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[Katsuaki Nakazawa](https://orcid.org/0000-0002-6056-5615), [Kazutaka Mitsuishi](https://orcid.org/0000-0002-9361-4057), Konstantin Iakoubovskii, [Shinji Kohara](https://orcid.org/0000-0001-9596-2680), [Koichi Tsuchiya](https://orcid.org/0000-0003-0267-2727)

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[Structure-dynamics relation in metallic glass revealed by 5-dimensional scanning transmission electron microscopy](https://mdr.nims.go.jp/datasets/aa072ea7-dadb-47d8-863a-2c1af406f9a4)

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Structure-dynamics relation in metallic glass revealed by 5-dimensional scanning transmission electron microscopyNakazawa et al. NPG Asia Materials           (2024) 16:57 https://doi.org/10.1038/s41427-024-00577-1 NPG Asia MaterialsART ICLE Open Ac ce s sStructure-dynamics relation in metallic glassrevealed by 5-dimensional scanning transmissionelectron microscopyKatsuaki Nakazawa 1, Kazutaka Mitsuishi2, Konstantin Iakoubovskii3, Shinji Kohara 2 and Koichi Tsuchiya1,4AbstractDynamical and structural heterogeneities play an important role in glass transition phenomena. However, the relationbetween these heterogeneities is not fully revealed. In this study, we simultaneously observed these heterogeneitiesnear the glass transition temperature in Zr50Cu40Al10 using five-dimensional scanning transmission electronmicroscopy, which can record the spatiotemporal distribution of diffraction patterns. The heterogeneities werevisualized with sub-nanometer resolution, and a correlation between them was measured up to the glass transitiontemperature. We verified that ordered structures had slow dynamics, and the order decreased as the temperatureincreased.IntroductionGlass transition is a universal phenomenon observed ina wide range of materials, including metals, polymers, andceramics, which were cooled from the melt quicklyenough to avoid crystallization and freeze the constituentatoms or molecules in disordered positions1,2. Since theglass phase has different physical properties comparedwith a liquid or a crystal, and the glass transition isstrongly related to crystallization and melting, this phe-nomenon is important for controlling physical and tech-nological properties such as moldability3. However, theprocess of freezing the atomic dynamics is still notunderstood. In the glass transition phenomenon, theviscosity changes rapidly near the glass transition tem-perature (Tg), even though the average structure remainsalmost unchanged4. Hence, to explain the viscosity var-iations, researchers focused on the microscopic structureof glasses and supercooled liquids. Dynamical hetero-geneity was discovered in simulations and experiments oncolloidal systems5,6, in which the motion of particles isheterogeneous and results in clustering. The dynamicalheterogeneity shows a divergent behavior near Tg and isexpected to explain the drastic change in viscosity duringthe glass transition. Furthermore, it has been revealed byelectron tomography and other methods that there is aspatial heterogeneity of atomic arrangement in glas-ses7–11. This heterogeneity is called structural hetero-geneity. The relation between dynamical and structuralheterogeneities is important. If a common atomic struc-ture of the slow-dynamics region in the dynamical het-erogeneity is detected, it may become possible to identifythe structures that cause the slow dynamics (high visc-osity) and are necessary for the glass transition. Sinceatomic motion is affected by the surrounding atomicstructure, there must be a relation between them. In fact,the relation between the structure and the temperaturedependence of viscosity (fragility) has already beenreported12,13, and a relation between heterogeneities hasbeen suggested,14–18 but has not been confirmed experi-mentally so far, possibly because of the scarcity lack ofobservation methods that can simultaneously probe boththe structural and dynamical heterogeneities. Thosemethods require a spatial resolution of a few nanometers,a time resolution of a few seconds, and the ability tomeasure the local structure of glass.