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[Ovidiu Cretu](https://orcid.org/0000-0002-1822-8172), [Han Zhang](https://orcid.org/0000-0003-0298-8502), [Koji Harano](https://orcid.org/0000-0001-6800-8023), [Koji Kimoto](https://orcid.org/0000-0002-3927-0492)

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Characterizing the effects of temperature on the thermal vibration properties of individual nanowiresViewOnlineExportCitationRESEARCH ARTICLE |  OCTOBER 02 2025Characterizing the effects of temperature on the thermalvibration properties of individual nanowiresOvidiu Cretu   ; Han Zhang  ; Koji Harano  ; Koji Kimoto J. Appl. Phys. 138, 134301 (2025)https://doi.org/10.1063/5.0288200Articles You May Be Interested InStructural and electronic properties of transferred graphene on yttrium iron garnet (111)J. Appl. Phys. (August 2025)Nanometer-scale mapping of defect-induced luminescence centers in cadmium sulfide nanowiresAppl. Phys. Lett. (March 2017) 06 October 2025 01:43:39https://pubs.aip.org/aip/jap/article/138/13/134301/3365793/Characterizing-the-effects-of-temperature-on-thehttps://pubs.aip.org/aip/jap/article/138/13/134301/3365793/Characterizing-the-effects-of-temperature-on-the?pdfCoverIconEvent=citejavascript:;https://orcid.org/0000-0002-1822-8172javascript:;https://orcid.org/0000-0003-0298-8502javascript:;https://orcid.org/0000-0001-6800-8023javascript:;https://orcid.org/0000-0002-3927-0492https://crossmark.crossref.org/dialog/?doi=10.1063/5.0288200&domain=pdf&date_stamp=2025-10-02https://doi.org/10.1063/5.0288200https://pubs.aip.org/aip/jap/article/138/6/064301/3358333/Structural-and-electronic-properties-ofhttps://pubs.aip.org/aip/apl/article/110/11/111904/32785/Nanometer-scale-mapping-of-defect-inducedhttps://e-11492.adzerk.net/r?e=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&s=-5E2HgWMyRqnOhEocVacG4H4P4sCharacterizing the effects of temperature onthe thermal vibration properties of individualnanowiresCite as: J. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200View Online Export Citation CrossMarkSubmitted: 30 June 2025 · Accepted: 13 September 2025 ·Published Online: 2 October 2025Ovidiu Cretu,1,a) Han Zhang,1 Koji Harano,1,2 and Koji Kimoto1AFFILIATIONS1Center for Basic Research on Materials (CBRM), National Institute for Materials Science (NIMS), Namiki 1-1, Tsukuba,Ibaraki 305-0044, Japan2Research Center for Autonomous Systems Materialogy (ASMat), Institute of Integrated Research, Institute of Science Tokyo,4259 Nagatsuda-cho, Midori-ku, Yokohama, Kanagawa 226–8501, Japana)Author to whom correspondence should be addressed: cretu.ovidiu@nims.go.jpABSTRACTWe study the effects of temperature on the properties of thermal vibrations of individual LaB6 single-crystal nanowires inside a transmissionelectron microscope using a method which combines high spatial resolution, high temporal resolution, and in situ temperature control.We find that the vibrations can be accurately modeled by classical formalisms, despite the small size of the resonator. We observe a vibrationfrequency decrease with temperature which enables us to measure the temperature coefficient of Young’s modulus, finding a value ofαE ffi �9� 10�5 K�1 over the 300–700 K temperature range. We additionally introduce a method to precisely measure the vibration ampli-tude, which agrees well with values predicted by the Boltzmann equipartition theorem over the entire temperature range.© 2025 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0288200I. INTRODUCTIONThe characterization of the vibration properties of nanometer-sized objects is important due to their applications as nanomechani-cal resonators.1–3 Evaluating these properties is also critical in caseswhere vibration has detrimental effects on the function of thesenanostructures, such as the loss of spatial coherence for electronsources.4,5 Understanding temperature effects on these properties isimportant for devices operating as high-temperature resonators6,7 orelectron emitters, where temperature is used to lower the work func-tion of the material and maintain a clean surface.8 In addition,thermal activation is interesting for designing self-powered devices.9Measuring vibration properties becomes increasingly challeng-ing as the size of individual objects decreases and requires solutionssuch as coupling with optical cavities.10 Electron microscopes offerexcellent spatial resolution, but