Temperature Dependence of Elastic Properties in Alkali Borate Binary Glasses
Mitsuru KAWASHIMA, Yu MATSUDA†, and Seiji KOJIMA* Graduate School of Pure and Applied Sciences, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan
Abstract The elastic properties of alkali borate glasses, xM2O▪(100-x)B2O3 (M = Li, Na, K, Rb, Cs x = 14, 28), have been investigated by Brillouin scattering spectroscopy from room temperature up to 1100 oC. Longitudinal sound velocity (VL) decreases markedly with increasing temperature above glass transition temperature (Tg). These changes in the elastic properties result from the disruption in the glass network with increasing temperature above Tg. Alkali borate family with the same x shows the similar behavior in the temperature variations of VL up to around Tg. Absorption coefficient (αL) increases gradually around Tg. With an increase in the size of alkali ion, the slope of VL just above Tg decreases. Since the alkali dependence of the fragility is related to the slope mentioned above, the present results suggest that the fragility of alkali borate increase with decreasing the size of alkali ion. Such alkali dependence of fragility is discussed on the basis of the degree of the fluctuation of the coordination number.
Keywords: alkali borate glass, elastic property, glass transition, fragility, relaxation, Brillouin scattering *Corresponding author. Tel.:+81 29 8535307; fax.:+81 29 8534490. E-mail address:
[email protected] (S. Kojima) †
Present address: Glass Research Center, Central Glass Co. Ltd, Matsusaka, Mie 515-0001, Japan
1
1. Introduction Pure B2O3 glass is a random three-dimensional network of BO3 triangles with a large fraction of almost planar B3O6 boroxol rings. It is known that alkali borate glasses show the anomalous composition dependences of physical properties, such as density [1], sound velocity [2, 3] and thermal expansion [4], by the additions of alkali oxide to pure B2O3 glass. Previous studies revealed that the structural origins of the anomalies observed are strongly related to the change in boron coordination from three to four and the formation of non-bridging oxygens [5]. The fourfold-coordinated boron atoms increase the network rigidity by cross-linking the borate framework. In contrast, the non-bridging oxygens destroy the borate network. The negative charge of the network sites is compensated by the positive charge of the alkali ions, M+, which do not directly participate in the network formation and which occupy interstitial voids. As a consequence, the structures of modified borate glasses are essentially built up from the covalently bonded structural units, while ionic bonds are made between M+ and the B-O anionic units, the strength of which depends on the specific alkaline cation. The study by nuclear magnetic resonance (NMR) [5] and Raman scattering measurement [6] revealed that the fraction of fourfold-coordinated boron atoms of alkali borate glass family at room temperature decrease with increasing the size of alkali ion, attributing it to the preference large alkalis to induce the creation of non-bridging oxygens. Therefore, in the case of same alkali composition, the elastic properties, such as sound velocity and elastic moduli, of alkali borate glasses increase with decreasing the size of alkali ion. The elastic properties far below a glass transition temperature (Tg) are relatively stable for the temperature variation above Tg. In contrast, depolymerization of the network starts at temperatures above Tg. The breakdown of the structural integrity is reflected in the rapidly decreasing rigidity. The network rigidity is directly connected and coupled with the structural (α) relaxation process characterized by Angell’s fragility. Therefore, to elucidate the 2
mechanism of the glass transition and nature of supercooled liquid, it is necessary to focus on the elastic properties over a wide temperature range. Moreover, the understanding of elastic properties at high temperatures themselves is important for glass manufacturing process. In this study, we employ Brillouin scattering spectroscopy to measure elastic properties at high temperatures up to 1100 ºC. Although the non-destructive and non-contact Brillouin scattering is powerful tool to investigate the elastic properties at high temperatures, only a few investigations were reported until now on elastic properties of alkali borate glass above Tg using Brillouin scattering. Masnik et al. [7] showed that temperature dependences of longitudinal elastic