Kinetic fragility of hydrous soda-lime-silica glasses

Kinetic fragility of hydrous soda-lime-silica glasses

Journal of Non-Crystalline Solids 354 (2008) 4713–4718 Contents lists available at ScienceDirect Journal of Non-Crystalline Solids journal homepage:...

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Journal of Non-Crystalline Solids 354 (2008) 4713–4718

Contents lists available at ScienceDirect

Journal of Non-Crystalline Solids journal homepage: www.elsevier.com/locate/jnoncrysol

Kinetic fragility of hydrous soda-lime-silica glasses J. Deubener a,*, H. Behrens b, R. Müller c, S. Zietka a, S. Reinsch c a b c

Institute of Non-Metallic Materials, Clausthal University of Technology, Germany Institute of Mineralogy, University of Hannover, Germany Federal Institute for Materials Research and Testing (BAM), Berlin, Germany

a r t i c l e

i n f o

Article history: Available online 26 August 2008 PACS: 66.20.Ej 83.80.Ab 64.70.ph . Keywords: Soda-lime-silica Fragility Viscosity Water in glass .

a b s t r a c t The effect of hydration on the kinetic fragility of soda-lime-silica glasses was investigated by viscometry in the glass transition range. Water-bearing glasses were prepared from industrial float glass (FG) and a ternary model glass (NCS = 16Na2O 10CaO 74SiO2 in mol%) by bubbling steam through the melt at 1480 °C and up to 7 bar. Additionally, a sodium borosilicate glass (NBS = 16Na2O 10B2O3 74SiO2 in mol%) was hydrated under equal conditions. As detected by infrared spectroscopy water dissolves in the glasses exclusively as OH-groups. The hydration resulted in a total water content CW up to  0.2 wt% for FG, NCS and NBS glasses. Kinetic fragility, expressed by the steepness index m, was determined from the temperature dependence of g at the glass transition. Viscosity data from previous studies on hydrous float glasses (CW > 1 wt%) were surveyed together with literature data on the (H2O)–Na2O– CaO–SiO2, (H2O)–Na2O–SiO2 and (H2O)–SiO2 systems to expand the range of water concentration and bulk composition. We could demonstrate that m decreases for all glasses although water is dissolved as OH and should depolymerize the network. An empirical equation of the general type m = a  b logCW where a, b are fitting parameters, enables m to be predicted, for each glass series as function of the water content CW. The enlarged data base shows that the parameter B of the Arrhenius viscosity-temperature relation decreases much stronger than the isokom temperature at the glass transition. Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction Water is an important minor component in industrial sodalime-silica melts. It changes the physical properties; particularly it decreases the Newtonian viscosity. The water content ranges between 0.03 and 0.04 wt% in conventionally fired glass, with electrical melting it decreases to 0.015–0.02 wt%, with oxy-combustion it increases to 0.05–0.06 wt% [1]. Thus, significant water-related viscosity variations are expected to take place if melting atmosphere or the redox conditions are significantly changed during glass production and forming. IR-spectroscopy reveals that water is dissolved predominantly as OH groups at concentrations up to 0.25 wt% [2]. In silicate glasses exceeding this water content both hydroxyl groups and molecular water diminishes the flow resistance. However, this influence of OH on viscosity is three- to sixtimes stronger than that of molecular water [3,4]. While a dependence of the viscosity and glass transition temperature on water content has been studied by several authors for synthetic [3–8] and natural melt [9–15] compositions, the water impact on fragility is less well established. Kinetic fragility, however, is of special

* Corresponding author. Tel.: +49 5323 72 2463; fax: +49 5323 72 3710. E-mail address: [email protected] (J. Deubener). 0022-3093/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jnoncrysol.2008.04.021

importance for glass technologists, since it resembles the classification of workability as ‘long’ and ‘short’ glasses used traditionally by glass markers in Europe. Kinetic fragility has been studied for a broad variety of anhydrous inorganic and organic liquids [16–19]. Non-Arrhenian viscosity vs. temperature behaviour is revealed if the temperature axis is scaled by Tg as proposed by Angell [20]. Details of this approach are discussed elsewhere [20–22]. From Angell’s plot it is apparent, that the viscosity data of anhydrous soda-lime-silica glasses fall between two extremes referred to ‘strong’ (tetrahedral network such as SiO2 and GeO2) and ‘fragile’ (e.g. nitrate melt). Kinetic fragility of an organic and inorganic liquid can be expressed by the steepness index m at glass transition [22]

dðlog gÞ m¼   T d Tg

;

