Boson Peak and Superstructural Groups in Na2O-B2O3 Glasses

Osipov, Armenak A.; Osipova, Leyla M.

doi:https://doi.org/10.1155/2018/6746023

Advances in Condensed Matter Physics

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Abstract Introduction Materials and Methods Results and Discussion Conclusions Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Research Article | Open Access

Volume 2018 | Article ID 6746023 | https://doi.org/10.1155/2018/6746023

Boson Peak and Superstructural Groups in Na₂O-B₂O₃ Glasses

Armenak A. Osipov¹and Leyla M. Osipova¹

Academic Editor: Luis L. Bonilla

Received20 Aug 2018

Revised30 Oct 2018

Accepted20 Nov 2018

Published03 Dec 2018

Abstract

Low-frequency Raman spectra of the sodium borate glasses with Na₂O content ranging from 0 to 30 mol% were measured and analyzed from the point of view of their structure in the intermediate range order. Our results show that there is a simple linear correlation between correlation length, , and an average size, <R>, of the area of ordered arrangement of atoms, obtained via the distribution of the (super)structural units and their representative size. Six types of the areas of ordered arrangement of atoms were determined, being related to the presence of the B₃O₃⌀₃ boroxol rings, B₃O₃ triborate rings, B₅O₆ pentaborate groups, B₈O₁₀ tetraborate groups, B₄O₅ diborate groups, and B₃ cyclic metaborate anions in the sodium borate glasses. It was shown that the size of the areas of ordered arrangement of atoms can be determined from the simple geometric analysis of the crystallographic data on the superstructural units.

1. Introduction

It is accepted to distinguish two hierarchical structural levels in the structure of borate glasses. These glasses may be considered as an assembly of different boron-oxygen polyhedra at the level of the short range order (SRO) (the first hierarchical level). The polyhedra can be structurally characterized and identified in terms of the bond length and angles. Numerous studies of the local structure of borate glasses and crystals have shown that the boron atoms may be both three-fold and four-fold coordinated by oxygen. It is accepted, in turn, to classify oxygen atoms into two types: bridging oxygen atoms (BO), which form B-O-B bridging bonds belonging to two boron atoms simultaneously, and nonbridging oxygen atoms (NBO or terminal oxygen atoms), which do not form B-O-B bonds and belong only to one boron atom. Thus, five basic structural units are usually distinguished in borates according to the coordination number of the boron atoms and to the number of BOs and NBOs belonging to the given boron atom: B⌀₃ symmetric triangle (⌀ is BO), [B⌀₄]^- borate tetrahedron, B⌀₂O^- metaborate triangle, B⌀ pyroborate unit, and B orthoborate anion. All of these basic structural units can be identified experimentally, e.g., by NMR or vibrational spectroscopies, and to date, the local structure of borate glasses is well studied both qualitatively and quantitatively. It was established that an addition of alkali oxides to B₂O₃ leads, first of all, to transformation of B⌀₃ symmetric triangles into [B⌀₄]^- tetrahedra and then to the formation of the structural units with NBOs. Thus, the BØ₃ symmetric triangles and [B⌀₄]^- tetrahedra are dominant structural units in structure of all alkali borate glasses with M₂O < 25-30 mol% (M = Li, Na, K, Rb and Cs). The concentration of the [B⌀₄]^- units, , does not depend (or slightly depends) on the type of alkali cation and as a function of mole fraction of alkali-metal oxide, x, follows x/(1-x) equation in the indicated compositional range [1–3].

In [3–5], however, it was noted that the scale of the short range order does not reflect all the complexity of borate glasses, whose structure is characterized by the presence of the so-called superstructural units (boroxol rings, triborate rings, pentaborate groups, diborate groups, etc.) in the next hierarchical level (intermediate range order (IRO)). The superstructural units consist of well defined arrangements of basic structural units with no internal degrees of freedom in the form of variable bond and/or torsion angles [6–8]. A rigidly defined atomic position in these groups allows interpreting the superstructural units as IRO structures of borate glasses. Investigation of distribution of the superstructural units directly, e.g., with using vibrational spectroscopy or NMR technique, is often problematic due to the ambiguity in identification of these groups [4, 5]. In turn, this leads to the problems of measurement of their concentration in glasses with various compositions. Therefore, experimental data on distribution of superstructural units are typically limited by area of their existence and by general tendencies of variation in their concentrations with change in modifier oxide content [9–11]. This fact does not allow to perform a depth study of the dependence of fraction of superstructural units on a glass composition and type of alkali cation.

