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Hirokazu Masai, [Yohei Onodera](https://orcid.org/0000-0002-3080-6991), Yasuhiro Fujii, Hideaki Hagihara, Kazuya Saito, Edison Sekiya, Nanami Misawa, Akitoshi Koreeda, [Shinji Kohara](https://orcid.org/0000-0001-9596-2680)

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[Structural ordering of SiO<sub>2</sub> glass exhibiting different fictive temperatures](https://mdr.nims.go.jp/datasets/bb2aba38-cafc-4cd6-b555-0ad0634eae69)

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Structural ordering of SiO2 glass exhibiting different fictive temperaturesFULL PAPERStructural ordering of SiO2 glass exhibiting different fictivetemperaturesHirokazu Masai1,³, Yohei Onodera2, Yasuhiro Fujii3,4, Hideaki Hagihara5, Kazuya Saito6,Edison Sekiya6, Nanami Misawa7, Akitoshi Koreeda7 and Shinji Kohara21National Institute of Advanced Industrial Science and Technology, 1–8–31 Midorigaoka, Ikeda, Osaka 563–8577, Japan2Center for Basic Research on Materials, National Institute for Materials Science, 1–2–1 Sengen, Tsukuba, Ibaraki 305–0047, Japan3Institute for Open and Transdisciplinary Research Initiatives, The University of Osaka,2–1 Yamada-Oka, Suita, Osaka 565–0871, Japan4Research Organization of Science and Technology, Ritsumeikan University, 1–1–1 Noji-higashi, Kusatsu, Shiga 525–8577, Japan5National Institute of Advanced Industrial Science and Technology, 1–1–1 Higashi, Tsukuba, Ibaraki 305–8560, Japan6Toyota Technological Institute, 2–12–1 Hisakata, Tempaku-ku, Nagoya 468–8511, Japan7Department of Physical Sciences, Ritsumeikan University, 1–1–1 Noji-higashi, Kusatsu, Shiga 525–8577, JapanThe physical and structural parameters of glass depend on its preparation conditions. Fictive temperature, Tf, isa standard for glass obtained from the super-cooled liquid. Although the Tf value is discussed from the viewpointof structural relaxation defined by infrared vibration, there should be structural correlations at the longerranges, which are worthy of exploration. Here, we demonstrate the structural change of the intermediate rangein SiO2 glasses with different Tf values using X-ray and neutron diffraction, inelastic light scattering, and posi-tron annihilation spectroscopy. By annealing the SiO2 glasses, i.e., decreasing Tf, an increase in the first sharpdiffraction peak (FSDP) heights and narrowing of the peak width are observed. Differential structure factor¦S(Q) of neutron diffraction reveals a formation of the thermally derived O–O inter-tetrahedral correlation inhigh-Tf glass. Spectroscopic analyses (Raman scattering, stimulated Brillouin scattering, and positron annihila-tion spectroscopy) suggest that a certain structural change has occurred in the SiO2 glass exhibiting higher Tfvalues, confirming that these approaches can be used as probes for structural ordering. Considering ¦S(Q) ofneutron diffraction, it is suggested that the structural changes in SiO2 glass with higher Tf values observed byspectroscopy correlate with oxygen-related structural change in the intermediate range. Since the observedstructures of each analysis are different, these multiscale and quantitative examinations are important forprecise examination of various random materials.Key-words : SiO2 glass, Fictive temperature, X-ray diffraction, Neutron diffraction, Spectroscopy[Received October 31, 2025; Accepted December 29, 2025]1. IntroductionAs oxide glass is a solidified supercooled liquid, thethermodynamically metastable structures and physicalproperties of the resultant glass depend on the preparationprocess.1,2) For example, the valence and local coordina-tion states of the constituent cations and homogeneity ofthe glass melt are affected by the preparation process, eventhough the nominal chemical composition is fixed.3)Therefore, the physical properties of oxide glass originatefrom how the supercooled liquid is treated above the glasstransition temperature, Tg, which is a threshold for thediffusion of constituent atoms. Although it is difficult toexamine all local coordination states in glass because ofthe “random network” in the long-range possessing amuch wider site distribution compared with that in corre-sponding crystal, such topological homogeneity is impor-tant for glass science from both scientific and industrialviewpoints. Recently, experimental and mathematical ap-proaches were combined to investigate the behavior ofrings and cavities in amorphous materials.4–10) However,although SiO2 glass is the most popular and typical oxideglass, the random network over the entire structural rangehas not yet been clarified. The random network, therefore,still fascinates many scientists.The structural ordering of SiO2 glass has been discussedusing various structural analysis techniques. The mostcommon method is neutron or X-ray diffraction measure-ment.1–29) A slightly sharp peak observed in structurefactor has been focused as a probe for evaluating thestructural ordering in the intermediate range. For example,³ Corresponding author: H. Masai; E-mail: hirokazu.masai@aist.go.jp‡ Preface for this article: DOI https://doi.org/10.2109/jcersj2.134.P4-1Journal of the Ceramic Society of Japan 134 [4] 246-256 2026DOI https://doi.org/10.2109/jcersj2.25149 JCS-Japan©2026 The Ceramic Society of Japan246This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/),which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.https://doi.org/10.2109/jcersj2.134.P4-1https://doi.org/10.2109/jcersj2.134.P4-1https://doi.org/10.2109/jcersj2.25149https://creativecommons.org/licenses/by/4.0/it is proposed that some periodic local atomic densityfluctuations correlate with the first sharp diffraction peak(FSDP).10) Since glass, especially SiO2 glass, containslarge cavities, the thermodynamically metastable structurescan be tuned semipermanently or transiently by applyinghigher pressure.3,20–24) In oxide glasses, in which variousmetastable structures exist, structural relaxation is one ofthe most interesting topics from both a scientific andindustrial perspective.Other probes for evaluating the structural ordering