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[Yuta Shuseki](https://orcid.org/0000-0003-4835-2841), [Shinji Kohara](https://orcid.org/0000-0001-9596-2680), Tomoaki Kaneko, [Keitaro Sodeyama](https://orcid.org/0000-0002-9228-0729), [Yohei Onodera](https://orcid.org/0000-0002-3080-6991), Chihiro Koyama, Atsunobu Masuno, Shunta Sasaki, Shohei Hatano, Motoki Shiga, Ippei Obayashi, Yasuaki Hiraoka, Junpei T. Okada, Akitoshi Mizuno, Yuki Watanabe, Yui Nakata, Koji Ohara, Motohiko Murakami, Matthew G. Tucker, Marshall T. McDonnell, Hirohisa Oda, Takehiko Ishikawa

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[Atomic and Electronic Structure in MgO–SiO<sub>2</sub>](https://mdr.nims.go.jp/datasets/dbe4af52-ed05-4980-9e4e-f5ffdaf90724)

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Atomic and Electronic Structure in MgO–SiO2Atomic and Electronic Structure in MgO−SiO2Yuta Shuseki, Shinji Kohara,* Tomoaki Kaneko, Keitaro Sodeyama, Yohei Onodera, Chihiro Koyama,Atsunobu Masuno, Shunta Sasaki, Shohei Hatano, Motoki Shiga, Ippei Obayashi, Yasuaki Hiraoka,Junpei T. Okada, Akitoshi Mizuno, Yuki Watanabe, Yui Nakata, Koji Ohara, Motohiko Murakami,Matthew G. Tucker, Marshall T. McDonnell, Hirohisa Oda, and Takehiko IshikawaCite This: J. Phys. Chem. A 2024, 128, 716−726 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Understanding disordered structure is difficult dueto insufficient information in experimental data. Here, weovercome this issue by using a combination of diffraction andsimulation to investigate oxygen packing and network topology inglassy (g-) and liquid (l-) MgO−SiO2 based on a comparison withthe crystalline topology. We find that packing of oxygen atoms inMg2SiO4 is larger than that in MgSiO3, and that of the glasses islarger than that of the liquids. Moreover, topological analysissuggests that topological similarity between crystalline (c)- and g-(l-) Mg2SiO4 is the signature of low glass-forming ability (GFA),and high GFA g-(l-) MgSiO3 shows a unique glass topology, whichis different from c-MgSiO3. We also find that the lowestunoccupied molecular orbital (LUMO) is a free electron-like state at a void site of magnesium atom arising from decreasedoxygen coordination, which is far away from crystalline oxides in which LUMO is occupied by oxygen’s 3s orbital state in g- and l-MgO−SiO2, suggesting that electronic structure does not play an important role to determine GFA. We finally concluded the GFAof MgO−SiO2 binary is dominated by the atomic structure in terms of network topology.■ INTRODUCTIONThe MgO−SiO2 system is very important in both glass scienceand geoscience1 since glassy (g)-MgO−SiO2 is a typical binarysilicate glass system and crystalline (c)-MgSiO3 (enstatite) andc-Mg2SiO4 (forsterite) are Mg-end members of maincomponents of the Earth’s mantle. Liquid (l)-Mg2SiO4 canbe classified as a fragile liquid, while l-MgSiO3 is a strongerliquid according to Angell.2 Particularly, viscosity under highpressure and high temperature is an important thermophysicalproperty to understand magma ocean solidification.3 Thestructures of g-MgSiO3 (high glass-forming ability (GFA)) andg-Mg2SiO4 (low GFA) have been widely studied because theuse of the levitation technique4 made it possible to synthesize abulk g-Mg2SiO4.5 Numerous studies using X-ray6−9 andneutron7−9 diffraction, NMR,5,10−13 Raman spectroscopy,14and reverse Monte Carlo (RMC)15−density functional (DF)theory simulation have been reported.9 The structure of liquid(l)-MgSiO3 has been studied by X-ray diffraction16,17 and DF−molecular dynamics (MD) simulation.9 In the case of l-Mg2SiO4, available data are very limited due to a high meltingpoint (1850 °C); only synchrotron X-ray diffraction data17 areavailable, while DF−MD simulation data are reported.9 Theprevious diffraction studies report that SiO4 tetrahedra arestable, and the Mg−O coordination number (CN) is around 5in l- and g-MgO−SiO2, although there are some discrepanciesin Mg−O CN’s in the previous reports. NMR spectroscopyconfirmed that the Q2 species (SiO4 chain) are dominant in g-and l-MgSiO3, while Si2O76− dimers and isolated SiO44− aredominant in g- and l-Mg2SiO4.In this article, we performed high-energy X-ray diffractionand neutron diffraction measurements on l-MgSiO3 and l-Mg2SiO4 to obtain more detailed structural information aboutthe liquids. To obtain atomic configurations with detailedelectronic structures of g- and l-MgO−SiO2, advanced DF−MD simulations for g- and l-MgO−SiO2 were conducted tounderstand the electronic structure in MgO−SiO2. Wemeasured the density of l-Mg2SiO4 by using an electrostaticlevitation furnace (ELF) under microgravity at the Interna-tional Space Station (ISS). Moreover, we performed severaltopological analyses (ring, polyhedral connection analysis, andpersistent homology) on crystalline (c-), g-, and l-MgO−SiO2to extract topological similarity among the crystal, glass, andReceived: August 17, 2023Revised: December 21, 2023Accepted: December 26, 2023Published: January 18, 2024Articlepubs.acs.org/JPCA© 2024 The Authors. Published byAmerican Chemical Society716https://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on