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Effects of thermal history on the acoustic attenuation of dry and wet B2O3 glasses
Materials Science and Engineering A 521–522 (2009) 263–267
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effects of thermal history on the acoustic attenuation of dry and wet B2 O3 glasses G. D’Angelo a,∗ , C. Crupi b , V. Conti Nibali a , M.A. Ramos c a
Dipartimento di Fisica, Università di Messina, Salita Sperone 31, S. Agata Messina 98166, Italy Istituto IPCF del CNR, sede di Messina, Salita Sperone, S. Agata Messina 98166, Italy c Departamento de Fısica de la Materia Condensada, C-III, Universidad Autonoma de Madrid, Cantoblanco, E-28049 Madrid, Spain b
a r t i c l e
i n f o
Article history: Accepted 2 October 2008 PACS: 61.40.Df 62.40 62.80.+f Keywords: Boron oxide glass Acoustic properties Low temperature relaxational dynamics
a b s t r a c t The acoustic properties at 10 and 30 MHz of dry and wet boron oxide samples have been investigated over the temperature range between 10 and 300 K. Significant differences in the temperature dependence of acoustic attenuation and longitudinal sound velocity as a function of the annealing treatment and water content have been revealed in the investigated glasses. Measurements, densely performed over the whole temperature range, together with a detailed analysis of the dispersive behaviors, allowed us to evidence the complexity of the relaxational dynamics, as due to the coexistence of different local motions. Above 150 K, the data analysis has been based on the existence of two relaxation processes, whose strengths result to be strictly dependent on the water content. Finally, a possible relation to the empty volume originated from the arrangement of the structural units on nanometer length scale has been put forward. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In the last decades, a great deal of experimental and theoretical work has been devoted to understand anomalous behaviors of acoustic properties [1–3] observed at low temperatures in amorphous materials. More precisely, the attenuation and velocity of ultrasounds show surprising trends, not normally found in crystals, which have been ascribed to thermally activated structural relaxations at high temperatures (T > 10 K) and to tunnelling motions at low temperatures (T < 10 K). To better understand the origin and the microscopic nature of structural defects causing these anomalies, a useful expedient would be to study how acoustic properties of glasses depend on specific physical or chemical treatments of samples made up of the same chemical compounds. As regards this issue, in fact, it has been shown that the rate of cooling may influence the properties of a glass as well as an annealing process if it is carried out below the glass transition temperature [4–7]. Vitreous B2 O3 appears to be a very promising glass for achieving this goal since some of its basic properties [4–6] show remarkable changes upon different stabilization temperature and water content [8]. This is a very good glass former, covalently bonded, whose molecular structure is built up by planar BO3 triangles set-
∗ Corresponding author. E-mail address: [email protected] (G. D’Angelo). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.10.076
tled in more elaborate symmetrical B3 O6 boroxol rings [9], the units being corner-linked by sharing common O atoms [10]. The arrangements of these structural units are not completely random, but show some correlations on the nanometer scale, as proved by neutron diffraction [11] and molecular dynamics studies [12]. Recently, structural investigations on B2 O3 samples subjected to different thermal histories have revealed no changes in the short range order [5]. This would suggest that the differences observed in the physical properties of these samples arise from undisclosed structural changes involving the medium range order. Structural modifications in boron oxide glass can arise from a progressive addition of water which induces a change in the boron coordination number from 3 to 4, as commonly observed when an alkali is added to the boron oxide [13]. The relative concentrations of BO3 and BO4 units depend strongly also on thermal history [14]. Glasses subjected to higher quenching rates contain fewer units based on four-coordinated boron atoms as compared to slowly cooled or annealed glasses. Recently, the change of the boron coordination number has been considered as the origin of the polymorphism experimentally observed in vitreous B2 O3 by applying elevated pressures [15,16]. The existence of vitreous polymorphs reveals a sort of structural instability of the systems, which can have important implication in explaining the phenomenology of the glassy state. This consideration sets the importance of studies devoted to the improving of knowledge of the relation existing between the microscopic structure and the physical properties of glasses.
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Table 1 Basic parameters of D-1 and W-2 glasses: hydroxyl ion concentrations [17], mass–density [17], longitudinal velocity vl [5], glass transition temperature Tg [17], values of the parameters related to thermally activated relaxations (Em , NBl2 ). Sample
Thermal treatment
[OH− ] (mol%)
(kg/m3 )
vl (m/s)
Tg (K)
Em1 /kB (K)
Em2 /kB (K)
2 NBl1 (10−13 J2 m−3 )
2 NBl2 (10−13 J2 m−3 )
D-1 W-2
As quenched 490 K, 100 h
0.27 5.8
1804 1866
3093 3355
570 537
3171 3169
1802 1835
0.26 6.01
5.76 1.45
In this work we have focused our attention on two different samples of glassy B2 O3 with the aim to study the influence of an annealing process and of water content on the attenuation and the propagation of ultrasonic waves. 2. Experimental details Two boron oxide samples (cf. Table 1), respectively named as dry (D-1) and wet (W-2) glasses, have been prepared by melting boron oxide pellets (Aldrich, 99.999% purity) in a platinum crucible, following different methods in order to obtain samples with (W-2) and without (D-1) a significant concentration of hydroxyl ions OH− . More precisely the dry sample was prepared by heating the material slowly up to 1050 ◦ C until bubbling has ceased after about 20 h. Then, the material was cooled and the process repeated in vacuum. The final step was to keep the melt at 1050 ◦ C for 24 h, and rapidly pouring the melt into the brass mould. The wet sample was prepared by heating the material at 300 ◦ C in air for 2 h, melting by heating up to 800 ◦ C also in air, holding for 4 h, and pouring into a brass mould. Finally the glass has been subjected to an annealing treatment of 100 h at a temperature of 490 K, near its glass transition temperature (Tg = 537 K). D-1 and W-2 glasses contain the 0.27% and the 5.8% of water content, respectively, as determined by infrared spectroscopy [17]. The mass–density of B2 O3 samples have been measured at room temperature [17] with an estimated experimental error of about ±0.003 g/cm3 . The main data characterizing these glasses are presented in Table 1. The attenuation and velocity of longitudinal ultrasound waves have been measured at frequencies of 10 and 30 MHz using a conventional pulse-echo ultrasonic technique. The thermal scanning was carried out in the temperature range from 10 to 300 K operating on a helium cryogenerator with a thermostatic control of about 0.1 K. The bonding agent between sample and transducer (a 10 MHz quartz) was N-Apiezon grease.