ofglassy materials are spectroscopy, which is commonlynon-destructive measurement of the materials, and theprecise numerical analysis is an advantage for the analysismethod. To examine the relationship between the coolingrate and frozen state of supercooled liquid, the concept offictive temperature, Tf, was introduced.30–32) The Tf haslong been a subject of research, and its correlation hasbeen discussed by various scientists.30–43) The value of Tf,which is determined by the Si–O–Si vibration mode,34) isthe fictive frozen state of glass and is one of the standardsfor structural relaxation, i.e., local structural rearrange-ment. The decrease of Tf means that structural relaxationof the SiO2 glass occurs by annealing. Changes in fictivetemperature not only change the wave number of Si–O–Sivibrations but also affect a wide range of physical prop-erties, such as the elastic modulus, thermal expansioncoefficient, and chemical durability. On the one hand, thiseffect is complex; some parameters increase, while othersdecrease. This is attributable to the fact that different struc-tures at different distance ranges contribute to differentphysical properties.On the other hand, inelastic light scattering has beenused as a spectroscopic probe for structural order-ing.1–3,25,26,44–49) In particular, the range of wavenumbersbelow 50 cm¹1 in inelastic light scattering is conventionallycalled the boson region, at which a peak above the densityof state estimated by the Debye rule in glass (random mate-rial) emerges. A correlation between the boson peak andFSDP has been discussed by many authors from viewpointof structural ordering.27) In addition, we have recently dem-onstrated other spectroscopic methods such as Brillouinscattering and positron annihilation spectroscopy can be aprobe to examine the structural ordering of glasses.49) Sincemany rings of different sizes exist in SiO2 glasses,5,7,8) it isnatural that cavities inevitably generated from rings affectthe nature of SiO2 glass. Therefore, a quantitative under-standing of cavities, which are characteristic of glass, isimportant. The structural ordering of the glass network hasbeen often discussed by limited analytic methods, i.e., acertain distance ranges. However, since structural orderingin a specific structural range should affect the ordering ofother ranges, it is preferable to use many analytical tech-niques toevaluatenon-periodicglassnetworks.In this study, we examined the structural ordering ofSiO2 glasses exhibiting different Tf values by differentanalysis methods: FSDP of high-energy X-ray diffractionand neutron diffraction, boson peak in Raman scattering,Brillouin scattering, and positron annihilation spectros-copy. By using these analyses, we examined the structuralchanges in the entire SiO2 network by thermal relaxationusing numerical values.2. Experimental2.1 Preparation of SiO2 glasses possessingdifferent Tf valuesThe base SiO2 glass was supplied by Tosoh QuartzCorp. The OH concentration was <50wt. ppm. The prepa-ration details have been presented in a previous paper.29)To examine the stimulated Brillouin scattering, the edgesof the samples were polished to obtain a mirror surface.2.2 Physicochemical analysisDensity was estimated according to a previous report.50)The refractive index of the samples was measured using aprism coupler (Metricon, N.J., U.S.A.) at 473, 633, and1319 nm. The error of the measurement was 3 © 10¹4. Tfwas estimated by the Si–O–Si vibration around 2260 cm¹1using a Model Spectrum 2000 (Perkin Elmer Inc.) with aresolution of 1 cm¹1.2.3 High-energy XRD measurementThe high-energy X-ray diffraction experiment was per-formed at the BL04B2 beamline at the SPring-8 synchro-tron radiation facility using a two-axis diffractometer dedi-cated to the study of disordered materials.51) The energy ofthe incident X-rays was 61.43 keV. The raw data werecorrected for polarisation, absorption, and background,and the contribution of Compton scattering was subtractedusing standard data analysis software.51) The corrected X-ray diffraction data were normalized to give the Faber–Ziman52) X-ray total structure factors, SX(Q).2.4 Neutron diffraction measurementNeutron diffraction measurements were conducted usinga high-intensity total diffractometer (NOVA) installed atBL21 of the Materials and Life Science ExperimentalFacility at the J-PARC spallation neutron source (Ibaraki,Japan). The wavelength range of the incident neutronbeam was 0.12¡ < ­ < 8.3¡. The glass sample (1.2 g)was transferred into a vanadium–nickel null alloy cell withan outer diameter of 6.0mm and thickness of 0.1mm. Theobserved scattering intensity for the sample was correctedfor instrumental background and attenuation of the sampleand cell, and then, normalized by the incident beam profileobtained from the scattering intensity of a vanadium stan-dard. The corrected neutron diffraction data were normal-ized to give the Faber–Ziman52) neutron total structurefactors, SN(Q).2.5 Raman spectroscopyConfocal micro-Raman measurements with a backscat-tering geometry were performed to analyse the boson peaks.Backscattering micro-Raman measurements were per-formed using a single-frequency diode-pumped solid-state(DPSS) laser oscillating at 532 nm (Oxxius LCX-532S-300). A home-built microscope consisting of ultra-narrowJournal of the Ceramic Society of Japan 134 [4] 246-256 2026 JCS-Japan247band notch filters (OptiGrate) and a 20© objective lens(Mitutoyo, M Plan APO SL20, NA = 0.28) was used tofocus the excitation laser and collect the Raman-scatteredlight. The scattered light was analysed using a singlemonochromator (Jovin-Yvon, HR320, 1200 grooves/mm)equipped with a charge-coupled device camera (Andor,DU420).2.6 Stimulated Brillouin spectroscopyBrillouin shifts ¯B of the glass were measured using afrequency-modulated stimulated Brillouin spectrome-ter.53,54) Two Miser-type Nd:YAG lasers with a wavelengthof 1.06¯m were utilized as pump and probe sources. Thebeams were arranged in a counterpropagating configura-tion within the sample, enabling a backscattering geometry.The frequency difference between the pump