© The Author(s) 2024OpenAccessThis article is licensedunder aCreativeCommonsAttribution 4.0 International License,whichpermits use, sharing, adaptation, distribution and reproductionin any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate ifchangesweremade. The images or other third partymaterial in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to thematerial. Ifmaterial is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtainpermission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.Correspondence: Katsuaki Nakazawa (NAKAZAWA.Katsuaki@nims.go.jp)1International Center for Young Scientists, National Institute for MaterialsScience, 1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, Japan2Center for Basic Research on Materials, National Institute for Materials Science,1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, JapanFull list of author information is available at the end of the article1234567890():,;1234567890():,;1234567890():,;1234567890():,;http://orcid.org/0000-0002-6056-5615http://orcid.org/0000-0002-6056-5615http://orcid.org/0000-0002-6056-5615http://orcid.org/0000-0002-6056-5615http://orcid.org/0000-0002-6056-5615http://orcid.org/0000-0001-9596-2680http://orcid.org/0000-0001-9596-2680http://orcid.org/0000-0001-9596-2680http://orcid.org/0000-0001-9596-2680http://orcid.org/0000-0001-9596-2680http://creativecommons.org/licenses/by/4.0/mailto:NAKAZAWA.Katsuaki@nims.go.jpExperimental methods for characterizing dynamics atthe atomic scale in glass began with measuring averagevalues using X-ray photon correlation microscopy(XPCS)19–21, progressed to probing local dynamics withelectron correlation microscopy (ECM)22,23, and advancedto visualizing dynamical heterogeneities using dark-fieldelectron correlation microscopy (DF-ECM)24. Thesemethods did contribute to the understanding of glassdynamics, but they suffered from low spatial resolution(XPCS), inabilities to observe the spatial distribution(ECM) or local structures (DF-ECM). However, a noveltechnique of 5-dimensional scanning transmission elec-tron microscopy (5D-STEM)25–27 that involves con-vergent electron beam diffraction (CBED) does meet therequirements mentioned above. 5D-STEM is an extensionof 4D-STEM28. It consists of 2D real-space scanning and2D diffraction patterns, with the addition of a timedimension, and enables the measurement of the spatio-temporal distribution of CBED patterns. These patternscan yield local information that is hard to retrieve in theconventional parallel-beam diffraction mode. When aparallel electron beam irradiates a macroscale volume of aglass, a halo pattern is observed. However, when theprobed volume shrinks to the nanoscale, intensity fluc-tuations, called speckles, appear instead29,30. The specklepattern reflects the local order of the atomic struc-ture31–34, and its temporal change reflects the motion ofthe local atomic structure22. Thus, as illustrated in Fig. 1,the local structure of a glass can be analyzed from thespatial distribution of diffraction patterns, and the localatomic rearrangement can be measured from the corre-sponding time sequences.In this study, we used 5D-STEM to simultaneouslyobserve dynamical and structural heterogeneities andanalyze the relation between them in a Zr50Cu40Al10metallic glass. We also conducted an in situ heatingexperiment to measure the temperature dependences ofthe dynamical and structural heterogeneities and thestructure-dynamics relation below Tg.Materials and methodsZr50Cu40Al10 metallic glass was fabricated by the tilt-melting method. Its glass transition and crystallization tem-peratures were 673K and 750K at the heating rate of1.4min/K35. TEM samples were fabricated by focused ionbeammilling. STEM observation was conducted at 200 kV inan aberration-corrected JEM-ARM200F microscope (JEOL.Ltd.) equipped with a cold field emission gun and a4DCanvas camera (JEOL. Ltd.). In the normal operationcondition, the convergence semi-angle of the electron probewas in the range of 10 to 30 mrad (which corresponds to 6.0to 18.0 nm–1). This value is much larger than the typicaldiffraction angle of speckles, and hence it was not possible toobserve them. Therefore, the condenser lens and one of thetransfer lenses of the corrector were adjusted to achieve anappropriate convergence semi-angle of 1.6mrad (0.95 nm–1)that results in a probe diameter of 0.78 nm (full width at halfmaximum). The probe current was 8.9 pA. We used a beamstop to save the detector from the transmitted electron beam.The shadow of the beam stop was excluded from the analysisby excluding this area from the calculation of eqs. (1) and (5).To investigate temperature dependences of dynamical andstructural heterogeneities and structure-dynamics relations,we heated the sample from 633 to 673K in 10K increments.Each diffraction pattern was acquired within 1ms at 633 and643K and within 0.5ms at 653, 663, and 673K. The numberof scan points and the step were 60 × 120 and 0.16 nm,respectively. The total observation area was 9.7 × 19.4 nm.Since 5D-STEM requires a sample edge for data calibration,we set the observation area as a horizontal rectangle. A totalof 106 diffraction patterns were acquired for each scan pointwith a 9.2 s time resolution at 633 and 643K and a 4.8 s timeresolution at 653, 663, and 673K. The total