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Definition of tetrahedral tilt. The tilt is defined as the O - O - O angle between linked tetrahedra as shown in ͑ a ͒ . The line between oxygen atoms that are bonded to the same silicon atom is an edge of a tetrahedron. The same angle is shown in the tetrahedral representation in ͑ b ͒ .
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Multiple small samples of amorphous silica have been generated and optimized using classical dynamics and the van Beest-Kramer-van Santen BKS empirical potential function. The samples were subsequently opti-mized and annealed using density functional theory DFT with both the local density and the generalized gradient approximations. A thorough anal...
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... the linked- tetrahedra model of silica, these angles may be thought of as the hinges between adjacent silica tetrahedra groups. The Si- O - Si angle distribution begins to show the intermediate- range structure of the system, because it is the angle between adjacent silica tetrahedra, and participates in ring structure. The data show that the Si- O - Si BAD is sensitive to changes in the cell volume ͑ volume relaxation ͒ , as well as the potential used. 31 The Si- O - Si BAD for the small glasses quenched using the BKS potential is very similar to that of the larger glass. Use of DFT, especially the GGA, results in smaller average Si- O - Si angles even before optimization of the volume ͑ see Table II ͒ . The BAD found using DFT-LDA is shifted slightly to smaller angles, and the BAD found using DFT-GGA is shifted even more than for DFT-LDA, consistent with the longer GGA Si- O bond lengths. With volume relaxation, the average Si- O - Si bond angle was consistently shifted toward smaller angles, and the distribution slightly narrowed. This effect was greatest when the samples were optimized using DFT-LDA, which is likely partially due to the greater sample density ͑ smaller optimum cell size ͒ obtained with the LDA. One way to quantify the connectivity of a network solid is through analysis of minimum ͑ primitive ͒ ring structures. For silica, an n -ring is defined counting only the participating silicon atoms ͑ see the Appendix ͒ . Quartz is composed of six-membered and eight-membered rings, while fully amor- phized silica is expected to have a peak at the six- and seven- membered rings. 56 Analysis of the ring structure of each sample was done using the method of Yuan et al. 56,57 The maximum ring size in the search was set to 19 silicon atoms. Figure 11 shows the ring size distribution ͑ RSD ͒ for each of the ten 72-atom samples used in this study. The dramatically different ring distributions for the ten glass samples show that the connectivity of each sample is significantly different. This selection of different connectivities is one way to try to sample a selection of the many local structures which are possible for a larger system. Since optimization with different potentials did not involve any changes to the connectivity, the ring structure is unchanged as well. Glasses 4, 6, and 10 show peaks at six-member and eight-member rings. The high proportion of six- and eight-membered rings in glass 6 could be considered an indication of incomplete melting, or crystalline character in a larger sample; however, examination of other structural characteristics does not reveal crystalline character ͑ see Fig. 4 ͒ . In addition, the presence of significant population of other sized rings prevents the sample from being crystalline. For the collection of small samples, regularity in the ring size distribution was not used as a criterion to eliminate samples. Figure 12 shows a comparison of the combined RSDs of the ten 72-atom samples with the RSD of the 1479-atom glass. The combined RSD has peaks at six-member and eight-member ring size, and is narrower than the RSD for the larger glass system. In particular, the tail of larger ring sizes is absent. It is clear that large rings are unavoidably underrepresented by small systems. The largest ring found in any of the small samples is a 13-ring. The three-membered rings are also underrepresented. The overall distribution of intermediate-sized rings is similar to that of the larger sample. The disproportionate representation of six-rings and eight-rings is due almost entirely to the influence of glass 6. Exclusion of glass 6 ͑ see Fig. 13 ͒ yields a combined RSD with the peak at seven-membered rings. Figure 14 shows the average torsion angle distribution of the 72-atom glasses and 1479-atom glass. The torsion angle is defined as the Si- O - Si- O angle between series of bonded atoms, as by Yuan and Cormack. 