Investigation of the low-frequency light scattering (Boson peak) plays important role for study of a glass structure. Today, there is no common opinion on the origin of the Boson peak and this problem is open for discussion. One idea is that the Boson peak is caused from vibrational excitations made up of acoustic phonons (most likely shear or transverse phonons) which scatter strongly from elastic inhomogeneities in the glass structure. The scattering leads to a drastic decrease of the mean free path of vibrations and can increase the vibrational density of states in a certain frequency range. The phonon localization may be viewed in terms of the Ioffe–Regel criteria (, where λ is phonon wavelength and is mean free phonon path). These criteria allow to define the correlation length, , through the Boson peak frequency, , and the sound velocity, [12]:

The study of the composition and concentration dependence of the low-frequency light scattering spectra of the borate glasses [13, 14] has shown that both the type of the alkali metal cation and the concentration of modifier oxide strongly affect the spectral properties of the Boson peak (intensity and Boson peak position) (see, e.g., Fig. 18 in ref. [13] or Fig. 7 in ref. [14]) and, hence, the dynamic correlation length . This clearly indicates that IRO structures of various alkali borate glasses are essentially different even if their local structure is qualitatively and quantitatively similar.

Significant progress in understanding of the structure of borate glasses at the level of superstructural units was achieved in the framework of the thermodynamic approach to modeling the properties and structure of the oxide glasses [15]. It was shown that the chemical structure of the lithium and sodium borate glasses and, therefore, the distribution of the superstructural units in these glasses, differ significantly (see, e.g., Fig. 19 in ref. [16] or Fig. 23 and 30 in ref. [8]). At the same time, their local structure is identical at 0 ≤ x ≤ 25-30 mol%. Thus, the results of the thermodynamic modeling also testify that the type of alkali cation strongly affects the IRO structures of alkali borate glasses.

The aim of our study is studying of an interrelationship between dynamic correlation length, , and distribution of the superstructural units in sodium borate glasses.

2. Materials and Methods

The glasses with composition xNa₂O-(100-x)B₂O₃ (where is the molar concentration of Na₂O ranging from 0 to 30 mol%) were prepared by the normal melt quenching method using Na₂CO₃ and H₃BO₃ as sources of sodium oxide and boron trioxide, respectively. The initial reagents were thoroughly mixed in the required ratios and placed in a platinum crucible (Pt). The batch (10 g) in a Pt crucible was placed into electrical furnace, where the temperature was gradually increased up to ~750-1000°C (depending on a glass composition). The fusion was carried out at the given temperatures for 2 hours, whereupon the melting was continued at 1100-1150°C for another one hour. Then, the clear and bubble free liquid was poured into a special steel mould preheated to the temperature close to the glass-transition temperature, , (below 5-10°C than ) to obtain the glassy parallelepiped (7 × 7 × 10 mm, approximately). All glassy samples were annealed at temperature close to for 3 hours. Two samples were prepared for each composition: one of them was used for the measurement of the low-frequency light scattering spectra and the other was used for determination of density ().

The density of each annealed glass sample was measured using Archimedes principle at room temperature using kerosene as a worked liquid. The density was calculated using the formula where and are the weights of the sample in air and in kerosene, respectively, and is the density of kerosene. The samples were weighted using an electronic digital balance (KERN ALS120-4) of uncertainty ± 0.0001 g.

The low-frequency Raman spectra were measured at a 90° scattering geometry using a double grating DFS-24 monochromator. Solid-state laser (LTI-701) with a wavelength of 532 nm (average power is 500 mW) was used as excitation source of spectra. An uncooled FEU-79 photomultiplier, operating in photon counting regime, was employed to collect the low-frequency Raman spectra. The spectral width of the slit was equal to 2 cm⁻¹ in all experiments.