modulus of sodium borate glasses and discussed a relaxation process above Tg in GHz frequency region. Ike et al. [8] reported the temperature dependences of the elastic properties of lithium borate glasses. Since their results focus on the effect of temperature and composition dependence, the influence of alkali ion and alkali dependence of fragility were not sufficiently discussed in detail. In this study, the temperature dependence of elastic property in alkali borate glasses xM2O∙ (100-x)B2O3 (M = Li, Na, K, Rb, Cs x = 14, 28), where x denotes the molar concentration (mol%), are investigated by Brillouin scattering up to 1100 oC. The influence of alkali cation to temperature dependence of the elastic properties and the variation of fragility are discussed
2. Experimental xM2O▪(100-x)B2O3 (M = Li, Na, K, Rb, Cs x = 14, 28) glasses were prepared by “solution method” [9]. This method is useful to obtain high homogeneity of the samples. Analytical-reagent-grade MOH and H3BO3, starting materials, were reacted in an aqueous solution to achieve the high homogeneity. Then the mixed solution was transferred to a dry box and after the complete evaporation of water a chemically synthesized powder was obtain. The
3
powder was melted in furnace at 1000 oC, and then the melt was quenched by pressing between two aluminum plates. The actual compositions of all samples were analyzed with respect to both x and (100-x) by the potentiometric titration chemical analysis [10]. The experimental setup of a Brillouin scattering apparatus is described elsewhere [8]. The features of this system are the combination of an optical microscope (Olympus BH-2) and a Sandercock-type 3 + 3 passes tandem multipass Fabry-Perot interferometer (FPI). The Brillouin scattering spectra were measured at a backward scattering geometry. A standard photon counting system and a multichannel analyzer were used to accumulate the signals. To measure the spectra at high temperatures up to 1100 ºC, we prepared the compact IR image furnace (Yonekura, IR-TP) specially customized for the present experiments. The combination of Brillouin apparatus and the IR image furnace enable us to prove elastic properties over a wide temperature range.
3. Results and Discussion 3.1 Temperature dependence of elastic property of alkali borate glasses The temperature dependence of Brillouin spectra in 28Rb2O▪72B2O3 are shown in Fig. 1. The obtained spectra contained one longitudinal acoustic (LA) mode and central peak. The Brillouin shift of LA mode decreased with increasing temperature, while the appearance of central peak was able to be confirmed above 700 oC. Then, the intensity of central peak increased with increasing temperature. The central peak was observed all samples at high temperature and the intensity of the central peak increased with decreasing the size of alkali ion. These Brillouin spectra were analyzed by convoluting a Lorentzian spectral function with a Gaussian broadening function. The longitudinal sound velocity (VL) and absorption
4
coefficient (αL) of the samples were calculated from Brillouin shift (Δν180) and FWHM (Γ) using the equations (1) and (2), VL
L
180 , 2n sin / 2
VL
(1)
(2)
,
where n is the refractive index, λ is the wavelength of the incident beam (532 nm) and θ is the scattering angle (180o). The values of n for each sample are taken from the data of refs. [11] and [12]. Since only room temperature value was available, it is assumed that the change of n is much smaller than that of Brillouin shift even above Tg. Figures 2 (a) and (b) show temperature dependences of VL and αL in 14M2O▪86B2O3. Figures 3 (a) and (b) show those of 28M2O ▪ 72B2O3. These temperature dependences generally observed by other Brillouin study for glass forming liquids [13, 14]. decreases very rapidly above an inflection point between 300
o
C and 400
Each VL o
C. This
characteristic inflection point can be identified as Tg. In the case of “strong” pure SiO2 glass, the elastic properties exhibit a steady increase with increasing temperature even above Tg [15]. The anomaly near Tg is remarkable in “fragile” alkali borate glasses of which anharmonicity are much stronger than that of pure SiO2 glass. At room temperature, VL increases with decreasing the size of alkali ion. The fraction of four-fold coordinated boron atoms at same alkali composition is larger with decreasing the size of alkali ion [5]. Its amount increases the network rigidity by cross-linking the borate framework with covalent B-O bonds, and subsequently yields to higher Tg. Therefore, the inflection point (Tg) shifts toward higher temperature with decreasing the size of alkali ion. On the other hand, with increasing the size of alkali ion, the amount of four-fold coordinated boron atoms decreases and non-bridging