53 Similar to the results shown in the same reference, there are peaks at 60°, and at 180°, which are related to the preference of the sample to be in a trans configuration, due to repulsion between oxygen atoms on neighboring silica tetrahedra. The TADs are quite noisy, and no significant differences can be seen between samples optimized with different methods, or between volume-optimized and fixed-volume results. It can be said qualitatively that the peak around 60° is more pronounced for the smaller samples as compared with the larger sample. Due to the relative rigidity of the silica tetrahedra, shown by the results for the O - Si- O BAD above, it is useful to determine the relative conformations given by the tilt and twist between neighboring tetrahedra. Figure 15 illustrates the structure of a small amorphous silica sample shown in the polyhedral representation. Each tetrahedron is centered on the position of a silicon atom, with oxygen atoms at each vertex. The tetrahedral tilt angle is defined as the O - O - O angle between linked tetrahedra, as shown in Fig. 16. Figure 17 shows the tetrahedral tilt distribution ͑ TLD ͒ for each set of glass samples. The tail at lower angles and the definite shoul- der in the smaller sample results suggest that there may be a secondary peak. A fit of two Gaussian functions yields peaks at around 90° and 140°. The twist between tetrahedra is defined as the torsion angle O - Si- Si- O, using the vector between neighboring silica tetrahedra as shown in Fig. 18. The tetrahedral twist distributions ͑ TWDs ͒ are shown in Fig. 19. The TWD shows peaks at 60° and 180° which are more clearly delineated than in the TAD presented above. These peaks are indicative of the repulsion between next-nearest-neighbor oxygen atoms. The TLD and TWD are strongly constrained in small ring structures, due to geometrical requirements. Comparison of the composite structure of an ensemble of small systems with the structure of a larger simulated system is valid because the convergence of structural properties with system size can be attributed to statistically capturing the key features of the large number of possible arrangements of the medium range structure. We have shown that the representation of the statistical distribution of structures can be achieved with an ensemble of small samples. For individual samples, finite-size effects have shown that silica glass is best studied by computer simulations using large system sizes. 7 This implies that studies of amorphous systems using techniques that require small system sizes are made possible by employing multiple small samples. This work shows that one of the most interesting structural characteristics to capture is the ring size distribution. The ring distribution is relatively straightforward to deter- mine quantitatively in atomic-level simulations. However, ring distribution is challenging to determine quantitatively by experiment. In Raman spectroscopy, small-sized rings may be detected, but larger rings are not easily distinguishable. 58 It can be important to match at least the small-ring-structure population because the increase in concentration of small- sized rings is correlated with enhanced reactivity of the silica structure. 59,60 ͓ Note that only one sample with three- membered rings was included in this study ͑ glass 10 ͒ , while all samples contained four-membered rings. ͔ Experimentally, the ring distribution, and the occurrence and concentration of coordination defects, may be controlled by the glass-forming history. 59,61 Some control of defect populations during annealing has also been shown to be possible in computer simulations. 32,62 With the small samples, we have shown that it is possible to form a variety of significantly different structures using the same glass simulation algorithm. This is uniquely different from using the melting, cooling, and annealing algo- rithms generally used to control structure, and the difference can be attributed to the small sample size. This work shows that a variety of intermediate-range structure can be obtained without attempting to control the cooling rate, in contrast to other recent work. 16,22 Care must be taken in sample selection because the average ring size distributions can be biased artificially. Samples with significantly different ring structures may have indistinguishable features in the short-range part of the TDFs. The pair and angle distribution functions, given by the Si- O, O - O, and Si- Si distances, O - Si- O and Si- O - Si bond angles, and the torsion, tilt, and twist angles, show that the selected sample ensemble has good agreement in the peak positions and widths as compared to a large simulated sample. The sample ensemble used in this work did not include defects that may contribute to the tails of the distributions of distances and angles observed in the larger sample. It is conceivable that more samples that contain three- membered rings should have been included in this study. By attempting to anneal structures to some other, lower- energy configuration it was determined that the structures formed by our primary method, as described above, are highly stable. It is possible that the system supercell size used is smaller than what might be needed to effect any simple transformations to other stable configurations. The Si- O bond is generally considered to have partial ionic character coupled with an otherwise covalent bond. The directional nature of the covalent bond should be seen in the width of the O - Si- O bond angle of the highly directional bonds that make up the silicon tetrahedron. The differences in the O - Si- O BAD seen between DFT and the BKS potential can be attributed to the ab initio method better represent- ing the directional nature of the Si- O bond. The BKS potential is spherical and achieves tetrahedral structure through a strictly repulsive interaction between oxygen atoms. In contrast, the DFT methods are able to describe the directional orbitals involved in bonding. The difference is ...