relatively poor temporal resolutionwhen compared to the vibration frequency of nanostructures,which can easily extend beyond the MHz regime.2 In order to over-come the temporal resolution limitation, previous studies havecombined scanning electron microscopes (SEMs) and fast signalacquisition electronics in order to study the dynamics of individualvibrating objects.11–15 In these cases, the measurements are limitedby the nanometer-level spatial resolution of the microscope. Anobvious solution is to use a transmission electron microscope(TEM), which is able to image nanomaterials with sub-angstromresolution. We have recently introduced a method to separate anddirectly image thermal vibration modes in a TEM,16 which showedexcellent qualitative agreement between the measured and calcu-lated mode shapes at room temperature.In the present study, we extend our previous work by varyingthe temperature of the sample in situ using a heating holder andinvestigating the effects of temperature on the properties of thermalvibrations. The first part of the paper provides a detailed analysis inthe time- and frequency domain of the signals which we collectduring the experiment, which includes a comparison with simu-lated data. The second part analyzes the temperature dependencyof the frequency variation with temperature, using mechanicalvibration theory in order to model it and derive the temperatureJournal ofApplied PhysicsMETHOD pubs.aip.org/aip/japJ. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200 138, 134301-1© Author(s) 2025 06 October 2025 01:43:39https://doi.org/10.1063/5.0288200https://doi.org/10.1063/5.0288200https://pubs.aip.org/action/showCitFormats?type=show&doi=10.1063/5.0288200http://crossmark.crossref.org/dialog/?doi=10.1063/5.0288200&domain=pdf&date_stamp=2025-10-02https://orcid.org/0000-0002-1822-8172https://orcid.org/0000-0003-0298-8502https://orcid.org/0000-0001-6800-8023https://orcid.org/0000-0002-3927-0492mailto:cretu.ovidiu@nims.go.jphttps://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://doi.org/10.1063/5.0288200https://pubs.aip.org/aip/japcoefficient of Young’s modulus. The third part of the paper intro-duces a method to precisely measure the vibration amplitude,which is modeled by using the Boltzmann equipartition theorem.Finally, the main challenges and limitations are discussed in detail.II. METHODSThe single-crystal LaB6 nanowires used in this study were syn-thesized following a procedure described previously.17 Briefly, BCl3gas and LaCl3 powder were introduced in a quartz tube furnaceand heated to 1150 °C; the nanowire growth occurred on aPt-coated Si substrate, placed downstream from the location of thepowder. An individual nanowire was deposited on the tip of a Taneedle using a nanomanipulator;18 the nanowire was aligned to theaxis of the needle. The Ta needle was then fixed on a 3 mm washerusing Ag epoxy. The final assembly could be installed into a stan-dard TEM sample holder. A low-magnification TEM image of thenanowire is displayed in Fig. S1 in the supplementary material,showing that the nanowire extends beyond the edge of the Taneedle by a distance of approximately 12 μm.The experiments were performed using a TFS Titan3 micro-scope, equipped with dual aberration-correctors and a monochro-mator. The microscope was operated at 80 kV in STEM (scanning)mode, with a convergence angle of 18 mrad, resulting in a probesize of less than 0.2 nm (FWHM). The probe current was set toapproximately 100 pA. The sample was installed in a single-tiltMelBuild furnace-type heating holder, which allows for heating upto 600 °C. The temperature of the nanowire was varied betweenroom temperature and 400 °C, with a soak time of more than30 min after each temperature change.An outline of the experimental setup is displayed in Fig. 1.The data were collected using a custom scanning and acquisitionsystem,16 composed of a scan controller implemented using aNational Instruments (NI) PXIe-7862 field-programmable gatearray (FPGA) based reconfigurable I/O module connected to thescan coils, together with a NI PXIe-5111 high-speed digitizer con-nected to a Gatan 806 high-angle annular dark-field (HAADF)detector. The data were acquired using NI LabVIEW and processedusing ImageJ19 and Gatan DigitalMicrograph. The experiment con-sisted of collecting the HAADF detector signal at high speed at eachpoint, over the entire scanned area, resulting in