enhanced intensity and shifts to higher temperatures as the frequency of the ultrasonic probe is increased, revealing a thermally activated nature of the underlying relaxation process. No trace of the high temperature peak observed in the wet glass is visible. The most surprising experimental evidence in the dry sample is the very extensive width of the revealed peak, hardly ascribable only to the randomness of the glassy structure. It seems more reasonable the hypothesis that different relaxation processes are working in this temperature range, with distinct but close activation energies, the broad peak experimentally observed being the outcome of overlapping losses. More clearly, the existence of different relaxations can be envisaged in the loss curve at 10 MHz, where a shoulder at about 150 K in addition to a peak at 50 K can be recognized. Moreover a third peak seems to emerge at higher temperatures, in the same interval of the high temperature peak revealed in the wet sample. By increasing frequency the intensity of each individual relaxation enhances, making difficult the possibility to discriminate the different contributions. The assumption of the existence in B2 O3 glass of at least two structural relaxations at low temperatures supplies a possible explanation also for the unexpected finding in the wet glass of a loss peak (the peak revealed at 50 K) shifted backwards by increasing frequency. This anomalous behavior can be believed as the result of combined effect of the increasing intensity and different activation energies that determine dissimilar temperature shift by increasing frequency.
3. Experimental results and discussion The temperature dependences of the ultrasonic attenuations ˛(T) of W-2 and D-1 glasses at frequencies of 10 and 30 MHz are plotted in Fig. 1(a) and (b), respectively. In the wet sample, a bump, typical of oxide glasses, is observed at temperatures below 100 K whose temperature position appears to shift toward lower values by increasing ultrasonic frequency. At higher temperatures the acoustic attenuation increases showing in the curve at 10 MHz a second peak at about 270 K. In the same temperature region (T > 150 K) we observe a fast increase of ˛(T) in the curve at 30 MHz, with an intensity about three times greater than the value at 10 MHz. Both these observations lead us to suppose that the upturn in ˛(T) is indicative of the existence of a peak centered at higher temperature. This peak should arise from the same loss mechanism observed at about 270 K in the 10 MHz curve; the increase of the intensity and the shift in temperature observed at 30 MHz being indicative of its thermally activated nature. The decreased content of water in the dry sample clearly gives rise to significant differences in the acoustic attenuation behavior and in its intensity. As a matter of fact a very broad peak, spread out over the whole investigated temperature range, is shown in ˛(T) curve of the D-1 glass (see Fig. 1(b)). This bump exhibits an
Fig. 1. Acoustic attenuation vs. temperature of: (a) W-2 boron oxide glass at 10 () and 30 MHz (); (b) D-1 boron oxide glass at 10 (䊉) and 30 MHz ().
G. D’Angelo et al. / Materials Science and Engineering A 521–522 (2009) 263–267
265
Fig. 3. Internal friction of W-2 boron oxide glass () and D-1 boron oxide glass (䊉) as a function of temperature. The solid lines represent the fit to experimental data obtained by supposing two relaxation peaks (indicated by arrows) for each sample.
Fig. 2. (a) The temperature dependence of longitudinal sound velocity (♦) and acoustic attenuation at 10 MHz () of W-2 boron oxide glass; (b) the temperature dependence of longitudinal sound velocity () and acoustic attenuation at 10 MHz (䊉) of D-1 boron oxide glass.