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... To characterize the nature of the bonding in amorphous Ti 2 C-MXene and its crystal counterpart, we have calculated the bond order (BO). The amorphous Ti 2 C produced in this work differs from both the traditional amorphous materials and the 2D phases of those, such as vitreous silica [23] or amorphous phases of graphene. [16] The [Ti 6 C] octahedra in MXenes are connected by sharing three M atoms, meaning that it is difficult for [Ti 6 C] octahedron to twist like a silicon oxygen tetrahedron after heating up. ...
The emergence of amorphous 2D materials has opened up new avenue for materials science and nanotechnology in the recent years. Their unique disordered structure, excellent large‐area uniformity, and low fabrication cost make them important for various industrial applications. However, there have no reports on the amorphous MXene materials. In this work, the amorphous Ti2C–MXene (a‐Ti2C–MXene) model is built by ab initio molecular dynamics (AIMD) approach. This model is a unique amorphous model, which is totally different from continuous random network (CRN) model for silicate glass and amorphous model for amorphous 2D BN and graphene. The structure analysis shows that the a‐Ti2C–MXene composited by [Ti5C] and [Ti6C] cluster, which are surrounded by the region of mixed cluster [TixC], [Ti–Ti] cluster, and [C–C] cluster. There is a high chemical activity for hydrogen evolution reaction (HER) in a‐Ti2C–MXene with |ΔGH| 0.001 eV, implying that they serve as the potential boosting HER performance. The work provides insights that can pave the way for future research on novel MXene materials, leading to their increased applications in various fields.
... The results indicate that both higher temperature and amorphization lead to an increase in Si-O bond length and a decrease in O-Si-O angle, consistent with previous works. 19,[56][57][58][59][60][61] The Si-O bond lengths vary from 1.60 to 1.63 Å as the temperature increases from 700 to 1000 K, which agrees with neutron scattering experimental results. 62 The O-Si-O bond angles remain within a narrow range of 109.0 • ± 0.2 • in all studied models. ...
The atomic scale solid–liquid interfacial process dominates the macro‐dissolution of silica, yet its direct experimental observation is challenging. Here we employed the reactive molecular dynamics to model this process in alkaline condition. An elevated temperature strategy under canonical ensemble (NVT) was applied to accelerate the process for sufficient sampling at temporal domain. A stepwise transformation from fully linked SiO4 network (Q³ and Q⁴) to reduced linkage and eventually aqueous species (Q⁰) was revealed. The simulated dissolution rate agrees well with the value predicted by empirical model. By tracing hydrogen atoms, we found that the dehydroxylated silica surfaces in alkaline electrolyte solutions underwent a transition from Si–O–Si bond cleavage‐dominated (mainly reacted with OH⁻) to hydroxylation‐dominated surface reactions. The free‐energy reconstruction of well‐tempered metadynamics reveals that 1500 K accelerates dissolution without altering the reaction pathways. These findings offer novel insights into the evolution of atomic‐scale surface configurations during the dissolution kinetics of silica.
... While ab initio techniques and first-principles calculations can be used 22,23 to get an understanding of a system, they quickly become computationally expensive given the large unit cells of silica polymorphs and the number of possible configurations. Furthermore, ab initio simulations of silica are often limited by length-time scales, that circumscribe them for the dynamics of small clusters 24,25 . Faster models are required to access longer time scales and accurately capture the dynamical evolution of the structural features like the angular distribution between the tetrahedral units and even features such as charge distribution, when subject to external stimuli [26][27][28] . ...