and probewaves, along with the resulting beat frequency, was con-tinuously monitored using a microwave frequency counter.This setup facilitated repetitive scanning and data averag-ing while preserving high spectral resolution. By employ-ing two lenses with a focal length of 30 cm, a spectralresolution of 20 kHz (HWHM) was achieved. The longi-tudinal sound velocity VL was calculated using the relationVL = ¯B­/2n1064, where ¯B, ­, n1064, are the Brillouin shift,the wavelength of the incident light (= 1064 nm), and therefractive index at 1064 nm, respectively. The n1064 valueswere calculated using the Cauchy relation with the refrac-tive indices at different wavelengths.2.7 Positron annihilation lifetime measure-mentPositron annihilation lifetime measurements were per-formed using a PSA TypeL-II (Toyo Seiko Co. Ltd.) withan anti-coincidence system.55) The 22Na source with adiameter of 15mm was encapsulated with Kaptonμ film.The accumulated count for each sample was 107.3. Results3.1 Comparison of the X-ray and neutronstructure factors S(Q) of SiO2 glassesexhibiting different Tf valuesFigures 1(a) and 1(b) show the X-ray total structurefactors SX(Q)29) and neutron total structure factors SN(Q)of SiO2 glasses with different Tf values, respectively. TheFSDP (Q1)3,5,7,22–24) is clearly observed at approximatelyQ = 1.5¡¹1 in both SX(Q) and SN(Q). On the contrary, aprincipal peak (PP) (Q2)3,5,7,22–24) at approximately Q =2.9¡¹1 is only observable in neutron diffraction data be-cause the O–O correlation, which is probed sensitively byneutrons, mainly contributes to this peak.5,7,22,23) The peakattributed to Q3 is observed at Q = 5.1¡¹1 [SX(Q)]3,24)and at Q = 5.3¡¹1 [SN(Q)],3,5,7,22–24) respectively. Thesethree peaks slightly altered their shape depending on the Tfvalue. Figures 1(c) and 1(d) show the enlarged SX(Q) andSN(Q) of SiO2 glasses with different Tf values in the FSDPregion. Each inset shows the FSDP height of the SiO2glasses as a function of Tf . The height of the FSDP linearly2.01.51.00.50.0432102.01.51.00.50.025201510502.01.51.00.50.043210Q (Å−1)SN(Q)Tf = 1300 K1403 K1493 K1610 K1743 KbdacQ (Å−1)SN(Q)Tf = 1300 K1403 K1493 K1610 K1743 K1.751.701.651.601.5517001600150014001300Fictive temperature Tf (K)Height  of FSDP2.01.51.00.50.025201510501.901.851.801.751.7017001600150014001300Fictive temperature Tf (K)Height  of FSDPSX (Q)SX (Q)Q (Å−1)Q (Å−1)Tf = 1300 K1403 K1493 K1610 K1743 KTf = 1300 K1403 K1493 K1610 K1743 KQ1 Q3 Q1Q2Q3Fig. 1. Comparison of the X-ray and neutron total structure factors S(Q) of SiO2 glasses exhibiting different Tfvalues. (a) X-ray total structure factors SX(Q)29) and (b) neutron total structure factors SN(Q) of SiO2 glassesexhibiting different Tf values. Enlarged SX(Q)29) (c) and SN(Q) (d) at the FSDP region with the fitting curve(dotted line). Insets of Figs. 1(c) and 1(d) show the heights of FSDP as a function of Tf values.Masai et al.: Structural ordering of SiO2 glass exhibiting different fictive temperaturesJCS-Japan248increased with decreasing Tf values, indicating that struc-tures correlated with the FSDP were preferentially orderedby thermal annealing.18,19,28,29) To examine the effect of Tfon the structural ordering in SiO2 glass more quantita-tively, the FSDP was fitted using a Lorentz function takinginto account the position, QFSDP, and full width at halfmaximum (FWHM), ¦QFSDP, of the FSDP:SðQÞ ¼ A0 �0:5�QFSDPðQ�QFSDPÞ2 þ ð0:5�QFSDPÞ2ð1Þwhere, A0, ¦QFSDP, and QFSDP are the fitting parameters.29)In this study, we fitted the S(Q) in the Q regions of 0.90–1.65¡¹1 for SX(Q) and 1.10–1.65¡¹1 for SN(Q). Thedotted curves in Figs. 1(c) and 1(d) represent the fittedcurves to the FSDP of SiO2 glass with Tf = 1743K.Figure 2 shows the fitting results of QFSDP (QXFSDP forX-ray and QNFSDP for neutron) and ¦QFSDP (¦QXFSDP forX-ray and ¦QNFSDP for neutron) as a function of Tf .Compared the values of QXFSDP [Fig. 2(a)] with those ofQNFSDP [Fig. 2(b)], the QXFSDP increases slightly withincreasing Tf values29) whereas the QNFSDP remains almostidentical. On the other hand, the FSDP width becomesbroader in both SX(Q) and SN(Q) [Figs. 2(c) and 2(d)].The diversity of the FSDP-related structure was evaluat-ed by examining the correlation length, 2³/¦QFSDP, as afunction of Tf [Figs. 2(c) and 2(d)]. The correlation lengthobtained from both SX(Q) and SN(Q) increases by thermalannealing (a decrease in Tf ), suggesting that annealinginduces the structural ordering consists of SiO4 network.The X-ray and neutron S(Q) of SiO2 glass exhibitedslightly different behavior in response to the Tf values, asshown in Figs. 1 and 2. In order to characterize the differ-ent behavior, we calculated the differential S(Q), ¦S(Q),for both SX(Q) and SN(Q); Using the S(Q) of SiO2 glasswith the Tf = 1300K as the reference data, ¦S(Q) wasobtained by subtracting the reference data from the S(Q) ofSiO2 glasses with the other Tf values (1403, 1493, 1610,and 1743K). Figures 3(a) and 3(b) show the X-ray andneutron ¦S(Q) of SiO2 glasses. In both X-ray and neutron¦S(Q), the clear changes corresponding to the Tf valueswere observed at the Q1, Q2, and Q3 regions. To clarify theorigin of the changes in each diffraction peak, the X-ray-and neutron-weighted partial structure factors Wij(Q)·Sij(Q) of Si–Si, Si–O, and O–O are shown in bottom ofFigs. 