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Shino Hayafune, Tatsuya Sakamaki, Haruki Ichikawa, [Yohei Onodera](https://orcid.org/0000-0002-3080-6991), [Shinji Kohara](https://orcid.org/0000-0001-9596-2680), Akio Suzuki

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[Formation of triclusters in silica melt under high pressure](https://mdr.nims.go.jp/datasets/d5480467-551a-436a-b386-527824fd8c44)

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Formation of triclusters in silica melt under high pressureEXPRESS LETTERFormation of triclusters in silica melt under high pressureShino Hayafune1,2, Tatsuya Sakamaki1, Haruki Ichikawa1,Yohei Onodera2, Shinji Kohara2,³ and Akio Suzuki11Department of Earth Science, Graduate School of Science, Tohoku University, Sendai 980–8578, Japan2Center for Basic Research on Materials, National Institute for Materials Science, Ibaraki 305–0047, JapanSilica (SiO2) is the major glass-forming material, and the structures of silica glass and melt have been extensivelystudied using X-ray and neutron diffraction techniques. The diffraction data of silica glass and melt show thefirst sharp diffraction peak (FSDP) at Q ³ 1.5¡¹1, which is a signature of intermediate-range order. In thisstudy, we performed classical molecular dynamics (MD) simulations at 2000K and 5GPa to understand thebehaviour of the diffraction peak associated with the modification of intermediate-range order. The high-pressure melt data obtained show the decrease in the height of FSDP with a shift of the peak position to the high-Q side in X-ray diffraction data, although the average coordination number of four was maintained. In addition,we observed the formation of OSi3 triclusters, which share an oxygen atom with a SiO4 tetrahedron. Thisunusually dense packed atomic arrangement is the result of high pressure and is associated with the very sharpprincipal peak observed at Q ³ 3¡¹1 in the O–O partial structure factor derived by MD simulation.Key-words : Silica, High pressure melt, Molecular dynamics simulation[Received March 17, 2025; Accepted April 9, 2025; Published online April 25, 2025]Glass is abundant in nature and has been manufacturedby humans for more than 3000 years. Glass has evolvedfrom basic structural materials such as art objects andwindow glasses to advanced electronic products, bio-logical products, photon products, and functional materialssuch as mass-produced window and fibre glasses. Silica isthe main oxide material for window, optical, and fibreglasses. The atomic structure of silica glass has been ex-tensively studied using quantum beam (X-ray and neu-tron) diffraction techniques because the diffraction dataare very sensitive to the intermediate-range order.1–10)Silica glass and melt exhibit a first sharp diffraction peak(FSDP)1–5,11,12) at Q ³ 1.5¡¹1 in both X-ray and neutrondiffraction data. The FSDP is a signature of intermediate-range order manifested by a periodicity of 4¡ and a co-herence length of 10¡.5) The peak position and height aresignificantly affected by temperature and pressure. Manydiffraction studies of silica glass under the conditionsranging from ambient temperature/pressure to high pres-sure,11–22) have been reported, but we are not aware ofdiffraction data of silica melt under high pressure/tem-perature due to experimental difficulties. The structuralchanges of silica melt under compression have been re-vealed by classical or first-principles molecular dynamics(MD) simulations.23–25)In this article, we report the results of classical MDsimulation of silica melt to understand the behaviour ofdiffraction peaks associated with the modification ofintermediate-range order under high pressure in compar-ison with previously reported X-ray diffraction12) and MDsimulation26) data of silica melt at ambient pressure andhot-compressed silica glasses.22)MD simulations of the SiO2 melt were performed usingthe Large-scale Atomic/Molecular Massively Parallel Sim-ulator code.27) The number of particles was 30000. Weemployed the empirical force field developed by Guillotand Sator28) with the NPT ensemble. The pressure was keptat 5GPa and the temperature at 2000K. The atomic numberdensity was 0.08635¡¹3. Ewald summations were usedto evaluate long-range Coulombic interactions. Periodicboundary conditions were imposed in the simulations, andthe time step was 1 fs. The simulations were started withrandom configuration and velocity. We first ran calculationsfor 50 ps at 5GPa and 3000K. The system was then cooledto 2000K for 10 ps and relaxed for 50 ps.Figure 1 shows the X-ray structure factor S(Q) of silicaglass