February 1, 2024 at 08:43:47 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuta+Shuseki"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shinji+Kohara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Tomoaki+Kaneko"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Keitaro+Sodeyama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yohei+Onodera"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Chihiro+Koyama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Atsunobu+Masuno"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Atsunobu+Masuno"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shunta+Sasaki"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shohei+Hatano"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Motoki+Shiga"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Ippei+Obayashi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yasuaki+Hiraoka"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Junpei+T.+Okada"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Junpei+T.+Okada"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Akitoshi+Mizuno"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuki+Watanabe"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yui+Nakata"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Koji+Ohara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Motohiko+Murakami"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Matthew+G.+Tucker"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Matthew+G.+Tucker"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Marshall+T.+McDonnell"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Hirohisa+Oda"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Takehiko+Ishikawa"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.jpca.3c05561&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=&ref=pdfhttps://pubs.acs.org/toc/jpcafh/128/4?ref=pdfhttps://pubs.acs.org/toc/jpcafh/128/4?ref=pdfhttps://pubs.acs.org/toc/jpcafh/128/4?ref=pdfhttps://pubs.acs.org/toc/jpcafh/128/4?ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/JPCA?ref=pdfhttps://pubs.acs.org/JPCA?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/liquid to understand the relationship between the topology andGFA.■ EXPERIMENTAL AND SIMULATION PROCEDURESStoichiometric mixtures of MgO and SiO2 were annealed in airin 12 h to obtain polycrystalline MgSiO3 and Mg2SiO4 forlevitation experiments. Spherical samples with a diameter of2−3 mm were prepared by melting the c-MgSiO3 and c-Mg2SiO4 using a CO2 laser heating on an aerodynamiclevitator. Samples of g-MgSiO3 were obtained during cooling,while 2−3 mm Mg2SiO4 was too large to be vitrified because ofits low GFA.The density of l-MgO−SiO2 was measured with an ELF atthe ISS. The following obstacles exist when measuring oxidematerials using an ELF on the ground: (1) A large voltage isrequired to overcome the gravity, but this voltage is discharged.(2) A vacuum is required to avoid discharge, but in that case,the oxides will volatilize. On the other hand, the above twoproblems can be avoided in space; this is why themeasurements must be performed on the ISS. A sample was2 mm in diameter. It was charged by friction or contact withother materials in ISS−ELF18 and then levitated to the centerbetween six electrodes that applied Coulomb force. Thesample position was stabilized by tuning voltages betweenelectrodes at 1000 Hz and monitoring the image of the samplebacklit with a He−Ne laser. The levitated sample was heatedand melted by four 40 W semiconductor lasers (980 nm)under 2 atm of dry air. The temperature of the sample wasmeasured by a pyrometer (1.45−1.8 μm). It was calibratedusing an emissivity calculated from the plateau temperature atrecalescence and the reference value of the melting point(MgSiO3: 1650 °C and Mg2SiO4: 1850 °C19). After melting,the nonspherical sample became spherical upon cooling aftershutting off the lasers. During cooling, the sample image wasobserved by ultraviolet back light and a CCD camera. Thepixel size was calibrated against an image of 2.0 mm stainlesssteel spheres, which was recorded under the same conditionsas the sample. The sample volume was calculated from itsdiameter obtained from the image. The density was calculatedfrom the volume and weight measured by UMX2 (MetlerTOLEDO) after the sample was returned to the earth.The X-ray diffraction measurements of l-MgSiO3 and l-Mg2SiO4 were performed at the BL04B2 beamline20 of SPring-8 using an aerodynamic levitator.21 The energy of the incidentX-rays was 61.4 keV. The 2 mm sample was levitated in dry airand heated by a 200 W CO2 laser. The temperature of thesample specimen was monitored by a two-color pyrometer (0.9and 1.05 μm). The instrument background was successfullyreduced by shielding the detectors and by optimizing a beamstop. The measured X-ray diffraction data were corrected forpolarization, absorption, and background, and the contributionof Compton scattering was subtracted using standard analysisprocedures.22The neutron diffraction measurements were conducted onthe Nanoscale-Ordered Materials Diffractometer (NOMAD)diffractometer23 at SNS of Oak Ridge National