3(a) and 3(b), respectively. In disordered materialscontaining n chemical species, the total structure factorS(Q) can be expressed using the X-ray or neutron weight-ing factors,Wij(Q), and partial structure factors, Sij(Q), fori-j correlations,SðQÞ¼Xni¼1Xnj¼1WijðQÞ � ½SijðQÞ�1�¼ 1þ 1hfðQÞi2Xni¼1Xnj¼1cicjfiðQÞfjðQÞ½SijðQÞ�1�ð2Þwhere ci is the atomic fraction of chemical species i, andfi(Q) is either a Q-dependent atomic form factor in X-raydiffraction or a Q-independent coherent scattering lengthin neutron diffraction, and0.700.650.600.550.501700160015001400130012.011.511.010.510.09.59.01.5241.5221.5201.5181.516170016001500140013000.640.620.600.580.560.540.521700160015001400130012.011.511.010.510.01.5421.5401.5381.5361.5341.5321.5301.52817001600150014001300bdFictive temperature Tf (K)acFictive temperature Tf (K)Position QNFSDP(Å−1)FWHM QNFSDP(Å−1)Correlation length 2/QNFSDP(Å)Fictive temperature Tf (K)Position QX FSDP(Å−1)Fictive temperature Tf (K)FWHM QX FSDP(Å−1)Correlation length 2/QX FSDP(Å)Fig. 2. The fictive temperature (Tf ) dependence of the FSDP in the X-ray and neutron diffraction data of SiO2glasses. Position of the FSDP in SX(Q)29) (a) and SN(Q) (b). (c) Full width half maximum (FWHM) of the FSDPin SX(Q), ¦QXFSDP, and the correlation length 2³/¦QXFSDP as a function of Tf .29) (d) FWHM of the FSDP inSN(Q), ¦QNFSDP, and the correlation length 2³/¦QNFSDP as a function of Tf .Journal of the Ceramic Society of Japan 134 [4] 246-256 2026 JCS-Japan249hfðQÞi ¼Xni¼1cifiðQÞ ð3ÞThe Sij(Q) data were calculated from the three-dimensional atomic configuration of SiO2 glass, whichwas constructed by a combination of molecular dynamics(MD) and reverse Monte Carlo (RMC) simulations basedon X-ray and neutron diffraction data.5) Further details ofthe MD-RMC simulations of SiO2 glass are described inRef. 5).As previously reported,29) the ¦SX(Q) is mainly domi-nated by the Si–Si and Si–O correlations. For instance, theSi–Si and Si–O correlations contribute to Q1 and Q3regions in the ¦SX(Q) [bottom of Fig. 3(a)] because X-rays are more sensitive to heavier atoms. The ¦SX(Q)exhibits a negative peak at the QXFSDP (= 1.5¡¹1), and thedepth of this negative peak increases uniformly withincreasing Tf , associated with the increases on both thelower- and higher-Q sides of the FSDP. This changesignifies the FSDP’s systematic broadening indicating thatthe intermediate-range structure becomes disordered withincreasing Tf . This behavior is consistent with the correla-tion length analysis results showing that annealing (low-ering Tf ) induces structural ordering in SiO2 glass. The Q3exhibited contrary alterations in direction between thelower- and higher-Q sides in the ¦SX(Q). This behavior inthe Q3 is consistent with that in the Si–Si partial structurefactor [see Wij(Q)·Sij(Q)]; the Si–Si correlation corre-sponds to the correlation between central Si atoms locatedin SiO4 tetrahedra interconnected by corner-sharing ofoxygen atoms in SiO2 glass. The change in the Q3 in the¦SX(Q) suggests that the annealing process affects the Si–O–Si correlation in SiO2 glass.29) In contrast to the Q1 andQ3, the Q2 exhibited no signs of change in the ¦SX(Q)since the positive Si–Si and O–O contributions are coun-terbalanced by the negative Si–O contribution in the Q2region.The ¦SN(Q) [Fig. 3(b)] exhibited changes in three dif-fraction peaks, including the Q2, in contrast to the ¦SX(Q).The Q1 (FSDP) in the ¦SN(Q) demonstrates a changeidentical to that in the ¦SX(Q), though the lower-Q sideunderwent a more significant alteration. This can be attri-buted to the fact that O–O correlation, which contributes tothe lower-Q side of the Q1 has a large weighting factor inneutron diffraction as shown in Wij·Sij(Q) in comparisonwith the Si–Si correlation. The positive contributions areobserved for the neutron-weighted O–O partial structurefactor in the Q2 and Q3 regions. Notably, the higher-Q sideof the Q2 in the SN(Q) is predominantly formed by the O–O correlation contribution. Thus, the evolution of thenegative peak observed at Q = 3.1¡¹1 in the ¦SN(Q) canbe attributed to the diminution of the Q2 in the O–O partialstructure factor, suggesting that oxygen-related structuraldisordering occurs as the Tf values increase. The Q2 peakin oxide glasses is correlated with the packing of oxygenatoms at the corner of polyhedral units (e.g., SiO4 tetra-hedron in SiO2 glass).3) Since the network structure ofinterconnected regular SiO4 tetrahedra is preserved in SiO2glasses with different Tf values, we suggest that inter-tetrahedral O–O correlation3,22,23) plays a major role in theoxygen-related structural disordering that occurs as the Tfincreases.3.2 Spectroscopic analysis of SiO2 glassexhibiting different Tf valuesRecently, we have examined network structure of glassthrough a combination of diffraction and spectroscopictechniques. It is found that inelastic light scattering(Raman and Brillouin scattering) and positron annihila-tion spectroscopy can be a probe of structural diversity ofoxide glass in addition to the high energy XRD and solidstate magic angle spinning NMR.49) Figure 4(a) shows theRaman spectra in the boson region of SiO2 glass exhibiting-0.15-0.10-0.050.000.050.100.15-0.15-0.10-0.050.000.050.10-2.0-1.5-1.0-0.50.00.51.0108642-1.5-1.0-0.50.00.51.0108642Q (Å−1)WijSij(Q)Si−OQ1 Q2 Q3ΔSN(Q) 1403 KΔSN(Q) 1493 KΔSN(Q) 1610 KΔSN(Q) 1743 KDifferential SN( Q), ΔSN(Q)Si−SiO−OQ (Å−1)DifferentialSX (Q), ΔSX (Q)Wij(Q)Sij(Q)Si−OSi−SiO−OQ1 (Q2) Q3ΔSX(Q) 1403 KΔSX(Q) 1493 KΔSx(Q) 1610 KΔSx(Q) 1743 KbaFig. 3. Comparison of the X-ray and neutron differential structure factors ¦SX,N(Q) of SiO2 glasses exhibitingdifferent Tf values. (a) ¦SX(Q)29) and (b) ¦SN(Q), which are obtained by subtracting S(Q) of SiO2 glass with theTf = 1300K (reference data) from S(Q) of SiO2 glasses with the other Tf values (1403, 1493, 1610, and 1743K).X-ray-weighted partial structure factors Wij(Q)·Sij(Q) and neutron-weighted partial structure factors Wij·Sij(Q)are also presented at the bottom of each figure. Vertical dot lines indicate Q values of each Qn peak.Masai et al.: Structural ordering of SiO2 glass exhibiting different fictive temperaturesJCS-Japan250the Tf = 1300K, as a representative. All Raman spectra ofSiO2 glasses exhibiting different Tf values are shown inFig. S1. We adopted a standard procedure to analyseBoson peaks with a log-normal function, i.e., the shape ofthe reduced spectrum is assumed to be the form given inEq. (4).46–48)»00ð¯Þ¯¼ Affiffiffiffiffiffi2³p·¯exp � ðln ¯�®Þ22·2� �; ð4Þwhere, ¯, A, e®, and · are the frequency shift, amplitude,median of the log-normal distribution, and standard devia-tion of the Gaussian peak in log-space, respectively. Thevalues of the ¯BPmax were calculated as e¯�·2using fittingresults. The values of ¯BPmax are plotted as a function of Tfin Fig. 4(b). The ¯BPmax shifts to the low-frequency side asTf decreases, and the amount of ¯BPmax change