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Structure and low energy vibrations in silver borate glasses with low silver content
Journal Pre-proof Structure and low energy vibrations in silver borate glasses with low silver content Cristina Crupi, Giovanni Carini, Jr., Giuseppe Carini, Mauro Federico, Andrea Mandanici, Valentino Romano, Giovanna D'Angelo PII:
S0022-3697(19)32150-X
DOI:
https://doi.org/10.1016/j.jpcs.2019.109304
Reference:
PCS 109304
To appear in:
Journal of Physics and Chemistry of Solids
Received Date: 23 September 2019 Revised Date:
12 November 2019
Accepted Date: 6 December 2019
Please cite this article as: C. Crupi, G. Carini Jr., G. Carini, M. Federico, A. Mandanici, V. Romano, G. D'Angelo, Structure and low energy vibrations in silver borate glasses with low silver content, Journal of Physics and Chemistry of Solids (2020), doi: https://doi.org/10.1016/j.jpcs.2019.109304. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
CRediT author statement D’Angelo Giovanna: Conceptualization, Methodology, Writing - Review & Editing; Supervision Crupi Cristina: Conceptualization, Methodology, Investigation Carini Giovanni Jr.: Investigation, Methodology, Carini Giuseppe: Conceptualization, Methodology, Writing - Review & Editing Federico Mauro: Formal analysis, Software Mandanici Andrea: Investigation, Formal analysis; Romano Valentino: Investigation, Formal analysis
STRUCTURE AND LOW ENERGY VIBRATIONS IN SILVER BORATE GLASSES WITH LOW SILVER CONTENT a
a
a,b
a
a
Cristina Crupi , Giovanni Carini Jr , Giuseppe Carini , Mauro Federico , Andrea Mandanici , a
Valentino Romano and Giovanna D’Angelo
a,b*
a
Dipartimento MIFT, Universita' di Messina, Viale F. Stagno d’Alcontres 31, I-98166 Messina, Italy
b
Istituto Processi Chimico-Fisici, Sezione di Messina–Consiglio Nazionale delle Ricerche, Viale F. Stagno d’Alcontres 37, I-98158 Messina, Italy
Structural changes of (Ag2O)x(B2O3)1-x glasses, over the range between X=0.0 and X=0.14, have been monitored by Raman spectroscopy. Low temperature heat capacity measurements have been also performed between 0.4 K and 25 K to investigate along with low frequency Raman scattering the behavior of the low-energy vibrational dynamics. A progressively decreasing intensity of the main band at 808 cm-1 and the appearance of a band at about 775 cm-1 with increasing Ag2O content have been observed and analyzed in detail. The strongly polarized band at 808 cm-1 is ascribed to the breathing vibration of boroxol rings and the decrease of its intensity indicates the reduction of the number of these units in the network. The band at 775 cm-1 is assigned to vibrations of pentaborate units, formed from two boroxol rings linked by a tetrahedral BO4 group. The rate of formation of BO4 groups appears to increase as X/(1-X). Raman investigation has been extended to very low frequencies, where a broad intense band, the Boson peak (BP), dominates the spectrum of all the samples below 100 cm-1. Addition of Ag2O shifts the BP position from 26 cm-1 up to 33 cm-1 and gives rise to a decrease of its intensity up to X=0.09 and a sudden increase for X=0.14, which has been explained as due to rattling motion of silver ions whose contribution is added to that of localized vibrations. The formation of tetrahedral BO4 groups stiffens the network and leads to a decrease of the excess heat capacity over the Debye prediction below 20 K, which is not taken into account by the simple hardening of the elastic continuum but seems to follow the reduction of boroxol rings. This result contrasts the observations on borate glasses with high Ag content and emphasizes the crucial role of the network continuity on the vibrational dynamics of a glass.
Keywords: Glasses, Vibrational dynamics, Raman scattering, Heat capacity, Boson peak *Corresponding author. E-mail address: [email protected]
PACS number: 63.50.Lm; 65.60.+a; 78.30.Ly 1
1. INTRODUCTION An excess of low-frequency vibrations over the Debye prediction is a common feature of amorphous materials and is universally observed below few THz, independently of the specific composition and stoichiometry [1-4]. This contribution is conventionally called the Boson peak (BP) and is also related to a bump in the low-frequency region of Raman spectra (below 150 cm-1) and to an excess lowtemperature (T<20 K) specific heat C [4-7], the latter appearing as a bump when reported as C/T3. In addition, the boson peak energy has also been associated with the position and the width of the socalled "first sharp diffraction peak" (FSDP) observed in the structure factor of many liquids and glasses [8-11], a correlation that calls into question the possibility of considering the characteristic length of medium range order of the glass structure as strongly involved in the development of the BP [10]. The FSDP is indeed considered as a manifestation of subtle correlations involving the medium-range order [9], mainly associated with some characteristic lengths or superstructural units in the network such as large rings of atoms [12,13]. A wide number of models has been proposed for explaining the nature of the BP, such as spatial fluctuations of the elastic constants [14,15], local inhomogeneities with small elastic constants schematized by soft potentials [16,17], or jamming transitions setting the mechanical stability of a system with the onset of excess vibrational modes [18,19]. All these different models, however, evidence some limitations when applied to explain the whole set of experimental observations [20]. Quite recently, we performed a number of studies to investigate the microscopic nature of low-energy vibrations using, as model systems, prototype glasses such as v-B2O3 [6], v-GeO2 [21,22] and v-SiO2 [23,24] compacted under very high pressures (GPa range) in order to increase the mass density. Increasing density causes a progressive decrease of additional low-energy vibrations contributing to the BP, leading to associate them to poorly packed and soft structural domains embedded in a rigid network. These soft regions are formed from connected boroxol rings formed by three corner sharing BO3 triangles in v-B2O3 [6] and from n-membered rings involving SiO4 or GeO4 tetrahedra in v-SiO2 [23] and v-GeO2 [25]. In particular, increasing density of v-B2O3 has also been obtained by changing the chemical bonding in the network [20], to promote the formation of tetra-coordinated boron atoms, but always preserving the stoichiometry. This has determined a growth of network connectivity as a result of higher average coordination, which caused the largest decrease of excess low-frequency vibrations among those observed in less compacted B2O3 glasses. To deepen our understanding on the relationship between atomic connectivity, structure and low energy dynamics in glasses, here we report and discuss the results of Raman and calorimetric investigations of (Ag2O)x(B2O3)1-x glasses. These samples can be prepared in a wide concentration range, evidencing structural transformations that lead to a remarkable increase of network connectivity, defined as the number of bridging oxygens per network forming ion (NFI). The addition of silver oxide modifier to 2
B2O3 significantly changes the boron coordination by forming
tetrahedral groups up to about
X=0.20 and non-bridging oxygens (NBO) for even higher concentrations. The rate of BO4 formation increases as R=X/(1-X) [26], i.e., there is the formation of two four-coordinated borons for each oxygen introduced by the metallic oxide. This structural mechanism increases the network connectivity from 3 to 3.25 at X=0.20, while the NBO formation due to the breaking of B-O-B linkages dominates the high concentration region and leads to the decrease of the network coherence [27]. In an earlier paper we have investigated the low-frequency region of Raman scattering (< 200 cm-1) of silver borate glasses, putting in evidence the role of Ag+ cation compared with Li+ cation in modifying the low frequency dynamics [28]. In the present study, the Raman investigation has been further extended over the frequency range up to 1100 cm-1 to follow the structural modifications of the network with increasing Ag2O concentration. Measurements of specific heat capacity over the temperature interval between 0.4 K and 30 K were also performed to evaluate the calorimetric BP. The range of Ag2O concentration has been limited up to X=0.14, in order to exclude the possible formation of NBO, which could introduce unwanted contributions to the low-energy vibrational dynamics. The results prove that addition of silver oxide promotes the formation of complex superstructural units, i.e. pentaborate groups, which seem to be connected to the systematic decrease of the calorimetric BP.
2. EXPERIMENTAL DETAILS Glasses of (Ag2O)x(B2O3)1-x system, where the molar fraction X ranges over the interval 0≤X≤0.14, were prepared from laboratory reagent 99.99 % purity grades of B2O3 and Ag2O (Aldrich) and stored by following the same specific procedures already described [29]. X-ray powder diffraction of samples was used to verify their amorphous character. The values of the density ρ, measured at room temperature by a Micromeritics Accupyc 1330 gas pycnometer under helium gas having a nominal accuracy of 0.03%, are reported in Table 1. The velocity of longitudinal (Vl) and shear (Vt) sound waves was measured at 10 MHz via a pulse-echo technique at room temperature and at 8 K, as described previously [29]. Their values together with those of the Debye sound velocity VD,
=
+
, and of the elastic Debye temperature ΘD used to
determine the low temperature Debye specific heat, are listed in Table 1. Raman spectra were recorded at room temperature for both VV geometry (incident and scattered light polarized vertical to the scattering plane) and VH geometry (perpendicular polarizations) using a double monochromator Jobin Yvon U-1000. The slits were set to give a measured resolution of 1 cm−1. The light source is an Ar+-ion laser operating at 514.5 nm with a typical output of 300 mW. The scattered light was detected by a cooled photomultiplier (Hamamatsu model R943). To remove the
3
effect of surface contamination, the sample surfaces have been polished before each run of measurement. Table 1. Values of density ρ, measured at room temperature, and of longitudinal (Vl) and shear (Vt) sound velocities, measured at 8 K. The calculated values of Debye sound velocity (VD) and elastic Debye temperature (ΘD) are also included.
ρ
(Ag2O)x(B2O3)1-x glasses
(kg m-3)
X=0.0
1826±0.6
X=0.04
Vl -1
(m s )
Vt -1
VD -1
ΘD
(m s )
(m s )
(K)
3337±3.3
1884±1.9
2095
267.9
2109±0.6
3551±3.6
1964±2.0
2188
283.4
X=0.09
2522±0.8
3890±3.9
2075±2.1
2318
305.9
X=0.14
2856±0.9
4167±4.2
2182±2.2
2440
322.9
For the specific-heat measurements, the standard thermal relaxation method in a 4He cryostat between 1.5 and 30 K and in a 3He cryostat between 0.4 and 2 K was applied [21]. The samples (with typical mass of about 20 mg) were bonded using Apiezon N vacuum grease to one side of a silicon chip, horizontally suspended with gilding metal threads having low thermal conductivity. SMD (surface mounting device) resistors of 15 kΩ (1.5-30 K) and 6 kΩ (0.4-2 K) were sanded and polished, calibrated, and glued to the other side of the silicon by using a thermosetting resin. As heater, we used a strain gage device (120 Ω at room temperature), also glued to the chip. The heat capacity of the empty sample holder together with the addenda was measured in a separate run, and their contribution to the total heat capacity was determined to be less than 30% of the overall mass (sample + sample holder).
3. RESULTS AND DISCUSSION A. Low and high frequency Raman scattering The scaled Raman spectra of (Ag2O)x(B2O3)1-x glasses are compared over the range between 8 and 600 cm-1 in Figure 1 and between 600 and 1100 cm-1 in Figure 2. The spectra have been scaled by the average number of atoms per unit volume (using as a reference that of v-B2O3) and the total integrated intensity Atot over the whole wavenumber range. Subtraction of background intensity Iback has been performed by considering the value at 1100 cm-1 where no vibrational contribution is present; in vB2O3, as an example, Iback at 1100 cm-1 has the same value observed at 1700 cm-1 where no band is expected [6]. The spectra show most vibrational features already observed in v-B2O3: a broad strong band below 100 cm-1 (the BP), a weak shoulder on the high frequency tail of BP at about 132 cm-1 ascribed to the first optical mode observed in crystalline B2O3, some broad and asymmetric bands between 350 and about 650 cm-1 due to bending vibrations of various borate segments, and an intense 4
and highly polarized band at 808 cm-1 associated with a localized breathing-type vibration of oxygen atoms inside the boroxol ring plane [6]. Addition of Ag2O causes the progressive decrease of the intensity I808 of the band at 808 cm-1 and the appearance of a further band at about 775 cm-1 whose intensity I775 increases with increasing X. The latter band was also observed in alkali borate glasses (M2O)x(B2O3)1-x with M=Li, Na, K, Cs and Rb and X≤0.2, and ascribed to breathing vibrations of pentaborate groups [30-32], super-structural units made up from two boroxol rings linked by a tetracoordinated boron atom (schematic illustration of pentaborate is reported in Figure 2).