5
oxygens increase at same alkali composition. Since the non-bridging oxygens connect with alkali ion by ionic bond, the strength strictly depends on alkali ion size. Moreover, the study by molecular dynamics simulation [16] showed that small alkali ions can enter into the matrix of pure B2O3 glass without inducing large modifications in the borate network, and when the other alkali ions are added to the initial structure, the network opens to accommodate the larger size of the cation. Thus, the loose structure increases with increasing alkali size. Above Tg, each VL decreases very rapidly. Such sudden decrease at Tg in Fig. 2(a) and Fig. 3(a) indicates that the structure of the glass network becomes weaker above Tg. This drastic change is caused by the disruption of glass network. The decrease in the fraction of the four-fold coordinated boron atoms with increasing temperature above Tg has been also confirmed by neutron diffraction [17]. The four-fold coordinated boron atoms are converted to the three-fold coordinated boron atoms. This decrease of coordination number induces a partial depolymerization of the network above Tg through the formation of non-bridging oxygen. Therefore, the temperature increase causes the decrease of coordination number of boron atoms, resulting in the creation of the planar weak structural units and non-bridging oxygen. Indeed, a molecular dynamic simulation of lithium borate glasses also found that the number of non-bridging oxygen in the vicinity of the Li ion increases with increasing temperature [18]. Moreover, the study by Raman scattering measurement of alkali borate glass with temperature revealed that the concentration of boroxol rings rapidly decreases above Tg because the boroxol rings open [19, 20]. Similarly, NMR data on sodium borate glasses have shown a decrease of the boron fraction in ring position [21]. As a result, the glass network is broken and random connections of BO3 triangular units are formed with increasing temperature. Therefore, the disruption in the glass network above Tg is due to the creation of random connections and non-bridging oxygen. On the other hand, the extents of connectivity in glass network remain unchanged from room temperature to Tg. Therefore, Above Tg, VL and absorption coefficient 6
change drastically and below Tg, their changes are very small. αL gradually increase at Tg and up to observed temperature range. The random connections and the non-bridging oxygens loosely connected to the network induce the energy dissipation of elastic wave propagation, thereby causing the damping of the sound wave to increase. Both temperature dependences of αL of x = 14 and 28 mol% do not depend on the size of alkali ion, and show similar behavior from room temperature around up to 850 oC. In this temperature region, we find that temperature dependences of αL are curve of the second order and can be represented by
L T 7.5 T 3502 275000
(x = 14 mol%)
(3)
L T 14.8 T 3502 275000
(x = 28 mol%).
(4)
These fitting results show inset of Figs. 2(b) and 3(b). Temperature dependences of αL of x = 28 mol% rises more rapidly than that of x = 14 mol% above around Tg. In high temperatures, αL increase higher with increasing the size of alkali ion.
3.2 Scaled sound velocity The temperature dependence of VL, which is showed in Figs. 2 (a) and 3(a), were scaled in such a way that VL and T are scaled by VL at Tg and Tg. Figures 4 and 5 show the scaled temperature dependence of VL. Despite the decrease of VL at room temperature with the alkali ion size, these figures were clearly scaled in same alkali composition from room temperature near Tg. In contrast, the scaled composition dependence of its temperature dependence of potassium borate glasses [22] cannot fall into the master curve (Fig. 6). Therefore, in the case of same alkali composition, the variations of structure with temperature up to around Tg is similar mechanism, while, in the case of different composition, the different variations of the 7
structure with temperature were observed. This means that the glass network at this temperature range is almost constructed by the boron and oxide atoms independent of influence of the alkali ion. On the other hand, at high temperature the influence of alkali ion appears.