3. Results and Discussion

Nominal glass compositions (in mol%), their designations as well as the velocity of transverse ultrasonic waves, , are presented in Table 1. In addition, the “real” composition of the glasses obtained on the basis of comparison of the density of studied glasses with the data from the literature [17–20] (see Figure 1) is shown in the third column of the Table 1. One can see that the difference between nominal and “real” glass compositions is in the reasonable limits and is less than 0.5 mol%. At the same time, our data are in a good agreement with those published in the literature. The “real” glass composition, therefore, will be used in further discussion.

The examples of the low-frequency Raman spectra for a series of sodium borate glasses are shown in Figure 2. Two main tendencies are observed with variation in modifier oxide content: (i) shift of the Boson peak maximum toward the higher wavenumbers and (ii) decrease in its intensity with an increase in Na₂O content. Similar behavior was found in ref. [21]. Furthermore, a comparison of the Boson peak position showed that our results are in a reasonable accordance (within the experimental errors) with the data published in ref. [21] (see Figure 3). Composition dependence of the dynamic correlation length calculated according to the Eq. (1) is shown in Figure 4. The function was obtained using velocity of transverse ultrasonic waves, , presented in Table 1. As seen from this figure, an increase in sodium oxide content leads to the systematic decrease in the dynamic correlation length from ~ 2.3 nm (g-B₂O₃) to ~ 1.7-1.8 nm (NB13 glass).

As shown in refs. [13, 21], some characteristic length, which we will denote here as L (L is not the same that ), can be determined through the analysis of the low-frequency Raman scattering spectra. The is the “short correlation length” according to ref. [13] or it is the intermolecular distance between the centers of interacting groups according to ref. [21]. Both these works show that systematically changes with the change in the glass composition and give L ~ 7.5-8 Å for g-B₂O₃. It is reasonable to consider a B₂O₃ structure in order to understand the meaning of this length.

It is known that the glassy B₂O₃ consists of B⌀₃ planar triangles. A major portion of these triangles (up to ~80% according to refs. [7, 22, 23]) is associated into the so-called B₃O₃⌀₃ boroxol rings, which contain three B⌀₃ units. The B₃O₃⌀₃ boroxol ring is a sole type of the superstructural units existing in the g-B₂O₃. Schematic illustration of the B₃O₃⌀₃ boroxol ring is shown in Figure 5. This figure is useful when considering the correlation between the structure of pure g-B₂O₃ and some characteristic length . For the fixed length of the B-O bonds (r = 1.365 Å [7]) and O-B-O angles (~120°) within the B⌀₃ units, a diameter of the boroxol ring ( = 4r) will be equal to ~5.5 Å. This value is less than characteristic length, L ~7.5-8 Å [13, 21], for the glassy B₂O₃. Hence it follows that the ordered arrangement of atoms in g-B₂O₃ is not limited by the size of the boroxol ring, but it noticeably in excess of its diameter. It was suggested [21] that the ordered arrangement of atoms in g-B₂O₃ may extend outside the boroxol ring, down to the nearest boron atoms, which are not included into the ring. In the given case, the 7.5 Å corresponds to the distance (see Figure 5). This distance is obtained if the B-O-B external angle, which is not included into the boroxol ring, is equal to 130°. A good agreement between experimental [13, 21] and theoretical (obtained via the simple geometric analysis) L values allows us to assume that the B-O-B angle is not changed completely at random. It is evident from Figure 5 that the characteristic length in the glassy B₂O₃ can be interpreted as a distance between the centers of two nearest-neighbor boroxol rings. Such interpretation is in accordance with assumption that the B₃O₃⌀₃ boroxol rings are not linked to each other completely at random in structure of g-B₂O₃ [13]. On the other hand, the geometric analysis allows interpreting the length as a distance, characterizing the size of the area of ordered arrangement of atoms in g-B₂O₃. From this point of view, it is obvious that the distance will change at an increase in concentration of modifier oxide; i.e., L is a function of the glass composition.