is approx-imately 5%. Although the data initially suggest a lineartrend, a minor deviation from linearity becomes evidentfor SiO2 glass with higher Tf value. If all data are used forlinear fitting, the coefficient of determination (R2) for thelinear regression becomes 0.944, while the R2 value be-comes 0.993 with the fitting using lower 4 data.It has been reported that there is a relationship amongfrequency of boson peak ¯BPmax, sound velocity ¯, andcorrelation length ², as shown in Eq. (5).46–48)² � v=¯BPmax ð5ÞAs shown in Fig. 4(b), the boson peak frequency de-creases with decreasing Tf . After annealing, which inducesa decrease in Tf , the spectral change indicated that thecorrelation length increased. Figure 4(c) shows the Tf de-pendence of the correlation length ² calculated usingEq. (5). The correlation length calculated from the value ofFSDP of neutron diffraction is also shown for comparison.In contrast to the linear relationship observed in the FSDPvalue, a minor deviation from linearity of the boson peakposition is observed owing to the ¯BPmax. The change ratesin the Tf range of 1300 to 1610K of boson peak and FSDPare ¹1.57 © 10¹2 and ¹4.42 © 10¹2%/K, respectively.As reported in previous papers, there is a relationshipbetween the positions of the boson peak and FSDP,48)whereas the boson peak position and density, i.e., FSDPposition, exhibit a non-linear dependence in a densifiedSiO2 glass.3) As in the previous paper,3) the present results,in which a deviation is observed in higher Tf glass, suggestthat the relationship between positions of boson peak andFSDP does not follow a linear correspondence.As in previous studies,56) Brillouin spectra have beenused to determine the sound velocity and elastic modulusof materials. In our previous study,29) Brillouin spectrawere fitted using the Voigt function to calculate theBrillouin shifts ¯B of SiO2 glass samples against differentTf values. Although an apparent linearity was observedbetween the c11 and Tf values in the previous paper,29) theconventional Brillouin measurement cannot be used forquantitative analysis of the Brillouin peak width of SiO2glass exhibiting different Tf values, because Brillouin peakwidth of SiO2 is narrower compared with other oxideglasses.49) We, therefore, examined the structural orderingemploying stimulated Brillouin scattering approach with aphase modulation. The details of the analysis are shown inthe previous paper.54)The stimulated Brillouin scattering spectra were fittedby the real and imaginary parts of the frequency-modulated Lorentzian functions as presented in Eq. (1) ofRef. 51) only with the electrostrictive coupling. Since thewavelength of the laser employed is twice that we reportedpreviously, the Brillouin shift in this study is approx-imately halved. Figure S2 shows the refractive index at1064 nm, which corresponds to the wavelength used forstimulated Brillouin scattering. With decreasing Tf, therefractive index decreases. Figures 5(a) and 5(b) show thestimulated Brillouin scattering spectra of SiO2 glasses ex-hibiting different Tf values of the real part (a) and imagi-nary part (b). The spectra of the real and imaginary partsaIntensity (arb. unit))1−Raman shift (cm0 50 100 150 2000.00.51.01.5(Å)FSDPNQ2Correlation length (K)fTFictive temperature )1−(cmBPmaxνcb(nm)Correlation length (K)fTFictive temperature 1300 1400 1500 1600 1700515253549.09.510.010.511.011.51300 1400 1500 1600 17003.653.703.753.803.853.90Fig. 4. Raman spectra of SiO2 glass exhibiting different Tfvalues. (a) Raman scattering spectra at boson region of SiO2 glassexhibiting Tf = 1300K as a representative. (b) ¯BPmax as a func-tion of Tf values. (c) Comparison of size parameters from bosonpeak and correlation length 2³/¦NQFSDP as a function of Tfvalues.Journal of the Ceramic Society of Japan 134 [4] 246-256 2026 JCS-Japan251can be fitted by the frequency-modulated Lorentzian re-sponse functions as shown in Fig. 5(c). The theoreticalcurves exhibit excellent agreement with the experimentaldata, enabling us to accurately determine the Brillouinshift and linewidth. The longitudinal elastic modulus c11values were calculated, as shown in Eq. (6),c11 ¼ μð¯B­=2n1064Þ ð6Þwhere ­, and n1064 are the Brillouin shift, the wavelengthof the incident light (1064 nm), and the refractive indexat 1064 nm, respectively. Figure 5(d) shows the Brillouinshift ¯B and the longitudinal elastic modulus c11 as a func-tion of Tf values. There appears to be a linear relationshipbetween Tf and these two parameters. On the contrary, theTf dependence of the Brillouin peak width !B exhibitsa quite different tendency, as shown in Fig. 5(e): the !Breaches its maximum when the Tf is approximately1600K, and then decreases. Generally, peak width !Bbecomes narrower with increasing frequency. The internalfriction, which is defined as !B/¯B, of this SiO2 glass, isalso shown in Fig. 5(e) as a function of Tf . Because thechange in !B (³5%) is larger than that in ¯B (³1%), thisconfirms that the size change of correlation length is mean-ingful. Thus, the obtained data suggest that not only theBrillouin peak width, but also internal friction do not showa linear dependence on temperature, and these parametersdecrease in SiO2 glasses exhibiting higher Tf values (Tf >1700K). Since Brillouin peak width is proportional to theultrasonic attenuation the decrease of !B indicates a qual-itative change in the phonon scattering mechanism in thelength scale of micrometer order across Tf ³ 1700K.Regarding the refractive index, we believe it does notaffect either the Raman or the Brillouin results. The bosonpeak, which reflects the vibrational density of states, isgenerally considered to be independent of the refractiveindex. Since no irregularity originating from the refractiveindex has been observed, we can conclude that the slightchange in the refractive index (<0.05%) is negligible inthe estimation of the c11 value, because the Brillouin shiftitself shows a variation of about 1%.Since it is expected that internal friction of SiO2 glassescorrelates with the cavity of SiO4 network, we performedpositron annihilation