at ambient pressure together with the X-ray S(Q) ofsilica melt at ambient pressure and 5Gpa. Experimentaldata of both silica glass (blue)29) and melt (cyan)12) underambient conditions show prominent FSDPs at Q ³1.5¡¹1, although the peak height of the melt is smallerthan that of the glass owing to the high temperature. TheMD data reported by Takada et al. (red)26) is in very goodagreement with the experimental data (cyan) reported bySkinner et al.12) Our simulation data (black) for the high-pressure melt shows an FSDP at Q ³ 1.9¡¹1, which is ahigher Q value owing to the high pressure (27% densi-fication), but the peak height of the high-pressure melt isidentical to that of the ambient-pressure melt.³ Corresponding author: S. Kohara; E-mail: KOHARA.Shinji@nims.go.jpJournal of the Ceramic Society of Japan 133 [6] 242-245 2025DOI https://doi.org/10.2109/jcersj2.25042 JCS-Japan©2025 The Ceramic Society of Japan242This 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/jcersj2.25042https://creativecommons.org/licenses/by/4.0/Figure 2(a) shows the partial pair distribution functionsgij(r) of silica melts obtained by MD simulation. Both theambient- and high-pressure melts show a prominent Si–Ocorrelation peak at 1.6¡, but the peak width decreases inthe high-pressure melt owing to the high pressure. Indeed,the average Si–O coordination number for both melts isapproximately four. The Si–O correlation of the ambient-pressure melt shows a zero-correlation region at 2.2–2.8¡,but this region almost disappears in the high-pressure melt.The O–O gij(r) of the two melts are identical because theintratetraheral O–O correlation is dominant in real space,whereas the Si–Si gij(r) of the two melts are significantlydifferent because the Si–Si correlation describes the corre-lation of the centres of SiO4 tetrahedra, which is significant-ly modified because of cavity squeezing22) by densification.Figure 2(b) shows the partial structure factors Sij(Q) ofsilica melts obtained by MD simulation. The three Sij(Q)have a positive peak at the FSDP position, which is in linewith the behaviour of the glass under ambient condi-tions.5,22) They show the peak shifting to the high-Q sideunder high pressure similarly to the FSDP of X-ray S(Q)shown in Fig. 1, but show a sharp constant in the high-pressure melt: both the heights of the Si–O and O–OFSDPs decrease, whereas that of the Si–Si FSDP in-creases. This behaviour is identical to that of hot com-pressed glass as reported by Onodera et al.22) In addition, apositive principal peak (PP)2) is found for Si–Si and O–OSij(Q), while a negative PP is found for Si–O Sij(Q) atQ ³ 3¡¹1. According to Zeidler and Salmon, the PP ob-served in neutron diffraction data reflects the packing frac-tion of the oxygen atoms because neutrons are sensitive tothe O–O correlation.30,31) This behaviour suggests that alarge difference in the height of the PP in O–O Sij(Q) re-flects the difference in the packing fraction of the oxygenatoms associated with cavity squeezing22) by densification.We also suggest that the negative PP in Si–O Sij(Q) reflectsthe zero-correlation region in Si–O gij(r) in Fig. 2(a)caused by the chemical difference between silicon (four-fold) and oxygen (twofold) atoms.Figure 3 shows the bond angle distributions (BADs) ofthe silica melts obtained by MD simulation. O–Si–O BADshows the symmetry of SiO4 tetrahedra, suggesting that thissymmetry is maintained in the high-pressure melt. A peakobserved at 60° of O–O–O BAD reflects O–O–O trianglesin a SiO4 tetrahedron and intertetrahedral O–O–O correla-tion.32) The difference between ambient- and high-pressuremelts is small. The profiles observed at angles greater than80° reflect intertetrahedral O–O–O correlation, in which asignificant difference is observed. Si–Si–Si BAD reflects21020151050 XRD 0 GPa/298 K glass29) XRD 0 GPa/1973 K12) MD 5 GPa/2000 K (this work) MD 0 GPa/2323 K26)Q (Å 1)S(Q)FSDPFig. 1. X-ray structure factor S(Q) of silica glass at ambientpressure together with X-ray S(Q) of silica melt at ambientpressure and 5GPa.