Laboratoryusing an aerodynamic levitator. The 3 mm sample waslevitated in dry argon and heated by a 400 W CO2 laser. Thetemperature of the sample specimen was monitored by a two-color pyrometer. The measured scattering intensities for thesamples were corrected for instrument background, absorptionof the samples, and multiple and incoherent scattering andthen normalized by the incident beam profile.The fully corrected data sets were normalized to give theFaber−Ziman24 total structure factor S(Q), and the totalcorrelation function T(r) was obtained by a Fourier transformof S(Q).The initial configurations for l-MgO−SiO2 were generatedby RMC modeling started with a random configuration usingboth X-ray and neutron diffraction data. The RMC++25 codewas used. The number of particles in the unit cells was 510 and511 for MgSiO3 and Mg2SiO4, respectively. DF−MDcalculations were performed using the CP2K code,26 whichis a software package for DF−MD calculations using the hybridGaussian (MOLOPT-DZVP-SR) and plane wave basis set.The generalized gradient approximation (GGA) of Perdew,Burke, and Ernzerhof27 was adopted for the exchange−correlation energy functional. The norm-conserving pseudo-potentials of Goedecker, Teter, and Hutter28 were adopted.The cutoff energy of the plane wave was set to 400 Ry. NVTsimulations were carried out using the Nose−Hoover chainmethod with three thermostats. We performed MDsimulations for 20 ps with the time step of 1 fs at 293 K forglass and at 2073 K for liquid.For the electronic structure calculations, we used thestructures of DF−MD at 10 ps for glasses and 10 and 20 psfor liquids. We employed the PHASE/0 code,29 which is DFcalculations using a plain wave basis set. The norm-conservingpseudo potentials30 were used for Mg and Si atoms, whileultrasoft pseudo potential31 was used for O atoms. The PBE0hybrid functional32 with fraction α = 0.3 was used for muchmore reliable estimation of band gap, where Γ is the fraction ofthe exact exchange term in the functional. The k-sampling was2 × 2 × 2 for the Γ point centered mesh with tetrahedronmethod. The cutoff energies of plane wave basis set and chargedensity were 25 and 225 Ry, respectively. For the evaluation ofthe exact exchange term, only the gamma point was sampled,and the real-space method was used for the deficit charge term.King ring size distributions were calculated by using R. I. N.G. S. code.33 The homology of atomic configurations for c-, g,and l-MgO−SiO2 was investigated using the PD1, which iscomprised of two-dimensional histograms showing a persistenthomology. Figure 1 shows the methodology of PD1.34 D1 of aset of atoms given by the following thickening process ofspheres: (i) place a sphere with a radius r at the center of eachatom, (ii) increase the radii of the spheres from 0 to asufficiently large value, and (iii) encode the pair of birth anddeath radii (bi, di) for each ring ci consisting of a set of spheres.The PD1 is then constructed by the two-dimensional histogramon the birth and death plane obtained by the pairs forindependent ci, (i = 1,···, K). Here, the birth (death) radius isdetected as the radius of spheres at which ring ci first appears(disappears). The birth radius has information about thedistances between atoms of the ring ci, and the death radiusFigure 1. Methodology of the persistent diagram.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726717https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig1&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asexhibits information about the size of the ring. The PD1provides statistical information on the shapes of all rings andthereby provides insight into intermediate-range ordering in adisordered structure. The rings detected by this process arerecorded for the computation of the PD1s; hence, theirgeometric shapes can be identified for further analyses. ThePD1s were calculated using the HomCloud package.35■ RESULTS AND DISCUSSIONDensity Data. Table 1 summarizes the published densitydata for MgO−SiO2. Note that density data for l-Mg2SiO4 isestimated in the supplemental data of ref 9. Density of l-Mg2SiO4 as a function of the temperature measured at the ISSusing ELF is depicted in Figure 2. The density showed a lineartemperature dependence, which can be fitted toT T( ) (2911 7) (0.13 0.003) (kg m )(1495 2270 C)3= ± ±° (1)with 99% confidence interval. The density is 2.678 g cm−3 at1800 °C, very close to the estimated value of 2.677 g cm−3given in Table 1. Experimental density data of l-xMgO−(100− x)SiO2 (x = 30, 40, 50, 60, 66.7, 70) were also obtained(Figure S1). Both the densities for g- and l-Mg2SiO4 are higherthan those of g- and l-MgSiO3, respectively. However, thedensity for c-Mg2SiO4 is comparable to that of c-MgSiO3despite the increase in MgO content. The densities of theliquids are lower than those for the glasses, which is a commontrend in oxide materials. It is worth mentioning that thedensity difference between c-MgSiO3 and g-MgSiO3 is muchlarger than that between c-Mg2SiO4 and g-Mg2SiO4.Diffraction Data. Figure 3 shows X-ray and neutron totalstructure factors, S(Q), for g-9 and l-MgSiO3 (a) and Mg2SiO4(b), respectively. And