3.3 Fragility of alkali borate glasses Angell has proposed a useful measure of the classification of glass-forming materials on the basis of temperature dependence of viscosity or structural relaxation time, using the concept of “strong” and “fragile” liquids [23]. For a strong liquid, the temperature dependence of characteristic relaxation time follows an Arrhenius behavior. On the other hand, the characteristic relaxation time of fragile liquid changes rapidly with super-Arrhenius temperature dependence and follows a Vogel-Fulcher behavior. The fragility is defined from the dependence of log η on Tg/T and, degree of the fragility is evaluated quantitatively by steepness index m m lim
T Tg
d log . d (T / Tg )
(5)
In the case of alkali borate glasses, it is known that the addition of alkali oxide to pure B2O3 glass causes a marked change of fragility from “strong” to “fragile” [24]. The slope of decrease in VL at Tg in Fig. 2 (a) and Fig. 3 (a) is a direct measure of the structural degradation of glass-forming liquids, because the Brillouin scattering technique can probe structural relaxation in the GHz frequency range. This slope in VL at Tg can be used as a measure of fragility [7, 25]. Very recently, we have shown that the slope of VL just above Tg of potassium borate glass increase with increasing K2O composition as well as the composition dependence of the fragility in ref [22]. The rate in Fig. 2(a) and Fig. 3(a) is more rapid with decrease size of alkali ion. Above Tg, VL decreases very rapidly. The alkali dependence of
8
dVL/dT just above Tg is shown in Fig. 7, where open symbols denote fragility indices of lithium (square) and sodium (circle) borate glass reported in ref [24], respectively. As can be seen in Fig. 7, dVL/dT just above Tg of alkali borate glasses increases with increasing the composition, and alkali dependence of fragility indicates that the fragility of alkali borate glasses increases with decreasing size of alkali ion, especially fragility of 28M2O▪72B2O3 shows a remarkable alkali dependence. Chryssikos et al. [26] suggested that lithium borate glass is more fragile than sodium borate glass from both the viscosity and specific heat data. Our result is agreement with their suggestion, and not only lithium and sodium borate glasses but also potassium, rubidium, and cesium borate glasses show alkali dependence of fragility. Even modest changes in the cation network interactions can have a significant impact on glass transition. Vilgis proposed the theoretical fragility model to understand the mechanism of glass-forming liquids near Tg [27, 28]. The summary of the model is that a degree of the fragility relates to a degree of the fluctuation of the coordination number. For instance, vitreous silica SiO2 belongs to the “strong” since it has a fixed covalent bonding of Si atom, which is four-coordinated to oxygen atoms. On the other hand, otherphenyl (OTP), one of the well-known molecular glass-formers, belongs to the typical “fragile” one since its coordination number fluctuates from 11 to 16 [28], indicating that the molecules strongly interact with each other cooperatively. In the case of alkali borate glasses, the coordination number of a boron atom changes from three to four by the additions of alkali oxide. Therefore, the more the fraction of four-fold coordinated boron atoms N4 approaches 0.5, the more the fluctuation of the coordination number of boron atom increases. Matsuda et al. experimentally revealed that the trends of the fragility and the fluctuation of the coordination number of boron atom in lithium borate glasses have the correlation over a wide composition range [29]. Zhong and Bray [5] showed that N4 in alkali borate glass decreases in the order Li ˃ Na ˃ K ˃ Rb ˃ Cs; also, the value of x for which N4 exhibits a maximum, decreases with increasing alkali ion size. 9
N4 of lithium borate glass, which is the highest in the same alkali compositions, exhibits a maximum, N4 = 0.4, at x = 40 mol%. From the alkali dependence of N4, the fluctuation of the coordination number of boron atoms decreases with increasing alkali ion size. Thus, the fluctuation in lithium borate glass is the highest and the fluctuation of cesium borate glass is the lowest in same composition. Therefore, Vilgis’s model gives the suggestion that the fragility of alkali borate glass increases with increasing composition up to at least x = 28 mol% and decreases with increasing alkali ion size. In Fig. 7, this suggestion is in agreement with the behavior of the slope in VL just above Tg. In other wards, the increase of composition and the decrease of alkali ion size make “fragile”, on the other hand, the decrease of composition and the increase of alkali ion size make “strong”. Fragility of 28M2O▪72B2O3 is expected to show the composition dependence more remarkably than that of 14M2O▪86B2O3, because the difference of formation of the four-coordinationed boron atom by alkali oxide becomes remarkable with increasing alkali composition [5, 30]. The prediction by Vilgis enabled us to explain alkali dependence of fragility estimated in present work. In the case of alkali borate glasses, the origin of fragility correlates to the formation of the 4-coordinationed boron atom.