lifetime spectroscopy to quantify thecavity size in materials.57–59) Figure 6(a) shows the posi-tron decay curves of the SiO2 glass with different Tf val-ues, where there is a slight difference in these curves. Forinsulators, the decay constant of ortho-positronium o-Ps(the third component in fitting the decay curve) was usedfor the size calculation. Figure 6(b) shows lifetime of o-Ps(on the left axis) and the relative intensity of total decaycomponents (on the right axis) as a function of Tf values.Both lifetime and intensity exhibit an inflection point at(MHz)BBrillouin linewidth cba)3−10×Internal friction ((K)fTFictive temperature (K)fTFictive temperature ed(GHz)BνBrillouin shift (GPa)11cmodulus Longitudinal elastic 77.077.578.01300 1400 1500 1600 1700 180016.2016.2516.3016.351.481.501.521.541300 1400 1500 1600 1700 180024.024.224.424.624.825.025.2ImaginaryReal= 1300 KfTIntensity (arb. units)Frequency shift (GHz)Intensity (arb. units)Frequency shift (GHz)Intensity (arb. units)Frequency shift (GHz)1743 K1610 K1763 K1493 K1403 K1300 K1743 K1610 K1763 K1493 K1403 K1300 K16.0 16.2 16.4 16.6 16.0 16.2 16.4 16.615.9 16.0 16.1 16.2 16.3 16.4 16.5Fig. 5. Stimulated Brillouin scattering spectra of SiO2 glass depending on Tf values. Stimulated Brillouinscattering spectra of SiO2 glasses exhibiting different Tf values; the real part (a) and imaginary part (b). (c) Fittingof stimulated Brillouin scattering spectra. Circles and solid lines are experimental and fitted data, respectively.(d) Tf dependence of Brillouin shift ¯B and longitudinal elastic modulus c11 as a function of Tf . (e) Brillouin peakwidth !B and internal friction of SiO2 glass possessing different Tf values.Masai et al.: Structural ordering of SiO2 glass exhibiting different fictive temperaturesJCS-Japan252the SiO2 glass whose Tf is 1656K. The cavity radii of thisSiO2 glass are plotted in Fig. 6(c) as a function of the Tfvalues. Although preliminary observations suggest anapparent consistency between cavity sizes of SiO2 and Tfvalues in the previous literatures; the cavity size increaseswith increasing Tf value,58) there is a different tendency athigher Tf-glass. The anomalous change of SiO2 glasseswith higher Tf will be discussed with other spectroscopicdata in the following section.4. DiscussionIn the previous paper,29) we assumed the Tf dependenceon the structural parameters of SiO2 glass to be linear.As shown in Tf-dependence of the FSDP of SX(Q), thechange of SX(Q), which is largely affected by the Si-related correlation, is roughly proportional to that of Tf . Onthe contrary, in the structure factor SN(Q), which is largelyaffected by the O–O correlation, the Tf-dependences of Qnpeaks are not identical to that in SX(Q). Figure 7 showsthe Qn peak height of ¦SN(Q) of SiO2 glasses exhibitingdifferent Tf values. In the case of Q1 (FSDP), the change islinear as observed in spectra change of ¦SX(Q). However,for Q2 and Q3 peaks, a steep change is observed for SiO2glass with Tf = 1743K. Comparing ¦SN(Q) with ¦SX(Q),the steep change is only observed in SN(Q). Therefore, weassume that the spectra change correlates with an oxygen-related structure. It is worth noting that the inter-tetrahedralO–O correlation observed in the present case seems to bedifferent from that observed in densified SiO2 glass, inwhich a significant density change is observed.3) In con-trast to pressure-driven structural change of densifiedglass,3) thermodynamic change from the supercooled stateshould change by undergoing a different pathway. It isexpected from the results of positron annihilation spec-troscopy that the formation of a smaller ring is the result ofhigh instability of the larger rings in higher Tf-glass.As shown in Fig. 6(c), an inflection point of structuralparameter with respect to the Tf values is also observed inpositron annihilation spectroscopy. It has been reportedthat small-membered rings, such as three-membered rings,exist in SiO2 glass exhibiting higher Tf values, and theserings induce higher refractive index, density, and elasticmodulus.60) Meanwhile, larger cavities are formed in SiO2glasses exhibiting higher Tf values as a counterpart.Although cavity sizes of the present result are in accor-dance with those in the literature for cavities of SiO2 withlower Tf values (<1650K),58) the deviation from linearityis observed at the higher-Tf region. It is notable that thisstudy is the first result to evaluate the cavity size of SiO2glasses with higher Tf (> 1700K) using the positron anni-hilation spectroscopy. It is reported that a positron line-shape parameter of SiO2 glass saturates after heat treatmentat 1673K.57) Although Brauer et al.57) used the positronlineshape parameter to evaluate the crystallinity of SiO2glass, it is suggested that the saturation behavior depend-ing on temperature is similar to our case.In both inelastic light scattering, while the boson peakfrequency ¯BPmax and Brillouin shift ¯B appear to be linearat lower Tf region, a slight nonlinearity is also discerniblein the high-Tf region. Here, we have compared Brillouinpeak width !B (Brillouin) and standard deviation of log-normal function · (Raman) concerning to spectral broad-10-410-310-210-11002520151050.2550.2500.245180017001600150014001300Fictive temperature Tf (K)Time (ns)Normalized countsCavity radius (nm)Tf = 1348 K1456 K1656 K1763 Kac1.681.661.641.621.6018001700160015001400130042.542.041.541.040.540.0Fictive temperature Tf (K)o-Ps lifetime (ns)o-Ps intensity (%)bFig. 6. Positron annihilation lifetime spectroscopy for determi-nation of cavity of SiO2 glasses exhibiting different Tf values.