observation timewas 1048 s at 633 and 643K and 524 s at 653, 663, and 673K.The pixel size and number of pixels for diffraction patternswere 0.058 nm–1 and 264 × 264. The diffraction patternswere 4 × 4 binned to increase the signal-to-noise ratio. Theresultant pixel size and the number of pixels were 0.23 nm–1and 66 × 66. The diffraction patterns near the sample edge(the left part of the sample) were too noisy for reliablemeasurements because of their thin thickness. Therefore, weused only the right half of the observed area whose thicknessrange is 40–50 nm in this article (see Fig. S1) to reducethickness dependence and eliminate spurious signals.Results and discussionThe local dynamics were evaluated from the temporalchange of the local diffraction patterns using the followingequations:16,20,21,36,37G Q; t1; t2ð Þ ¼ I Q; t1ð ÞI Q; t2ð Þh iϕI Q; t1ð Þh iϕ I Q; t2ð Þh iϕð1Þg Q; tð Þ ¼ G Q; t1; tð Þh it1 ð2ÞHere Q is the position vector in reciprocal space, itsabsolute value Q is the spatial frequency and t, t1 and t2are acquisition times. G Q; t1; t2ð Þ measures the correla-tion between diffractions acquired at times t1 and t2.I Q; t1ð Þ is the signal intensity at Q and t1, and 〈⋯〉ϕ thesubscript ϕ indicates that the averaging is performed onthe ensemble of pixels over a range of spatial frequency. Inthis study, we limited the frequency to the range of4.2–4.6 nm–1 that covered the first sharp diffractionpeaks. Strong speckles are observed when the electronbeam irradiates an ordered atomic structure along itssymmetry axis. Speckles are formed when the electronbeam irradiates an ordered atomic structure along itsNakazawa et al. NPG Asia Materials           (2024) 16:57 Page 2 of 7    57 symmetry axis. Thus, this method probes the dynamics ofthe ordered atomic structures whose crystal symmetryaxis is aligned to the beam direction. g Q; tð Þ takes theaverage of G Q; t1; t2ð Þ over t1, at a fixed delay time, t ¼ t2�t1. The Kohlrausch-Williams-Watts (KWW) functionwas fitted to g Q; tð Þ to measure the dynamics.g Q; tð Þ � 1 ¼ β exp �2tτ� �γ� �ð3ÞHere β, τ and γ are a scaling constant, the relaxation time,and the stretch factor, respectively. The stretch factorrepresents the nonlinearity of relaxation and indicateswhether relaxation is compressed (γ>1) or stretched(γ<1) as compared to the simple exponent. Relaxation timeis an indicator of dynamics; long relaxation time indicatesslow dynamics and vice versa. We measured the relaxationtime from all scan points to obtain a relaxation time map thatdirectly reflects the dynamical heterogeneity. The relaxationtime map for 633 K is presented in Fig. 2a. As seen from themap, the relaxation time spatially varies from 200 s to 5000 srevealing a heterogeneity of local dynamics. As shown in Fig.2b–e, although the relaxation times vary, the dynamicalheterogeneity has been observed at different temperatures.The average relaxation time is plotted in Fig. 2f; it shortens asthe temperature approaches Tg, indicating an increase inatomic mobility. These values show good agreement with theprevious research of Zr–Cu–Al systems, and such tempera-ture dependence was observed in a series of metallic glassesusing various measuring methods38–40. In samples withsimilar composition (Cu59Zr41), the relaxation process belowTg is thought of as β-relaxation. From the energy landscapeperspective, β-relaxation is recognized as hopping acrosssub-basins inside an identical mega-basin. The activationenergy to cross the sub-basins can be estimated from thetemperature dependence of the relaxation time below Tg.The relation between relaxation time and activation energy isFig. 1 Schematic of measurements of dynamical and structural heterogeneities by 5D-STEM. V Qð Þ is calculated from each diffraction patternand averaged over time to make fluctuation map. g Q; tð Þ is calculated from sequential CBED images at each position according to equations (1) and(2). By fitting the KWW function to g Q; tð Þ at each position, relaxation time map can be obtained. Examples of sequential CBED images whoserelaxation times are slow and fast are shown in bottom left and their g Q; tð Þ are shown in bottom center panel.Nakazawa et al. NPG Asia Materials           (2024) 16:57 Page 3 of 7    57 expressed by the Arrhenius law.