However, further investigations at different frequencies and temperatures are needed to solve this obscure point. By pursuing the aim to resolve better the supposed multiple relaxations, measurements of longitudinal velocity at 10 MHz have been performed as a function of temperature. In Fig. 2(a) and (b) the temperature dependences of the 10 MHz longitudinal sound velocity, vl (T ), of D-1 and W-2 glasses are shown. In the same figures the acoustic attenuation curves at the same frequency are also reported in order to have a comparison between the temperature positions of the contributions observed in both sound velocity and attenuation. Firstly, it has to be considered that the presence of a higher number of OH− hydroxyls in the wet sample induces a great number of tetrahedral boron atoms [13] which increases the connectivity and the rigidity of this glass, as monitored by the higher value of the sound velocity with respect to the dry sample. It is evident that in the wet glass the longitudinal velocity decreases quite linearly with temperature in the whole investigated range (see Fig. 2(a)), although clear signs of dispersion (inflexion points marked by arrows in Fig. 2(a)) are visible around 50, 80, and 275 K. We can observe that the dispersions at 50 and 80 K correspond, in the loss curve below 150 K, to a peak followed by a shoulder, while the dispersion at 275 K is associated to the high temperature loss peak ascribed to the relaxation of OH− hydroxyls [18]. It has to be remarked that ill-defined dispersions can be envisaged around 175 and 250 K. The temperature dependence of velocity in the dry sample shows an alternation of linear behaviors with changing slope and inflexion points particularly evident at about 125, 175 and 250 K (see arrows in Fig. 2(b)). These dispersions indicate the existence of relaxations in a temperature region where the acoustic attenuation displays a visible asymmetric broadening of the high temperature
tail of the loss peak, showing the complexity of the structural relaxations in this glass. The thorough analysis of dispersions in the velocity curves shows that in both dry and wet samples the same relaxation processes are active, although with strengths strongly dependent on the water content. Considering the role of water in determining the main characteristics of structural relaxations in boron oxide glasses, the following analysis will be focused on the acoustic behavior above 150 K, where the high water content of the wet glass results in a high temperature peak, well suitable for an unquestionable investigation. With the aim of directly comparing the sound attenuation of D-1 and W-2 glasses, the temperature dependences of internal friction Q−1 (= 2˛v/ω, where v is the sound velocity and ω is the ultrasonic angular frequency) at 10 MHz are reported in Fig. 3. The internal friction value measured at the lowest temperature in the experiment has been assumed to arise mainly from parasitic (static) dissipative mechanisms and has been subtracted from the experimental data. A quantitative analysis has been performed on the internal friction data for both samples, at temperatures higher than 150 K, by supposing the existence of two loss peaks ˛1 and ˛2 , both arising from a thermally activated relaxation: Q −1 =
2v (˛1 + ˛2 ) ω
(1)
In Eq. (1), ˛1 accounts for the loss peak observed at 300 K, clearly visible in the wet glass. It is believed that this relaxation process comes from local motions of hydroxyl groups, largely present in W-2 sample but barely in the dry glass. The second loss peak ˛2 has been included to account for the significant loss observed in this temperature region in the dry glass, which is related to the relaxation process contributing to the sound velocity dispersion at 175 K. It is supposed that this relaxation process arises from intrinsic structural defects, sensitive to the water presence too. For ˛1 and ˛2 separately, the following equation has been used [19]: ˛=
Bl2
P(E)
4v3l kB T
ω2 (E) dE 1 + ω2 2 (E)
(2)
In Eq. (2), Bl is the deformation potential that refers to the coupling between the ultrasonic longitudinal stress and the system, T the absolute temperature, kB the Boltzmann constant, P(E) is a distribution function of activation energy E and is the relaxation time, that is related to the activation energy E of the process and to the frequency factor 0−1 by an Arrhenius-type equation:
−1 = 0−1 exp −
E kB T
(3)
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Taking into account the topological disorder of glassy materials, it is quite reasonable assuming P(E) as a Gaussian distribution: N
P(E) = √ exp ( 2)E0
−
(E − Em )2 2E02
,
(4)
N being the total number of relaxing particles per unit volume, Em and E0 are the most probable value and the width of the distribution, respectively. From the data analysis, the values of Em , E0 , NBl2 , and were obtained by least-squares fits of the results using a Minuit minimum search program. The theoretical internal friction curves together with their distinct components for both the samples are shown in Fig. 3 as solid and dashed lines, respectively. The values of the parameters Em and NBl2 are reported in Table 1, while the width of distribution Eo /kB and the characteristic frequency −1 −1 o−1 are: Eo1 /kB = 411 K, o1 = 4.5 × 1013 s−1 , Eo2 /kB = 400 K, o2 = −1 0.2 × 1013 s−1 (W-2 glass); Eo1 /kB = 480 K, o1 = 0.7 × 1013 s−1 ,
−1 Eo2 /kB = 550 K, o2 = 0.7 × 1013 s−1 (D-1 glass). It has to be observed that the use of two distinct relaxations lets to get a very good fit of the experimental data in both samples. More importantly, the mean activation energies Em1 ad Em2 are exactly the same in the wet and dry glasses, suggesting that the local arrangements of the relaxing particles are not greatly influenced by water addition. Moreover the value of Em1 agrees exactly with the activation energy of 26.4 kJ/mol previously derived by Krause and 2 and N B2 for Kurkjian [18]. In addition to this, the products N1 Bl1 2 l2 each of investigated glasses change in direct and inverse relation to the amount of OH− groups, respectively, revealing that both relaxations strictly depend on water content. This findings support the hypothesis that the defects originating ˛1 and ˛2 are the same in the W-2 and D-1 glasses. 2 values obtained in the present glasses and the By using the N1 Bl1 value of 0.21 eV for the deformation potential Bl [19], we deduce a value of 5.3 × 1020 cm−3 and 2.3 × 1019 cm−3 for the number N1 of relaxing particles in W-2 and D-1 glasses. These values are in good agreement with the number of OH− impurities estimated from infrared measurements (see Table 1) and equal to 9.36 × 1020 cm−3 (W-2 glass) and 4.21 × 1019 cm−3 (D-1 glass). Otherwise, the attribution of this first attenuation peak to relaxation modes of hydroxyl ions is once more supported by calculations on the decrement of its intensity by going from W-2 to D-1 sample. By the best fit values of ˛1 intensity for the two glasses a reduction of 96% has been estimated in perfect agreement with the decrease of 95% of water content between the wet and dry boron oxide glass. Unlikely, the attribution of a definite microscopic origin of the relaxing centres giving rise to the second attenuation peak ˛2 requires further analysis in the sight of the really complex behaviors shown by the acoustic attenuation curves of both systems. However, we can put forward a hypothesis referring to known structural changes occurring in pure borate glass because of the addition of water. In this regard, the strong decrease of ˛2 intensity from dry to wet sample can be explained by assuming a direct relation to the decrease of three coordinated boron atoms following the addition of water. It is plausible to associate the ˛2 peak of D-1 sample to local motion of structural units containing BO3 groups. Otherwise, in the W-2 glass, the presence of water content causes the transformation of BO3 planar units in tetrahedral BO4 groups with a consequent decreased number of the associated relaxation modes. We believe that the complexity of the relaxations we have observed below room temperature in B2 O3 glass has an intrinsic structural origin. BO3 triangles, on which B2 O3 structure is based, are expected to have a great freedom of movement to arrange by bending, taking advantage of the empty space inside the network.