ð1Þ

T¼T g

where g is the Newtonian shear viscosity and Tg the glass transition temperature. Conventionally for inorganic glasses, the Vogel–Fulcher–Tammann (VFT) relation is used to describe the temperature dependence of g:

log g ¼ A þ

B ; T  T0

ð2Þ

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where A, B, and T0 are the VFT parameters with g and B, T0 being in units of Pa s and K, respectively. If one defines the glass transition temperature at the isokom temperature T12 for which the Newtonian viscosity is 1012 Pa s (T12 = Tg) and utilises Eqs. (1), (2) m equals [23]





B

T 12 1  TT120

ð3Þ

2 :

However, if viscosity data are limited to a narrow temperature range at the glass transition, Newtonian viscosity g can be described in first approximation by an Arrhenius equation (T0 = 0 in Eq. (2)) of the form:

B log g ¼ A þ : T

ð4Þ

When using Arrhenius Eq. (4) at the glass transition range the steepness index can be expressed as



B ¼ 12  A: T 12

ð5Þ

In the case of industrial glass melt compositions previous studies on fragility are restricted to anhydrous melts. To our knowledge, solely Del Gaudio et al. [4] investigated m as a function of CW of hydrated float glasses using in situ high pressure viscometry. Generally, one would aspect that m increases with increasing water content, if water depolymerises the melt network. However, Del Gaudio et al. [4] did not found any variation of m for float glass in the range of water contents of 0–5 wt% with concentrations of H2O molecules and OH groups up to 3.5 wt.% and 1.5 wt%, respectively. The apparent discrepancy is due to the relatively low concentration of OH groups in the glass, increasing the number of non-bridging oxygen per tetrahedral cation (NBO/T) from 0.77 to 0.91. It was shown that m depends non-linearly on NBO/T. While m is increasing strongly for NBO/ T < 0.5 the dependence flattens for NBO/T > 1 [17]. Thus, the relative large scatter of the presented data in Ref. [4] could have masked the effect of increasing OH groups on kinetic fragility. The aim of the present study is therefore to (1) revisit the float glass system using viscometry at ambient pressure in the concentration range where molecular water is not yet present (CW < 1 wt%) and (2) to expand the range of m data on other melt compositions (sodium borosilicate and silica glasses). This is accomplished also by surveying literature data on the temperature dependence of the Newtonian viscosity at the glass transition range. 2. Experiments 2.1. Glass preparation As starting materials commercial glass beads (FG = 72.5SiO2, 13.7Na2O, 9.8CaO, 3.3MgO, 0.4Al2O3, 0.2FeO + Fe2O3, 0.1K2O in