Silica is an abundant and technologically attractive material. Due to the structural complexities of silica polymorphs coupled with subtle differences in Si–O bonding characteristics, the development of accurate models to predict the structure, energetics and properties of silica polymorphs remain challenging. Current models for silica range from computationally efficient Buckingham formalisms (BKS, CHIK, Soules) to reactive (ReaxFF) and more recent machine-learned potentials that are flexible but computationally costly. Here, we introduce an improved formalism and parameterization of BKS model via a multireward reinforcement learning (RL) using an experimental training dataset. Our model concurrently captures the structure, energetics, density, equation of state, and elastic constants of quartz (equilibrium) as well as 20 other metastable silica polymorphs. We also assess its ability in capturing amorphous properties and highlight the limitations of the BKS-type functional forms in simultaneously capturing crystal and amorphous properties. We demonstrate ways to improve model flexibility and introduce a flexible formalism, machine-learned ML-BKS, that outperforms existing empirical models and is on-par with the recently developed 50 to 100 times more expensive Gaussian approximation potential (GAP) in capturing the experimental structure and properties of silica polymorphs and amorphous silica.
... Therefore, the MXene may have decomposed before reaching the melting temperature. Different from the connection of (SiO 4 ) tetrahedra in classical amorphous SiO 2 by bridging oxygen, [9] the (M 6 C) octahedra in MXenes are connected by sharing three M atoms, meaning that it is difficult for an (M 6 C) octahedron to twist like a (SiO 4 ) tetrahedron upon heating. Thus, it is hard to synthesize amorphous MXenes by traditional preparation methods. ...
Recently, novel amorphous nanomaterials formed by introducing atomic irregular arrangement factors have been successfully fabricated, showing superior performance in catalysis, energy storage, and mechanics. Among them, 2D amorphous nanomaterials are the stars, as they combine the benefits of both 2D structure and amorphous. Up to now, many research studies have been published on the study of 2D amorphous materials. However, as one of the most important parts of 2D materials, the research on MXenes mainly focuses on the crystalline counterpart, while the study of highly disordered forms is much less. This work will provide insight into the possibility of MXenes amorphization, and discusses the application prospect of amorphous MXenes materials.
... 27 To generate the amorphous silica structures, we performed a melt-quench method by first-principles MD calculations. [28][29][30][31][32] We melted both models at 5000 K for 10 ps (1 fs  10 000 steps) and decreased the temperature from 5000 to 0 K at a rate of À 50 K/ps. Then, structural optimization calculations were performed for each structure, and we investigated the characteristic local structures. ...
Potassium-ion electrets, which mainly consist of amorphous silica and permanently store negative charge, are vital elements of small autonomous vibration-powered generators. However, negative charge decay is sometimes observed to cause issues for applications. In this study, we propose an improved guideline for the fabrication of potassium-ion electrets by first-principles calculations based on density functional theory, which shows that yield reduction can be suppressed by additional oxidation. Moreover, we experimentally confirm that the additional oxidation step effectively extends the lifetime of potassium-ion electrets.
... From eq 1, the available "reactive area" per 0.169 mol from 0.169 mol dm −3 (SiO 2 ) amorphous silica particle of radius 17.5 nm dispersion is 8 × 10 5 cm 2 . If a tetrahedrally coordinated structure of both species of dissolved SiO 2 is assumed with a distance between the O atoms of 0.26 nm, 58 a tetrahedral base area of ∼0.03 nm 2 can be estimated. The 0.002 mol dm −3 dissolved SiO 2 (0.012%) in equilibrium with the silica dispersion will have a "reactive area" of 3.6 × 10 5 cm 2 per 0.002 mol SiO 2 if every Langmuir pubs.acs.org/Langmuir ...