It is supposed that in the dry sample, not subjected to annealing treatment, a variety of arrangements between the BO3 triangles on nanometer scale are possible during the quenching of melt, giving rise to voids of different sizes. The structural units overlooking these voids are likely responsible for local motions originating the observed relaxations. Each significant difference in the size of these voids corresponds to observable changes in the activation energy for the same local motion. This would explain the multiplicity of relaxations active over the same temperature range. The annealing treatment and the increase of connectivity (due to the presence of four-coordinated boron atoms) lead to a reduction of the free volume, precluding some structural relaxations. The acoustic loss curve below room temperature is consequently changed as concerning its shape and intensity. It has been observed that the reduction of internal volume is testified by the increase of mass density, equal to 3.4% in the W-2 sample (see Table 1). Further investigations in B2 O3 samples subjected to different thermal histories are in progress in order to confirm these suggestive suppositions for the origin of structural relaxations in boron oxide glass. 4. Conclusion Low temperature ultrasonic measurements have been carried out on dry and wet boron oxide samples. The temperature dependences of acoustic attenuation and sound velocity as a function of the annealing process and water content have revealed significant differences in these glasses. In the wet glass it has been observed a big loss peak around room temperature ascribed to thermally activated relaxation process of hydroxyl ions. In the dry sample it has been observed a large and wide peak, spreading over the whole investigated temperature range, which arises from the overlap of different relaxation processes. A quantitative analysis of the internal friction curves above 150 K has revealed that the relaxation processes working in this temperature region have the same origin in both dry and wet glasses and are strictly depend on the water content. It is supposed that, in the dry glass, a variety of arrangements between the BO3 triangles on nanometer scale are possible during the quenching of melt, giving rise to voids of different sizes. Assisted by temperature, groups of atoms lying in these empty spaces are supposed to be able of relaxing with less constraints than in the wet sample giving rise to a more complex acoustic spectrum. References [1] S. Hunklinger, M.v. Schickfus, in: W.A. Phillips (Ed.), Amorphous Solids: Lowtemperature Properties, Springer, Berlin, 1981, p. 81. [2] R. Orbach, Science 231 (1986) 814 (and references therein). [3] D.A. Parshin, Phys. Solid State 36 (1994) 991 (and references therein). [4] N.V. Surovtsev, A.P. Shebanin, M.A. Ramos, Phys. Rev. B 67 (2003) 024203. [5] N.V. Surovtsev, J. Wiedersich, A.E. Batalov, V.N. Novikov, M.A. Ramos, E. Rossler, J. Chem. Phys. 113 (2000) 5891. [6] E. Perez-Enciso, M.A. Ramos, S. Vieira, Phys. Rev. B 56 (1997) 32. [7] G.K. White, J.A. Birch, Phys. Chem. Glasses 6 (1965) 85. [8] F.C. Eversteijn, J.M. Stevels, H.I. Waterman, Phys. Chem. Glasses 1 (1960) 123. [9] R.J. Bell, A. Carnevale, Philos. Mag. B 43 (1981) 389; F.L. Galeener, G. Lucovsky, J.C. Mikkelsen Jr., Phys. Rev. B 22 (1980) 3983. [10] A.C. Hannon, D.I. Grimley, R.A. Hulme, A.C. Wright, R.N. Sinclair, J. Non-Cryst. Solids 177 (1994) 299. [11] J. Swenson, L. Borjesson, W.S. Howells, Phys. Rev. B 52 (1995) 9310. [12] M.A. Gonzalez, C. Mondelli, G. D’Angelo, C. Crupi, M.R. Johnson, J. Non-Cryst. Solids 354 (2008) 203. [13] P.J. Bray, J. Zhong, J. Non-Cryst. Solids 111 (1989) 67. [14] J.F. Stebbins, S.E. Ellsworth, J. Am. Ceram. Soc. 79 (1996) 2247; S. Sen, Z. Xu, J.F. Stebbins, J. Non-Cryst. Solids 226 (1998) 29. [15] J. Nicholas, S. Sinogeikin, J. Kieffer, J. Bass, Phys. Rev. Lett. 92 (2004) 215701. [16] S. Murugavel, B. Roling, Phys. Rev. B 76 (2007) 180202.
G. D’Angelo et al. / Materials Science and Engineering A 521–522 (2009) 263–267 [17] M.A. Ramos, J.A. Moreno, S. Vieira, C. Prieto, J.F. Fernandez, J. Non-Cryst. Solids 221 (1997) 170; M.A. Ramos, S. Vieira, C. Prieto, J.F. Fernandez, in: A.C. Wright, S.A. Feller, A.C. Hannon (Eds.), Borate Glasses, Crystals and Melts, The Society of Glass Technology, Sheffield, 1997, pp. 207–214.