1.0
Ir/IBP
80
0.5
Ir/Atot
60
0
50
100 -1
40
freq. shift (cm )
20
0 0
100
200
300
400
500
600
-1
frequency shift (cm ) Figure 1.
Room temperature scaled Raman spectra (VV configuration) measured between 8 cm-1 and 600 cm-1 in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), solid line; X=0.04, (O); X=0.09, (∆); X=0.14, (∇). Inset reports Ir/IBP for glasses with X=0.0, X=0.04, and X=0.14, using the same symbols.
5
20
Ir/Atot
80
10
60 700
750
800
850 -1
Ir/Atot
freq. shift (cm )
boroxol
40
pentaborate
20
0 600
800
1000 -1
frequency shift (cm ) Figure 2.
Room temperature scaled Raman spectra (VV configuration) between 600 cm-1 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses; symbols are the same of Figure 1. Inset shows the modes at 775 cm-1 and 808 cm-1 in the glass with X=0.14 and the Lorentzian fit; dotted and solid lines show the single bands and their addition, respectively. Schematic illustration of planar boroxol ring (B3O6) and pentaborate group is also included.
A Lorentzian fit has been used to decompose both the bands in two separate peaks and the results for the glass with X=0.14 are shown in the inset of Fig. 2. The values of the integrated intensity and the full width at half height ∆ν for both the vibrational modes are reported in Table 2. Analysis of the bands by a pseudo-Voigt profile has been also performed, obtaining results for the main characteristics (integrated intensity, frequency and full width) of the two peaks in very close agreement with those from Lorentzian fit. The frequency region below 100 cm-1 of all samples, is dominated by the presence of the BP, whose intensity IBP, after an early decrease up to X=0.09, becomes higher than that of v-B2O3. Interestingly, detailed inspection of data reveals a shift of the BP frequency νBP from 26 cm-1 in X=0.0 up to about 6
33 cm-1 in X=0.14, as shown by the inset of Fig. 1 where the Raman intensity scaled by IBP is reported, to evidence the shift. This is in contrast with the observations for I808 and I775 bands which strictly preserve their frequency positions with increasing X. The observed variations of the spectral features with increasing Ag2O content arise from structural modifications involving both the short- and medium-range orders of the network. The changes in the short-range order are due to the formation of four-coordinated boron atoms that give rise to pentaborate Table 2. Integrated intensity Iν, frequency νi and full width at half height ∆νi of the bands at 775 cm- 1 and 808 cm-1 for (Ag2O)x(B2O3)1-x glasses by Lorentzian fit. The calculated fractions of boroxol rings are also included.
(Ag2O)x(B2O3)1-x
I775
glasses X=0.0
X=0.04
X=0.09
X=0.14
-
ν1
∆ν775
cm-1
(cm-1)
-
-
ν2
∆ν808
Boroxol
cm-1
(cm-1)
fraction
1806.2
808.4
14.64
0.54
±36.0
±0.01
±0.041
I808
143.6
772.6
25.8
1348.1
807.9
12.54
±24.58
±1.68
±5.84
±16.2
±0.06
±0.19
329.8
775.1
23.1
1124.6
808.5
14.42
±20.46
±0.55
±1.85
±15.79
±0.08
±0.25
470.7
777.2
25.1
510.8
807.9
15.9
±17.83
±0.35
±1.16
±14.05
±0.15
±0.5
0.40
0.34
0.15
units containing one tetrahedral BO4 group and have a symmetric ring-breathing vibration centered at about 775 cm-1 [31,32]. As determined by NMR spectroscopy measurements in silver borate glasses [26], the fraction N4 of B(4) increases as X/(1-X) up to X ≤0.25, in very close agreement with the behavior observed in lithium borate glasses and quite differently from borate glasses with heavy alkaline ions, such as Rb and Cs, which disclose significant deviations [32,33]. The intensity I775 is given by ANpent, where A is the Raman cross section of this mode and Npent (equal to N4) the fraction of pentaborate units. Thus, it is expected that I775 increases with increasing X following the concentration increase of Npent, as proved by the data reported in Figure 3, where I775 scaled to its value at the highest content (X=0.14) is reported. It is worth noting that formation of tetra-coordinated boron atoms also leads to a substantial stiffening of the network, as shown by the increase of the Debye sound velocity (Table 1). Conversely, the decrease of I808 band is associated with a progressively smaller number of boroxol rings, the building blocks of the medium-range order in v-B2O3. Also in this case, I808 is given by BNring, where B is the Raman cross section of this mode and Nring the fraction of boroxol rings. I808 7
scaled by its highest value at X=0.0 evidences a linear decrease with increasing X, Figure 3. A similar linear decrease of boroxol rings with increasing alkali oxide content has been predicted by a model developed to explain the structural changes in potassium borate glasses, observed by NMR and Raman spectroscopy measurements [34]. Tentatively, we try to evaluate the fraction of boroxol rings contributing to I808 in (Ag2O)x(B2O3)1-x glasses, using as a reference the integrated value of I808 in vB2O3. It was found, from NMR spectroscopy measurements in v-B2O3, that a fraction f=0.78 of boron atoms is involved in boroxol rings [35], the resulting network being formed by quite close fractions of rings (0.54) and oxygen-sharing BO3 triangles (0.46). It is worth noting that the network of v-B2O3 is formed by a roughly even mixture of boroxol rings and BO3 triangular units, which would be exactly 1:1 if 0.75 of boron atoms were in rings, because each ring contains three borons [34]. Assuming that I808 in v-B2O3 is determined by a ring fraction of 0.54, we have evaluated the fraction of boroxol rings contributing to I808 in (Ag2O)x(B2O3)1-x glasses, which is found to be reduced by more than one third in the glass with X=0.14, see Table 2. Since in B2O3 the BP is ascribed to localized out-of-plane rigid librations of rings [6,36] connected via a single bridging oxygen atom [37,38], the observed reduction of the BP in borate glasses with X≤0.09 has been assumed to be related to the decrease of boroxol rings. As regards the increase of IBP observed in the glass with X=0.14, it is believed to be a consequence of the particular morphology of silver borate glasses, that also involves the contribution of local vibrations of loosely coupled Ag+ cations in the low-energy vibrational dynamics. In fact, a previous study on borate glasses of high Ag content (X≥ 0.20) [39] revealed that localized rattling modes of silver atoms within voids of the glassy network influence substantially the low-energy vibrational dynamics of silver borate glasses, because they introduce a contribution which adds to that of excess vibrations of borate network, determining an increase of IBP and shifting the BP position to higher frequency [39]. Of course, rattling atoms exist also in the whole set of alkali borate glasses [39,40], but only the rattling of heavy loose ions can influence the BP energy range [40]. In lithium borate glasses, the rattling frequencies of light Li atoms fall beyond the frequency range of BP, so their contribution lies in the BP tail and does not influence the low energy dynamics [39]. On this basis, the present
8
I775/I775,max
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
I808/I808,max
1.0
0.0 0.00
0.05
0.10
0.15
R=X/(1-X) Figure 3.
Plot of the scaled band intensities at 775 cm-1 (O) and 808 cm-1 (∆) against the mole fraction R=X/(1-X) of Ag2O. Linear fits to the data are reported as dotted and dashed lines, respectively.
observations concerning the BP can be explained by considering the competitive effect of two contributions: the low-frequency librations of connected boroxol rings and rattling modes of Ag+ cations. In fact, for X≤0.09, the rattling contribution is quite small and the BP decreases as a consequence of the decreasing number of librations of coupled boroxols, while for X>0.09 the Ag rattling contribution increases and contrasts the libration decrease, resulting in an overall BP which is higher than that observed in v-B2O3.
B. Low temperature specific heat. In Figure 4(a), the specific heat capacity C(T) of (Ag2O)x(B2O3)1-x glasses between 1.5 K and 25 K is compared to that of v-B2O3, measured between 0.4 and 20 K. In Figure 4(b) the same data are reported as C(T)/T3 vs T, a representation that reveals the existence of the calorimetric BP as a characteristic broad peak. As generally found in amorphous solids, the magnitude of this peak is always larger than C
2 π2
the respective elastic Debye contributions TD3 = 5 ħ
(dashed lines in Figure 4(b)), implying an excess
heat capacity over the Debye prediction. In v-B2O3 and marginally also in glasses with X=0.09 and X=0.14, it is observed an upturn in C/T3 below about 2 K, which arises from the nearly linear contribution of two-level systems (TLS) [41]. Increasing Ag2O content progressively depresses the bump in C(T)/T3 up to X=0.09, the glass with X=0.14 disclosing a heat capacity quite close to that of the latter, and shifts the peak temperature Tpeak from about 5.7 K in v-B2O3 up to 8.0 K in the glass with 9
X=0.14 and the temperature of the minimum Tmin from 1 K up to about 2 K. The decrease of the bump with the associated shift of Tpeak are reminiscent of the behaviors observed for IBP and νBP, which have been explained in terms of the competitive contributions of soft vibrations and rattling modes in the host borate network. Growing addition of silver oxide modifier leads to the decrease of boroxol rings with their librations and to the increase of guest atoms (Ag+ ions) with their rattling modes. The assignments of the Ag rattling modes at the low-energy region have been made in silver borate crystal by Raman scattering and in silver borate glasses by far-FTIR spectroscopy [32,39]. Therefore, we have evaluated the rattling contribution to the specific heat capacity of (Ag2O)x(B2O3)1-x glasses, by applying the procedure previously explained [39]. To be more in detail, three Einstein terms (a) 0
-1
10
-2
10
-3
20 2
10
C/T (mJ/molK )
C (J/molK)
10
15 10 5 0
5
10 15 2
2
T (K )
10
-4
1
T (K)
10
(b)
4
C/T (mJ/molK )
1.0
0.0 0.04 0.09 0.14
3
0.5
0.0 0
5
10
15
20
25
T (K)
Figure 4.
(a) The temperature dependence of the specific heat capacity C in (Ag2O)x(B2O3)1-x glasses: X=0.0 (vB2O3), (●); X=0.04, (∆); X=0.09, (O); X=0.14, (∇). Inset reports specific heat capacity data of glasses with X=0.0 (●), X=0.09 (O); X=0.14, (∇), plotted as C(T)/T vs T2, together with SPM quadratic fits (solid lines). (b) The temperature dependence of C(T)/T3 for (Ag2O)x(B2O3)1-x glasses; symbols are the same of (a). The Debye levels CD(T)/T3 are reported as dashed lines, with X growing from the top to the bottom. Rattling contributions to C/T3 for glasses with X=0.04 (▲) and X=0.14 (▼) are also included.
10
CE1, CE2, and CE3 were considered to describe the motions of Ag+ ions into structural voids: C =A1CE1 + A2CE2 + A3CE3, where Ai=3NAkBsi. The term
=
"
!
#
$ν %
! $&
represents the fraction of atoms per
formula unit contributing to the Einstein heat capacity CEi, being Itot =Σi Iνi. Tentatively, it has been assumed that the three Raman components Iνi, observed in silver borate crystal, preserve their relative shape and frequency also in borate glasses, keeping unchanged their frequency with increasing Ag2O content (this feature being supported by FTIR observations in the same glasses up to X=0.20 [32]). Thus, the values calculated for the Einstein temperatures θEi(=hνi/kB) and the corresponding fractions Iνi/Itot are: θE1 =50 K and Iν1/Itot =0.18, θE2 =66 K and Iν2/Itot =0.19, θE3 =93 K and Iν3/Itot = 0.63 for the Raman lines observed at 35, 46, and 66 cm−1, respectively. Since one mole of oscillators provides a heat capacity of 3R =24.95 Jmol−1K−1 and by knowing the relative molar fraction of Ag+ ions, we anticipate a contribution to the heat capacity from Ag+ rattling of 1.513 Jmol−1K−1 (split into A1 = 0.27 Jmol−1K−1, A2 = 0.29 Jmol−1K−1, and A3 = 0.95 Jmol−1K−1) in the glass having the highest concentration of Ag+ ions (X=0.14, 5.93% of silver atoms). This means that the rattling contribution is quite negligible compared to the total heat capacity of silver borate glasses, becoming slightly significant only in the glass with X=0.14, as it can be observed in Figure 4(b) where the rattling contributions for two glasses are reported. Over the temperature region up to about Tpeak, the data can be described as [42], C(T)=CTLST+CDT3+CSPMT5
(1)
where CTLST represents the linear TLS contribution, CDT3 marks the contribution of Debye vibrational modes, and CSPMT5 denotes the contribution of soft harmonic oscillators (HO), predicted by the Soft Potential Model (SPM) [43]. All these low-energy vibrational excitations determine the excess specific heat capacity and are substantially accounted by the SPM in terms of soft anharmonic oscillator potentials which include TLS and soft HO. The model is able to reproduce the results of TLS model and also gives an exhaustive explanation of the strong rise of the HO vibrational density of states with increasing frequency. A crossover to delocalization of soft harmonic oscillators changes the initial strong rise of the vibrational density of states (∝E4) to a weaker energy dependence (∝E). Inset of Fig. 4(a) reports the polynomial fit of C/T vs T2 for v-B2O3 and for glasses with X=0.09 and X=0.14, because only these glasses evidence a minimum followed by a defined increase in C/T3 with decreasing temperature, which are behaviors marking the crossover to the region regulated by TLS. The upper temperature limit of the fit has been set at T=5 K [24], considering the deviation from a T5-dependence of C(T) due to the discussed variation of HO distribution with increasing energy. The values of the parameters obtained from quadratic fits are reported in Table 3.