wt%, from Potters-Ballotini) and cullets of two ternary model glasses (NCS = 16Na2O 10CaO 74SiO2 and NBS = 16Na2O 10B2O3 74SiO2 in mol%) were used. Dry glasses were re-melted in a pressure vessel by bubbling compressed steam through the melt at 1450 °C under various pressures (1–7 bar) for different durations (0.5–3 h). For doing so, anhydrous glasses were poured in a 350 mL Pt/Rh crucible. The covered crucible was inserted into the pressure vessel and connected with an alumina capillary tube of a high-pressure water pump. The pump provided a somewhat higher water pressure than the internal gas pressure of the vessel (adjusted by argon) to allow vapour bubbles ascending in the melt. After the hydration time the glasses were cooled under pressure to room temperature. From the dry and hydrated glasses cylinders for parallel plate viscometry were cored out of the crucibles to fit sizes 6  6 (height  diameter in mm). Coplanar surfaces were prepared by grinding and polishing of the cylinder faces. 2.2. Water analysis IR absorption spectra of doubly polished sections were recorded with an FTIR spectrometer Bruker IFS88. For this purpose residual parts of the drilled cylinders were used and polished to thin slices of approx. 0.7 mm thickness. Bulk spectra were measured in the mid-infrared (spectral range of 500–4000 cm1) while mounting samples on a hole aperture 4 mm in diameter. Measurement conditions for the mid-infrared were: globar light source, KBr beamsplitter, DTGS detector, spectral resolution of 2 cm1. The peak height of the fundamental OH stretching vibration at 2850 cm1 (FG glass), 3550 cm1 and 2800 cm1 (NCS glass), and 3590 cm1 (NBS) was used for total water determination. The results of the spectroscopic investigations are summarised in Table 1. 2.3. Viscometry Creep experiments were performed under constant load using a vertical dilatometer (Bähr VIS 404). Cylindrical glass samples were compressed in axial direction under isothermal conditions. The sample was heated by a vertical tube furnace mounted on a support frame consisting of two half shells to open the furnace for sample loading and unloading. The glass sample was placed between the top and bottom plates (silica glass discs 8 mm in diameter and 1 mm thick). A heating rate of 5 K/min was chosen in all experiments to reach the desired temperature. After a dwell time for allowing structural relaxation the load to the sample was adjusted by placing various static weights (corresponding to F = 0.01–10 N) on top of the probe rod. Sample compression was monitored continuously by a vertical, counter-weighted, silica glass probe rod and overhead LVDT assembly. The viscosity g is cal-

Table 1 Spectroscopic data Sample FG1 FG2 FG3 FG4 NCS1 NCS2 NCS3 NBS1 NBS2

A3590

0.148 1.710

A3550

A2850

Thickness (cm)

Density (g/L)

Cw (wt%)

0.0544 0.5133 0.8445

0.131 0.294 0.695 0.771 0.0961 0.6084 1.1054

0.0765 0.0790 0.0754 0.0731 0.0788 0.0726 0.0752 0.0779 0.0803

2505 2504 2503 2502 2505 2503 2502 2455 2464

0.0307 0.0665 0.1650 0.1890 0.0130 0.1130 0.1862 0.0253 0.2821

Notes: Linear molar absorption coefficients of 40.2 L mol1 cm1 for the band at 2850 cm1 and was used to calculate water concentration from the absorbance A (peak height) for FG glass [34]. For the NCS glasses the two band model using the molar absorption coefficients of 70 L mol1 cm1 for the band at 3550 cm1 and 150 L mol1 cm1 for the band at 2800 cm1 (background correction at 4250 cm1).For the NBS glasses a molar absorption coefficient of 55.2 L mol1 cm1 for the band at 3590 cm1was used (background correction at 4000 cm1) [35].Absorption coefficients always refer to mol H2O in this paper. Densities of NBS were measured using Archimedes buoyancy in water (Behrens, unpublished data). Density of FG and NCS were calculated using the relation q = 2505  14.6CW (see Ref. [34]).

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culated by measuring the rate of deformation of the cylindrical height [24]:



Fh0 ; ln h 3V d dt

ð6Þ

where F is the applied load, V is the cylinder volume, and h is the actual and h0 is the initial height of the cylinder. The experiments were carried out in the temperature range from 533 to 670 °C, controlling the temperature to within ±1 K. However, the maximum error on the temperature is ±5 K due to the accuracy of the thermal elements and measurement equipment. The system was calibrated by the standard glass G1 of the Physikalisch-Technische Bundesanstalt (PTB) [25]. The error in viscosity is ±0.1 log units. 3. Results The Newtonian viscosity was determined in the range from 1012.2 to 107.5 Pa s (Table 2). The temperature dependence was analysed for each glass series using an Arrhenian relation (see Eq. (4)). The small number of samples within the narrow temperature range does not allow evaluating a possible non-linear variation of log viscosity in such plots (Figs. 1–3). The values of A and B determined by linear regression for the dry and hydrated glasses are summarised together with the calculated steepness index m of