a 3D data set.Data-cubes of 128 × 128 × 8192 voxels were collected at each temper-ature, using acquisition rates of 2 and 20MHz at each scan point.In order to better understand the experimental results, thesignals were simulated by generating square-wave functions andconvoluting them with Gaussians, followed by Fourier analysis.Noise was also added to the calculated signals; however, it did notmake any significant difference to the results. The calculations wereperformed using GNU Octave. The code used for the calculationscan be found in the supplementary material.III. RESULTSA. Time-domain analysisThe signal collected by a STEM detector is usually constant ateach scan position; in the case of a HAADF detector, it is approxi-mately proportional to Z1.7t, where Z is the average atomic numberof the sample at that point and t is the thickness.20 However, in ourcase, this signal is modulated by the thermal vibration of the nano-wire. This is schematically illustrated in Fig. 2(a). Here, the nano-wire vibrates between two extreme positions marked by orange andpurple contours, its trajectory described by a sine function. Whenthe electron beam is fixed in a position along this vibration path,the detector signal will be high (H) when the nanowire covers thebeam and low (L) otherwise. Thus, the signal at the detector will bea square wave with the same period as the vibration of the nano-wire. If the position of the beam is close to the outside contour[marked as “position 1” in Fig. 2(a)], the signal will be low formost of the vibration period, resulting in a low duty cycle. On thecontrary, if the beam is fixed close to the inside contour [markedas “position 2” in Fig. 2(a)], it will be covered by the nanowireduring most of the vibration period, resulting in a high duty cycle.It is important to note that the middle point of the vibration,marked by a black contour, is the only location where the signalhas a 50% duty cycle.This idealized explanation can be compared with the twoexperimental signals in Fig. 2(c), extracted from points “1” and“2” of the HAADF image in Fig. 2(b). While there is good agree-ment with respect to the duty cycle, the main differencewith Fig. 2(a) is that the experimental signals appear rounded(softened). There are two main reasons for this, which will be dis-cussed in detail in the later sections of the paper: the fact that thenanowire edge is not perfectly flat and the finite response time ofthe HAADF detector. A much closer match is obtained by com-paring experimental data with the square-wave calculations inFig. S2 in the supplementary material, which are described indetail below.The signals in Fig. 2(c) can also be used in order to estimatethe amount of noise present in our measurements. The bottomFIG. 1. Schematic description of the experiment.Journal ofApplied PhysicsMETHOD pubs.aip.org/aip/japJ. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200 138, 134301-2© Author(s) 2025 06 October 2025 01:43:39https://doi.org/10.60893/figshare.jap.c.8032819https://doi.org/10.60893/figshare.jap.c.8032819https://doi.org/10.60893/figshare.jap.c.8032819https://pubs.aip.org/aip/jappart of the black curve (corresponding to point “1”) shows thedetector signal in the absence of the nanowire; the noise level is rel-atively low. The top part of the red curve (corresponding to point“2”) shows the detector signal while the beam is covered by thenanowire; this curve appears noisy; however, this is the actualsignal due to the overlap of the various vibration modes of thenanowire.B. Frequency-domain analysisFurther insight can be gained by converting the time-domaindata-cube into the frequency domain, which is done by applying aFourier transform to the time-domain signal collected at eachpoint. Figure 3(a) shows a HAADF image of the scanned area atthe tip of the nanowire, while Fig. 3(d) shows the average FFT spec-trum from the entire area. The two strongest peaks represent the1st and 2nd harmonics of the first (fundamental) vibration modeof the nanowire. Mapping these two peaks over the entire scannedarea produces the images in Figs. 3(b) and 3(c), respectively. Theimage in Fig. 3(b) represents the vibration profile of the nanowire,and we have previously shown that this type of analysis can beextended to the higher order vibration modes.16It is interesting to note that the map in Fig. 3(c) shows aminimum. This is also visible in Fig. 3(e), which