also, Figure S2 shows X-ray totalstructure factors, S(Q), for l-xMgO−(100 − x)SiO2 werecorrected using density data from Figure S1. The liquid datashow broader features in comparison with the glass data due tothe high temperature in Figure 3. A first sharp diffraction peak(FSDP)39 is observed at Q ∼ 2 and 2.2 Å−1 in the X-ray andneutron S(Q) for MgSiO3 and Mg2SiO4, respectively. AnFSDP is considered the symbol of intermediate-range orderwhich is composed of corner-sharing of SiO4 tetrahedra acrossthe void. A principal peak (PP)40 is observed at Q ∼ 2.8 Å−1 inonly the neutron S(Q) because the PP reflects the packingfraction of oxygen atoms,41 which neutrons are more sensitiveto. The position of the FSDP in g-MgSiO3 is higher in Q thanthat of g-SiO29 and that in g-Mg2SiO4 is higher in Q than thatof g-MgSiO3 because the network comprised by the corner-sharing of SiO4 tetrahedra is broken down into MgSiO3 andMg2SiO4 by the addition of MgO associated with the reductionof the cavity volume.9 On the other hand, the position of thePP in the neutron S(Q) is almost identical, but the peakheights for glasses are greater than those for liquids. This trendis consistent with density data because the PP reflects thepacking fraction of the oxygen atoms as mentioned earlier.The total correlation functions, T(r), for MgO−SiO2 glassesand liquids are shown in Figure 3. The real-space resolution inthe glass data is better than that in the liquid data because wehave measured the glass data with a wider Q range. In addition,the liquid structure is inherently more disordered than theglass structure, making peak assignment more difficult in theliquid data, as shown in Figure 3d. As can be seen in Figure 3c,we observe well-defined Si−O, Mg−O, and O−O peaks atapproximately 1.63, 2.02, and 2.71 Å, respectively, but both theMg−O and the O−O atomic distances in g-Mg2SiO4 areslightly longer than those in g-MgSiO3. We evaluated CNsusing experimental and simulation data (Figure S3 and TablesS1 and S2), and it shows that the Si−O and Mg−O CNs areapproximately 4 and 5 in both MgSiO3 and Mg2SiO4, althoughthe Mg−O CNs in the glasses are slightly larger than those inthe liquids, and those in Mg2SiO4 are larger than those inMgSiO3. These behaviors are in line with the behaviors of thePP in the neutron S(Q) and density data because the glassesare much denser than the liquids, and g- and l-Mg2SiO4 aredenser than g- and l-MgSiO3. The average CNMg−O of DF−MD model of g-MgSiO3 shows 5.0 and the distribution of thevalue CNMg−O gives [4]Mg (21.6%), [5]Mg (55.9%), and [6]Mg(22.5%) using the cutoff distance 2.60 Å. The previous resultsobtained by neutron diffraction, RMC, and empirical potentialstructure refinement (EPSR) show CNMg−O around 4.50,424.50,43 and 4.48,44 respectively. Our DF−MD model hashigher CNMg−O than those because a lot of [5]Mg exist. On theother hand, [4]Mg is predominant in other previous models; itmight be our model slightly overestimates the Mg−Ocoordination.Partial Structure and Short-Range Structure Derived fromDF−MD Simulation. X-ray and neutron total structure factors,S(Q), for g-MgO−SiO2 and l-MgO−SiO2 derived from DF−MD simulations are shown in Figure 4. Figure 5a shows thepartial structure factors, Sij(Q), for MgO−SiO2. The Sij(Q)except SSi−Mg(Q) exhibits a negative peak at the FSDPposition. Similar behavior is found in 22.7R2O−77.3SiO2glasses (R=Na and/or K).45 The cation−oxygen Sij(Q)(SSi−O(Q) and SMg−O(Q)) exhibit a positive peak at the PPposition, while the cation−cation Sij(Q) (SSi−Si(Q), SSi−Mg(Q),and SMg−Mg(Q)) and SO−O(Q) exhibit a positive peak. Thealkali−oxygen Sij(Q) in 22.7R2O−77.3SiO2 glasses do notexhibit such a negative peak at the PP position because alkaliTable 1. Density (g cm−3) Data for MgO−SiO2MgSiO3 Mg2SiO4crystal 3.21036 3.22037glass 2.7407,9 2.9309liquid 2.51138 2.6779Figure 2. Measured density of l-Mg2SiO4 as a function oftemperature. Error bar was estimated to be 3%.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726718https://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig2&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asand magnesium have different valences, which results indifferent oxygen coordination numbers. Indeed, oxygencoordination numbers are mostly smaller than 5 in22.7R2O−77.3SiO2 glasses. The partial pair distributionfunctions, gij(r), for MgO−SiO2 derived from the DF−MDsimulations are shown in Figure 5b. The first correlation peaksfor the glasses are sharper than those of the liquids. The firstcorrelation peaks of gSi−Si(r) in MgSiO3 are sharper than thosein Mg2SiO4 and the first correlation peaks of gMg−Mg(r) inMg2SiO4 are sharper than those in MgSiO3, which reflect thecomposition difference between MgSiO3 (MgO−SiO2) andMg2SiO4 (2MgO−SiO2).It is confirmed that both the Si−O and Mg−O CNs derivedfrom the DF−MD simulations are comparable to theexperimental data. These behaviors suggest that there is noconsiderable structural difference in cation−oxygen coordina-tion between MgSiO3 and Mg2SiO4 and between liquids andglasses. On the other hand, gO−O(r) shows significantdifferences between them, although the difference in oxygenatomic fractions between MgSiO3 (atomic fraction is 0.6) andMg2SiO4 (atomic fraction is 0.57) is subtle. The O−O CNs forg-MgSiO3, g-Mg2SiO4, l-MgSiO3, and l-Mg2SiO4 are found tobe 12.17, 12.70, 11.24, and 11.80, respectively. The differencebetween MgSiO3 and Mg2SiO4 and between liquids and glassesis large, which agrees well with the behavior of the PP inneutron S(Q). These results suggest that differences in packingfraction of oxygen atoms46 are an important parameter tounderstand the glass structure.Three Body Correlations. Figure 6a shows the bond angledistributions (BAD) for Mg−SiO2 glasses and liquids. It isworth mentioning that l-MgSiO3, l-Mg2SiO4, and g-Mg2SiO4data are very similar, and only g-MgSiO3 exhibits a differencein fine structure in the Mg−O−Si and Mg−O−Mg BADs.Especially, the Mg−O−Mg BAD exhibit that the MgOxpolyhedra of g-MgSiO3 have a unique connectivity because c-MgSiO3 shows only a single broad peak at ∼97° (no peak at∼120°). The O−Mg−O BADs of g-MgSiO3 and g-Mg2SiO4have two distinct peaks at ∼90 and ∼180°, which are verydifferent from a single well-defined peak for O−Si−O (109°),suggesting that MgOx polyhedra are octahedral, although theMg−O CN is 5. The O−Mg−O BADs are rather similar toO−Er−O of l-Er2O3 (Er−O CN is 6.1)47 and O−Al−O of g-Al2O3 (Al−O CN is 4.7). Note that the Er2O3 is a nonglass-forming liquid and Al2O3 glass can be obtained only byelectrochemical method48 since Al2O3 is classified intointermediate (nonglass former).49Topological Analysis. From previous research,9 theaddition of MgO decreases SiO4 tetrahedra rings becauseMgO worked as intermediate oxide. Especially, g-Mg2SiO4 hasno SiO4 tetrahedra rings, and SiO4 monomer and Si2O7 dimerFigure 3. Diffraction data for MgO−SiO2 glasses and liquids. (a) Neutron (upper) and X-ray (lower) structure factors, S(Q) for g-7,9 and l-MgSiO3.(b) Neutron (upper) and X-ray (lower) structure factors, S(Q) for g-7,9 and l-Mg2SiO4. (c) Neutron (upper) and X-ray (lower) total correlationfunctions, T(r) for g-7,9 MgSiO3 (bule line) and Mg2SiO4 (red line). (d) Neutron (upper) and X-ray (lower) total correlation functions, T(r) for l-MgSiO3 (blue line) and Mg2SiO4 (red line). Dashed lines are guides for the eyes.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726719https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig3&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asare predominant silicate species. In this research, we focusedon the ring statistics for −O−Si(Mg)−O− rings in MgO−SiO2, and these data are shown in Figure 6b. Our ring statisticsdata are slightly different from those reported previously.9 Weattribute this discrepancy to the different modeling approaches,i.e., RMC modeling in ref 9 vs a DF−MD simulation in ourstudy. Fourfold rings are the dominant rings in all MgO−SiO2.Intriguingly, all ring size distributions are very similar inMg2SiO4, while g- and l-MgSiO3 have larger-sized rings incomparison with c-MgSiO3. It is suggested that g- and l-MgSiO3 are topologically disordered,50 which is a typicalbehavior of high GFA glass, while g- and l-Mg2SiO4 aretopologically very similar to c-Mg2SiO4. Table 2 summarizesthe results of the polyhedral connections and Qn analyses forMgO−SiO2. It is found that most of MgO−SiO2 are within thecorner-sharing motif for SiO4−SiO4 connectivities, althoughsmall fractions of edge-sharing are observed in g-Mg2SiO4 andliquid MgO−SiO2. SiO4−MgOx connectivities for c-MgSiO3show a corner-sharing motif, too, but the fraction of edge-sharing is increased in g-MgSiO3 and shows the maximumvalue in l-MgSiO3 due to disorder. However, SiO4−MgOxconnectivities in Mg2SiO4 show completely different behavior.The fraction of edge-sharing is increased in l-Mg2SiO4 incomparison with g-Mg2SiO4, but the fraction of that in c-Mg2SiO4 shows the maximum value. Moreover, the ratio ofcorner-sharing and edge-sharing is exactly the same betweenSiO4−MgOx connectivities and MgOx−MgOx connectivitiesbetween c-Mg2SiO4 and g- and l-Mg2SiO4. The fraction ofcorner-sharing in MgOx−MgOx connectivities in c-Mg2SiO4 issmaller than that in g-Mg2SiO4 and l-Mg2SiO4. On the otherhand, MgOx−MgOx connectivities in c-MgSiO3 show onlyedge-sharing, while the g-MgSiO3 shows a small fraction ofedge-sharing in addition to corner-sharing and the fraction ofedge-sharing slightly decreases in l-MgSiO3. Thus, the behavioris quite different between MgSiO3 and Mg2SiO4, and the lattershows similarity between c-Mg2SiO4 and g-/l-Mg2SiO4 becauseit is noted that the SiO4−SiO4 connectivities are subtle in g-/l-Mg2SiO4 owing to the breakdown of SiO4 network.Qn distributions summarized in Table 2 provide us withconnectivities of SiO4 polyhedra. c-MgSiO3 shows quite uniqueconnectivity, because we can observe only Q2 chain network.Indeed, it is demonstrated that SiO4 tetrahedra form a corner-sharing chain network and MgOx polyhedra form only an edge-sharing network, which form a layer structure in c-MgSiO3.More than 50% of the Q2 chain transforms into Q1 and Q3 inboth g-MgSiO3 and l-MgSiO3, suggesting that the structuraltransformation between c-MgSiO3 and g-/l-MgSiO3 requiresquite significant structural modifications. On the other hand, c-Mg2SiO4 shows only Q0 because the SiO4 tetrahedra areisolated. Moreover, the fractions of Q0 in g- and l-Mg2SiO4 areFigure 4. Neutron and X-ray total structure factors, S(Q), for g,l-MgO−SiO2 derived from DF−MD simulations (blue line) and experimental (redline) data.