Eq. (5) and the isokom temperature T12 for which the Newtonian viscosity is 1012 Pa s (T12 ffi Tg) in Table 3. For the hydrated glasses FG3, FG4, NCS2, NCS3 and NBS2 the viscosity was measured only up to 1011 Pa s. For these glasses it is assumed that the determined Arrhenian dependence is also valid at the calculated glass transition temperature. 4. Discussion To reveal a possible dependence of the kinetic fragility on the water content of the FG; NCS, and NBS glasses, B is plotted vs. T12 (Fig. 4). Also, to visualise this relation for an enlarged data basis of hydrous melts, literature data of the Newtonian viscosity in the systems (H2O)–Na2O–CaO–SiO2 [8], (H2O)–Na2O–SiO2 [7], and (H2O)–SiO2 [5,26] were evaluated (Table 4) and plotted in Fig. 4. According to Eq. (5) a straight line through the origin indicates constant fragility. Though a linear dependence is evident for all glass series, extrapolated straight lines through the data do not intersect the origin. Accordingly, fragility is a function of the water content. In contrast the data of Ref. [5] for hydrous silica glass intersect the origin for B/T12  15. Using characteristic values for the relaxation time at T12 = 102 s and for the atomic attempt frequency kT/h = 1013 s1 for silicate glasses, a theoretical lower fragility limit mmin = 15 has been calculated, which corresponds to a theoretical

Table 2 Newtonian viscosity of dry and hydrated FG, NCS and NBS glasses T (°C)

log g (g in Pa s) FG 1

533 545 545 550 550 560 560 560 561 569 570 571 571 577 577 578 580 588 589 590 591 598 598 599 600 603 610 624 625 630 630 637 638 649 650 651 653 660 670 689

NCS 2

3

4

1

NBS 2

3

11.00

11.00 10.47 10.47

12.20 12.19 11.65

10.80

10.46 10.42 10.32 10.26

1

2

11.25 10.95

10.27 9.99

10.67

10.54 10.23 10.20 10.17

11.52

10.78

11.45

9.93

10.20 10.17 10.16 10.87

10.77 11.75 11.57

10.48 10.28

9.55

10.21 10.08 11.18 10.33 10.21

9.47

9.35

10.11 9.69

8.35 9.99

9.43

8.32 8.46

7.88 7.84 9.64 9.58 7.61

8.25

7.86 7.8

8.33 7.82

8.36

8.71 7.80 7.51

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12

log Newton viscosity η (η in Pa s)

log Newton viscosity η (η in Pa s)

12

11

10

9

FG1 FG2 FG3

8

11

10

9

NBS1

8

NBS2

FG4 1.05

1.10

1.15

1.20

1.05

1.25

1.10

1.20

1.25

-1

1000/T (K ) Fig. 1. Logarithm of the Newtonian viscosity vs. reciprocal temperature for anhydrous and hydrated float glasses FG.

Fig. 3. Logarithm of the Newtonian viscosity vs. reciprocal temperature for anhydrous and hydrated sodium borosilicate glasses NBS.

Table 3 Arrhenius parameters A and B of Eq. (4) (by linear regression analysis), calculated isokom temperature T12, and steepness index m (Eq. (5)) of FG, NCS and NBS glasses

12

log Newton viscosity η (η in Pa s)

1.15

1000/T (K )

-1

11

10

Glass

A

B (K)

T12 (K)

m

FG1 FG2 FG3 FG4 NCS1 NCS2 NCS3 NBS1 NBS2

21.5 ± 0.8 22.4 ± 1.2 19.7 ± 0.4 17.4 ± 1.1 23.0 ± 0.9 18.6 ± 1.5 17.8 ± 0.9 27.9 ± 1.0 20.7 ± 1.1

27769 ± 627 28320 ± 992 25412 ± 313 23375 ± 888 28885 ± 679 24175 ± 1149 23147 ± 679 34052 ± 886 26061 ± 889