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[18] J.T. Krause, C.R. Kurkjian, in: L.D. Pye, V.D. Fréchette, N.J. Kreidl (Eds.), Borate Glasses, vol. 12, Plenum Press, New York and London, 1978, pp. 577–585. [19] G. Carini, G. Carini, G. D’Angelo, G. Tripodo, A. Bartolotta, G. Salvato, Phys. Rev. B 72 (2005) 14201.
Contents lists available at ScienceDirect
Materials Science and Engineering A journal homepage: www.elsevier.com/locate/msea
Effects of thermal history on the acoustic attenuation of dry and wet B2 O3 glasses G. D’Angelo a,∗ , C. Crupi b , V. Conti Nibali a , M.A. Ramos c a
Dipartimento di Fisica, Università di Messina, Salita Sperone 31, S. Agata Messina 98166, Italy Istituto IPCF del CNR, sede di Messina, Salita Sperone, S. Agata Messina 98166, Italy c Departamento de Fısica de la Materia Condensada, C-III, Universidad Autonoma de Madrid, Cantoblanco, E-28049 Madrid, Spain b
a r t i c l e
i n f o
Article history: Accepted 2 October 2008 PACS: 61.40.Df 62.40 62.80.+f Keywords: Boron oxide glass Acoustic properties Low temperature relaxational dynamics
a b s t r a c t The acoustic properties at 10 and 30 MHz of dry and wet boron oxide samples have been investigated over the temperature range between 10 and 300 K. Significant differences in the temperature dependence of acoustic attenuation and longitudinal sound velocity as a function of the annealing treatment and water content have been revealed in the investigated glasses. Measurements, densely performed over the whole temperature range, together with a detailed analysis of the dispersive behaviors, allowed us to evidence the complexity of the relaxational dynamics, as due to the coexistence of different local motions. Above 150 K, the data analysis has been based on the existence of two relaxation processes, whose strengths result to be strictly dependent on the water content. Finally, a possible relation to the empty volume originated from the arrangement of the structural units on nanometer length scale has been put forward. © 2009 Elsevier B.V. All rights reserved.
1. Introduction In the last decades, a great deal of experimental and theoretical work has been devoted to understand anomalous behaviors of acoustic properties [1–3] observed at low temperatures in amorphous materials. More precisely, the attenuation and velocity of ultrasounds show surprising trends, not normally found in crystals, which have been ascribed to thermally activated structural relaxations at high temperatures (T > 10 K) and to tunnelling motions at low temperatures (T < 10 K). To better understand the origin and the microscopic nature of structural defects causing these anomalies, a useful expedient would be to study how acoustic properties of glasses depend on specific physical or chemical treatments of samples made up of the same chemical compounds. As regards this issue, in fact, it has been shown that the rate of cooling may influence the properties of a glass as well as an annealing process if it is carried out below the glass transition temperature [4–7]. Vitreous B2 O3 appears to be a very promising glass for achieving this goal since some of its basic properties [4–6] show remarkable changes upon different stabilization temperature and water content [8]. This is a very good glass former, covalently bonded, whose molecular structure is built up by planar BO3 triangles set-
∗ Corresponding author. E-mail address: [email protected] (G. D’Angelo). 0921-5093/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.msea.2008.10.076
tled in more elaborate symmetrical B3 O6 boroxol rings [9], the units being corner-linked by sharing common O atoms [10]. The arrangements of these structural units are not completely random, but show some correlations on the nanometer scale, as proved by neutron diffraction [11] and molecular dynamics studies [12]. Recently, structural investigations on B2 O3 samples subjected to different thermal histories have revealed no changes in the short range order [5]. This would suggest that the differences observed in the physical properties of these samples arise from undisclosed structural changes involving the medium range order. Structural modifications in boron oxide glass can arise from a progressive addition of water which induces a change in the boron coordination number from 3 to 4, as commonly observed when an alkali is added to the boron oxide [13]. The relative concentrations of BO3 and BO4 units depend strongly also on thermal history [14]. Glasses subjected to higher quenching rates contain fewer units based on four-coordinated boron atoms as compared to slowly cooled or annealed glasses. Recently, the change of the boron coordination number has been considered as the origin of the polymorphism experimentally observed in vitreous B2 O3 by applying elevated pressures [15,16]. The existence of vitreous polymorphs reveals a sort of structural instability of the systems, which can have important implication in explaining the phenomenology of the glassy state. This consideration sets the importance of studies devoted to the improving of knowledge of the relation existing between the microscopic structure and the physical properties of glasses.