-8-6-4-20246151050S ij(Q)Q (Å 1)Si SiO OSi OFSDP PP14121086420876543210g ij(r)r (Å)Si SiO OSi O(a) (b)Fig. 2. Partial pair distribution functions gij(r) (a) and partial structure factors Sij(Q) (b) of silica melts obtainedby MD simulation. Black curves, 5GPa/2000K; red curves, 0GPa/2323K.26)Journal of the Ceramic Society of Japan 133 [6] 242-245 2025 JCS-Japan243the symmetry of intertetrahedral Si–(O)–Si4 hypertetrahe-dra.21,22,30) The symmetry of hypertetraheda of ambient-pressure melt is far from that of the regular tetrahedra ofsilica glass,22,32) and the symmetry is broken in the high-pressure melt similarly to the glass under high pressure asreported by Kono et al.21) Si–O–Si BAD reflects theintertetrahedral correlation and has been extensivelydiscussed.33) The ambient-pressure melt has a peak at³150°, whereas the high-pressure melt does not have awell-defined peak. This behaviour is similar to the differ-ence between pristine and hot-compressed glasses,22) andfar from the recent results obtained by machine learn-ing MD simulation, which shows a large difference in peakposition between pristine and hot-compressed glasses.34)O–Si–Si BAD also reflects intertetrahedral correlation, andthe peak heights observed at ³15° and ³105° decrease inthe high-pressure melt, which is consistent with the behav-iour of the hot-compressed glass.22) O–O–Si BAD reflectsboth intra- and intertetrahedral correlations, which showssignificant differences between ambient- and high-pressuremelts. The peak profile of the ambient-pressure melt isidentical to that of the hot-compressed glass reported byOnodera et al.,22) but that of the high-pressure melt is verydifferent from that of the hot-compressed glass. The peakobserved at ³30° indicates the intratetrahedral O–O–Sicorrelation, the peak height of which is smaller in the high-pressure melt than that in the ambient-pressure melt.However, the peak profile in the large-angle (>60°) regionof the high-pressure melt, which is considered to indicatethe intertetrahedral O–O–Si correlation, is far from thatof the ambient-pressure melt. This behaviour is similarto that of O–O–O BAD, and understanding O–O–Si andO–O–O BADs is important to understand the structure ofthe high-pressure melt.On the basis of the above discussion, we attempted toanalyse the intertetrahedral correlation. We calculated thefraction of OSi3 triclusters in the melts and found that it isonly 0.3% in the ambient-pressure melt, but it is approx-imately ten times higher in the high-pressure melt. Thetypical local atomic arrangement of an OSi3 triclustercombined with a SiO4 tetrahedron is illustrated in Fig. 4.Note that the number of silicon atoms around the siliconatom in the centre of the SiO4 tetrahedron is five, althoughthe number of bridging oxygen atoms around the siliconatom in the centre of SiO4 tetrahedron is four. The forma-tion of the tricluster is out of Zachariasen’s rule,35) whereoxygen atoms should be twofold, and we suggest that thisunusual atomic arrangement in silica melt is induced byhigh pressure. It is also shown that this highly denselypacked atomic arrangement is associated with the verysharp PP in the O–O Sij(Q) observed at Q ³ 3¡¹1 inFig. 2(b). In addition, this atomic arrangement is consis-tent with the “zip model” proposed by Zeidler et al.18) forsilica glass under high pressure at room temperature.In this article, we have presented the results of classicalMD simulation of the silica melt under high pressure.432101801501209060300B(θ)/sinθ (arb. unit)Angle (degree)B (θ )/sinθ (arb. unit)Angle (degree)B (θ)/ sinθ (arb. unit)Angle (degree)B(θ)/sinθ (arb. unit)Angle (degree)B(θ )/sinθ (arb. unit)Angle (degree)B(θ )/sinθ (arb. unit)Angle (degree)432101801501209060300432101801501209060300432101801501209060300432101801501209060300432101801501209060300Si Si Si Si O Si O Si SiO Si O O O Si O O OFig. 3. Bond angle distributions of the silica melts obtained by MD simulation. Black curves, 5GPa/2000K;red curves, 0GPa/2323K.26)OSi3tricluster SiO4tetrahedronFig. 4. Typical atomic arrangement formed by the combinationof a SiO4 tetrahedron and an OSi3 tricluster. Only the highlightedoxygen atom forms a tricluster.Hayafune et al.: Formation of triclusters in silica melt under high pressureJCS-Japan244The comparison with the ambient-pressure melt and hot-compressed glass is very useful for understanding theeffect of pressure on the intermediate-range order of themelt manifested by FSDP and PP in diffraction data. Wefound a very unusually densely packed atomic arrange-ment in the high-pressure melt, and it is likely that suchan arrangement is also observed in amorphous alumina(Al2O3) because it has a large number of triclusters.36) Wealso suggest that this atomic arrangement indicates theonset of the transformation from four- to five- and sixfoldSi–O polyhedra through the recombination of Si–O bonds.Acknowledgments We are grateful to Dr. Akira Takadafor providing the MD simulation data of silica melt at ambi-ent pressure. This research was carried out with the supportof JSPS KAKENHI Grant Numbers 20H05878, 20H05881,JP21K18641, and JP23K22588. 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