830 823 802 794 826 789 777 854 797

33.5 34.4 31.7 29.4 35.0 30.6 29.8 39.9 32.7

9 NCS1

40000

NCS2

8

sodium trisilicate 35000 Ref. 7

NCS3 1.05

1.10

1.15

1.20

SiO2 Ref. 5 NBS NCS FG this work

1.25

-1

1000/T (K )

value of A ffi 3 (for g in units of Pa s) in Eq. (5) [21] which intersects the origin (out of display range). However, from an inspection of the viscosity temperature dependence of 38 anhydrous oxide glasses an average value of A = 5.1 ± 2.0 was calculated [19]. The most striking effect is, that contrary to the expected trend, fragility decreases if the water content is increased (Fig. 5). The dependence of m on the water concentration can be approximated by an apparent straight line of the general type m = a  b  logCW where a, b are fitting parameters (Table 5). It should be noted, that this trend is only valid within the investigated range of CW, where water is present as OH. Water speciation in silicate glasses is highly dependent on glass composition and quenching rate, i.e. fictive temperature. Dissolution of OH in the glass network is limited to 1.5 wt% for FG [27], 2.0 wt% for NCS [27], and  3.5 wt% for so-

SiO2 Ref. 26

B (K)

Fig. 2. Logarithm of the Newtonian viscosity vs. reciprocal temperature for anhydrous and hydrated soda-lime-silica glasses NCS.

30000

25000

NCS Ref. 8 20000

15000

mmin = 15 10000 600

800

1000

1200

1400

1600

T12 (K) Fig. 4. Arrhenian parameter B vs. isokom temperature T12. The dashed line corresponds to the lower fragility limit mmin = 15 as proposed in Ref. [21] which intersects the origin (out of display range). The narrow dashed lines through the data series are intended only as guide for the eyes.

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J. Deubener et al. / Journal of Non-Crystalline Solids 354 (2008) 4713–4718 Table 4 Water content CW, viscosity range and calculated parameters T12 and m (Eq. (5)) of glasses in the systems (H2O)–Na2O–CaO–SiO2 [8], (H2O)–Na2O–SiO2 [7] and (H2O)– SiO2 [5,26] CW (wt%)

Range of logg (g in Pa s)

15Na2O, 2K2O, 0.012 0.029 0.032 0.050 0.085

3MgO, 6CaO, 2Al2O3, 1B2O3, 71SiO2 in wt% 11.30–7.95 25485 10.97–7.68 25030 10.84–7.71 23810 10.63–7.61 22974 10.33–7.33 22822

B (K)

T12 (K)

m

Ref.

804 795 790 783 775

31.7 31.5 30.1 29.3 29.4

[8] [8] [8] [8] [8]

25.59 Na2O, 74.41SiO2 in wt% 0.0033 12.8–10.2 0.0051 12–11 0.0057 12–11 0.0070 12–11 0.0110 12–11 0.0131 12.5–10.0 0.0183 12–11 0.0242 12–11 0.0263 12–11 0.0550 12.5–9.9

35837 33870 31248 32996 34089 31467 31904 31467 27970 27314

749 748 748 748 748 742 744 742 738 729

47.8 45.3 41.8 44.1 45.6 42.4 42.9 42.4 37.9 37.5

[7] [7] [7] [7] [7] [7] [7] [7] [7] [7]

100 SiO2 in wt% 0.0003 13.5–9.0 0.027 12.5–8.6 0.04 12.5–8.6 0.12 12.0–8.3 0.0535 13.03–12.22 0.0696 12.89–12.02 1.00 13.85–13.29

37300 33800 28600 26700 20891 22928 16399

1463 1432 1382 1355 1496 1475 1030

25.5 23.6 20.7 19.7 14.0 15.5 15.9

[5] [5] [5] [5] [26] [26] [26]