τ ¼ τ1 expEβRT� �; ð4ÞWhere τ∞ is the relaxation time at infinite temperature, Eβis the activation energy and R is the gas constant. Theactivation energy was calculated as 97 ± kJ/mol. Thisvalue falls within the range of the previously reportedvalues, namely, 46 kJ/mol by internal friction measure-ments in Cu59Zr4141, 96–159 kJ/mol by MD simulationsof the Zr-Cu system42–44, and 62–174 kJ/mol by dynamicmechanical analysis of Zr-Cu-Al alloys45–47.To evaluate the structural heterogeneity, we measuredthe intensity fluctuation along the azimuthal directionaround the halo pattern. This intensity fluctuation mainlyoriginates from the speckle pattern. The fluctuation isevaluated by the following equation:V Q; rð Þ ¼I Q; rð Þ2� �ϕI Q; rð Þh i2ϕ� 1 ð5ÞSince the speckle pattern reflects the local atomicstructure, so does the value of V Q; rð Þ—a higherV Q; rð Þ corresponds to a more ordered structure32,48. Itshould be noted that the value of V Q; rð Þ is alsoinfluenced by the direction of the symmetry axis.However, since glass is isotropic, such effects can begreatly reduced by statistical sampling, making V Q; rð Þ areliable indicator for measuring overall trends andcorrelations. In this experiment, V Q; rð Þ was measuredfrom diffractions whose spatial frequency ranged from 3.0to 5.8 nm–1. We measured V Q; rð Þ for all scanning pointsand averaged it over time. Figure 3a shows the calculatedfluctuation map at 633 K. The values range from 0.45 to0.75 and show heterogeneous distribution, indicating thecoexistence of different local atomic structures. Thisimage directly visualizes the structural heterogeneity ofmetallic glass. Thus, it was confirmed that the localatomic structure was heterogeneous. As shown in Fig.3b–e, although the V Q; rð Þ values vary, the structuralheterogeneity has been observed at different tempera-tures. The temperature dependence of average V Q; rð Þ isshown in Fig. 3f. The average V Q; rð Þ slightly decreasedwith temperature from 0.56 to 0.52, reflecting thedecrease in atomic order. A similar slight decrease inthe average local order was theoretically predicted forZr47.5Cu47.5Al5 glass49.As mentioned above, the dynamical and structuralheterogeneities can be measured simultaneously by 5D-STEM. The structure-dynamics relation was evaluatedfrom these heterogeneities by correlating the maps ofrelaxation time and V Q; rð Þ. Since the local order wasFig. 2 Visualized dynamical heterogeneities. Maps of relaxation time at a 633 K, b 643 K, c 653 K, d 663 K, and e 673 K. f Temperature dependenceof the spatially averaged relaxation time. The error bar shows the distribution of relaxation time.Nakazawa et al. NPG Asia Materials           (2024) 16:57 Page 4 of 7    57 probed by the speckle pattern and the local relaxationtime was measured from the temporal change of the samepattern, the local atomic order and atomic rearrange-ments were measured from the same nanostructure, andthe correlation between dynamical and structural het-erogeneities directly reflects the structure-dynamic rela-tion. The degree of relaxation depends both on therelaxation time and the value of γ50. To simplify theanalysis, considering that γ values are close to 1 (see Figs.S1 and S2), we fixed γ at 1.0. The correlation was calcu-lated by Spearman’s rank correlation, where the correla-tion value can range from −1 to 1. Positive and negativevalues mean positive and negative correlations betweenthe maps of relaxation time and V Q; rð Þ, while 0 meanslack of correlation. A scatter plot is shown in Fig. 4 withV Q; rð Þ on the vertical axis and relaxation time on thehorizontal axis. At 633 K, the distribution of the points isstretched from the center to the upper right, and thecorrelation value is 0.39, statistically indicating thatregions with a long relaxation time and regions with apartial order tend to coincide. Thus, ordered regions tendto have slow dynamics. This tendency is also observed insimulations of polydisperse particles14. It is noteworthythat not all structural heterogeneities exhibit correlationswith dynamical heterogeneities. Structural heterogeneitiescalculated by density or potential energy fields do notexhibit a positive correlation with dynamical hetero-geneities14,51. Simulation studies have demonstrated thatthe multi-body effects such as flexibility17, deviations fromsterically favored structures14, or softness18 are significantin explaining dynamical heterogeneity, as the relaxationprocess is affected by surrounding atoms or particles. Thediffraction or speckle pattern formed by the interferenceof electrons scattered by atoms naturally includes infor-mation about surrounding atoms31. Therefore, a positivecorrelation has been observed between structural het-erogeneity measured by V Qð Þ and dynamical hetero-geneity. The same tendency is observed at highertemperatures, as shown in Fig. 4b–e, and especially in Fig.4f, which superimposes the scatter plots for all tempera-tures. Figure 4f reveals that the relaxation time shortens athigher temperatures. Meanwhile, the shift in the dis-tribution toward the lower left corner indicates that thenumber of less regular structures that exhibit higheratomic mobility increases at high temperatures.In summary, our results can be interpreted as follows: atlow temperatures, the atomic rearrangement was slow. Asthe temperature increased, the atomic motion sped up,and the degree of local atomic order decreased. Theatomic motion was slow for ordered regions regardless oftemperature. The atomic motion accelerated near Tg fortwo reasons: (1) an increase in the number of structuresFig. 