(a) Neutron (upper) and X-ray (lower) structure factors, S(Q) for g-7,9 MgSiO3. (b) Neutron (upper) and X-ray (lower) structurefactors, S(Q) for g-7,9 Mg2SiO4. (c) Neutron (upper) and X-ray (lower) structure factors, S(Q) for l-MgSiO3. (d) Neutron (upper) and X-ray(lower) structure factors, S(Q) for l-Mg2SiO4.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726720https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig4&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asdecreased to less than 40% and Q1 (Si2O76− dimers7) isdominant (43.8% in glass and 45.2% in liquid), while thefractions of Q2 are about 16%. In addition, a small fraction ofQ3 (1.4%) and Q4 (0.1%) is observed in l-Mg2SiO4. It issuggested from these behaviors that the transformation from g/l-Mg2SiO4 into c-Mg2SiO4 seems to be easier than that inMgSiO3 because only the breakdown of chains or dimers isrequired while the formation of chains is required in thetransformation from g/l- MgSiO3 into c-MgSiO3. The averageQn values of MgO−SiO2 are 2.00 (c-MgSiO3), 2.03 (g-MgSiO3), 2.02 (l-MgSiO3), 0 (c-Mg2SiO4), 0.77 (g-Mg2SiO4),and 0.82 (l-Mg2SiO4). Both g- and l-SiO2 with high GFA havethe value of that average Qn are almost 4.0, which suggestedthat the number of average Qn is an indicator of GFA.Figure 7a shows the Si-centric persistence diagrams, PD1s. Itis well-known that g-SiO2 shows a prominent vertical profilealong with the death axis at bk ∼ 2.2 Å2 in both the Si-centricand O-centric PD1s due to the formation of SiO4 tetrahedralnetwork with corner-sharing of oxygen atoms.51,52 Similarprofiles are only observed in the Si-centric PD1 for g- and l-MgSiO3 at bk ∼ 2.4 Å2, but c-MgSiO3 does not show such aprofile since c-MgSiO3 has only a Q2 chain network, which isnot three-dimensional. Mg2SiO4 does not show such a profile,either, because there is almost no Q3 or Q4 three-dimensionalSiO4 network. The O-centric PD1s are shown in Figure 7b.The small death profiles are observed along with the diagonalin PD1s because the death values reflect significantly highpacking of oxygen atoms and high density. It is found that thedeath value is a maximum in l-MgSiO3 (minimum density) anda minimum in c-MgSiO3 (maximum density). Figure 7c showsMg-centric PD1s. The PD1s for g-MgSiO3 and g-Mg2SiO4 havea profile along with the death axis at bk ∼ 3.0 Å2, which are thesignature for the formation of the Mg−O network. The PD1sfor c-Mg2SiO4 have a profile at the same bk position, while c-MgSiO3 does not have such a profile because of the absence ofwell-defined three-dimensional Mg−O network. Moreover, it issuggested that all of the liquid data are very similar to glassdata and that c-Mg2SiO4 data are very similar to g-Mg2SiO4,Figure 5. Partial structure for MgO−SiO2 glasses and liquids.(a) Partial structure factors, Sij(Q). (b) Partial pair distribution functions, gij(r). Black,l-MgSiO3; red, g-MgSiO3; blue, l-Mg2SiO4; cyan, g-Mg2SiO4. Dashed lines are a guide to the eyes.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726721https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig5&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asFigure 6. Analysis of intermediate-range structure in MgO−SiO2. (a) BADs. (b) King ring size distributions for −O−Si(Mg)−O− rings. Black, l-MgSiO3; red, g-MgSiO3; blue, l-Mg2SiO4; cyan, g-Mg2SiO4.Figure 7. Topological analysis for MgO−SiO2. (a) Si-centric PD1, (b) O-centric PD1, and (c) Mg-centric PD1.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726722https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig7&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig7&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asbut c-MgSiO3 data are very different from g/l-MgSiO3 data.This trend is consistent with ring size distributions,demonstrating that we can see similarity in homology inMg2SiO4, but the homology of c-MgSiO3 is quite differentfrom that of g- and l-MgSiO3.Electronic Structures. Figure 8 shows electron density ofstates (DOS) for g-and l-MgO−SiO2 calculated employingPBE053 with a fraction of exact exchange of α = 0.3, which willbe referred to as PBE0 (0.3) below. It is known that GGA−PBE underestimates the band gap, and we performed severalbenchmark tests for crystalline MgO, SiO2 (α-quartz),MgSiO3, and Mg2SiO4 (see Table S3) and confirmed thatPBE0 (0.3) shows the best agreement with experimental data;hence, we compare GGA−PBE (blue) and PBE0 (0.3) (red)in Figure S4. It is suggested from the DF−MD calculationsthat the lowest unoccupied molecular orbitals (LUMOs) are 3sorbitals and free electron-like state at the void sites nearmagnesium atoms (see Figure 9a for g-MgSiO3 as a typicalexample and Figure S5 for l-MgSiO3 and g-/l-Mg2SiO4) arisingfrom a decreased oxygen coordination, and the highestoccupied molecular orbitals (HOMOs) are oxygen’s 2p orbitalstates. These behaviors are in line with our previous study onCaO−Al2O3 glass54 but very different