11
Table 3. Values of the parameters CTLS, CD and CSPM which assess contributions from TLS, Debye vibrational modes and harmonic oscillators to the specific heat capacity C below 5 K (Eq. 1). The values of Debye contributions, CD,el, obtained from elastic data at 8 K are also included for comparison.
(Ag2O)x(B2O3)1-x glasses
CTLS -6
CD 2
(10 J/molK )
-6
CSPM 4
(10 J/molK )
-6
CD,el 6
(10 J/molK )
-6
(10 J/molK4)
X=0.0
0.09±0.006
0.56±0.007
0.05±0.001
0.50
X=0.09
0.14±0.04
0.30±0.015
0.03±0.001
0.33
X=0.14
0.29±0.07
0.22±0.019
0.03±0.001
0.27
Differently from silver borate glasses where the limited lowest temperature in the experiment (1.5 K) prevents reliable considerations on the TLS contribution, the value of CTLS obtained in v-B2O3 is accurate, and it is found close to those determined in samples having similar OH contents [44]. The progressive decrease of the parameter CSPM with increasing Ag2O content points to a well-defined reduction of soft HO contribution, i.e. of the low-energy vibrations determining the excess specific heat, as observed. Moreover, the obtained CD values are in reasonable agreement with those (CD,el) from elastic data at 8 K. An elastic continuum, which becomes increasingly stiffer, leads to a decrease of the low temperature specific heat capacity. In principle, the stiffening of borate network, due to the increase of connectivity because of the formation of tetrahedral BO4 groups, could account for the observed decrease of the excess C(T). Figure 5 compares C(T)-Crattl/CD,el(T) vs T/ΘD (also ΘD is evaluated by elastic data) in silver borate glasses, disclosing an increase of the peak intensity with increasing Ag2O content and a shift of the maxima compared to that of v-B2O3. This observation implies that variations of low-energy vibrational dynamics of borate network modified by Ag2O addition are not explainable by simple modification of elastic continuum. This finding contrasts with the results obtained for borate glasses with high Ag content (X≥0.20) [39]. In those glasses, after subtraction of the rattling contribution and rescaling to the CD values, the specific heats are found to overlap exactly, proving that the observed differences of excess specific heat are compensated by the changes of the Debye value. It is worth noting that in low silver content glasses, here discussed, the rattling contribution (reported in Fig. 4) represents a very small fraction of the specific heat and no change from the behaviors shown in Fig. 5 was observed after its subtraction, even for the X=0.14 glass with the highest content of silver ions. We infer that the discrepancy between glasses with low and high silver content is strictly connected to the breaking of B-O-B bonds and the consequent formation of NBO, found in large amounts already in the glass with X=0.20 [27]. This concentration, in fact, marks the incoming softening of the glass
12
Figure 5
1.0
3
(C/T )/(C/T )peak
5
0.5
C-Crattl/CD,el
3
4
3
0.0
0
1
2
3
4
T/Tpeak
2
1
0.00
0.05
0.10
T/ΘD Figure 5.
Comparison of C(T)/CD,el vs T/ΘD of (Ag2O)x(B2O3)1-x glasses: (●) X=0.0, (∆) X=0.04, (O) X=0.09 and (∇) X=0.14. Inset shows C/T3 scaled by (C/T3)peak vs T/Tpeak for same borate glasses and also for X=0.20 (+) [from Ref. 39]; dashed and solid lines refer to v-Se [from Ref. 46] and v-SiO2 [from Ref. 24], respectively.
matrix, as clearly indicated by the decrease of the glass transition temperature by further increasing X [45]. This result points out to the crucial role of the network continuity in affecting the vibrational dynamics of a glass. Further interesting considerations turn out from the scaling plot in the inset of Figure 5, which reports C/T3 scaled by (C/T3)peak and plotted vs T/Tpeak for different glasses. It shows that the curves of silver borate glasses are definitely narrower than those of v-B2O3, v-Se [46] and v-SiO2 [24], the behaviors of the last two glasses having been also included for a more exhaustive comparison. In principle, increasing connectivity and rigidity of the glassy network should lead to a narrowing of the energy distribution of vibrations as evidenced by going from v-Se (connectivity of 2), through vB2O3 (connectivity of 3), to SiO2 (connectivity of 4). However, the structural modifications, induced by growing Ag2O addition to the network borate and associated to a change of the connectivity from 3.10 (X=0.04) to 3.25 (X=0.20), appear to be more efficient in reducing the spectral width of vibrational excitations that originate the peak in C/T3. 13
The decrease of the excess low-energy vibrations with increasing content of silver oxide modifier is consistent with the decrease of boroxol rings determined by formation of four-coordinated boron atoms which link two rings in a single pentaborate unit, as observed by Raman spectra reported in Figure 2. As discussed above, in fact, the vibrations underlying both Raman and calorimetric BP in v-B2O3 are identified as low-frequency librations of connected boroxol rings [6,37]. Pentaborate groups are expected to hinder the librational modes of the rings forming them, leading to the observed decrease of the excess heat capacity.
4. CONCLUSIONS Raman light scattering measurements performed at room temperature over the frequency range between 6 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses reveal that the structural variations of borate network due to the addition of silver oxide modifier concern both the short- and medium-range order. Analysis of the high-frequency region shows that the main vibrational band at 808 cm-1, arising from the localized breathing-type vibration of oxygen atoms inside boroxol rings, preserves its frequency but decreases progressively its intensity with increasing Ag2O content up to X=0.14. This decrease is closely related to the appearance of a band at 775 cm-1 assigned to vibrations of groups containing fourcoordinated boron atoms, whose intensity increases with increasing X. These observations imply decrease of boroxol rings and increasing formation of pentaborate units, which are formed by two boroxol rings linked by one tetra-coordinate boron atom and enhance the network connectivity by variations in the chemical bonding. Low-frequency Raman scattering below 150 cm-1 evidences a BP which increases its frequency from 26 cm-1 up to 33 cm-1 with growing silver oxide content. The BP decreases in magnitude up to X=0.09, showing a sudden increase for further Ag2O addition. It is suggested that the reduction of BP, mainly due to localized out-of-plane rigid librations of planar boroxol rings, follows from the decrease of rings, while its increase observed in the glass with X=0.14 arises from rattling modes of Ag+ cations loosely linked with the rest of covalently connected host matrix. Localized rattling modes of silver atoms within voids of glassy network influence substantially the vibrational dynamics below 100 cm-1 determining a contribution which adds to that of excess vibrations of borate network, determining an increase of IBP and its slight shift to higher frequency. The decrease of boroxol rings leads also to a progressive decrease of the excess heat capacity observed below 20 K, not taken into account by the hardening of elastic continuum, and to the shift to higher temperatures of the calorimetric BP. Evaluation of the contribution of rattling modes shows that it is quite negligible compared to the total heat capacity of silver borate glasses, becoming a little significant only in the glass with X=0.14. Moreover, it has been shown that structural modification of the glassy network induced by growing addition of Ag2O leads to a substantial reduction of the spectral width of vibrational excitations leading to the peak in C/T3. All the observations are consistent with a low14
energy vibrational dynamics of silver borate glasses that appears to be related to the boroxol rings, these glassy units being connected to the network by simple or complex links. The experimental results of the heat capacity C are also compared with the theoretical descriptions of the soft potential model, resulting in qualitative agreement with the main predictions of this model. It is worth emphasizing that silver borate glasses are materials of current great interest because they are used in electrochemical devices such as high-energy and high-power solid state batteries [47,48], even if some technical problems limit their large-scale application. Their use as components of composite electrolytes permits to enhance the ionic conductivity of the overall system. Very recently it has been found that the mechanical stability of ionic clusters is directly related to diffusion pathway for the mobile ions: the less stable the clusters are, the faster the ion transport is [49]. Soft modes [50] and Boson peak [51] are suggested as appropriate indicators of the structural stability of clusters in amorphous solids. This aspect makes the investigation of the structural changes and of the low energy dynamics, experienced by borate matrix with silver oxide addition, of great importance to gain insights into the mechanisms underlying ionic diffusion.
15
REFERENCES [1]
T. Nakayama, Boson peak and terahertz frequency dynamics of vitreous silica, Reports on Progress in Physics 65 (2002) 1195, https://doi.org/10.1088/0034-4885/65/8/203.
[2]
U. Buchenau, N. Nücker, A. J. Dianoux, Neutron scattering study of the low-frequency vibrations in vitreous silica, Phys. Rev. Lett. 53 (1984) 2316, https://doi.org/10.1103/PhysRevLett.53.2316.
[3]
V. K. Malinovsky, V. N. Novikov, P. P. Parshin, A. P. Sokolov, M. G. Zemlyanov, Universal form of the low-energy (2 to 10 meV) vibrational spectrum of glasses, Europhys. Lett. 11 (1990) 43, https://doi.org/10.1209/0295-5075/11/1/008.
[4]
G. D’Angelo, C. Crupi, G. Tripodo, G. Salvato, Relation between low-temperature thermal conductivity and the specific heat of cesium borate glasses, J. Phys. Chemistry B 114 (2010) 24672475, https://doi.org/10.1021/jp907152y.
[5]
R. O. Pohl, in Amorphous Solids: Low-Temperature Properties, edited by W. A. Phillips (Springer, Berlin, 1981) p. 27.
[6]
G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, G. Di Marco, C. Vasi, E. Gilioli, Influence of packing on low energy vibrations of densified glasses, Phys. Rev. Lett. 111 (20134) 245502, https://doi.org/10.1103/PhysRevLett.111.245502.
[7]
G. D’Angelo, G. Carini, C. Crupi, M. Koza, G. Tripodo, C. Vasi, Boson peak in alkaline borate glasses: Raman spectroscopy, neutron scattering, and specific-heat measurements, Phys. Rev. B 79 (2009) 014206, https://doi.org/10.1103/PhysRevB.79.014206.
[8]
P. S. Salmon, R. A. Martin, P. E. Mason, G. J. Cuello, Topological versus chemical ordering in network
glasses
at
intermediate
and
extended
length
scales, Nature 435
(2005)
75,
https://doi.org/10.1038/nature03475. [9]
S. R. Elliott, Origin of the first sharp diffraction peak in the structure factor of covalent glasses, Phys. Rev. Lett. 67 (1991) 711, https://doi.org/10.1103/PhysRevLett.67.711.
[10] V. N. Novikov and A. P. Sokolov, A correlation between low-energy vibrational spectra and first sharp diffraction peak in chalcogenide glasses, Solid State Comm. 77 (1991) 243-247, https://doi.org/10.1016/0038-1098(91)90341-R. [11] Q. Mei, C. J. Benmore, S. Sen, R. Sharma, and J. L. Yarger, Intermediate range order in vitreous silica
from
a
partial
structure
factor
analysis,
Phys.
Rev.