50 FG, this work NCS, this work NBS, this work NCS, Ref. 8 NS, Ref. 7 S, Ref. 5 S, Ref. 26

steepness index m

40

dium trisilicate [28]. To our knowledge a lack of comprehensive data is evident for silica glasses. Utilising the spectroscopic data reported in Ref. [26], we assume a maximum concentration of OH  1.5 wt% in silica glass. For concentrations exceeding these limits excess water is dissolved exclusively as water molecules. However, spectroscopy reveals that dissolution of water as molecules starts already in hydrous FG and NCS glasses at CW  0.5 wt% [27]. The influence of water molecules on the kinetic fragility is anticipated to be only weak. Thus, the lines through the data in Fig. 4 will merge in straight lines through the origin, reflecting constant m for water rich glasses containing H2O molecules. To support this assumption, m of FG is compared with data of waterrich float glasses from a previous study (Fig. 6). Despite the large scatter of the high pressure data, a deviation from the apparent linear decrease is evident for glasses with CW > 0.5 wt%. It should be noted that the viscosity data of water rich float glasses of Ref. [4] were determined by high pressure viscometry, i.e. a parallel plate viscometer operating in an internally heated pressure vessel (IHPV) at pressures up to 400 MPa. Viscosity determined by the IHPV viscometer is of larger uncertainty (for details see [4,29]) than the viscosity data determined in this study using an ambient pressure viscometer. At ambient pressure, water escape from the hydrated samples may change viscosity during measurement. However, viscosity was found to be independent on measuring time. Repeating measurement of the same cylinder resulted in the same viscosity (within the uncertainty of 0.1 log units). Thus, effects based on possible water release were neglected. Previous indentation studies support this conclusion [10,16,30–32]. Those authors measured the homogeneity and stability of dissolved water in hydrous alumosilicate glasses by FTIR spectroscopy before and after micro-penetration viscometry at 1012–108.5 Pa s and did not observe any detectable water loss. In any case one should be aware that the displayed dependencies of fragility on water content may be affected by other impurities and components (nominally NBO/T is calculated as zero for the anhydrous silica glass). This is crucial especially for silica glasses with low total water content, see for instance the review by Mysen and Richet for further details [33]. Interaction of water (as proton)

30

50

10 1E-4

1E-3

0.01

0.1

1

10

water content CW (wt%) Fig. 5. Steepness index m vs. water content CW. Straight lines indicate the best fit through the data (Table 5).

steepness index m

20

40

30

Table 5 Coefficients a and b of the equation m = a  b  log CW (by linear regression) and number of non-bridging oxygens per tetrahedral cation NBO/T of the anhydrous melts calculated as molar components: (Na + K + 2Ca + 2Mg–B–Al)/(Si + Al + B) Glass

NBO/T

Number of data points

a

b

FG, this work NCS, this work Sodium trisilicate [7] NCS [8] NBS, this work SiO2 [5] SiO2 [26]

0.77 0.70 0.67 0.66 0.13 0 0

4 3 10 5 2 4 4

29 ± 1 27 ± 1 30 ± 3 26 ± 2 29 19 ± 2 14 ± 2

3.4 ± 1.2 4.4 ± 1.1 7.0 ± 1.7 3.1 ± 1.0 6.8 2.1 ± 0.8 –

FG, Ref. 4 FG, this work 20

0.1

1

10

water content c w (wt%) Fig. 6. Steepness index m vs. water content CW for float glass FG. The full line indicates the best fit according to Fig. 8 and Table 5. The dashed line is intended to demonstrate the discrepancy to the Data of Ref. [4].

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with alkali cations was reported in Ref. [26] for the T12 isokom for hydrous alkali silicate melts. 5. Conclusions The structural role of OH is found to be complex. On one side a ‘strengthened’ effect on m and on the other side a fluxing effect on viscosity (like alkali ions) is evident if OH is enriched in the studied FG, NCS and NBS glasses. Thus, it is inferred that OH acts as an anomalous network modifier. Acknowledgement The research was supported by the German Research Foundation DFG under Grants De 598/4, Be 1720/9 and Mu 963/4.