from α-quartz, c-MgO, c-MgSiO3, and c-Mg2SiO4, in which LUMOs and HOMOs areoxygen’s 3s and 2p orbitals, respectively. Electron band gapscalculated by PBE0 (0.3) are found to be 7.97, 6.30, and 2.71Table 2. Polyhedral Connections and Qn Analyses for MgO−SiO2polyhedral connections QnSiO4−SiO4 SiO4−MgOx MgOx−MgOx Q0 Q1 Q2 Q3 Q4c-MgSiO3 corner 100 92.3 0 0 0 100 0 0edge 0 7.7 100face 0 0 0g-MgSiO3 corner 100 82.7 65.9 4.9 22.6 44.1 21.4 7.0edge 0 17.3 30.7face 0 0 3.4l-MgSiO3 corner 98.5 77.1 69.6 5.8 20.3 44.3 25.7 3.9edge 1.5 22.5 27.9face 0 0.4 2.5c-Mg2SiO4 corner 0 66.7 66.7 100 0 0 0 0edge 0 33.3 33.3face 0 0 0g-Mg2SiO4 corner 96.6 79.3 71.5 39.6 43.8 16.6 0 0edge 3.4 20.7 27.4face 0 0 1.1l-Mg2SiO4 corner 98.4 76.2 68.5 37.1 45.2 16.2 1.4 0.1edge 1.6 23.2 28.3face 0 0.6 3.2Figure 8. Electronic structure of MgO−SiO2 glasses and liquids. Electron DOSs for (a) MgSiO3 and (b) Mg2SiO4 glasses and liquids calculated byDF−MD simulations employing PBE0 (0.3).The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726723https://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig8&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig8&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(10 ps)/3.69 (20 ps) eV, for c-, g, and l-MgSiO3 and 8.37, 5.64,and 3.43 (10 ps)/3.81 (20 ps) eV, for c-, g, and l-Mg2SiO4.Note that liquid data have more fluctuations due to the hightemperature. It is found that band gap values become small inthe order of crystal, glass, and liquid (see Figure 9b) and theband gap of g-Mg2SiO4 is narrower than that of g-MgSiO3. Wediscuss these behaviors in Figure 9. The LUMO levels ofglasses can be stabilized due to void site arising from adecreased oxygen coordination from six in the crystals to fivein the glasses (Figure 9c). The LUMO levels of the liquid canbe more stabilized due to the high temperature. HOMO can bedestabilized in glasses due to inherent structural disorder,especially between oxygen atoms. This feature is enhanced inthe liquid due to high temperature (see Figure 9d) manifestedby decreased minimum oxygen−oxygen atomic distancesshown in the inset of Figure 5b.■ CONCLUSIONSIn this article, we have discussed the atomic and electronicstructures of MgSiO3 and Mg2SiO4 to understand the networktopology and relationship between structure and GFA. Thedensity measurement at the ISS confirmed that our previousestimated density for l-Mg2SiO4 is very close to experimentaldata. The packing of oxygen atoms in Mg2SiO4 is larger thanthat in MgSiO3, and that of the glasses is larger than that of theliquids. Diffraction measurements and DF−MD simulationsdemonstrated that the packing of oxygen atoms is an importantstructural descriptor to understand the difference betweenMgSiO3 and Mg2SiO4 and between glass and liquid. Theanalysis of electronic and topological structures reasonablyexplained the behaviors of electron band gaps and topologicalsimilarity in crystals, glasses, and liquids. These results suggestthat an electronic state does not change quite a lot betweenMgSiO3 and Mg2SiO4, also the topological similarity betweencrystalline (c)- and g-(l-) Mg2SiO4 is the signature of low GFAand high GFA g-(l-) MgSiO3 shows a unique glass topology,which is different from c-MgSiO3. This means the atomicstructure in terms of network topology is an important factorto understand GFA. We demonstrated that systematiccomparison among crystal, glass, and liquid is important tounderstand the nature and glass and liquid. The utilization ofcontainerless techniques and understanding of behavior ofoxygen atoms, as well as network topology, provide us withcrucial information to discuss glass-forming ability.■ ASSOCIATED CONTENTData Availability StatementThe data sets used and/or analyzed during the current studyavailable from the corresponding author on reasonable request.*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561.Experimental and computational details; density data ofl− xMgO−(100 − x)SiO2; X-ray total structure factors,S(Q), for l− xMgO−(100 − x)SiO2; pair functionanalysis; electron density of states; Isosurface plots of thepartial charge density; coordination numbers obtainedby pair function analysis; coordination number obtainedby DF−MD; electron band gaps of GGA−PBE andPBE0 (PDF).■ AUTHOR INFORMATIONCorresponding AuthorShinji Kohara − Center for Basic Research on Materials,National Institute for Materials Science (NIMS), Tsukuba,Ibaraki 305-0047, Japan; orcid.org/0000-0001-9596-2680; Email: KOHARA.Shinji@nims.go.jpAuthorsYuta Shuseki − Graduate School of Engineering, KyotoUniversity, Kyoto 615-8520, Japan; Center for BasicResearch on Materials, National Institute for MaterialsScience (NIMS), Tsukuba, Ibaraki 305-0047, Japan;orcid.org/0000-0003-4835-2841Tomoaki Kaneko − Department of Computational Scienceand Technology, Research Organization for InformationScience and Technology (RIST), Tokyo 105-0013, JapanFigure 9. Behaviors of HOMO and LUMO in MgO−SiO2.