As mentioned in “Introduction”, addition of the sodium oxide leads to the changes in the SRO and IRO structures in sodium borate glasses. The changes of SRO structures are related to the increase in coordination number of boron atoms from 3 to 4. In turn, the formation of the [B⌀₄]^- tetrahedra is reflected in IRO structures: the boroxol rings are transformed into the other superstructural units with [B⌀₄]^- tetrahedra. According to the results of the thermodynamic modeling [5, 24], an increase in concentration of Na₂O, first, leads to appearance of the B₃O₃ triborate rings and B₅O₆ pentaborate groups, simultaneously, and then, the B₄O₅ diborate groups and B₃ cyclic metaborate anions start to appear in the structure of studied glasses. An increase in the fraction of B₃O₃ triborate and B₅O₆ pentaborate groups is accompanied by a decrease in concentration of the B₃O₃⌀₃ boroxol rings. In turn, an increase in concentration of B₄O₅ diborate and B₃ metaborate groups is accompanied by a decrease in fraction of pentaborate and triborate groups (see Fig. 5 in ref. [24]).

By the definition given in the “Introduction", each of the above mentioned superstructural units is the area of ordered arrangement of atoms. Thus, for the glass with any given composition, an average size, <R>, of the area of ordered arrangement of atoms can be expressed as follows:Here, and are the concentration and representative size of the area of the ordered arrangement of atoms, respectively, near or within the limits of the superstructural group. Subscript i indicates the type of superstructural units: i = B (boroxol ring), T (triborate ring), P (pentaborate group), D (diborate group), and M (metaborate ring). All necessary data on the concentration of the superstructural units can be readily obtained from refs. [4, 24]. The compositional dependencies of various superstructural units within the range under consideration are shown in Figure 6. One can see that, to calculate the average size <R>, four representative sizes (for the B₃O₃ triborate ring, B₅O₆ pentaborate group, B₄O₅ diborate group, and B₃ cyclic metaborate anion) should be determined in the studied composition range (0 ≤ x ≤ 30 mol%).

It is evident that the linear size of the ring-type superstructural units, such as triborate and metaborate rings, at the first approximation, can be considered to be equal to the diameter of circle circumscribed around of the boroxol ring, i.e., = = = ~ 5.5 Å (see Figure 5). The strict location of atoms in the pentaborate group (Figure 7), as shown in ref. [25], leads to the fact that this group can be unambiguously described via seven independent parameters: four lengths of B-O bonds and three O-B-O angles (see Table 6 in ref. [25]). Based on these data, one can estimate the linear sizes of the pentaborate group. As seen from Figure 7, the pentaborate group has a maximum size along X-axis ( = 2), whereas its sizes along Y and Z axes will be equal ( = ) and less than = 2 (for the orientation presented in the figure). Taking into account that the characteristic size of the ring-type superstructural units is the diameter of circle circumscribed around of such groups, it was assumed that, among two specific sizes of the pentaborate group, and = , the maximum size should be used for calculation of the <R>(x) function according to Eq. (3). Thus, using the data published in ref. [25], we have found that = = 2 ~5.84 Å.

Diborate group (Figure 8) consists of two B⌀₃ symmetric triangles and two [B⌀₄]^- tetrahedra. The fixed position of atoms in this group is described by nine independent parameters: five lengths of B-O bonds and four O-B-O/B-O-B angles [25, 26]. Figure 8 shows that this group can be described by three linear sizes, , and (linear size along Z-axis is not shown), and size, obviously, is a maximum size. We have found that the linear size of the diborate group along X-axis, , is equal to ~5.7 Å, based on the data presented in Table 7 in ref. [25]. Therefore, the representative size of the area of ordered arrangement of atoms within the limit of diborate group, , was accepted to be 5.7 Å.

Thus, we have all necessary data (concentrations of superstructural units (Figure 6) and representative sizes of the areas of ordered arrangement of atoms: = 7.5 Å, = 5.84 Å, = 5.7 Å and = = 5.5 Å) to calculate the average size <R>, according to Eq. (3). The results of calculation are shown in Figure 9 (black dotted line). One can see that the theoretic curve is changed monotonously only in the limited composition ranges (0 ≤ x ≤ 20 mol%) and it remains practically unchanged with further increasing in Na₂O content. Therefore, a simple linear correlation between and <R>(x) values is observed also in only the limited composition range (x ≤ 15-20 mol%) and strong deviation from the linear behavior is observed at higher concentration of sodium oxide (see Figure 10(a)). This result can be explained if we assume that some type of the area of ordered arrangement of atoms was ignored in our calculations.