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G. D’Angelo et al. / Materials Science and Engineering A 521–522 (2009) 263–267
Table 1 Basic parameters of D-1 and W-2 glasses: hydroxyl ion concentrations [17], mass–density [17], longitudinal velocity vl [5], glass transition temperature Tg [17], values of the parameters related to thermally activated relaxations (Em , NBl2 ). Sample
Thermal treatment
[OH− ] (mol%)
(kg/m3 )
vl (m/s)
Tg (K)
Em1 /kB (K)
Em2 /kB (K)
2 NBl1 (10−13 J2 m−3 )
2 NBl2 (10−13 J2 m−3 )
D-1 W-2
As quenched 490 K, 100 h
0.27 5.8
1804 1866
3093 3355
570 537
3171 3169
1802 1835
0.26 6.01
5.76 1.45
In this work we have focused our attention on two different samples of glassy B2 O3 with the aim to study the influence of an annealing process and of water content on the attenuation and the propagation of ultrasonic waves. 2. Experimental details Two boron oxide samples (cf. Table 1), respectively named as dry (D-1) and wet (W-2) glasses, have been prepared by melting boron oxide pellets (Aldrich, 99.999% purity) in a platinum crucible, following different methods in order to obtain samples with (W-2) and without (D-1) a significant concentration of hydroxyl ions OH− . More precisely the dry sample was prepared by heating the material slowly up to 1050 ◦ C until bubbling has ceased after about 20 h. Then, the material was cooled and the process repeated in vacuum. The final step was to keep the melt at 1050 ◦ C for 24 h, and rapidly pouring the melt into the brass mould. The wet sample was prepared by heating the material at 300 ◦ C in air for 2 h, melting by heating up to 800 ◦ C also in air, holding for 4 h, and pouring into a brass mould. Finally the glass has been subjected to an annealing treatment of 100 h at a temperature of 490 K, near its glass transition temperature (Tg = 537 K). D-1 and W-2 glasses contain the 0.27% and the 5.8% of water content, respectively, as determined by infrared spectroscopy [17]. The mass–density of B2 O3 samples have been measured at room temperature [17] with an estimated experimental error of about ±0.003 g/cm3 . The main data characterizing these glasses are presented in Table 1. The attenuation and velocity of longitudinal ultrasound waves have been measured at frequencies of 10 and 30 MHz using a conventional pulse-echo ultrasonic technique. The thermal scanning was carried out in the temperature range from 10 to 300 K operating on a helium cryogenerator with a thermostatic control of about 0.1 K. The bonding agent between sample and transducer (a 10 MHz quartz) was N-Apiezon grease.
enhanced intensity and shifts to higher temperatures as the frequency of the ultrasonic probe is increased, revealing a thermally activated nature of the underlying relaxation process. No trace of the high temperature peak observed in the wet glass is visible. The most surprising experimental evidence in the dry sample is the very extensive width of the revealed peak, hardly ascribable only to the randomness of the glassy structure. It seems more reasonable the hypothesis that different relaxation processes are working in this temperature range, with distinct but close activation energies, the broad peak experimentally observed being the outcome of overlapping losses. More clearly, the existence of different relaxations can be envisaged in the loss curve at 10 MHz, where a shoulder at about 150 K in addition to a peak at 50 K can be recognized. Moreover a third peak seems to emerge at higher temperatures, in the same interval of the high temperature peak revealed in the wet sample. By increasing frequency the intensity of each individual relaxation enhances, making difficult the possibility to discriminate the different contributions. The assumption of the existence in B2 O3 glass of at least two structural relaxations at low temperatures supplies a possible explanation also for the unexpected finding in the wet glass of a loss peak (the peak revealed at 50 K) shifted backwards by increasing frequency. This anomalous behavior can be believed as the result of combined effect of the increasing intensity and different activation energies that determine dissimilar temperature shift by increasing frequency.
3. Experimental results and discussion The temperature dependences of the ultrasonic attenuations ˛(T) of W-2 and D-1 glasses at frequencies of 10 and 30 MHz are plotted in Fig. 1(a) and (b), respectively. In the wet sample, a bump, typical of oxide glasses, is observed at temperatures below 100 K whose temperature position appears to shift toward lower values by increasing ultrasonic frequency. At higher temperatures the acoustic attenuation increases showing in the curve at 10 MHz a second peak at about 270 K. In the same temperature region (T > 150 K) we observe a fast increase of ˛(T) in the curve at 30 MHz, with an intensity about three times greater than the value at 10 MHz. Both these observations lead us to suppose that the upturn in ˛(T) is indicative of the existence of a peak centered at higher temperature. This peak should arise from the same loss mechanism observed at about 270 K in the 10 MHz curve; the increase of the intensity and the shift in temperature observed at 30 MHz being indicative of its thermally activated nature. The decreased content of water in the dry sample clearly gives rise to significant differences in the acoustic attenuation behavior and in its intensity. As a matter of fact a very broad peak, spread out over the whole investigated temperature range, is shown in ˛(T) curve of the D-1 glass (see Fig. 1(b)). This bump exhibits an
Fig. 1. Acoustic attenuation vs. temperature of: (a) W-2 boron oxide glass at 10 () and 30 MHz (); (b) D-1 boron oxide glass at 10 (䊉) and 30 MHz ().
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Fig. 3. Internal friction of W-2 boron oxide glass () and D-1 boron oxide glass (䊉) as a function of temperature. The solid lines represent the fit to experimental data obtained by supposing two relaxation peaks (indicated by arrows) for each sample.
Fig. 2. (a) The temperature dependence of longitudinal sound velocity (♦) and acoustic attenuation at 10 MHz () of W-2 boron oxide glass; (b) the temperature dependence of longitudinal sound velocity () and acoustic attenuation at 10 MHz (䊉) of D-1 boron oxide glass.