3 Visualized structural heterogeneities. Maps of V Q; rð Þ at a 633 K, b 643 K, c 653 K, d 663 K, and e 673 K. f The average V Qð Þ at alltemperatures. The errorbar shows the distribution of V Qð Þ. Q is the spatial frequency and ranged from 3.0 to 5.8 nm−1 in this calculation.Nakazawa et al. NPG Asia Materials           (2024) 16:57 Page 5 of 7    57 that have a low degree of order and hence a high atomicmobility, and (2) an increase in the atomic mobility instructures with any degree of order.Structural and dynamical heterogeneities are importantfor elucidating the mechanism of glass transition. How-ever, the relationship between these heterogeneities isdifficult to analyze because of the lack of experimentalmethods that can simultaneously measure these hetero-geneities. In this study, we simultaneously visualized thedynamical and structural heterogeneities in aZr50Cu40Al10 metallic glass by recording the spatio-temporal distribution of diffraction patterns via 5D-STEM. We also measured the temperature dependen-cies of relaxation time and structural order. The resultsdirectly reveal a positive correlation between dynamicaland structural heterogeneities, indicating that atomicrearrangement is slower in more ordered atomic struc-tures. This study demonstrates the high potential of 5D-STEM in monitoring the dynamical and structural het-erogeneities in glasses, yet the reported calculation ofV Q; rð Þ can only hint at the presence of the orderedstructure. Therefore, a better correlation of structure anddynamics would require the development of new analy-tical methods for diffraction patterns that can identifytranslational symmetry, rotational symmetry, and whetherthe structural order is energy-driven or entropy-driven, asproposed for atomic structures in real space52.AcknowledgementsWe thank Ms. K. Shiomi for her help with the preparation of the sample andProf. T. Sannomiya for advice on STEM electron optics. We also would like tothank Profs. T. Ichitsubo and H. Kato for fruitful discussions. This work wassupported by JSPS KAKENHI Grant Number JP23K13076. This research isfounded by JSPS KAKENHI Grant Number JP23K13076.Author details1International Center for Young Scientists, National Institute for MaterialsScience, 1-2-1, Sengen, Tsukuba, Ibaraki 305-0047, Japan. 2Center for BasicResearch on Materials, National Institute for Materials Science, 1-2-1, Sengen,Tsukuba, Ibaraki 305-0047, Japan. 3Department of Physics, National Universityof Singapore, Singapore 117551, Singapore. 4Research Center for StructuralMaterials, National Institute for Materials Science, 1-2-1, Sengen, Tsukuba,Ibaraki 305-0047, JapanAuthor contributionsK.N., S.K., and K.M. conceived the idea and experiments. K.T. prepared bulkZr50Cu40Al10 metallic glass, and K.N. processed the TEM sample. K.N., K.M., andK.I. measured relaxation time. K.N. and K.I. analyzed the data and wrote themanuscript. K.N. and S.K. prepared the figures. All the authors participated inthe manuscript review.Conflict of interestThe authors declare no competing interests.Fig. 4 Correlation between dynamical and structural heterogeneities. Scatter plots of relaxation time and V Qð Þ at a 633 K, b 643 K, c 653 K,d 663 K, e 673 K. f Superimposed scatter plots at all temperatures.Nakazawa et al. NPG Asia Materials           (2024) 16:57 Page 6 of 7    57 Publisher’s noteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.Supplementary information The online version contains supplementarymaterial available at https://doi.org/10.1038/s41427-024-00577-1.Received: 2 April 2024 Revised: 9 October 2024 Accepted: 14 October 2024References1. Angell, C. A. Perspective on the glass transition. J. Phys. Chem. Solids 49,863–871 (1988).2. Berthier, L. & Biroli, G. Theoretical perspective on the glass transition andamorphous materials. Rev. Mod. Phys. 83, 587–645 (2011).3. 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Tanaka, H., Tong, H., Shi, R. & Russo, J. Revealing key structural features hiddenin liquids and glasses. Nat. Rev. Phys. 1, 333–348 (2019).Nakazawa et al. NPG Asia Materials           (2024) 16:57 Page 7 of 7    57 https://doi.org/10.1038/s41427-024-00577-1 Structure-dynamics relation in metallic glass revealed by 5-dimensional scanning transmission electron microscopy Introduction Materials and methods Results and discussion Acknowledgements