(a)

(b)

There are numerous works [9, 11, 14, 27–31] where it was shown that B₈O₁₀ tetraborate groups are also present in structure of the sodium borate glasses in addition to those presented in Figure 6. The B₈O₁₀ tetraborate group is not a superstructural unit [8, 16], because it consists of B₅O₆ pentaborate group and B₃O₃ triborate ring, which are connected to each other by bridging oxygen atom (see Figure 11). For this reason, the tetraborate groups are absent in the distribution of the superstructural units [24] and, hence, they were ignored initially. Nevertheless, the B₈O₁₀ group represents the local area of the ordered arrangement of atoms and, hence, it should be taken into account for calculation of the <R>(x) function according to Eq. (3). Unfortunately, no unambiguous information is known on the concentration of tetraborate groups in structure of the sodium borate glasses. For this reason, at the first approximation, the concentration of the tetraborate group was defined as a product of concentrations of triborate and pentaborate groups. New distribution of the IRO structures obtained under this assumption is shown in Figure 12.

The linear size of the B₈O₁₀ tetraborate group may be estimated on the basis of new distribution of IRO structures: size can be chosen so that the correlation factor, R², between , and <R>, will be more than any preassigned value (R² ≥ 0.98 in this work). It was found that a good correlation between correlation length, , and average size, <R>, is observed at ~9.5-9.6 Å. It is evident that value may match to the linear size of the tetraborate group along X-axis for the orientation presented in Figure 11. New <R>(x) dependence is shown in Figure 9 by red solid line.

On the other hand, one can estimate this size based on the data about the structure of crystalline sodium tetraborate [32]. Such estimation provides the maximum linear size of the tetraborate group of 10 Å, approximately. This result is consistent with previously found of ~9.5-9.6 Å. Thus, the inclusion in consideration of the B₈O₁₀ tetraborate group leads to the fact that between and <R>(x) dependencies a simple linear correlation is observed (see Figure 10(b)).

4. Conclusions

The low-frequency light-scattering spectra of a series of sodium borate glasses with sodium oxide content ranging from 0 to 30 mol% were measured. The spectra were analyzed to find a compositional dependence of the correlation length, , and its interrelation with the IRO structures in the studied glasses. The correlation length was determined according with Ioffe–Regel criteria and it decreases systematically with the increase in Na₂O content. In turn, the average size, <R>, of the area of ordered arrangement of atoms was determined via the data of the thermodynamic modeling of the distribution of the superstructural units and the geometric analysis of the superstructural units. Six types of areas of the ordered arrangement of atoms were determined. Each of them was related to the presence of the B₃O₃⌀₃ boroxol rings, B₃O₃ triborate rings, B₅O₆ pentaborate groups, B₈O₁₀ tetraborate groups, B₄O₅ diborate groups, and B₃ cyclic metaborate anions. For the ring-type groups, such as boroxol ring, triborate ring, and cyclic metaborate anion, the representative size can be expressed through the diameter of the circle circumscribed around them. If the shape of the large grouping significantly differs from the ring (e.g., pentaborate group, tetraborate group, and diborate group), then the representative size of the area of the ordered arrangement of atoms is determined by the maximum linear size of such groups. In case of the pure g-B₂O₃, the area of the ordered arrangement of atoms (7.5 Å) exceeds the diameter of the boroxol ring that indicates the extension of the ordered arrangement of atoms beyond the ring. The representative size of the area of the ordered arrangement of atoms does not exceed the maximum linear size of the corresponding group in all other cases (5.5, 5.84, 9.4-9.5, 5.7, and 5.5 Å for the triborate ring, pentaborate group, tetraborate group, diborate group, and metaborate ring, resp.). It was found that there is a simple linear correlation between the correlation length, , and the average size, <R>, of the area of ordered arrangement of atoms.

Data Availability

The data (density, sound velocity, low-frequency Raman spectra, and distribution of the superstructural groups) used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that there are no conflicts of interest regarding the publication of this paper.

Acknowledgments

This work was supported by state contract [AAAA-A16-116012510127-9 and state task no. 11.9643.2017/BCh of the Ministry of Education and Science of Russia.

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Copyright © 2018 Armenak A. Osipov and Leyla M. Osipova. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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