B
78
(2008)
144204,
https://doi.org/10.1103/PhysRevB.78.144204. [12] C. Crupi, G. Carini, M. A. González, G. D'Angelo, Origin of the first sharp diffraction peak in glasses. Phys. Rev. B 92 (2015) 134206, https://doi.org/10.1103/PhysRevB.92.134206. [13] M. A. González, C. Mondelli, G. D’Angelo, C. Crupi, M. R. Johnson, A molecular dynamics study of the role of the cation in modifying the structure of alkali borate glasses, J. Non-Crystall. Solids 354 (2008) 203-207, https://doi.org/10.1016/j.jnoncrysol.2007.08.079. [14] T. S. Grigera, V. Martin-Mayor, G. Parisi, P. Verrocchio, Phonon interpretation of the ‘boson peak’in supercooled liquids, Nature 422 (2003) 289, https://doi.org/10.1038/nature01475
16
[15] W. Schirmacher, G. Ruocco, T. Scopigno, Acoustic attenuation in glasses and its relation with the boson peak, Phys. Rev. Lett. 98 (2007) 025501, https://doi.org/10.1103/PhysRevLett.98.025501 [16] V. L. Gurevich, D. A. Parshin, H. R. Schober, Anharmonicity, vibrational instability, and the Boson peak in glasses, Phys. Rev. B 67 (2003) 094203, https://doi.org/10.1103/PhysRevB.67.094203 and references therein. [17] E. Duval, A. Mermet, L. Saviot, Boson peak and hybridization of acoustic modes with vibrations of nanometric heterogeneities in glasses, Phys. Rev. B 75 (2007) 024201, https://doi.org/10.1103/PhysRevB.75.024201. [18] L. E. Silbert, A. J. Liu, S. R. Nagel, Vibrations and diverging length scales near the unjamming transition, Phys. Rev. Lett. 95 (2005) 098301, https://doi.org/10.1103/PhysRevLett.95.098301. [19] N. Xu, M. Wyart, A. J. Liu, S. R. Nagel, Excess vibrational modes and the boson peak in model glasses, Phys. Rev. Lett. 98 (2007) 175502, https://doi.org/10.1103/PhysRevLett.98.175502. [20] G. Carini Jr, G. Carini, G. D’Angelo, E. Gilioli, C. Vasi, Origin of excess low-energy vibrations in densified B2O3 glasses, Phil. Mag. 95 (2015) 2596-2606, https://doi.org/10.1080/14786435.2015.1067733. [21] G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, L. Orsingher, A. Fontana, Low temperature specific heats of permanently densified glassy GeO2, Phil. Mag. 91 (2011) 1877-1886, https://doi.org/10.1080/14786435.2010.530617. [22] L. Orsingher, M. Calicchio, G. Carini Jr, R. Dal Maschio, D. Fioretto, A. Fontana, ... F. Rossi, Optical and spectroscopic characterization of permanently densified GeO2 glasses, Phil. Mag. 88 (2008) 3907-3914, https://doi.org/10.1080/14786430802247213. [23] A. I. Chumakov, G. Monaco, A. Fontana, A. Bosak, R. P. Hermann, D. Bessas, … G. Baldi, Role of disorder in the thermodynamics and atomic dynamics of glasses, Phys. Rev. Lett. 112 (2014) 025502, https://doi.org/10.1103/PhysRevLett.112.025502. [24] G. Carini Jr, G. Carini, D. Cosio, G. D’Angelo, F. Rossi, Low temperature heat capacity of permanently densified SiO2 glasses, Phil. Mag. 96 (2016) 761-773, https://doi.org/10.1080/14786435.2015.1122845. [25] L. Orsingher, A. Fontana, E. Gilioli, G. Carini Jr, G. Carini, G. Tripodo, ..., U. Buchenau, Vibrational dynamics of permanently densified GeO2 glasses: Densification-induced changes in the boson peak, J. Chem. Phys. 132 (2010) 124508, https://doi.org/10.1063/1.3360039. [26] K. S. Kim, P. J. Bray, 11B Nuclear Magnetic Resonance Studies of the System Ag2O-B2O3, J. Non Met. 2 (1974) 95-101. [27] M. C. Abramo, G. Carini, G. Pizzimenti, Ag2O-B2O3 glassy systems: network coherence behaviour as seen from molecular dynamics calculations, Journal of Physics C: Solid State Physics 21 (1988) 527, https://doi.org/10.1088/0022-3719/21/3/009. [28] G. D’Angelo, C. Vasi, A. Bartolotta, G. Carini, C. Crupi, G. Di Marco, G. Tripodo, Low-frequency Raman scattering of silver borate glasses, Phil. Mag. 84 (2004) 1631-1638, https://doi.org/10.1080/14786430310001644413.
17
[29] G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, A. Bartolotta, G. Salvato, Ultrasonic relaxations, anharmonicity, and fragility in lithium borate glasses, Phys. Rev. B 72 (2005) 014201, https://doi.org/10.1103/PhysRevB.72.014201. [30] B. N. Meera, J. Ramakrishna, Raman spectral studies of borate glasses, J. of Non-Crystal. Solids 159 (1993) 1-21, https://doi.org/10.1016/0022-3093(93)91277-A. [31] E. I. Kamitsos, G. D. Chryssikos, Borate glass structure by Raman and infrared spectroscopies, J. of Mol. Structure 247 (1991) 1-16, https://doi.org/10.1016/0022-2860(91)87058-P. [32] J. A. Kapoutsis, E. Kamitsos and G. D. Chryssikos, Proc. of Second Int. Conf. on Borate Glasses, Crystals and Melts, edited by A. C. Wright, S. A. Feller and A. C. Hannon (Soc. Glass Technology, Sheffield, UK, 1997), pp.303-312. [33] J. Zhong and P. Bray, J. Non-Cryst. Solids 111 (1989) 67, https://doi.org/10.1016/00223093(89)90425-0. [34] R. E. Youngman and J. W. Zwanziger, J. Phys. Chem. 100 (1996) 16720-16728, https://doi.org/10.1021/jp961439+ [35] V. V. Brazhkin, I. Farnan, K. I. Funakoshi, M. Kanzaki, Y. Katayama, A. G. Lyapin, H. Saitoh, Structural transformations and anomalous viscosity in the B2O3 melt under high pressure, Phys. Rev. Lett. 105 (2010) 115701, https://doi.org/10.1103/PhysRevLett.105.115701. [36] G. Simon, B. Hehlen, E. Courtens, E. Longueteau, R. Vacher, Hyper-Raman scattering from vitreous boron oxide: coherent enhancement of the boson peak, Phys. Rev. Lett. 96 (2006) 105502, https://doi.org/10.1103/PhysRevLett.96.105502. [37] F. L. Galeener, M. F. Thorpe, Rings in central-force network dynamics, Phys. Rev. B 28 (1983) 5802, https://doi.org/10.1103/PhysRevB.28.5802. [38] G. Carini Jr, G. Carini, G. D'Angelo, D. Fioretto, G. Tripodo, Identification of relaxing structural defects in densified B2O3 glasses, Phys. Rev. B 90 (2014) 140204, https://doi.org/10.1103/PhysRevB.90.140204. [39] G. D’Angelo, C. Crupi, G. Carini, C. Vasi, Rattling ions and the anomalous vibrational dynamics of glasses, Phys. Rev. B 84 (2011) 172201, https://doi.org/10.1103/PhysRevB.84.172201. [40] C. Crupi, G. D’Angelo, C. Vasi, Low-energy vibrational dynamics of cesium borate glasses, J. Phys. Chem. B 116 (2012) 6499-6505, https://doi.org/10.1021/jp301230s. [41] W. A. Phillips, Two-level states in glasses, Rep. Progr. Phys. 50 (1987) 1657, https://doi.org/10.1088/0034-4885/50/12/003. [42] M. A. Ramos, Are the calorimetric and elastic Debye temperatures of glasses really different?, Phil. Mag. 84 (2004) 1313, https://doi.org/10.1080/14786430310001644053. [43] D. A. Parshin, Interactions of soft atomic potentials and universality of low-temperature properties of glasses, Phys. Rev. B 49 (1994) 9400, https://doi.org/10.1103/PhysRevB.49.9400. [44] J. C. Lasjaunias, D. Thoulouze, F. Pernot, Solid State Comm. 14 (1974) 957-961, https://doi.org/10.1016/0038-1098(74)90402-5.
18
[45] E. N. Boulos and N. J. Kreidl, Structure and properties of silver borate glasses, J. Am. Ceram. Soc. 54 (1971) 368-375, https://doi.org/10.1111/j.1151-2916.1971.tb12324.x. [46] A. Avogadro, S. Aldrovandi, F. Borsa, G. Carini, Specific-heat study of low-energy excitations in glasses, Phil. Mag. B 56 (1987) 227-236, https://doi.org/10.1080/13642818708208529. [47] J. G. Kim, B. Son, S. Mukherjee, N. Schuppert, A. Bates, O. Kwon, ... S. Park, A review of lithium and non-lithium based solid state batteries, J. Power Sources 282 (2015) 299-322, https://doi.org/10.1016/j.jpowsour.2015.02.054. [48] C. Jiang, H. Li, C. Wang, Recent progress in solid-state electrolytes for alkali-ion batteries, Science Bull. 62 (2017) 1473-1490, https://doi.org/10.1016/j.scib.2017.10.011. [49] Y. S. Choi, J. C. Lee, Electronic and mechanistic origins of the superionic conductivity of sulfidebased solid electrolytes, J. Power Sources 415 (2019) 189-196, https://doi.org/10.1016/j.jpowsour.2019.01.071. [50] V. K. Tewary, B. Yang, Singular behavior of the Debye-Waller factor of graphene, Phys. Rev. B 79 (2009) 125416, https://doi.org/10.1103/PhysRevB.79.125416. [51] M. Sharma, S. Yashonath, Correlation between conductivity or diffusivity and activation energy in amorphous solids, J. Chem. Phys. 129 (2008) 144103, https://doi.org/10.1063/1.2990744.
19
FIGURE CAPTIONS
Figure 1.
Room temperature scaled Raman spectra (VV configuration) measured between 8 cm-1 and 600 cm-1 in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), solid line; X=0.04, (O); X=0.09, (∆); X=0.14, (∇). Inset reports Ir/IBP for glasses with X=0.0, X=0.04, and X=0.14, using the same symbols.
Figure 2.
Room temperature scaled Raman spectra (VV configuration) between 600 cm-1 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses; symbols are the same of Figure 1. Inset shows the modes at 775 cm-1 and 808 cm-1 in the glass with X=0.14 and the Lorentzian fit; dotted and solid lines show the single bands and their addition, respectively. Schematic illustration of planar boroxol ring (B3O6) and pentaborate group is also included.
Figure 3.
Plot of the scaled band intensities at 775 cm-1 (O) and 808 cm-1 (∆) against the mole fraction R=X/(1-X) of Ag2O. Linear fits to the data are reported as dotted and dashed lines, respectively.
Figure 4.
(a) The temperature dependence of the specific heat capacity C in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), (●); X=0.04, (∆); X=0.09, (O); X=0.14, (∇). Inset reports specific heat capacity data of glasses with X=0.0 (●), X=0.09 (O); X=0.14, (∇), plotted as C(T)/T vs T2, together with SPM quadratic fits (solid lines). (b) The temperature dependence of C(T)/T3 for (Ag2O)x(B2O3)1-x glasses; symbols are the same of (a). The Debye levels CD(T)/T3 are reported as dashed lines, with X growing from the top to the bottom. Rattling contributions to C/T3 for glasses with X=0.04 (▲) and X=0.14 (▼) are also included.
Figure 5.
Comparison of C(T)/CD vs T/ΘD of (Ag2O)x(B2O3)1-x glasses: (●) X=0.0, (∆) X=0.04, (O) X=0.09 and (∇) X=0.14. Inset shows C/T3 scaled by (C/T3)peak vs T/Tpeak for same borate glasses and also for X=0.20 (+) [from Ref. 39]; dashed and solid lines refer to vSe [from Ref. 46] and v-SiO2 [from Ref. 24], respectively.
20
Highlights 1. Raman scattering and heat capacity measurements on silver borate glasses evidenced remarkable changes in structure and low- energy vibrational dynamics. 2. Rattling of silver ions and soft vibrations determine the profile of the low-energy vibrational spectrum. 3. The crucial role of the network continuity on the vibrational dynamics of a glass is pointed out.