The interaction of amorphous silica nanoparticles with phospholipid monolayers and bilayers has received a great deal of interest in recent years and is of importance for assessing potential cellular toxicity of such species, whether natural or synthesized for the purpose of nanomedical drug delivery and other applications. This present communication studies the rate of silica nanoparticle adsorption on to phospholipid monolayers in order to extract a heterogeneous rate constant from the data. This rate constant relates to the initial rate of growth of an adsorbed layer of nanoparticles as SiO2 on a unit area of the monolayer surface from unit concentration in dispersion. Experiments were carried out using the system of dioleoyl phosphatidylcholine (DOPC) monolayers deposited on Pt/Hg electrodes in a flow cell. Additional studies were carried out on the interaction of soluble silica with these layers. Results show that the rate constant is effectively constant with respect to silica nanoparticle size. This is interpreted as indicating that the interaction of hydrated SiO2 molecular species with phospholipid polar groups is the molecular initiating event (MIE) defined as the initial interaction of the silica particle surface with the phospholipid layer surface promoting the adsorption of silica nanoparticles on DOPC. The conclusion is consistent with the observed significant interaction of soluble SiO2 with the DOPC layer and the established properties of the silica-water interface.
... Classical force fields and DFT methods complemented each other in the melting-quenching procedure to obtain an amorphous state, but DFT methods are often used only for local energy optimization after classical MD as in Ref. [6] where the SIESTA code [7] is used for the energy optimization. In Ref. [8], silica glass is obtained from melts of various density using classical MD with BKS potentials, where the BKS abbreviation corresponds to names of authors of Ref. [9], but then glass samples are annealed at 3000 K by ab initio MD employing the VASP program (Vienna ab initio simulation program) [10][11][12]. In contrast to quartz crystal containing only 6-and 8-membered rings, glass samples prepared in Ref. [8] contain rings of a wide range of sizes, constructed from 3 to 13 SiO 4 -tetrahedra. ...
... In Ref. [8], silica glass is obtained from melts of various density using classical MD with BKS potentials, where the BKS abbreviation corresponds to names of authors of Ref. [9], but then glass samples are annealed at 3000 K by ab initio MD employing the VASP program (Vienna ab initio simulation program) [10][11][12]. In contrast to quartz crystal containing only 6-and 8-membered rings, glass samples prepared in Ref. [8] contain rings of a wide range of sizes, constructed from 3 to 13 SiO 4 -tetrahedra. Densities of amorphous (glassy) states of silicon dioxide obtained in [5,6,8] are close to the experimental value of 2.20-2.14 ...
... In contrast to quartz crystal containing only 6-and 8-membered rings, glass samples prepared in Ref. [8] contain rings of a wide range of sizes, constructed from 3 to 13 SiO 4 -tetrahedra. Densities of amorphous (glassy) states of silicon dioxide obtained in [5,6,8] are close to the experimental value of 2.20-2.14 g/cm 3 (at T=0) [5], 2.18-2.23 g/cm 3 (using different DFT methods) [6] and 2.24-2.33 ...
Ab initio molecular dynamics modeling in the NPT ensemble is used to obtain amorphous states by melting SiO2, ZrO2 and HfO2 crystals. A wide range of melt stabilization temperatures are used. Two types of SiO2 amorphous states are obtained. For melt temperatures below 4500 K, a perfect silica glass is obtained without any point defects. For melt temperatures above 4500 K, silica point defects such as threefold coordinated oxygen atoms, edge-sharing SiO4-tetrahedra, and others together with a wide range of Si-O-Si rings including 3-, and 4-membered rings appear. When the temperature of the melt exceeds the ZrO2 and HfO2 crystal melting point by 100 – 400 K, a sharp drop in the density of amorphous states is observed, accompanied by a decrease in atomic coordination, but this does not lead to the formation of defect states in the depth of the band gap of hafnium and zirconium dioxides.
