ps and the $k$-averaged normalization gives $2700\\pm900$ ps. In the experimental nanowire, local $g_2$ maps flag domains whose relaxation time exceeds the experiment duration as immobile crystals, and two-time maps show the exact wait time at which newly formed domains crystallize.","pith_inferences":["Because the paper diagnoses the elevated baseline as a consequence of sampling a $k$-range over which the time-averaged intensity varies, the same correction should be needed for any small-probe correlation experiment, such as a scanning X-ray nanobeam, whose detector spans more than one speckle; a direct test would be to apply the time-and-azimuthal normalization to such data.","The paper attributes the remaining scatter between $c_2$ and the self-intermediate scattering function to ECM seeing only the subset of atoms that scatter strongly; a testable consequence is that a diffraction-weighted self-intermediate scattering function computed from the molecular-dynamics trajectory should agree with $c_2$ better than the unweighted one does.","The method relies on two hand-chosen parameters, the 60-degree azimuthal averaging window and the $\\tau>1600$ s crystal cutoff in the experimental data. A fully automated pipeline would need a data-driven rule for both, for example choosing the window from measured ring ellipticity or speckle width and setting the crystal threshold from the distribution of local relaxation times rather than the to"],"forward_implications":["With the proposed $g_2$, a molecular-dynamics benchmark returns $\\langle\\tau\\rangle=395.0\\pm0.9$ ps and $\\langle\\beta\\rangle=0.653\\pm0.002$, versus self-intermediate-scattering-function values of $349.4\\pm0.5$ ps and $0.670\\pm0.001$; the two competing normalizations miss by tens of percent to an order of magnitude.","Stable relaxation times and exponents can be obtained with experiment durations around $20\\langle\\tau\\rangle$ instead of the roughly $40\\langle\\tau\\rangle$ needed for time-averaged normalization; runs shorter than $5\\langle\\tau\\rangle$ are unreliable regardless.","Stretching exponents larger than 1 reported in previous short-duration electron correlation studies are likely artifacts of too-short observation windows, not evidence of compressed-exponential dynamics.","Unchanging nanoscale crystalline domains become visible as regions with local relaxation time exceeding the experiment duration, and crystallization events appear as high-correlation patches in two-time maps at the moment of transformation, so crystallization can be localized in both space and time.","Previous results from both nanobeam and tilted dark-field electron correlation studies may need re-examination: time-averaged normalization can miss crystals entirely, while $k$-averaged normalization with shifted stretched-exponential background fitting can return relaxation times whose uncertainty exceeds the estimate."],"supporting_citations":[{"why":"Provides the experimental time-resolved 4D STEM Pt-nanowire dataset and the time-averaged normalization whose artifacts this paper identifies.","marker":"Huang & Voyles, 2024"},{"why":"Established tilted dark-field ECM and the time-averaged normalization, and reported that the relaxation time converges only for experiment durations near 40 time constants.","marker":"Zhang et al., 2018"},{"why":"The nanobeam ECM study using k-averaged normalization and a shifted stretched-exponential background that this paper argues is unreliable for immobile domains.","marker":"Nakazawa & Mitsuishi, 2025"},{"why":"Supplies the mathematical argument that subtracting the sample mean from a time series forces negative autocorrelation at long lags.","marker":"Percival, 1993"},{"why":"Provides the interatomic potential used for the CuZr molecular-dynamics trajectory that serves as the benchmark.","marker":"Mendelev et al., 2009"},{"why":"Provides the multislice simulation method used to generate nanobeam diffraction patterns from the molecular-dynamics snapshots.","marker":"Madsen & Susi, 2021"},{"why":"An earlier tilted dark-field ECM study whose images may contain undetected crystalline regions, used as motivation for reanalysis.","marker":"Chatterjee et al., 2021"},{"why":"A short-duration tilted dark-field ECM dataset with stretching exponents above 1 that the paper attributes to truncation artifacts.","marker":"Vaerst et al., 2023"},{"why":"Introduced the shifted stretched-exponential fit with a constant background whose application to nanobeam ECM data is criticized.","marker":"Zhang et al., 2023"}],"fun_headline_variants":["Ring-averaged intensities fix electron correlation artifacts","New normalization removes false dynamics in electron correlation","Ring averaging corrects electron microscopy dynamics artifacts","Fixing electron correlation artifacts with ring-averaged intensities","Ring-averaged normalization unmasked nanoscale dynamics"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The method assumes the expected scattering intensity at each pixel is time-invariant and depends only on $|k|$, so the time- and azimuthal-averaged ring intensity is the correct denominator; if the sample is anisotropic, has thickness or ellipticity gradients that survive the 60-degree moving window, or evolves structurally during the experiment, this reference is biased, and the paper's choices of a hand-picked 60-degree window and a $\\tau>1600$ s crystal cutoff are not subjected to sensitivity analysis.","fun_headline_variants_meta":{"raw":{"variants":["Ring-averaged intensities fix electron correlation artifacts","New normalization removes false dynamics in electron correlation","Ring averaging corrects electron microscopy dynamics artifacts","Fixing electron correlation artifacts with ring-averaged intensities","Ring-averaged normalization unmasked nanoscale dynamics"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000653,"raw_usage":{"total_tokens":3063,"prompt_tokens":1082,"completion_tokens":1981,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":698,"completion_tokens_details":{"reasoning_tokens":1909}},"tokens_in":698,"tokens_out":1981,"duration_ms":34300,"temperature":1.0,"reasoning_tokens":1909,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:12:45.949351+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the molecular-dynamics validation on a simulated anisotropic or slowly crystallizing sample and compare $g_2$ and $c_2$ against the self-intermediate scattering function while sweeping the azimuthal averaging window ($\\pm10^\\circ$, $\\pm30^\\circ$, $\\pm60^\\circ$, $\\pm90^\\circ$) and the crystalline fraction. If the recovered relaxation time and stretching exponent stay within fitted uncertainty for all window widths and crystal fractions, the central claim survives; if the relaxation time drifts with the window width or with global structure-factor evolution, the time- and azimuthal-averaged reference still carries a residual, method-specific bias.","supporting_citations":[{"cited_title":"Ritchie and Andrew M","cited_arxiv_id":null,"evidence_quote":"Introduced the shifted stretched-exponential fit with a constant background whose application to nanobeam ECM data is criticized."}],"review_version":1}