AUTHOR DECLARATION
On Behalf of all the authors, I wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. Yours sincerely
23/09/2019
S0022-3697(19)32150-X
DOI:
https://doi.org/10.1016/j.jpcs.2019.109304
Reference:
PCS 109304
To appear in:
Journal of Physics and Chemistry of Solids
Received Date: 23 September 2019 Revised Date:
12 November 2019
Accepted Date: 6 December 2019
Please cite this article as: C. Crupi, G. Carini Jr., G. Carini, M. Federico, A. Mandanici, V. Romano, G. D'Angelo, Structure and low energy vibrations in silver borate glasses with low silver content, Journal of Physics and Chemistry of Solids (2020), doi: https://doi.org/10.1016/j.jpcs.2019.109304. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.
CRediT author statement D’Angelo Giovanna: Conceptualization, Methodology, Writing - Review & Editing; Supervision Crupi Cristina: Conceptualization, Methodology, Investigation Carini Giovanni Jr.: Investigation, Methodology, Carini Giuseppe: Conceptualization, Methodology, Writing - Review & Editing Federico Mauro: Formal analysis, Software Mandanici Andrea: Investigation, Formal analysis; Romano Valentino: Investigation, Formal analysis
STRUCTURE AND LOW ENERGY VIBRATIONS IN SILVER BORATE GLASSES WITH LOW SILVER CONTENT a
a
a,b
a
a
Cristina Crupi , Giovanni Carini Jr , Giuseppe Carini , Mauro Federico , Andrea Mandanici , a
Valentino Romano and Giovanna D’Angelo
a,b*
a
Dipartimento MIFT, Universita' di Messina, Viale F. Stagno d’Alcontres 31, I-98166 Messina, Italy
b
Istituto Processi Chimico-Fisici, Sezione di Messina–Consiglio Nazionale delle Ricerche, Viale F. Stagno d’Alcontres 37, I-98158 Messina, Italy
Structural changes of (Ag2O)x(B2O3)1-x glasses, over the range between X=0.0 and X=0.14, have been monitored by Raman spectroscopy. Low temperature heat capacity measurements have been also performed between 0.4 K and 25 K to investigate along with low frequency Raman scattering the behavior of the low-energy vibrational dynamics. A progressively decreasing intensity of the main band at 808 cm-1 and the appearance of a band at about 775 cm-1 with increasing Ag2O content have been observed and analyzed in detail. The strongly polarized band at 808 cm-1 is ascribed to the breathing vibration of boroxol rings and the decrease of its intensity indicates the reduction of the number of these units in the network. The band at 775 cm-1 is assigned to vibrations of pentaborate units, formed from two boroxol rings linked by a tetrahedral BO4 group. The rate of formation of BO4 groups appears to increase as X/(1-X). Raman investigation has been extended to very low frequencies, where a broad intense band, the Boson peak (BP), dominates the spectrum of all the samples below 100 cm-1. Addition of Ag2O shifts the BP position from 26 cm-1 up to 33 cm-1 and gives rise to a decrease of its intensity up to X=0.09 and a sudden increase for X=0.14, which has been explained as due to rattling motion of silver ions whose contribution is added to that of localized vibrations. The formation of tetrahedral BO4 groups stiffens the network and leads to a decrease of the excess heat capacity over the Debye prediction below 20 K, which is not taken into account by the simple hardening of the elastic continuum but seems to follow the reduction of boroxol rings. This result contrasts the observations on borate glasses with high Ag content and emphasizes the crucial role of the network continuity on the vibrational dynamics of a glass.
Keywords: Glasses, Vibrational dynamics, Raman scattering, Heat capacity, Boson peak *Corresponding author. E-mail address: [email protected]
PACS number: 63.50.Lm; 65.60.+a; 78.30.Ly 1
1. INTRODUCTION An excess of low-frequency vibrations over the Debye prediction is a common feature of amorphous materials and is universally observed below few THz, independently of the specific composition and stoichiometry [1-4]. This contribution is conventionally called the Boson peak (BP) and is also related to a bump in the low-frequency region of Raman spectra (below 150 cm-1) and to an excess lowtemperature (T<20 K) specific heat C [4-7], the latter appearing as a bump when reported as C/T3. In addition, the boson peak energy has also been associated with the position and the width of the socalled "first sharp diffraction peak" (FSDP) observed in the structure factor of many liquids and glasses [8-11], a correlation that calls into question the possibility of considering the characteristic length of medium range order of the glass structure as strongly involved in the development of the BP [10]. The FSDP is indeed considered as a manifestation of subtle correlations involving the medium-range order [9], mainly associated with some characteristic lengths or superstructural units in the network such as large rings of atoms [12,13]. A wide number of models has been proposed for explaining the nature of the BP, such as spatial fluctuations of the elastic constants [14,15], local inhomogeneities with small elastic constants schematized by soft potentials [16,17], or jamming transitions setting the mechanical stability of a system with the onset of excess vibrational modes [18,19]. All these different models, however, evidence some limitations when applied to explain the whole set of experimental observations [20]. Quite recently, we performed a number of studies to investigate the microscopic nature of low-energy vibrations using, as model systems, prototype glasses such as v-B2O3 [6], v-GeO2 [21,22] and v-SiO2 [23,24] compacted under very high pressures (GPa range) in order to increase the mass density. Increasing density causes a progressive decrease of additional low-energy vibrations contributing to the BP, leading to associate them to poorly packed and soft structural domains embedded in a rigid network. These soft regions are formed from connected boroxol rings formed by three corner sharing BO3 triangles in v-B2O3 [6] and from n-membered rings involving SiO4 or GeO4 tetrahedra in v-SiO2 [23] and v-GeO2 [25]. In particular, increasing density of v-B2O3 has also been obtained by changing the chemical bonding in the network [20], to promote the formation of tetra-coordinated boron atoms, but always preserving the stoichiometry. This has determined a growth of network connectivity as a result of higher average coordination, which caused the largest decrease of excess low-frequency vibrations among those observed in less compacted B2O3 glasses. To deepen our understanding on the relationship between atomic connectivity, structure and low energy dynamics in glasses, here we report and discuss the results of Raman and calorimetric investigations of (Ag2O)x(B2O3)1-x glasses. These samples can be prepared in a wide concentration range, evidencing structural transformations that lead to a remarkable increase of network connectivity, defined as the number of bridging oxygens per network forming ion (NFI). The addition of silver oxide modifier to 2
B2O3 significantly changes the boron coordination by forming
tetrahedral groups up to about
X=0.20 and non-bridging oxygens (NBO) for even higher concentrations. The rate of BO4 formation increases as R=X/(1-X) [26], i.e., there is the formation of two four-coordinated borons for each oxygen introduced by the metallic oxide. This structural mechanism increases the network connectivity from 3 to 3.25 at X=0.20, while the NBO formation due to the breaking of B-O-B linkages dominates the high concentration region and leads to the decrease of the network coherence [27]. In an earlier paper we have investigated the low-frequency region of Raman scattering (< 200 cm-1) of silver borate glasses, putting in evidence the role of Ag+ cation compared with Li+ cation in modifying the low frequency dynamics [28]. In the present study, the Raman investigation has been further extended over the frequency range up to 1100 cm-1 to follow the structural modifications of the network with increasing Ag2O concentration. Measurements of specific heat capacity over the temperature interval between 0.4 K and 30 K were also performed to evaluate the calorimetric BP. The range of Ag2O concentration has been limited up to X=0.14, in order to exclude the possible formation of NBO, which could introduce unwanted contributions to the low-energy vibrational dynamics. The results prove that addition of silver oxide promotes the formation of complex superstructural units, i.e. pentaborate groups, which seem to be connected to the systematic decrease of the calorimetric BP.
2. EXPERIMENTAL DETAILS Glasses of (Ag2O)x(B2O3)1-x system, where the molar fraction X ranges over the interval 0≤X≤0.14, were prepared from laboratory reagent 99.99 % purity grades of B2O3 and Ag2O (Aldrich) and stored by following the same specific procedures already described [29]. X-ray powder diffraction of samples was used to verify their amorphous character. The values of the density ρ, measured at room temperature by a Micromeritics Accupyc 1330 gas pycnometer under helium gas having a nominal accuracy of 0.03%, are reported in Table 1. The velocity of longitudinal (Vl) and shear (Vt) sound waves was measured at 10 MHz via a pulse-echo technique at room temperature and at 8 K, as described previously [29]. Their values together with those of the Debye sound velocity VD,
=
+
, and of the elastic Debye temperature ΘD used to
determine the low temperature Debye specific heat, are listed in Table 1. Raman spectra were recorded at room temperature for both VV geometry (incident and scattered light polarized vertical to the scattering plane) and VH geometry (perpendicular polarizations) using a double monochromator Jobin Yvon U-1000. The slits were set to give a measured resolution of 1 cm−1. The light source is an Ar+-ion laser operating at 514.5 nm with a typical output of 300 mW. The scattered light was detected by a cooled photomultiplier (Hamamatsu model R943). To remove the
3
effect of surface contamination, the sample surfaces have been polished before each run of measurement. Table 1. Values of density ρ, measured at room temperature, and of longitudinal (Vl) and shear (Vt) sound velocities, measured at 8 K. The calculated values of Debye sound velocity (VD) and elastic Debye temperature (ΘD) are also included.
ρ
(Ag2O)x(B2O3)1-x glasses
(kg m-3)
X=0.0
1826±0.6
X=0.04
Vl -1
(m s )
Vt -1
VD -1
ΘD
(m s )
(m s )
(K)
3337±3.3
1884±1.9
2095
267.9
2109±0.6
3551±3.6
1964±2.0
2188
283.4
X=0.09
2522±0.8
3890±3.9
2075±2.1
2318
305.9
X=0.14
2856±0.9
4167±4.2
2182±2.2
2440
322.9
For the specific-heat measurements, the standard thermal relaxation method in a 4He cryostat between 1.5 and 30 K and in a 3He cryostat between 0.4 and 2 K was applied [21]. The samples (with typical mass of about 20 mg) were bonded using Apiezon N vacuum grease to one side of a silicon chip, horizontally suspended with gilding metal threads having low thermal conductivity. SMD (surface mounting device) resistors of 15 kΩ (1.5-30 K) and 6 kΩ (0.4-2 K) were sanded and polished, calibrated, and glued to the other side of the silicon by using a thermosetting resin. As heater, we used a strain gage device (120 Ω at room temperature), also glued to the chip. The heat capacity of the empty sample holder together with the addenda was measured in a separate run, and their contribution to the total heat capacity was determined to be less than 30% of the overall mass (sample + sample holder).
3. RESULTS AND DISCUSSION A. Low and high frequency Raman scattering The scaled Raman spectra of (Ag2O)x(B2O3)1-x glasses are compared over the range between 8 and 600 cm-1 in Figure 1 and between 600 and 1100 cm-1 in Figure 2. The spectra have been scaled by the average number of atoms per unit volume (using as a reference that of v-B2O3) and the total integrated intensity Atot over the whole wavenumber range. Subtraction of background intensity Iback has been performed by considering the value at 1100 cm-1 where no vibrational contribution is present; in vB2O3, as an example, Iback at 1100 cm-1 has the same value observed at 1700 cm-1 where no band is expected [6]. The spectra show most vibrational features already observed in v-B2O3: a broad strong band below 100 cm-1 (the BP), a weak shoulder on the high frequency tail of BP at about 132 cm-1 ascribed to the first optical mode observed in crystalline B2O3, some broad and asymmetric bands between 350 and about 650 cm-1 due to bending vibrations of various borate segments, and an intense 4
and highly polarized band at 808 cm-1 associated with a localized breathing-type vibration of oxygen atoms inside the boroxol ring plane [6]. Addition of Ag2O causes the progressive decrease of the intensity I808 of the band at 808 cm-1 and the appearance of a further band at about 775 cm-1 whose intensity I775 increases with increasing X. The latter band was also observed in alkali borate glasses (M2O)x(B2O3)1-x with M=Li, Na, K, Cs and Rb and X≤0.2, and ascribed to breathing vibrations of pentaborate groups [30-32], super-structural units made up from two boroxol rings linked by a tetracoordinated boron atom (schematic illustration of pentaborate is reported in Figure 2).
1.0
Ir/IBP
80
0.5
Ir/Atot
60
0
50
100 -1
40
freq. shift (cm )
20
0 0
100
200
300
400
500
600
-1
frequency shift (cm ) Figure 1.