However, further investigations at different frequencies and temperatures are needed to solve this obscure point. By pursuing the aim to resolve better the supposed multiple relaxations, measurements of longitudinal velocity at 10 MHz have been performed as a function of temperature. In Fig. 2(a) and (b) the temperature dependences of the 10 MHz longitudinal sound velocity, vl (T ), of D-1 and W-2 glasses are shown. In the same figures the acoustic attenuation curves at the same frequency are also reported in order to have a comparison between the temperature positions of the contributions observed in both sound velocity and attenuation. Firstly, it has to be considered that the presence of a higher number of OH− hydroxyls in the wet sample induces a great number of tetrahedral boron atoms [13] which increases the connectivity and the rigidity of this glass, as monitored by the higher value of the sound velocity with respect to the dry sample. It is evident that in the wet glass the longitudinal velocity decreases quite linearly with temperature in the whole investigated range (see Fig. 2(a)), although clear signs of dispersion (inflexion points marked by arrows in Fig. 2(a)) are visible around 50, 80, and 275 K. We can observe that the dispersions at 50 and 80 K correspond, in the loss curve below 150 K, to a peak followed by a shoulder, while the dispersion at 275 K is associated to the high temperature loss peak ascribed to the relaxation of OH− hydroxyls [18]. It has to be remarked that ill-defined dispersions can be envisaged around 175 and 250 K. The temperature dependence of velocity in the dry sample shows an alternation of linear behaviors with changing slope and inflexion points particularly evident at about 125, 175 and 250 K (see arrows in Fig. 2(b)). These dispersions indicate the existence of relaxations in a temperature region where the acoustic attenuation displays a visible asymmetric broadening of the high temperature
tail of the loss peak, showing the complexity of the structural relaxations in this glass. The thorough analysis of dispersions in the velocity curves shows that in both dry and wet samples the same relaxation processes are active, although with strengths strongly dependent on the water content. Considering the role of water in determining the main characteristics of structural relaxations in boron oxide glasses, the following analysis will be focused on the acoustic behavior above 150 K, where the high water content of the wet glass results in a high temperature peak, well suitable for an unquestionable investigation. With the aim of directly comparing the sound attenuation of D-1 and W-2 glasses, the temperature dependences of internal friction Q−1 (= 2˛v/ω, where v is the sound velocity and ω is the ultrasonic angular frequency) at 10 MHz are reported in Fig. 3. The internal friction value measured at the lowest temperature in the experiment has been assumed to arise mainly from parasitic (static) dissipative mechanisms and has been subtracted from the experimental data. A quantitative analysis has been performed on the internal friction data for both samples, at temperatures higher than 150 K, by supposing the existence of two loss peaks ˛1 and ˛2 , both arising from a thermally activated relaxation: Q −1 =
2v (˛1 + ˛2 ) ω
(1)
In Eq. (1), ˛1 accounts for the loss peak observed at 300 K, clearly visible in the wet glass. It is believed that this relaxation process comes from local motions of hydroxyl groups, largely present in W-2 sample but barely in the dry glass. The second loss peak ˛2 has been included to account for the significant loss observed in this temperature region in the dry glass, which is related to the relaxation process contributing to the sound velocity dispersion at 175 K. It is supposed that this relaxation process arises from intrinsic structural defects, sensitive to the water presence too. For ˛1 and ˛2 separately, the following equation has been used [19]: ˛=
Bl2
P(E)
4v3l kB T
ω2 (E) dE 1 + ω2 2 (E)
(2)
In Eq. (2), Bl is the deformation potential that refers to the coupling between the ultrasonic longitudinal stress and the system, T the absolute temperature, kB the Boltzmann constant, P(E) is a distribution function of activation energy E and is the relaxation time, that is related to the activation energy E of the process and to the frequency factor 0−1 by an Arrhenius-type equation:
−1 = 0−1 exp −
E kB T
(3)
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Taking into account the topological disorder of glassy materials, it is quite reasonable assuming P(E) as a Gaussian distribution: N
P(E) = √ exp ( 2)E0
−
(E − Em )2 2E02
,
(4)
N being the total number of relaxing particles per unit volume, Em and E0 are the most probable value and the width of the distribution, respectively. From the data analysis, the values of Em , E0 , NBl2 , and were obtained by least-squares fits of the results using a Minuit minimum search program. The theoretical internal friction curves together with their distinct components for both the samples are shown in Fig. 3 as solid and dashed lines, respectively. The values of the parameters Em and NBl2 are reported in Table 1, while the width of distribution Eo /kB and the characteristic frequency −1 −1 o−1 are: Eo1 /kB = 411 K, o1 = 4.5 × 1013 s−1 , Eo2 /kB = 400 K, o2 = −1 0.2 × 1013 s−1 (W-2 glass); Eo1 /kB = 480 K, o1 = 0.7 × 1013 s−1 ,
−1 Eo2 /kB = 550 K, o2 = 0.7 × 1013 s−1 (D-1 glass). It has to be observed that the use of two distinct relaxations lets to get a very good fit of the experimental data in both samples. More importantly, the mean activation energies Em1 ad Em2 are exactly the same in the wet and dry glasses, suggesting that the local arrangements of the relaxing particles are not greatly influenced by water addition. Moreover the value of Em1 agrees exactly with the activation energy of 26.4 kJ/mol previously derived by Krause and 2 and N B2 for Kurkjian [18]. In addition to this, the products N1 Bl1 2 l2 each of investigated glasses change in direct and inverse relation to the amount of OH− groups, respectively, revealing that both relaxations strictly depend on water content. This findings support the hypothesis that the defects originating ˛1 and ˛2 are the same in the W-2 and D-1 glasses. 2 values obtained in the present glasses and the By using the N1 Bl1 value of 0.21 eV for the deformation potential Bl [19], we deduce a value of 5.3 × 1020 cm−3 and 2.3 × 1019 cm−3 for the number N1 of relaxing particles in W-2 and D-1 glasses. These values are in good agreement with the number of OH− impurities estimated from infrared measurements (see Table 1) and equal to 9.36 × 1020 cm−3 (W-2 glass) and 4.21 × 1019 cm−3 (D-1 glass). Otherwise, the attribution of this first attenuation peak to relaxation modes of hydroxyl ions is once more supported by calculations on the decrement of its intensity by going from W-2 to D-1 sample. By the best fit values of ˛1 intensity for the two glasses a reduction of 96% has been estimated in perfect agreement with the decrease of 95% of water content between the wet and dry boron oxide glass. Unlikely, the attribution of a definite microscopic origin of the relaxing centres giving rise to the second attenuation peak ˛2 requires further analysis in the sight of the really complex behaviors shown by the acoustic attenuation curves of both systems. However, we can put forward a hypothesis referring to known structural changes occurring in pure borate glass because of the addition of water. In this regard, the strong decrease of ˛2 intensity from dry to wet sample can be explained by assuming a direct relation to the decrease of three coordinated boron atoms following the addition of water. It is plausible to associate the ˛2 peak of D-1 sample to local motion of structural units containing BO3 groups. Otherwise, in the W-2 glass, the presence of water content causes the transformation of BO3 planar units in tetrahedral BO4 groups with a consequent decreased number of the associated relaxation modes. We believe that the complexity of the relaxations we have observed below room temperature in B2 O3 glass has an intrinsic structural origin. BO3 triangles, on which B2 O3 structure is based, are expected to have a great freedom of movement to arrange by bending, taking advantage of the empty space inside the network.