... For this reason it is sufficient to consider only one of the two torsion angles which we will call ω. From the analysis reported in the literature [38,41], it is found that ω varies as a function of the Si-O-Si bond angle and that, for θ in the 140-160°range, it has three maxima of around 60°, 180°, and 300°. These values correspond to the three staggered conformations of the O 3 Si-O-SiO 3 moiety, as viewed along the Si-Si axis, and are such that next-nearest-neighbor oxygen atoms are at a maximum distance. ...
Due to its unique properties, amorphous silicon dioxide (a-SiO2) or silica is a key material in many technological fields, such as high-power laser systems, telecommunications, and fiber optics. In recent years, major efforts have been made in the development of highly transparent glasses, able to resist ionizing and non-ionizing radiation. However the widespread application of many silica-based technologies, particularly silica optical fibers, is still limited by the radiation-induced formation of point defects, which decrease their durability and transmission efficiency. Although this aspect has been widely investigated, the optical properties of certain defects and the correlation between their formation dynamics and the structure of the pristine glass remains an open issue. For this reason, it is of paramount importance to gain a deeper understanding of the structure–reactivity relationship in a-SiO2 for the prediction of the optical properties of a glass based on its manufacturing parameters, and the realization of more efficient devices. To this end, we here report on the state of the most important intrinsic point defects in pure silica, with a particular emphasis on their main spectroscopic features, their atomic structure, and the effects of their presence on the transmission properties of optical fibers.
... Many models for describing silica have been proposed for fixed-charge force fields, 20-33 reactive potentials, [34][35][36][37][38][39][40][41][42] and electronic structure-based interactions. 38,[43][44][45][46][47][48][49][50][51][52][53][54][55] Each of these approaches has advantages and disadvantages depending upon the phenomena that are of interest. ...
... 35 Other reactive force fields include one based on the dissociative water model by Garofalini and co-workers, 40,41 which was used to examine the dissolution of a-SiO 2 silica in water. 42 Electronic structure-based descriptions of silica surfaces using periodic boundary conditions are becoming increasingly accessible, 38,[43][44][45][46][47][48][49][50][51][52][53]55 providing better insight into reactivity of silica surfaces. They are still limited, however, to relatively small system sizes and timescales of not more than a few tens of picoseconds. ...
... It is considered as the archetypal network glass. Its structural [3][4][5][6][7][8][9][10][11] and dynamical [12][13][14][15][16][17][18][19][20][21] properties have been extensively studied both theoretically [8][9][10][11][12][13][14][15][16][17] and experimentally [4][5][6][7][18][19][20][21], but persistent challenges remain. Many computer-simulation-based structural models have been performed for creating realistic structural models of amorphous silica. ...
... It is considered as the archetypal network glass. Its structural [3][4][5][6][7][8][9][10][11] and dynamical [12][13][14][15][16][17][18][19][20][21] properties have been extensively studied both theoretically [8][9][10][11][12][13][14][15][16][17] and experimentally [4][5][6][7][18][19][20][21], but persistent challenges remain. Many computer-simulation-based structural models have been performed for creating realistic structural models of amorphous silica. ...
... This can be explained by the lack of a Si-Si short-range attraction term in the BKS potential. First-principles calculations [8] performed on smaller samples (72 atoms) of amorphous silica have also shown smaller values for the Si-Si distances (3.1 Å) compared to those found with the BKS potential (3.12 Å). A densification can also decrease the Si-Si pair distances. ...
Ten small size samples of amorphous silica containing 78 atoms have been prepared using classical molecular dynamics and the van Beest-Kramer-van Santen (BKS) empirical potential. Our final goal is to use such samples in a forthcoming publication to compute accurately the thermal properties of silica from first principles calculations. The structural characteristics of these ten samples are in good agreement with experimental data. Dynamical properties, like the mean-square displacement, the vibrational density of states or the dynamic structure factor, have also been investigated and compare relatively well with data from neutron scattering experiments. These small dynamically stable structures can therefore be used subsequently to study more complicated physical properties, like the thermal conductivity or the diffusivity at a reduced computational cost.