Room temperature scaled Raman spectra (VV configuration) measured between 8 cm-1 and 600 cm-1 in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), solid line; X=0.04, (O); X=0.09, (∆); X=0.14, (∇). Inset reports Ir/IBP for glasses with X=0.0, X=0.04, and X=0.14, using the same symbols.
5
20
Ir/Atot
80
10
60 700
750
800
850 -1
Ir/Atot
freq. shift (cm )
boroxol
40
pentaborate
20
0 600
800
1000 -1
frequency shift (cm ) Figure 2.
Room temperature scaled Raman spectra (VV configuration) between 600 cm-1 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses; symbols are the same of Figure 1. Inset shows the modes at 775 cm-1 and 808 cm-1 in the glass with X=0.14 and the Lorentzian fit; dotted and solid lines show the single bands and their addition, respectively. Schematic illustration of planar boroxol ring (B3O6) and pentaborate group is also included.
A Lorentzian fit has been used to decompose both the bands in two separate peaks and the results for the glass with X=0.14 are shown in the inset of Fig. 2. The values of the integrated intensity and the full width at half height ∆ν for both the vibrational modes are reported in Table 2. Analysis of the bands by a pseudo-Voigt profile has been also performed, obtaining results for the main characteristics (integrated intensity, frequency and full width) of the two peaks in very close agreement with those from Lorentzian fit. The frequency region below 100 cm-1 of all samples, is dominated by the presence of the BP, whose intensity IBP, after an early decrease up to X=0.09, becomes higher than that of v-B2O3. Interestingly, detailed inspection of data reveals a shift of the BP frequency νBP from 26 cm-1 in X=0.0 up to about 6
33 cm-1 in X=0.14, as shown by the inset of Fig. 1 where the Raman intensity scaled by IBP is reported, to evidence the shift. This is in contrast with the observations for I808 and I775 bands which strictly preserve their frequency positions with increasing X. The observed variations of the spectral features with increasing Ag2O content arise from structural modifications involving both the short- and medium-range orders of the network. The changes in the short-range order are due to the formation of four-coordinated boron atoms that give rise to pentaborate Table 2. Integrated intensity Iν, frequency νi and full width at half height ∆νi of the bands at 775 cm- 1 and 808 cm-1 for (Ag2O)x(B2O3)1-x glasses by Lorentzian fit. The calculated fractions of boroxol rings are also included.
(Ag2O)x(B2O3)1-x
I775
glasses X=0.0
X=0.04
X=0.09
X=0.14
-
ν1
∆ν775
cm-1
(cm-1)
-
-
ν2
∆ν808
Boroxol
cm-1
(cm-1)
fraction
1806.2
808.4
14.64
0.54
±36.0
±0.01
±0.041
I808
143.6
772.6
25.8
1348.1
807.9
12.54
±24.58
±1.68
±5.84
±16.2
±0.06
±0.19
329.8
775.1
23.1
1124.6
808.5
14.42
±20.46
±0.55
±1.85
±15.79
±0.08
±0.25
470.7
777.2
25.1
510.8
807.9
15.9
±17.83
±0.35
±1.16
±14.05
±0.15
±0.5
0.40
0.34
0.15
units containing one tetrahedral BO4 group and have a symmetric ring-breathing vibration centered at about 775 cm-1 [31,32]. As determined by NMR spectroscopy measurements in silver borate glasses [26], the fraction N4 of B(4) increases as X/(1-X) up to X ≤0.25, in very close agreement with the behavior observed in lithium borate glasses and quite differently from borate glasses with heavy alkaline ions, such as Rb and Cs, which disclose significant deviations [32,33]. The intensity I775 is given by ANpent, where A is the Raman cross section of this mode and Npent (equal to N4) the fraction of pentaborate units. Thus, it is expected that I775 increases with increasing X following the concentration increase of Npent, as proved by the data reported in Figure 3, where I775 scaled to its value at the highest content (X=0.14) is reported. It is worth noting that formation of tetra-coordinated boron atoms also leads to a substantial stiffening of the network, as shown by the increase of the Debye sound velocity (Table 1). Conversely, the decrease of I808 band is associated with a progressively smaller number of boroxol rings, the building blocks of the medium-range order in v-B2O3. Also in this case, I808 is given by BNring, where B is the Raman cross section of this mode and Nring the fraction of boroxol rings. I808 7
scaled by its highest value at X=0.0 evidences a linear decrease with increasing X, Figure 3. A similar linear decrease of boroxol rings with increasing alkali oxide content has been predicted by a model developed to explain the structural changes in potassium borate glasses, observed by NMR and Raman spectroscopy measurements [34]. Tentatively, we try to evaluate the fraction of boroxol rings contributing to I808 in (Ag2O)x(B2O3)1-x glasses, using as a reference the integrated value of I808 in vB2O3. It was found, from NMR spectroscopy measurements in v-B2O3, that a fraction f=0.78 of boron atoms is involved in boroxol rings [35], the resulting network being formed by quite close fractions of rings (0.54) and oxygen-sharing BO3 triangles (0.46). It is worth noting that the network of v-B2O3 is formed by a roughly even mixture of boroxol rings and BO3 triangular units, which would be exactly 1:1 if 0.75 of boron atoms were in rings, because each ring contains three borons [34]. Assuming that I808 in v-B2O3 is determined by a ring fraction of 0.54, we have evaluated the fraction of boroxol rings contributing to I808 in (Ag2O)x(B2O3)1-x glasses, which is found to be reduced by more than one third in the glass with X=0.14, see Table 2. Since in B2O3 the BP is ascribed to localized out-of-plane rigid librations of rings [6,36] connected via a single bridging oxygen atom [37,38], the observed reduction of the BP in borate glasses with X≤0.09 has been assumed to be related to the decrease of boroxol rings. As regards the increase of IBP observed in the glass with X=0.14, it is believed to be a consequence of the particular morphology of silver borate glasses, that also involves the contribution of local vibrations of loosely coupled Ag+ cations in the low-energy vibrational dynamics. In fact, a previous study on borate glasses of high Ag content (X≥ 0.20) [39] revealed that localized rattling modes of silver atoms within voids of the glassy network influence substantially the low-energy vibrational dynamics of silver borate glasses, because they introduce a contribution which adds to that of excess vibrations of borate network, determining an increase of IBP and shifting the BP position to higher frequency [39]. Of course, rattling atoms exist also in the whole set of alkali borate glasses [39,40], but only the rattling of heavy loose ions can influence the BP energy range [40]. In lithium borate glasses, the rattling frequencies of light Li atoms fall beyond the frequency range of BP, so their contribution lies in the BP tail and does not influence the low energy dynamics [39]. On this basis, the present
8
I775/I775,max
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
I808/I808,max
1.0
0.0 0.00
0.05
0.10
0.15
R=X/(1-X) Figure 3.
Plot of the scaled band intensities at 775 cm-1 (O) and 808 cm-1 (∆) against the mole fraction R=X/(1-X) of Ag2O. Linear fits to the data are reported as dotted and dashed lines, respectively.
observations concerning the BP can be explained by considering the competitive effect of two contributions: the low-frequency librations of connected boroxol rings and rattling modes of Ag+ cations. In fact, for X≤0.09, the rattling contribution is quite small and the BP decreases as a consequence of the decreasing number of librations of coupled boroxols, while for X>0.09 the Ag rattling contribution increases and contrasts the libration decrease, resulting in an overall BP which is higher than that observed in v-B2O3.
B. Low temperature specific heat. In Figure 4(a), the specific heat capacity C(T) of (Ag2O)x(B2O3)1-x glasses between 1.5 K and 25 K is compared to that of v-B2O3, measured between 0.4 and 20 K. In Figure 4(b) the same data are reported as C(T)/T3 vs T, a representation that reveals the existence of the calorimetric BP as a characteristic broad peak. As generally found in amorphous solids, the magnitude of this peak is always larger than C
2 π2
the respective elastic Debye contributions TD3 = 5 ħ
(dashed lines in Figure 4(b)), implying an excess
heat capacity over the Debye prediction. In v-B2O3 and marginally also in glasses with X=0.09 and X=0.14, it is observed an upturn in C/T3 below about 2 K, which arises from the nearly linear contribution of two-level systems (TLS) [41]. Increasing Ag2O content progressively depresses the bump in C(T)/T3 up to X=0.09, the glass with X=0.14 disclosing a heat capacity quite close to that of the latter, and shifts the peak temperature Tpeak from about 5.7 K in v-B2O3 up to 8.0 K in the glass with 9
X=0.14 and the temperature of the minimum Tmin from 1 K up to about 2 K. The decrease of the bump with the associated shift of Tpeak are reminiscent of the behaviors observed for IBP and νBP, which have been explained in terms of the competitive contributions of soft vibrations and rattling modes in the host borate network. Growing addition of silver oxide modifier leads to the decrease of boroxol rings with their librations and to the increase of guest atoms (Ag+ ions) with their rattling modes. The assignments of the Ag rattling modes at the low-energy region have been made in silver borate crystal by Raman scattering and in silver borate glasses by far-FTIR spectroscopy [32,39]. Therefore, we have evaluated the rattling contribution to the specific heat capacity of (Ag2O)x(B2O3)1-x glasses, by applying the procedure previously explained [39]. To be more in detail, three Einstein terms (a) 0
-1
10
-2
10
-3
20 2
10
C/T (mJ/molK )
C (J/molK)
10
15 10 5 0
5
10 15 2
2
T (K )
10
-4
1
T (K)
10
(b)
4
C/T (mJ/molK )
1.0
0.0 0.04 0.09 0.14
3
0.5
0.0 0
5
10
15
20
25
T (K)
Figure 4.
(a) The temperature dependence of the specific heat capacity C in (Ag2O)x(B2O3)1-x glasses: X=0.0 (vB2O3), (●); X=0.04, (∆); X=0.09, (O); X=0.14, (∇). Inset reports specific heat capacity data of glasses with X=0.0 (●), X=0.09 (O); X=0.14, (∇), plotted as C(T)/T vs T2, together with SPM quadratic fits (solid lines). (b) The temperature dependence of C(T)/T3 for (Ag2O)x(B2O3)1-x glasses; symbols are the same of (a). The Debye levels CD(T)/T3 are reported as dashed lines, with X growing from the top to the bottom. Rattling contributions to C/T3 for glasses with X=0.04 (▲) and X=0.14 (▼) are also included.
10
CE1, CE2, and CE3 were considered to describe the motions of Ag+ ions into structural voids: C =A1CE1 + A2CE2 + A3CE3, where Ai=3NAkBsi. The term
=
"
!
#
$ν %
! $&
represents the fraction of atoms per
formula unit contributing to the Einstein heat capacity CEi, being Itot =Σi Iνi. Tentatively, it has been assumed that the three Raman components Iνi, observed in silver borate crystal, preserve their relative shape and frequency also in borate glasses, keeping unchanged their frequency with increasing Ag2O content (this feature being supported by FTIR observations in the same glasses up to X=0.20 [32]). Thus, the values calculated for the Einstein temperatures θEi(=hνi/kB) and the corresponding fractions Iνi/Itot are: θE1 =50 K and Iν1/Itot =0.18, θE2 =66 K and Iν2/Itot =0.19, θE3 =93 K and Iν3/Itot = 0.63 for the Raman lines observed at 35, 46, and 66 cm−1, respectively. Since one mole of oscillators provides a heat capacity of 3R =24.95 Jmol−1K−1 and by knowing the relative molar fraction of Ag+ ions, we anticipate a contribution to the heat capacity from Ag+ rattling of 1.513 Jmol−1K−1 (split into A1 = 0.27 Jmol−1K−1, A2 = 0.29 Jmol−1K−1, and A3 = 0.95 Jmol−1K−1) in the glass having the highest concentration of Ag+ ions (X=0.14, 5.93% of silver atoms). This means that the rattling contribution is quite negligible compared to the total heat capacity of silver borate glasses, becoming slightly significant only in the glass with X=0.14, as it can be observed in Figure 4(b) where the rattling contributions for two glasses are reported. Over the temperature region up to about Tpeak, the data can be described as [42], C(T)=CTLST+CDT3+CSPMT5
(1)
where CTLST represents the linear TLS contribution, CDT3 marks the contribution of Debye vibrational modes, and CSPMT5 denotes the contribution of soft harmonic oscillators (HO), predicted by the Soft Potential Model (SPM) [43]. All these low-energy vibrational excitations determine the excess specific heat capacity and are substantially accounted by the SPM in terms of soft anharmonic oscillator potentials which include TLS and soft HO. The model is able to reproduce the results of TLS model and also gives an exhaustive explanation of the strong rise of the HO vibrational density of states with increasing frequency. A crossover to delocalization of soft harmonic oscillators changes the initial strong rise of the vibrational density of states (∝E4) to a weaker energy dependence (∝E). Inset of Fig. 4(a) reports the polynomial fit of C/T vs T2 for v-B2O3 and for glasses with X=0.09 and X=0.14, because only these glasses evidence a minimum followed by a defined increase in C/T3 with decreasing temperature, which are behaviors marking the crossover to the region regulated by TLS. The upper temperature limit of the fit has been set at T=5 K [24], considering the deviation from a T5-dependence of C(T) due to the discussed variation of HO distribution with increasing energy. The values of the parameters obtained from quadratic fits are reported in Table 3.