(a) Isosurface plots of the partial charge density around the HOMO and the LUMOlevels for g-MgSiO3. (b) Schematic illustration for HOMOs and LUMOs in crystals, glasses, and liquids. (c) Schematic illustration of LUMO inglasses and liquids. (d) Schematic illustration for electron repulsions in liquids.The Journal of Physical Chemistry A pubs.acs.org/JPCA Articlehttps://doi.org/10.1021/acs.jpca.3c05561J. Phys. Chem. A 2024, 128, 716−726724https://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.jpca.3c05561/suppl_file/jp3c05561_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Shinji+Kohara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0001-9596-2680https://orcid.org/0000-0001-9596-2680mailto:KOHARA.Shinji@nims.go.jphttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Yuta+Shuseki"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-4835-2841https://orcid.org/0000-0003-4835-2841https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Tomoaki+Kaneko"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Keitaro+Sodeyama"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig9&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpca.3c05561?fig=fig9&ref=pdfpubs.acs.org/JPCA?ref=pdfhttps://doi.org/10.1021/acs.jpca.3c05561?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asKeitaro Sodeyama − Center for Basic Research on Materials,National Institute for Materials Science (NIMS), Tsukuba,Ibaraki 305-0047, Japan; orcid.org/0000-0002-9228-0729Yohei Onodera − Center for Basic Research on Materials,National Institute for Materials Science (NIMS), Tsukuba,Ibaraki 305-0047, JapanChihiro Koyama − Human Spaceflight TechnologyDirectorate, Japan Aerospace Exploration Agency (JAXA),Tsukuba, Ibaraki 305-8505, JapanAtsunobu Masuno − Graduate School of Engineering, KyotoUniversity, Kyoto 615-8520, Japan; Center for BasicResearch on Materials, National Institute for MaterialsScience (NIMS), Tsukuba, Ibaraki 305-0047, JapanShunta Sasaki − Graduate School of Science and Technology,Hirosaki University, Hirosaki, Aomori 036-8561, JapanShohei Hatano − Graduate School of Science and Technology,Hirosaki University, Hirosaki, Aomori 036-8561, JapanMotoki Shiga − Unprecedented-Scale Data Analytics Center,Tohoku University, Sendai, Miyagi 980-8578, Japan;Graduate School of Information Science, Tohoku University,Sendai, Miyagi 980-8579, Japan; RIKEN Center forAdvanced Intelligence Project, Tokyo 103-0027, JapanIppei Obayashi − Center for Artificial Intelligence andMathematical Data Science, Okayama University, Okayama700-8530, JapanYasuaki Hiraoka − Institute for the Advanced Study of HumanBiology (WPI-ASHBi), Kyoto University, Kyoto 606-8303,JapanJunpei T. Okada − Institute for Materials Research, TohokuUniversity, Sendai, Miyagi 980-8577, JapanAkitoshi Mizuno − National Institute of Technology,Hakodate College, Hakodate, Hokkaido 042-8510, Japan;orcid.org/0000-0002-5238-1971Yuki Watanabe − Advanced Engineering Services Co., Ltd.,Tsukuba, Ibaraki 305-0032, JapanYui Nakata − Advanced Engineering Services Co., Ltd.,Tsukuba, Ibaraki 305-0032, JapanKoji Ohara − Faculty of Materials for Energy, ShimaneUniversity, Matsue, Shimane 690-8504, Japan; orcid.org/0000-0002-3134-512XMotohiko Murakami − Department of Earth Sciences, ETHZürich, Zürich 8092, SwitzerlandMatthew G. Tucker − Neutron Scattering Division, Oak RidgeNational Laboratory, Oak Ridge, Tennessee 37831, UnitedStates; orcid.org/0000-0002-2891-7086Marshall T. McDonnell − Computer Science andMathematics Division, Oak Ridge National Laboratory, OakRidge, Tennessee 37830, United States; orcid.org/0000-0002-3713-2117Hirohisa Oda − Human Spaceflight Technology Directorate,Japan Aerospace Exploration Agency (JAXA), Tsukuba,Ibaraki 305-8505, JapanTakehiko Ishikawa − Institute of Space and AstronauticalScience, Japan Aerospace Exploration Agency (JAXA),Tsukuba, Ibaraki 305-8505, JapanComplete contact information is available at:https://pubs.acs.org/10.1021/acs.jpca.3c05561Author ContributionsS.K. designed the research. A.M. prepared the samples. Y.S.,S.K., C.K. A.M., Y.W., Y.N. H.O, and T.I. measured density ofl-Mg2SiO4. Y.S., S.K., Y.O., C.K., A.M., S.S., S.H., Y.W., andK.O. performed X-ray diffraction measurements. S.K., Y.O.,C.K., J.T.O. A.M., Y.N., M.G.T., and M.T.M. performedneutron diffraction measurements. T.K. and K.S. conductedDF−MD simulations. Y.S., S.K., T.K., K.S., Y.O., M.S., I.O.,Y.H., M.M. H.O., and T.I. analyzed data. Y.S. and S.K. wrotethe paper, with comments provided by all authors.NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThe synchrotron radiation experiments were performed withthe approval of the Japan Synchrotron Radiation ResearchInstitute (JASRI) (proposal nos. 2018A1096 and 2022A1074).The neutron data were collected on the NOMAD instrumentat the Spallation Neutron Source, a DOE Office of ScienceUser Facility operated by the Oak Ridge National Laboratory.This research was supported by JSPS Grant-in-Aid forTransformative Research Areas (A) “Hyper-Ordered Struc-tures Science” Grant Numbers 20H05878 (to M.S. and S.K.),20H05881 (to S.K. and Y.O.), 20H05882 (to T.I.), 20H05884(to M.S.), and KAKENIHI Grant Number 19K05648 (toY.O.)). Discussion with Yuji Higo is gratefully appreciated.■ REFERENCES(1) Mysen, B.; Richet, P. Silicate Glasses and Melts, Second ed.;Elsevier, 2019.(2) Angell, C. A. 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