plots the intensi-ties of the 1st and 2nd harmonics of the first vibration mode alongthe direction indicated by a white arrow. The explanation for thisminimum can be found in the mathematical properties of the har-monics of square waves. A numerical simulation of this effect isshown in Fig. S2 in the supplementary material, which displayshow the FFT spectrum of a square-wave changes as the duty cycleis increased, while all the other parameters are kept constant. Thedata show that, in the special case of a 50% duty cycle, all of theeven harmonics are suppressed. This agrees well with our explana-tion in Fig. 2(a), where we pointed out that this corresponds to themiddle point of the vibration of the nanowire. This can further-more be interpreted as the position of the nanowire in the absenceof any vibrations. The calculations are summarized in Fig. 3(f ),which can be compared to the experimental data in Fig. 3(e). Thereis qualitative agreement between the two figures, with the biggestdifference being that the peaks in Fig. 3(e) are asymmetric. This isdue to the finite response time of the HAADF detector and will bediscussed in detail below.C. Temperature dependency of the vibrationfrequencyBy performing the analysis in Fig. 3(d) for each temperature,we can determine the variation of the vibration frequency withtemperature, which is plotted in Fig. 4(a). This phenomenon canbe modeled using mechanical vibration theory. The fundamentalvibration frequency of a beam which is clamped at one end isgiven by21,22f ¼ 12πa2ffiffiffiffimpffiffiffiffiffiEIL3r, (1)where a = 1.88, m is the mass, E is Young’s modulus, L is thelength, and I is the cross-sectional area momentum of inertiaÐy2dA� �. Considering that LaB6 has cubic symmetry, we canassume isotropic thermal expansion,I ¼ I0(1þ αΔT)4; L ¼ L0(1þ αΔT); E ¼ E0(1þ αEΔT), (2)where α is the thermal expansion coefficient and αE is the thermalcoefficient of Young’s modulus. Combining Eqs. (1) and (2), weobtainf ¼ 12πa2ffiffiffiffimpffiffiffiffiffiffiffiffiffiE0I0L30s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi(1þ αΔT)(1þ αEΔT)pffi f0 1þ α þ αE2ΔT� �:(3)An identical expression can be obtained for each of thehigher modes of vibration by changing the value of the parameterFIG. 2. Time-domain analysis. (a) Schematic illustration. (b) HAADF image of the tip of the nanowire. (c) Detector signal from points marked “1” and “2” in the image. Thetwo signals have been manually offset for clarity.Journal ofApplied PhysicsMETHOD pubs.aip.org/aip/japJ. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200 138, 134301-3© Author(s) 2025 06 October 2025 01:43:39https://doi.org/10.60893/figshare.jap.c.8032819https://pubs.aip.org/aip/japa. The corresponding experimental data for the second and thirdmodes are given in Figs. 4(b) and 4(c). Due to the higher fre-quencies, the data acquisition rate is higher, resulting in lowerfrequency resolution and, thus, higher measurement uncertaintyfor the second and third modes. The third mode compensates forthe loss of frequency resolution by having a larger variationinterval; however, it has the disadvantage of having a significantlyreduced amplitude.Using the experimental data in Fig. 4(a), we can determine theslope as α þ αE ffi �8:28� 10�5 K�1. Considering the thermalexpansion coefficient as α ffi 7� 10�6 K�1,23 we finally getαE ffi �9� 10�5 K�1. Although we did not find any otherFIG. 3. Frequency-domain analysis. (a) HAADF image of the tip of the nanowire. (b) and (c) Maps of the 1st and 2nd harmonics of the first vibration mode in (d), respec-tively. (d) FFT spectrum extracted from the entire area in (a). (e) Averaged profiles along the direction marked by white arrows in (b) and (c). (f ) Calculated intensities ofthe 1st and 2nd harmonics of a square wave, relative to the duty cycle.FIG. 4. Temperature dependency of the nanowire vibration frequency for the first three modes of vibration.Journal ofApplied PhysicsMETHOD pubs.aip.org/aip/japJ. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200 138, 134301-4© Author(s) 2025 06 October 2025 01:43:39https://pubs.aip.org/aip/japexperimental data for this parameter, our value agrees well with the�1:5� 10�424 and �1:2� 10�4 K�125 values obtained by calcula-tions, which confirms the validity of our method. It is important tomention that Eq. (3) does not require any prior knowledge or mea-surement of the nanowire’s geometry or properties, which elimi-nates potential sources of error. Finally, it is interesting to note thatthe two thermal coefficients have opposite signs. Therefore, thedecrease in frequency with temperature is due to the much largertemperature coefficient of Young’s modulus. In the absence of thisvariation, due to thermal expansion alone, the frequency shoulddisplay the opposite behavior and increase.The absolute value of the frequency can be used to determinethe exact length of the suspended part of the nanowire.Equation (1) can be re-written asf ¼ a22πL2ffiffiffiffiffiffiEIρAs! L ¼ affiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12πfffiffiffiffiffiffiEIρAsvuut , (4)where ρ is the density and A is the area of the cross section of thenanowire. This expression is particularly convenient for caseswhere the cross section is not a simple geometric shape, such as thenanowire. An image of the cross section is shown in Fig. S3 in thesupplementary material; these data were obtained by tomography,as described previously.16,26 From the cross-sectional image,parameters A and I can be determined numerically; we obtainA = 2.95 × 103 nm2 and I = 7.68 × 105 nm4. Using these values, aswell as ρ = 4720 kg/m3 and E = 467 GPa,27 we obtain L = 15 μm.This length is significantly different from the 12 μm which can bemeasured in Fig. S1 in the supplementary material, implying thatthe suspended length of the nanowire extends approximately 3 μminside the area covered by the Ta needle. Further proof that thepart of the nanowire located close to the edge of the needle isvibrating is given in Fig. S4 in the supplementary material, whichshows a high-resolution image of the nanowire lattice in that area.The profiles show that the lattice along the direction of the vibra-tion (“Y”) is much less resolved than the perpendicular direction(“X”), which should not be the case considering the cubic lattice ofLaB6 and is a result of blurring introduced by the vibration.D. Temperature dependency of the vibrationamplitudeThe vibration amplitude can be obtained by fitting the profileof the 1st harmonic of the fundamental vibration mode in Fig. 3(e).We have found that a suitable expression for performing this fit isthe “asymmetric peak” function implemented in Gatan’sDigitalMicrograph software. This expression is defined asg(x) ¼ A s c1_w4(x � x0)2 þ _w2� �þ (1� s)c2_we�c3x�x0_wð Þ2� �  , (5)where _w ¼ x � E þ w, c1 ¼ 2/π, c2 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 ln (2)/πp, c3 ¼ 4ln(2), A isthe scale, x0 is the position for E = 0, w is the FWHM for E = 0, E isthe asymmetry factor, and s is the shape factor. All of the parame-ters in Eq. (5) are fitting parameters, except for x which is the inde-pendent variable. With respect to Fig. 3(e), x0 is the location of thecenter of the curve (which indicates the equilibrium position of thenanowire), while _w0 ¼ x0 � E þ w represents the width (which isproportional to the vibration amplitude). The results of fitting theprofile at each temperature are plotted in Fig. 5, by considering thevibration amplitude as _w0/2.The amplitude of the vibration can be modeled consideringBoltzmann’s equipartition theorem, which assigns each vibrationmode an energy of 1/2 kT,21z ¼ 2ffiffiffi2pa2ffiffiffiffiffiffikTp ffiffiffiffiffiL3EIr, (6)where k is Boltzmann’s constant. Using the previously determinedvalues for L and I, we obtain z ¼ 2:88� 10�10ffiffiffiffiTp. This is in excel-lent agreement with the red curve in Fig. 5, which is obtained byfitting the experimental data z ¼ 3:07� 10�10ffiffiffiffiTp.It is interesting to note that, somewhat counterintuitively, thismethod cannot be used to obtain the amplitudes of the highervibration modes. This is because the higher order modes are modu-lated by the fundamental mode. This modulation has the effect ofextending the signal of the higher order vibrations to the entirearea covered by the first mode. The opposite also holds; however,the effect should be less pronounced owing to the much smalleramplitudes of the higher order modes. Nevertheless, this couldexplain the slightly higher experimental value in the previousparagraph.IV. DISCUSSIONThere are two factors which complicate our measurementsand analysis. The first and arguably the most important is the factthat the nanowire has an irregular, rounded cross section, as shownin Fig. S2 in the supplementary material. This distorts the time-domain signals in Fig. 2 and broadens the FFT intensity profiles inFig. 