11
Table 3. Values of the parameters CTLS, CD and CSPM which assess contributions from TLS, Debye vibrational modes and harmonic oscillators to the specific heat capacity C below 5 K (Eq. 1). The values of Debye contributions, CD,el, obtained from elastic data at 8 K are also included for comparison.
(Ag2O)x(B2O3)1-x glasses
CTLS -6
CD 2
(10 J/molK )
-6
CSPM 4
(10 J/molK )
-6
CD,el 6
(10 J/molK )
-6
(10 J/molK4)
X=0.0
0.09±0.006
0.56±0.007
0.05±0.001
0.50
X=0.09
0.14±0.04
0.30±0.015
0.03±0.001
0.33
X=0.14
0.29±0.07
0.22±0.019
0.03±0.001
0.27
Differently from silver borate glasses where the limited lowest temperature in the experiment (1.5 K) prevents reliable considerations on the TLS contribution, the value of CTLS obtained in v-B2O3 is accurate, and it is found close to those determined in samples having similar OH contents [44]. The progressive decrease of the parameter CSPM with increasing Ag2O content points to a well-defined reduction of soft HO contribution, i.e. of the low-energy vibrations determining the excess specific heat, as observed. Moreover, the obtained CD values are in reasonable agreement with those (CD,el) from elastic data at 8 K. An elastic continuum, which becomes increasingly stiffer, leads to a decrease of the low temperature specific heat capacity. In principle, the stiffening of borate network, due to the increase of connectivity because of the formation of tetrahedral BO4 groups, could account for the observed decrease of the excess C(T). Figure 5 compares C(T)-Crattl/CD,el(T) vs T/ΘD (also ΘD is evaluated by elastic data) in silver borate glasses, disclosing an increase of the peak intensity with increasing Ag2O content and a shift of the maxima compared to that of v-B2O3. This observation implies that variations of low-energy vibrational dynamics of borate network modified by Ag2O addition are not explainable by simple modification of elastic continuum. This finding contrasts with the results obtained for borate glasses with high Ag content (X≥0.20) [39]. In those glasses, after subtraction of the rattling contribution and rescaling to the CD values, the specific heats are found to overlap exactly, proving that the observed differences of excess specific heat are compensated by the changes of the Debye value. It is worth noting that in low silver content glasses, here discussed, the rattling contribution (reported in Fig. 4) represents a very small fraction of the specific heat and no change from the behaviors shown in Fig. 5 was observed after its subtraction, even for the X=0.14 glass with the highest content of silver ions. We infer that the discrepancy between glasses with low and high silver content is strictly connected to the breaking of B-O-B bonds and the consequent formation of NBO, found in large amounts already in the glass with X=0.20 [27]. This concentration, in fact, marks the incoming softening of the glass
12
Figure 5
1.0
3
(C/T )/(C/T )peak
5
0.5
C-Crattl/CD,el
3
4
3
0.0
0
1
2
3
4
T/Tpeak
2
1
0.00
0.05
0.10
T/ΘD Figure 5.
Comparison of C(T)/CD,el vs T/ΘD of (Ag2O)x(B2O3)1-x glasses: (●) X=0.0, (∆) X=0.04, (O) X=0.09 and (∇) X=0.14. Inset shows C/T3 scaled by (C/T3)peak vs T/Tpeak for same borate glasses and also for X=0.20 (+) [from Ref. 39]; dashed and solid lines refer to v-Se [from Ref. 46] and v-SiO2 [from Ref. 24], respectively.
matrix, as clearly indicated by the decrease of the glass transition temperature by further increasing X [45]. This result points out to the crucial role of the network continuity in affecting the vibrational dynamics of a glass. Further interesting considerations turn out from the scaling plot in the inset of Figure 5, which reports C/T3 scaled by (C/T3)peak and plotted vs T/Tpeak for different glasses. It shows that the curves of silver borate glasses are definitely narrower than those of v-B2O3, v-Se [46] and v-SiO2 [24], the behaviors of the last two glasses having been also included for a more exhaustive comparison. In principle, increasing connectivity and rigidity of the glassy network should lead to a narrowing of the energy distribution of vibrations as evidenced by going from v-Se (connectivity of 2), through vB2O3 (connectivity of 3), to SiO2 (connectivity of 4). However, the structural modifications, induced by growing Ag2O addition to the network borate and associated to a change of the connectivity from 3.10 (X=0.04) to 3.25 (X=0.20), appear to be more efficient in reducing the spectral width of vibrational excitations that originate the peak in C/T3. 13
The decrease of the excess low-energy vibrations with increasing content of silver oxide modifier is consistent with the decrease of boroxol rings determined by formation of four-coordinated boron atoms which link two rings in a single pentaborate unit, as observed by Raman spectra reported in Figure 2. As discussed above, in fact, the vibrations underlying both Raman and calorimetric BP in v-B2O3 are identified as low-frequency librations of connected boroxol rings [6,37]. Pentaborate groups are expected to hinder the librational modes of the rings forming them, leading to the observed decrease of the excess heat capacity.
4. CONCLUSIONS Raman light scattering measurements performed at room temperature over the frequency range between 6 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses reveal that the structural variations of borate network due to the addition of silver oxide modifier concern both the short- and medium-range order. Analysis of the high-frequency region shows that the main vibrational band at 808 cm-1, arising from the localized breathing-type vibration of oxygen atoms inside boroxol rings, preserves its frequency but decreases progressively its intensity with increasing Ag2O content up to X=0.14. This decrease is closely related to the appearance of a band at 775 cm-1 assigned to vibrations of groups containing fourcoordinated boron atoms, whose intensity increases with increasing X. These observations imply decrease of boroxol rings and increasing formation of pentaborate units, which are formed by two boroxol rings linked by one tetra-coordinate boron atom and enhance the network connectivity by variations in the chemical bonding. Low-frequency Raman scattering below 150 cm-1 evidences a BP which increases its frequency from 26 cm-1 up to 33 cm-1 with growing silver oxide content. The BP decreases in magnitude up to X=0.09, showing a sudden increase for further Ag2O addition. It is suggested that the reduction of BP, mainly due to localized out-of-plane rigid librations of planar boroxol rings, follows from the decrease of rings, while its increase observed in the glass with X=0.14 arises from rattling modes of Ag+ cations loosely linked with the rest of covalently connected host matrix. Localized rattling modes of silver atoms within voids of glassy network influence substantially the vibrational dynamics below 100 cm-1 determining a contribution which adds to that of excess vibrations of borate network, determining an increase of IBP and its slight shift to higher frequency. The decrease of boroxol rings leads also to a progressive decrease of the excess heat capacity observed below 20 K, not taken into account by the hardening of elastic continuum, and to the shift to higher temperatures of the calorimetric BP. Evaluation of the contribution of rattling modes shows that it is quite negligible compared to the total heat capacity of silver borate glasses, becoming a little significant only in the glass with X=0.14. Moreover, it has been shown that structural modification of the glassy network induced by growing addition of Ag2O leads to a substantial reduction of the spectral width of vibrational excitations leading to the peak in C/T3. All the observations are consistent with a low14
energy vibrational dynamics of silver borate glasses that appears to be related to the boroxol rings, these glassy units being connected to the network by simple or complex links. The experimental results of the heat capacity C are also compared with the theoretical descriptions of the soft potential model, resulting in qualitative agreement with the main predictions of this model. It is worth emphasizing that silver borate glasses are materials of current great interest because they are used in electrochemical devices such as high-energy and high-power solid state batteries [47,48], even if some technical problems limit their large-scale application. Their use as components of composite electrolytes permits to enhance the ionic conductivity of the overall system. Very recently it has been found that the mechanical stability of ionic clusters is directly related to diffusion pathway for the mobile ions: the less stable the clusters are, the faster the ion transport is [49]. Soft modes [50] and Boson peak [51] are suggested as appropriate indicators of the structural stability of clusters in amorphous solids. This aspect makes the investigation of the structural changes and of the low energy dynamics, experienced by borate matrix with silver oxide addition, of great importance to gain insights into the mechanisms underlying ionic diffusion.
15
REFERENCES [1]
T. Nakayama, Boson peak and terahertz frequency dynamics of vitreous silica, Reports on Progress in Physics 65 (2002) 1195, https://doi.org/10.1088/0034-4885/65/8/203.
[2]
U. Buchenau, N. Nücker, A. J. Dianoux, Neutron scattering study of the low-frequency vibrations in vitreous silica, Phys. Rev. Lett. 53 (1984) 2316, https://doi.org/10.1103/PhysRevLett.53.2316.
[3]
V. K. Malinovsky, V. N. Novikov, P. P. Parshin, A. P. Sokolov, M. G. Zemlyanov, Universal form of the low-energy (2 to 10 meV) vibrational spectrum of glasses, Europhys. Lett. 11 (1990) 43, https://doi.org/10.1209/0295-5075/11/1/008.
[4]
G. D’Angelo, C. Crupi, G. Tripodo, G. Salvato, Relation between low-temperature thermal conductivity and the specific heat of cesium borate glasses, J. Phys. Chemistry B 114 (2010) 24672475, https://doi.org/10.1021/jp907152y.
[5]
R. O. Pohl, in Amorphous Solids: Low-Temperature Properties, edited by W. A. Phillips (Springer, Berlin, 1981) p. 27.
[6]
G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, G. Di Marco, C. Vasi, E. Gilioli, Influence of packing on low energy vibrations of densified glasses, Phys. Rev. Lett. 111 (20134) 245502, https://doi.org/10.1103/PhysRevLett.111.245502.
[7]
G. D’Angelo, G. Carini, C. Crupi, M. Koza, G. Tripodo, C. Vasi, Boson peak in alkaline borate glasses: Raman spectroscopy, neutron scattering, and specific-heat measurements, Phys. Rev. B 79 (2009) 014206, https://doi.org/10.1103/PhysRevB.79.014206.
[8]
P. S. Salmon, R. A. Martin, P. E. Mason, G. J. Cuello, Topological versus chemical ordering in network
glasses
at
intermediate
and
extended
length
scales, Nature 435
(2005)
75,
https://doi.org/10.1038/nature03475. [9]
S. R. Elliott, Origin of the first sharp diffraction peak in the structure factor of covalent glasses, Phys. Rev. Lett. 67 (1991) 711, https://doi.org/10.1103/PhysRevLett.67.711.
[10] V. N. Novikov and A. P. Sokolov, A correlation between low-energy vibrational spectra and first sharp diffraction peak in chalcogenide glasses, Solid State Comm. 77 (1991) 243-247, https://doi.org/10.1016/0038-1098(91)90341-R. [11] Q. Mei, C. J. Benmore, S. Sen, R. Sharma, and J. L. Yarger, Intermediate range order in vitreous silica
from
a
partial
structure
factor
analysis,
Phys.
Rev.