[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26]

References

[27] [28]

[1] F. Geotti-Bianchini, L. De Riu, Glastech. Ber. Glass Sci. Technol. 71 (1998) 230. [2] H. Behrens, A. Stuke, Glass Sci. Technol. 76 (2003) 176. [3] J. Deubener, R. Müller, H. Behrens, G. Heide, J. Non-Cryst. Solids 330 (2003) 268. [4] P. Del Gaudio, H. Behrens, J. Deubener, J. Non-Cryst. Solids 353 (2007) 223. [5] G. Hetherington, K.H. Jack, J.C. Kennedy, Phys. Chem. Glasses 5 (1964) 130. [6] C.-K. Wu, J. Non-Cryst. Solids 41 (1980) 381. [7] J.E. Shelby, G.L. McVay, J. Non-Cryst. Solids 20 (1976) 439. [8] S. Sakka, K. Matusita, T. Watanabe, K. Kamiya, Yogyo Kyokai Shi 89 (1981) 577. [9] P. Richet, A.-M. Lejeune, F. Holtz, J. Roux, Chem. Geol. 128 (1996) 185. [10] D. Giordano, D.B. Dingwell, C. Romano, J. Volcanol. Geotherm. Res. 103 (2000) 239.

[29] [30] [31] [32] [33] [34] [35]

D.B. Dingwell, Phys. Earth Planet Int. 107 (1998) 1. A. Whittington, P. Richet, Y. Linard, F. Holtz, Chem. Geol. 174 (2001) 209. A. Whittington, P. Richet, F. Holtz, Geochim. Cosmochim. Acta 64 (2000) 3725. D. Giordano, A.R.L. Nichols, D.B. Dingwell, J. Volcanol. Geotherm. Res. 103 (2000) 239. Y. Morizet, A.R.L. Nichols, S.C. Kohn, R.A. Brooker, D.B. Dingwell, Eur. J. Mineral. 19 (2007) 657. K.-U. Hess, D.B. Dingwell, Am. Mineral. 81 (1996) 297. D. Giordano, D.B. Dingwell, J. Phys. Condens. Matter 15 (2003) S945. E. Rössler, K.-U. Hess, V.N. Novikov, J. Non-Cryst. Solids 223 (1998) 207. M.L.F. Nascimento, C. Aparicio, J. Phys. Chem. Solids 68 (2007) 104. C.A. Angell, Strong and fragile liquids, in: K. Ngai, G.B. Wright (Eds.), Relaxation in Complex Systems, pp. 3–11. C.A. Angell, J. Phys. Chem. Solids 49 (1988) 863. C.A. Angell, J. Non-Cryst. Solids 131–133 (1991) 13. R. Böhmer, K.L. Ngai, C.A. Angell, D.J. Plazek, J. Chem. Phys. 99 (1993) 4201. D.R. Neuville, P. Richet, Geochim. Cosmochim. Acta 55 (1991) 1011. N. Böse, G. Klingenberg, G. Meerlender, Glastech. Ber. Glass Sci. Technol. 74 (2001) 115. S. Zietka, J. Deubener, H. Behrens, R. Müller, Phys. Chem. Glasses: Eur. J. Glass Sci. Technol. B 48 (2007) 380. A. Stuke, H. Behrens, B.C. Schmidt, R. Dupree, Chem. Geol. 229 (2006) 64. M. Tomozawa, M. Takata, J. Acocella, E.B. Watson, T. Takamori, J. Non-Cryst. Solids 56 (1983) 343. F. Schulze, H. Behrens, W. Hurkuck, Am. Mineral. 84 (1999) 1512. D.B. Dingwell, K.-U. Hess, C. Romano, Earth Planet Sci. Lett. 158 (1998) 31. C. Romano, B. Poe, V. Minicione, K.-U. Hess, D.B. Dingwell, Chem. Geol. 174 (2001) 115. F. Vetere, H. Behrens, V. Misiti, G. Ventura, F. Holtz, R. De Rosa, J. Deubener, Chem. Geol. 245 (2007) 89. B.O. Mysen, P. Richet, Silicate Glasses and Melts, Elsevier, Amsterdam, 2005. pp 144. H. Behrens, A. Stuke, Glass Sci. Technol. 76 (2003) 1. L. Wondraczek, S. Sen S, H. Behrens, R.E. Youngman, Phys. Rev. B 76 (2007) 014202.