3. Additionally, this complicates our modeling becauseFIG. 5. Temperature dependency of the nanowire vibration amplitude.Journal ofApplied PhysicsMETHOD pubs.aip.org/aip/japJ. Appl. Phys. 138, 134301 (2025); doi: 10.1063/5.0288200 138, 134301-5© Author(s) 2025 06 October 2025 01:43:39https://doi.org/10.60893/figshare.jap.c.8032819https://doi.org/10.60893/figshare.jap.c.8032819https://doi.org/10.60893/figshare.jap.c.8032819https://doi.org/10.60893/figshare.jap.c.8032819https://pubs.aip.org/aip/japestablished expressions for simple geometrical shapes cannot beused. An even more straight-forward example of this problem isillustrated in Fig. S5 in the supplementary material, which showsaveraged plots of the nanowire’s width at different temperatures.There is no obvious broadening of the profiles, despite the increas-ing amplitude of the vibration.Another important issue is the temporal resolution of thesystem, which is determined by the response time of the HAADFdetector. The Gatan 806 detector has a scintillator/photomulti-plier (PMT) design; the scintillator used is yttrium aluminumperovskite (YAP), which has a reported decay time constant ofτ ∼ 27 ns,28,29 resulting in a pulse width of 3τ ∼ 100 ns. However,the PMT and downstream electronics broaden this pulse to∼400–500 ns.30 This is likely due to design considerations sincesuch a detector is mainly optimized for high gain and low noise.This becomes an issue when collecting square-wave signals with avery high dwell-time since, as illustrated in Fig. 2(a), the timewhen the signal is low can be much shorter than the ∼2.5 μsvibration period of the nanowire, preventing the detector signalfrom returning to its initial level. Since these high dwell-timesignals are located toward the interior of the nanowire, this couldexplain why the peaks in Fig. 3(e) show an asymmetry in thatregion. While the current setup is limited in terms of time resolu-tion to ∼10 MHz, the latest generation of fast scintillator detec-tors have shown response times down to ∼1 ns,31 which wouldallow vibration measurements into the GHz regime and extendthe methods shown here to a wide variety of nanoresonators.Lastly, the agreement between the measured and calculatedvibration amplitudes allows us to infer that there is no differencebetween the actual temperature of the nanowire and the value setusing our heating holder. This fits well with estimates accordingto which the temperature of ceramics should increase by lessthan 0.1 K when using a 100 pA electron probe.32 Another argu-ment comes from the fact that the irradiated region of the nano-wire shown in Figs. 2(b) and 3(a) is ∼150 nm in length, whichrepresents ∼1% of the total volume of the nanowire, consideringthe 15 μm length estimated earlier. Therefore, we can confidentlystate that heating by the electron beam is negligible in ourexperiments.V. CONCLUSIONSIn conclusion, we have combined the well-known spatial reso-lution of the TEM with the high temporal resolution of our customacquisition system and with temperature control in order to gaininsight into how temperature influences the thermal vibrationproperties of individual nanowires. Within the constraints of ourexperiments, the nanowire vibration can be accurately modeled byclassical formalisms, such as mechanical vibration theory andBoltzmann’s equipartition theory, despite the small size. We havetaken advantage of this in order to measure material propertieswhich would otherwise be difficult to determine, such as the tem-perature coefficient of Young’s modulus.SUPPLEMENTARY MATERIALSee the supplementary material for a low-magnificationimage of the nanowire (Fig. S1), square-wave signals andcorresponding FFTs (Fig. S2), nanowire cross section (Fig. S3),nanowire high-resolution data near the end of the Ta needle(Fig. S4), and HAADF profiles of the nanowire at various tempera-tures (Fig. S5).ACKNOWLEDGMENTSThis work was supported by JSPS KAKENHI Grant Nos.JP24K08253 (O.C.), JP23H04874 (K.H.), and JP22H05145 (K.K.).AUTHOR DECLARATIONSConflict of InterestThe authors have no conflicts to disclose.Author ContributionsOvidiu Cretu: Conceptualization (lead); Formal analysis (lead);Funding acquisition (equal); Investigation (lead); Methodology(lead); Writing – original draft (lead); Writing – review & editing(lead). 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