(a) Positron decay curves of SiO2 glasses exhibiting different Tfvalues. (b) Lifetime of ortho-positronium (o-Ps) ¸3 and theintensity I3 as a function of a function of Tf values. (c) Correlationbetween cavity radius and Tf of SiO2 glasses.3Q2Q1Q 310= 2) n()Q(NSΔpeak height of nQ= 1, 3)n()Q(NSΔpeak height of nQ(K)fTFictive temperature 0-10-20-30-40-501300 1400 1500 1600 17000.00-0.05-0.10-0.15Fig. 7. Qn peak height of ¦SN(Q) of SiO2 glasses as a functionof Tf values.Journal of the Ceramic Society of Japan 134 [4] 246-256 2026 JCS-Japan253ening, i.e. the structural diversity. Figure 8 shows Brillouinpeak width !B and standard deviation of log-normal func-tion · as a function of Tf values. In both parameters, inflec-tion points can be observed, which suggests that somestructural change occurred in SiO2 glass with higher Tfvalue. In SiO2 glass exhibiting a lower Tf value, the num-ber of 6-membered rings (the most thermally stable struc-ture) is increased. If there are many large-membered ringswith a cavity, the refractive index and elastic modulus,which reflect the number of bridging bonds per unit vol-ume, decrease. Such a cavity, i.e., free volume, acts as adisturbance to the phonon propagation of sound velocity,and consequently, a decrease in the propagation distanceof the ultrasonic wave. The propagation distance of theultrasonic wave is inversely proportional to !B. In thepresent study (at approximately 33GHz, 180 nm), themean free path was calculated as 73¯m (Tf = 1300K) and77¯m (Tf = 1763K). The values show that phonon scat-tering is high in SiO2 glass with a low Tf value, indicat-ing the formation of 6-membered rings with a significantfraction of cavities. We assume that the observed structuralchanges do not originate from structural heterogeneity be-cause of the nature of experimental techniques. AlthoughSiO2 glasses with the Tf of more than 1700K were rapidlyquenched, the samples were polished for both spectro-scopic and optical measurements. In addition, for Ramanspectra, the areas close to the surface were observedwhereas stimulated Brillouin spectra reflect information ofbulk area. Since Raman and Brillouin spectra exhibit simi-lar dependence on Tf, the glass can be treated as a struc-turally uniform medium for the purposes of this analysis.Thus, we can conclude that the thermal history affects theformation of various rings during the vitrification.Here we discuss a plausible reason for the observedchange based on a formation of 6-membered rings andother smaller- or larger-membered rings. As a 6-memberedring is the most thermally stable structure, an increase in thenumber of 6-membered rings will induce a decrease in sitedistribution as observed in SiO2 glass with lower Tf . It isreported that both smaller- and larger-membered rings areformed with increasing Tf . The formation of various ringsis reflected in the change of the Brillouin shift, the standarddeviation of the boson peak, and the width of the Brillouinpeak. In the case of SN(Q), a formation of structures is ob-served at the Q region below 1¡¹1 [see Figs. 1(d) and3(b)]. In addition, Tf-dependences of peak height of¦SN(Q) of SiO2 glasses are different. It is thought thatthe degree of ordering or disordering is determined by thedifference in the distance range observed. Since the tem-perature dependence of Brillouin peak width is slightlydifferent from the other spectroscopic data, it is expectedthat the width reflects longer-distance structure, althoughthe distance also belongs to the intermediate-range (not thelong-range ordering, i.e. crystalline structure).Since glass possesses metastable network quenched ata certain temperature, although the actual construction ofSiO2 glass is difficult to determine because of coexistenceof various non-symmetric rings, recent ring analysisallows for the visualization of plausible random networkstructures.3–10,61) On the other hand, as shown in the pres-ent data, rearrangement of network structure upon anneal-ing (relaxation) is still complicated. Since there is noanalytical method to determine the network structure ofglasses with different distance range, a combination ofmultiple measurement techniques is important for under-standing the nature of the glass network.5. ConclusionsTransparent SiO2 glasses with different Tf values wereexamined using several measurement approaches. TheHEXRD and neutron diffraction results suggest the for-mation of a more disordered structure in SiO2 glass withhigher Tf values, and oxygen-related species correlate thestructural change. The correlation length of the boson peakshowed a slightly different tendency to that of the FSDP,indicating that the structural origin of the boson peak isnot the same as that of FSDP. Data from the stimulatedBrillouin scattering spectra suggest that structural changesoccurred in SiO2 glass with higher Tf values, which is alsodetected by positron annihilation spectroscopy. We havedemonstrated Brillouin peak width and standard deviationof log-normal function can be used as a probe for thestructural ordering of glass. Although the direct atomisticobservation of glass is very difficult, these multiscale andquantitative examinations are milestones in the evaluationof various random materials.Acknowledgments High-energy XRD measurementswere performed on the BL04B2 beamline at SPring-8 withthe approval of the Japan Synchrotron Radiation ResearchInstitute (JASRI) (Proposal Numbers 2015A1313 and2024B1004). Neutron diffraction measurements were per-formed on the BL21 beamline at J-PARC with the permissionfrom J-PARC (Proposal Number 2017A0232). This work waspartially supported by the Japan Society for the Promotion ofScience Grant-in-Aid for Scientific Research (B) Numbers18H01714 and 22H01785 (H.M.), Grant-in-Aid for ScientificResearch (C) Number 24K08045 (Y.F.), and for Transforma-tive Research Areas (A) Numbers 20H05881 (Y.O. and S.K.)and 20H05882 (H.M.). This work was also supported by theTokyo Ohka Foundation for the Promotion of Science andTechnology. The discussions with Prof. P. S. Salmon aregratefully appreciated.)3−(cmnormal function Standard deviation of log-(K)fTFictive temperature (MHz)BBrillouin linewidth 1051101151201251300 1400 1500 1600 1700 180024.024.224.424.624.825.025.2Fig. 8. Brillouin peak width !B and standard deviation of log-normal function · as a function of Tf values.Masai et al.: Structural ordering of SiO2 glass exhibiting different fictive temperaturesJCS-Japan254Additional information The authors declare no compet-ing financial interests.References1) G. N. Greaves and S. Sen, Adv. Phys. 56, 1 (2007).2) C. A. Angell, K. L. Ngai, G. B. McKenna, P. F.McMillan and S. W. Martin, J. Appl. Phys. 88, 3113(2000).3) Y. Onodera, S. Kohara, P. S. Salmon, A. Hirata, N.Nishiyama, S. Kitani, A. Zeidler, M. Shiga, A. Masuno,H. Inoue, S. Tahara, A. Polidori, H. E. Fischer, T. Mori,S. Kojima, H. Kawaji, A. I. Kolesnikov, M. B. Stone,M. G. Tucker, M. T. McDonnell, A. C. Hannon, Y.Hiraoka, I. Obayashi, T. Nakamura, J. Akola, Y. Fujii,K. Ohara, T. Taniguchi and O. Sakata, NPG Asia Mater.12, 85 (2020).4) S. Kohara, J. Ceram. Soc. Jpn. 125, 799 (2017).5) Y. Onodera, S. Kohara, S. Tahara, A. Masuno, H. Inoue,M. Shiga, A. Hirata, K. Tsuchiya, Y. Hiraoka, I.Obayashi, K. Ohara, A. Mizuno and O. Sakata,J. Ceram. Soc. Jpn. 127, 853 (2019).6) Y. Shi, J. Neuefeind, D. Ma, K. Page, L. A. Lamberson,N. J. Smith, A. Tandia and A. P. Song, J. Non-Cryst.Solids 516, 71 (2019).7) S. Kohara, M. Shiga, Y. Onodera, H. Masai, A. Hirata,M. Murakami, T. Morishita, K. Kimura and K. Hayashi,Sci. Rep.-UK 11, 22180 (2021).8) M. Shiga, A. Hirata, Y. Onodera and H. Masai,Commun. Mater. 4, 91 (2023).9) S. Kohara, S. Sato, M. Shiga, Y. Onodera, H. Masai, T.Wakihara, A. Masuno, A. Hirata, N. Kitamura, Y.Idemoto, K. Kimura and K. Hayashi, J. Ceram. Soc.Jpn. 132, 653 (2024).10) A. Hirata, S. Sato, M. Shiga, Y. Onodera, K. Kimotoand S. Kohara, NPG Asia Mater. 16, 25 (2024).11) S. R. Elliott, Nature 354, 445 (1991).12) S. R. Elliott, J. Phys.-Condens. Mat. 4, 7661 (1992).13) A. C. Wright, J. Non-Cryst. Solids 179, 84 (1994).14) P. H. Gaskell and D. J. Wallis, Phys. Rev. Lett. 76, 66(1996).15) Q. Mei, C. J. Benmore and J. K. R. Weber, Phys. Rev.Lett. 98, 057802 (2007).16) S. Susman, K. J. Volin, D. L. Price, M. Grimsditch, J. P.Rino, R. K. Kalia, P. Vashishta, G. Gwanmesia, Y. Wangand R. C. Liebermann, Phys. Rev. B 43, 1194 (1999).17) S. Kohara, J. Akola, L. Patrikeev, M. Ropo, K. Ohara,M. Itou, A. Fujiwara, J. Yahiro, J. T. Okada, T.Ishikawa, A. Mizuno, A. Masuno, Y. Watanabe and T.Usuki, Nat. Commun. 5, 5892 (2014).18) L. Hennet, V. Cristiglio, J. Kozaily, I. Pozdnyakova,H. E. Fischer, A. Bytchkov, J. W. E. Drewitt, M.Leydier, D. Thiaudière, S. Gruner, S. Brassamin, D.Zanghi, G. J. Cuello, M. Koza, S. Magazù, G. N.Greaves and D. L. Price, Eur. Phys. J.-Spec. Top. 196,151 (2011).19) L. B. Skinner, C. J. Benmore, J. K. R. Weber, M. C.Wilding, S. K. Tumber and J. B. Parise, Phys. Chem.Chem. Phys. 15, 8566 (2013).20) L. Stixrude and M. S. T. Bukowinski, Phys. Rev. B 44,2523 (1999).21) P. S. Salmon and A. Zeidler, Phys. Chem. Chem. Phys.15, 15286 (2013).22) A. Zeidler and P. S. Salmon, Phys. Rev. B 93, 214204(2016).23) P. S. Salmon, A. Zeidler, M. Shiga, Y. Onodera and S.Kohara, Phys. Rev. B 107, 144203 (2023).24) H. Masai, S. Kohara, T. Wakihara, Y. Shibazaki, Y.Onodera, A. Masuno, S. Sukenaga, K. Ohara, Y. Sakai,J. Haines, C. Levelut, P. Hébert, A. Isambert, D. A.Keen and M. Azuma, Commun. Chem. 6, 269 (2023).25) A. P. Sokolov, A. Kisliuk, M. Soltwisch and D.Quitmann, Phys. Rev. Lett. 69, 1540 (1992).26) L. Börjesson, A. K. Hassan, J. Swenson, L. M. Torelland A. Fontana, Phys. Rev. Lett. 70, 1275 (1993).27) T. Nakayama, Rep. Prog. Phys. 65, 1195 (2002).28) T. Gerber and B. Himmel, J. Non-Cryst. Solids 92, 407(1987).29) H. Masai, S. Kohara, Y. Onodera, A. Koreeda, K. Saito,E. H. Sekiya and N. Kitamura, J. Ceram. Soc. Jpn. 128,1038 (2020).30) A. Q. Tool, J. Am. Ceram. Soc. 29, 240 (1946).31) D. B. Fraser, J. Appl. Phys. 39, 5868 (1968).32) R. Brückner, J. Non-Cryst. Solids 5, 123 (1970).33) T. Moynihan, A. J. Easteal, M. A. Debolt and J. Tucker,J. Am. Ceram. Soc. 59, 12 (1976).34) A. Agarwal, K. M. Davis and M. Tomozawa, J. Non-Cryst. Solids 185, 191 (1995).35) M. D. Ediger, C. A. Angell and S. R. Nagel, J. Phys.Chem. 100, 13200 (1996).36) A. Agarwal and M. Tomozawa, J. Non-Cryst. Solids209, 166 (1997).37) K. Tsujikawa, K. Tajima and M. Ohashi, J. LightwaveTechnol. 18, 1528 (2000).38) H. Kakiuchida, K. Saito and A. J. Ikushima, J. Appl.Phys. 94, 777 (2003).39) S. Sen, R. L. Andrus, D. E. Baker and M. T. Murtagh,Phys. Rev. Lett. 93, 125902 (2004).40) V. Lubchenko and P. G. Wolynes, J. Chem. Phys. 121,2852 (2004).41) A. E. Geissberger and F. L. Galeener, Phys. Rev. B 28,3266 (1983).42) N. Shimodaira, K. Saito, N. Hiramitsu, S. Matsushitaand A. J. Ikushima, Phys. Rev. B 71, 024209 (2005).43) T. Watanabe, K. Saito and A. J. Ikushima, J. Appl. Phys.94, 4824 (2003).44) R. Shuker and R. W. Gamon, Phys. Rev. Lett. 25, 222(1970).45) P. F. McMillan, B. T. Poe, P. H. Gillet and B. Reynard,Geochim. Cosmochim. Ac. 58, 3653 (1994).46) V. K. Malinovsky, V. N. Novikov and A. P. Sokolov,Phys. Lett. A 153, 63 (1991).47) S. R. Elliott, Europhys. Lett. 19, 201 (1992).48) H. Masai, Y. Fujii, N. Kitamura and M. Yamawaki,J. Non-Cryst. Solids 576, 121248 (2022).49) H. Masai, T. Ohkubo, Y. Onodera, Y. Fujii, S. Shimonoand A. Koreeda, J. Ceram. Soc. Jpn. 133, 1 (2025).50) H. Kakiuchida, E. H. Sekiya, N. Shimodaira, K. Saitoand A. J. Ikushima, J. Non-Cryst. Solids 353, 568(2007).51) S. Kohara, M. Itou, K. Suzuya, Y. Inamura, Y. Sakurai,Y. Ohishi and M. Takata, J. Phys.-Condens. Mat. 19,506101 (2007).52) T. E. Faber and J. M. Ziman, Philos. Mag. 11, 153(1965).53) T. Sonehara, Y. Konno, H. Kaminaga, S. Saikan and S.Journal of the Ceramic Society of Japan 134 [4] 246-256 2026 JCS-Japan255Ohno, J. Opt. Soc. Am. B 24, 1193 (2007).54) T. Sonehara, H. Kaminaga, E. Tatsu, S. Saikan and S.Ohno, J. Non-Cryst. Solids 354, 1768 (2007).55) M. Yamawaki, Y. Kobayashi, K. Hattori and Y.Watanabe, Jpn. J. Appl. Phys. 50, 086301 (2011).56) Y. Onodera, S. Kohara, H. Masai, A. Koreeda, S.Okamura and T. Ohkubo, Nat. Commun. 8, 15449(2017).57) G. Brauer and G. Boden, Appl. Phys. 16, 119 (1978).58) M. Ono, K. Hara, M. Fujinami and S. Ito, Appl. Phys.Lett. 101, 164103 (2012).59) M. Zanatta, G. Baldi, R. S. Brusa, W. Egger, A.Fontana, E. Gilioli, S. Mariazzi and G. Monaco, Phys.Rev. Lett. 112, 045501 (2014).60) J. Kushibiki, T.-C. Wei, Y. Ohashi and A. Tada, J. Appl.Phys. 87, 3113 (2000).61) H. Masai, J. Non-Cryst. Solids X 15, 100105 (2022).Masai et al.: Structural ordering of SiO2 glass exhibiting different fictive temperaturesJCS-Japan256