B
78
(2008)
144204,
https://doi.org/10.1103/PhysRevB.78.144204. [12] C. Crupi, G. Carini, M. A. González, G. D'Angelo, Origin of the first sharp diffraction peak in glasses. Phys. Rev. B 92 (2015) 134206, https://doi.org/10.1103/PhysRevB.92.134206. [13] M. A. González, C. Mondelli, G. D’Angelo, C. Crupi, M. R. Johnson, A molecular dynamics study of the role of the cation in modifying the structure of alkali borate glasses, J. Non-Crystall. Solids 354 (2008) 203-207, https://doi.org/10.1016/j.jnoncrysol.2007.08.079. [14] T. S. Grigera, V. Martin-Mayor, G. Parisi, P. Verrocchio, Phonon interpretation of the ‘boson peak’in supercooled liquids, Nature 422 (2003) 289, https://doi.org/10.1038/nature01475
16
[15] W. Schirmacher, G. Ruocco, T. Scopigno, Acoustic attenuation in glasses and its relation with the boson peak, Phys. Rev. Lett. 98 (2007) 025501, https://doi.org/10.1103/PhysRevLett.98.025501 [16] V. L. Gurevich, D. A. Parshin, H. R. Schober, Anharmonicity, vibrational instability, and the Boson peak in glasses, Phys. Rev. B 67 (2003) 094203, https://doi.org/10.1103/PhysRevB.67.094203 and references therein. [17] E. Duval, A. Mermet, L. Saviot, Boson peak and hybridization of acoustic modes with vibrations of nanometric heterogeneities in glasses, Phys. Rev. B 75 (2007) 024201, https://doi.org/10.1103/PhysRevB.75.024201. [18] L. E. Silbert, A. J. Liu, S. R. Nagel, Vibrations and diverging length scales near the unjamming transition, Phys. Rev. Lett. 95 (2005) 098301, https://doi.org/10.1103/PhysRevLett.95.098301. [19] N. Xu, M. Wyart, A. J. Liu, S. R. Nagel, Excess vibrational modes and the boson peak in model glasses, Phys. Rev. Lett. 98 (2007) 175502, https://doi.org/10.1103/PhysRevLett.98.175502. [20] G. Carini Jr, G. Carini, G. D’Angelo, E. Gilioli, C. Vasi, Origin of excess low-energy vibrations in densified B2O3 glasses, Phil. Mag. 95 (2015) 2596-2606, https://doi.org/10.1080/14786435.2015.1067733. [21] G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, L. Orsingher, A. Fontana, Low temperature specific heats of permanently densified glassy GeO2, Phil. Mag. 91 (2011) 1877-1886, https://doi.org/10.1080/14786435.2010.530617. [22] L. Orsingher, M. Calicchio, G. Carini Jr, R. Dal Maschio, D. Fioretto, A. Fontana, ... F. Rossi, Optical and spectroscopic characterization of permanently densified GeO2 glasses, Phil. Mag. 88 (2008) 3907-3914, https://doi.org/10.1080/14786430802247213. [23] A. I. Chumakov, G. Monaco, A. Fontana, A. Bosak, R. P. Hermann, D. Bessas, … G. Baldi, Role of disorder in the thermodynamics and atomic dynamics of glasses, Phys. Rev. Lett. 112 (2014) 025502, https://doi.org/10.1103/PhysRevLett.112.025502. [24] G. Carini Jr, G. Carini, D. Cosio, G. D’Angelo, F. Rossi, Low temperature heat capacity of permanently densified SiO2 glasses, Phil. Mag. 96 (2016) 761-773, https://doi.org/10.1080/14786435.2015.1122845. [25] L. Orsingher, A. Fontana, E. Gilioli, G. Carini Jr, G. Carini, G. Tripodo, ..., U. Buchenau, Vibrational dynamics of permanently densified GeO2 glasses: Densification-induced changes in the boson peak, J. Chem. Phys. 132 (2010) 124508, https://doi.org/10.1063/1.3360039. [26] K. S. Kim, P. J. Bray, 11B Nuclear Magnetic Resonance Studies of the System Ag2O-B2O3, J. Non Met. 2 (1974) 95-101. [27] M. C. Abramo, G. Carini, G. Pizzimenti, Ag2O-B2O3 glassy systems: network coherence behaviour as seen from molecular dynamics calculations, Journal of Physics C: Solid State Physics 21 (1988) 527, https://doi.org/10.1088/0022-3719/21/3/009. [28] G. D’Angelo, C. Vasi, A. Bartolotta, G. Carini, C. Crupi, G. Di Marco, G. Tripodo, Low-frequency Raman scattering of silver borate glasses, Phil. Mag. 84 (2004) 1631-1638, https://doi.org/10.1080/14786430310001644413.
17
[29] G. Carini Jr, G. Carini, G. D’Angelo, G. Tripodo, A. Bartolotta, G. Salvato, Ultrasonic relaxations, anharmonicity, and fragility in lithium borate glasses, Phys. Rev. B 72 (2005) 014201, https://doi.org/10.1103/PhysRevB.72.014201. [30] B. N. Meera, J. Ramakrishna, Raman spectral studies of borate glasses, J. of Non-Crystal. Solids 159 (1993) 1-21, https://doi.org/10.1016/0022-3093(93)91277-A. [31] E. I. Kamitsos, G. D. Chryssikos, Borate glass structure by Raman and infrared spectroscopies, J. of Mol. Structure 247 (1991) 1-16, https://doi.org/10.1016/0022-2860(91)87058-P. [32] J. A. Kapoutsis, E. Kamitsos and G. D. Chryssikos, Proc. of Second Int. Conf. on Borate Glasses, Crystals and Melts, edited by A. C. Wright, S. A. Feller and A. C. Hannon (Soc. Glass Technology, Sheffield, UK, 1997), pp.303-312. [33] J. Zhong and P. Bray, J. Non-Cryst. Solids 111 (1989) 67, https://doi.org/10.1016/00223093(89)90425-0. [34] R. E. Youngman and J. W. Zwanziger, J. Phys. Chem. 100 (1996) 16720-16728, https://doi.org/10.1021/jp961439+ [35] V. V. Brazhkin, I. Farnan, K. I. Funakoshi, M. Kanzaki, Y. Katayama, A. G. Lyapin, H. Saitoh, Structural transformations and anomalous viscosity in the B2O3 melt under high pressure, Phys. Rev. Lett. 105 (2010) 115701, https://doi.org/10.1103/PhysRevLett.105.115701. [36] G. Simon, B. Hehlen, E. Courtens, E. Longueteau, R. Vacher, Hyper-Raman scattering from vitreous boron oxide: coherent enhancement of the boson peak, Phys. Rev. Lett. 96 (2006) 105502, https://doi.org/10.1103/PhysRevLett.96.105502. [37] F. L. Galeener, M. F. Thorpe, Rings in central-force network dynamics, Phys. Rev. B 28 (1983) 5802, https://doi.org/10.1103/PhysRevB.28.5802. [38] G. Carini Jr, G. Carini, G. D'Angelo, D. Fioretto, G. Tripodo, Identification of relaxing structural defects in densified B2O3 glasses, Phys. Rev. B 90 (2014) 140204, https://doi.org/10.1103/PhysRevB.90.140204. [39] G. D’Angelo, C. Crupi, G. Carini, C. Vasi, Rattling ions and the anomalous vibrational dynamics of glasses, Phys. Rev. B 84 (2011) 172201, https://doi.org/10.1103/PhysRevB.84.172201. [40] C. Crupi, G. D’Angelo, C. Vasi, Low-energy vibrational dynamics of cesium borate glasses, J. Phys. Chem. B 116 (2012) 6499-6505, https://doi.org/10.1021/jp301230s. [41] W. A. Phillips, Two-level states in glasses, Rep. Progr. Phys. 50 (1987) 1657, https://doi.org/10.1088/0034-4885/50/12/003. [42] M. A. Ramos, Are the calorimetric and elastic Debye temperatures of glasses really different?, Phil. Mag. 84 (2004) 1313, https://doi.org/10.1080/14786430310001644053. [43] D. A. Parshin, Interactions of soft atomic potentials and universality of low-temperature properties of glasses, Phys. Rev. B 49 (1994) 9400, https://doi.org/10.1103/PhysRevB.49.9400. [44] J. C. Lasjaunias, D. Thoulouze, F. Pernot, Solid State Comm. 14 (1974) 957-961, https://doi.org/10.1016/0038-1098(74)90402-5.
18
[45] E. N. Boulos and N. J. Kreidl, Structure and properties of silver borate glasses, J. Am. Ceram. Soc. 54 (1971) 368-375, https://doi.org/10.1111/j.1151-2916.1971.tb12324.x. [46] A. Avogadro, S. Aldrovandi, F. Borsa, G. Carini, Specific-heat study of low-energy excitations in glasses, Phil. Mag. B 56 (1987) 227-236, https://doi.org/10.1080/13642818708208529. [47] J. G. Kim, B. Son, S. Mukherjee, N. Schuppert, A. Bates, O. Kwon, ... S. Park, A review of lithium and non-lithium based solid state batteries, J. Power Sources 282 (2015) 299-322, https://doi.org/10.1016/j.jpowsour.2015.02.054. [48] C. Jiang, H. Li, C. Wang, Recent progress in solid-state electrolytes for alkali-ion batteries, Science Bull. 62 (2017) 1473-1490, https://doi.org/10.1016/j.scib.2017.10.011. [49] Y. S. Choi, J. C. Lee, Electronic and mechanistic origins of the superionic conductivity of sulfidebased solid electrolytes, J. Power Sources 415 (2019) 189-196, https://doi.org/10.1016/j.jpowsour.2019.01.071. [50] V. K. Tewary, B. Yang, Singular behavior of the Debye-Waller factor of graphene, Phys. Rev. B 79 (2009) 125416, https://doi.org/10.1103/PhysRevB.79.125416. [51] M. Sharma, S. Yashonath, Correlation between conductivity or diffusivity and activation energy in amorphous solids, J. Chem. Phys. 129 (2008) 144103, https://doi.org/10.1063/1.2990744.
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FIGURE CAPTIONS
Figure 1.
Room temperature scaled Raman spectra (VV configuration) measured between 8 cm-1 and 600 cm-1 in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), solid line; X=0.04, (O); X=0.09, (∆); X=0.14, (∇). Inset reports Ir/IBP for glasses with X=0.0, X=0.04, and X=0.14, using the same symbols.
Figure 2.
Room temperature scaled Raman spectra (VV configuration) between 600 cm-1 and 1100 cm-1 in (Ag2O)x(B2O3)1-x glasses; symbols are the same of Figure 1. Inset shows the modes at 775 cm-1 and 808 cm-1 in the glass with X=0.14 and the Lorentzian fit; dotted and solid lines show the single bands and their addition, respectively. Schematic illustration of planar boroxol ring (B3O6) and pentaborate group is also included.
Figure 3.
Plot of the scaled band intensities at 775 cm-1 (O) and 808 cm-1 (∆) against the mole fraction R=X/(1-X) of Ag2O. Linear fits to the data are reported as dotted and dashed lines, respectively.
Figure 4.
(a) The temperature dependence of the specific heat capacity C in (Ag2O)x(B2O3)1-x glasses: X=0.0 (v-B2O3), (●); X=0.04, (∆); X=0.09, (O); X=0.14, (∇). Inset reports specific heat capacity data of glasses with X=0.0 (●), X=0.09 (O); X=0.14, (∇), plotted as C(T)/T vs T2, together with SPM quadratic fits (solid lines). (b) The temperature dependence of C(T)/T3 for (Ag2O)x(B2O3)1-x glasses; symbols are the same of (a). The Debye levels CD(T)/T3 are reported as dashed lines, with X growing from the top to the bottom. Rattling contributions to C/T3 for glasses with X=0.04 (▲) and X=0.14 (▼) are also included.
Figure 5.
Comparison of C(T)/CD vs T/ΘD of (Ag2O)x(B2O3)1-x glasses: (●) X=0.0, (∆) X=0.04, (O) X=0.09 and (∇) X=0.14. Inset shows C/T3 scaled by (C/T3)peak vs T/Tpeak for same borate glasses and also for X=0.20 (+) [from Ref. 39]; dashed and solid lines refer to vSe [from Ref. 46] and v-SiO2 [from Ref. 24], respectively.
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Highlights 1. Raman scattering and heat capacity measurements on silver borate glasses evidenced remarkable changes in structure and low- energy vibrational dynamics. 2. Rattling of silver ions and soft vibrations determine the profile of the low-energy vibrational spectrum. 3. The crucial role of the network continuity on the vibrational dynamics of a glass is pointed out.
AUTHOR DECLARATION
On Behalf of all the authors, I wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. Yours sincerely
23/09/2019