It is supposed that in the dry sample, not subjected to annealing treatment, a variety of arrangements between the BO3 triangles on nanometer scale are possible during the quenching of melt, giving rise to voids of different sizes. The structural units overlooking these voids are likely responsible for local motions originating the observed relaxations. Each significant difference in the size of these voids corresponds to observable changes in the activation energy for the same local motion. This would explain the multiplicity of relaxations active over the same temperature range. The annealing treatment and the increase of connectivity (due to the presence of four-coordinated boron atoms) lead to a reduction of the free volume, precluding some structural relaxations. The acoustic loss curve below room temperature is consequently changed as concerning its shape and intensity. It has been observed that the reduction of internal volume is testified by the increase of mass density, equal to 3.4% in the W-2 sample (see Table 1). Further investigations in B2 O3 samples subjected to different thermal histories are in progress in order to confirm these suggestive suppositions for the origin of structural relaxations in boron oxide glass. 4. Conclusion Low temperature ultrasonic measurements have been carried out on dry and wet boron oxide samples. The temperature dependences of acoustic attenuation and sound velocity as a function of the annealing process and water content have revealed significant differences in these glasses. In the wet glass it has been observed a big loss peak around room temperature ascribed to thermally activated relaxation process of hydroxyl ions. In the dry sample it has been observed a large and wide peak, spreading over the whole investigated temperature range, which arises from the overlap of different relaxation processes. A quantitative analysis of the internal friction curves above 150 K has revealed that the relaxation processes working in this temperature region have the same origin in both dry and wet glasses and are strictly depend on the water content. It is supposed that, in the dry glass, a variety of arrangements between the BO3 triangles on nanometer scale are possible during the quenching of melt, giving rise to voids of different sizes. Assisted by temperature, groups of atoms lying in these empty spaces are supposed to be able of relaxing with less constraints than in the wet sample giving rise to a more complex acoustic spectrum. References [1] S. Hunklinger, M.v. Schickfus, in: W.A. Phillips (Ed.), Amorphous Solids: Lowtemperature Properties, Springer, Berlin, 1981, p. 81. [2] R. Orbach, Science 231 (1986) 814 (and references therein). [3] D.A. Parshin, Phys. Solid State 36 (1994) 991 (and references therein). [4] N.V. Surovtsev, A.P. Shebanin, M.A. Ramos, Phys. Rev. B 67 (2003) 024203. [5] N.V. Surovtsev, J. Wiedersich, A.E. Batalov, V.N. Novikov, M.A. Ramos, E. Rossler, J. Chem. Phys. 113 (2000) 5891. [6] E. Perez-Enciso, M.A. Ramos, S. Vieira, Phys. Rev. B 56 (1997) 32. [7] G.K. White, J.A. Birch, Phys. Chem. Glasses 6 (1965) 85. [8] F.C. Eversteijn, J.M. Stevels, H.I. Waterman, Phys. Chem. Glasses 1 (1960) 123. [9] R.J. Bell, A. Carnevale, Philos. Mag. B 43 (1981) 389; F.L. Galeener, G. Lucovsky, J.C. Mikkelsen Jr., Phys. Rev. B 22 (1980) 3983. [10] A.C. Hannon, D.I. Grimley, R.A. Hulme, A.C. Wright, R.N. Sinclair, J. Non-Cryst. Solids 177 (1994) 299. [11] J. Swenson, L. Borjesson, W.S. Howells, Phys. Rev. B 52 (1995) 9310. [12] M.A. Gonzalez, C. Mondelli, G. D’Angelo, C. Crupi, M.R. Johnson, J. Non-Cryst. Solids 354 (2008) 203. [13] P.J. Bray, J. Zhong, J. Non-Cryst. Solids 111 (1989) 67. [14] J.F. Stebbins, S.E. Ellsworth, J. Am. Ceram. Soc. 79 (1996) 2247; S. Sen, Z. Xu, J.F. Stebbins, J. Non-Cryst. Solids 226 (1998) 29. [15] J. Nicholas, S. Sinogeikin, J. Kieffer, J. Bass, Phys. Rev. Lett. 92 (2004) 215701. [16] S. Murugavel, B. Roling, Phys. Rev. B 76 (2007) 180202.
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