5. Conclusions At room temperature, VL of alkali borate glasses increase with decreasing the size of alkali ion. From room temperature to Tg, the extents of connectivity in glass network remain unchanged. In this temperature region, the glass network is almost constructed by the boron and oxide atoms independent of influence of the alkali ion. In contrast, above Tg, since the glass network is completely disintegrated, random connections and non-bridging oxygen are created. Therefore, VL of alkali borate decreases drastically and αL increases with increasing
10
temperature. It is found that the fragility of alkali borate increase with decreasing the size of alkali ion. This experimental evidence is consistent with the suggestion in previous study. The formation of the 4-coordinated boron atom plays the dominate role in the fragility of the borate glass system.
Acknowledgement One of the authors (Y. M.) is thankful for the JSPS Research Fellowship 19-574.
11
References [1] M. Kodama, T. Matsushita, and S. Kojima: Jpn. J. Appl. Phys. 34 (1994) 2570. [2] Y. Matsuda, Y. Fukawa, M. Kawashima, S. Mamiya, M. Kodama, and S. Kojima: Phys. Chem. Glasses 50 (2009) 95. [3] M. Kawashima, Y. Matsuda, Y. Fukawa, S. Mamiya, M. Kodama, and S. Kojima: Jpn. J. Appl. Phys. 48 (2009) 07GA03. [4] J. E. Shelby: J. Am. Ceram. Soc. 66 (1983) 501. [5] J. Zhong and P. Bray: J. Non-Cryst. Solids 111 (1989) 67. [6] G. D. Chryssikos, E. I. Kamitsos, and M. A. Karakassides: Phys. Chem. Glasses 31 (1990) 109. [7] J. E. Masnik, J. Kieffer, and J. D. Bass: J. Chem. Phys. 103 (1995) 9907. [8] Y. Ike, Y. Matsuda, S. Kojima, and M. Kodama: Jpn. J. Appl. Phys. 34 (2006) 4474. [9] M. Kodama: J. Non-Cryst. Solids 127 (1991) 65. [10] M. Kodama, K. Iizuka, M. Miyashita, N. Nagai, W. Clarida, S. A. Feller, and M. Affatigato: Glass Technol. 44 (2003) 50. [11] R. I. Bresker and K. S. Evstropiev: Zh. Prikl. Khim. 25 (1952) 905 [in Russian]. [12] K. Terashima, S. H. Kim, and T. Yoko: J. Am. Ceram. Soc., 78 (1983) 1601. [13] D. L. Sidebottom, P. E. Green, and R. K. Brow: J. Mol. Struct. 479 (1999) 219. [14] L. M. Torell: J. Chem. Phys. 76 (1982) 3467. [15] R. E. Youngman, J. Kieffer, J. D. Bass, and L. Duffrene: J. Non-Cryst. Solids 222 (1997) 190. [16] M. A. Gonzalez, C. Mondelli, G. Angelo, C. Crupi, and M. R. Johnson: J. Non-Cryst. Solids 354 (2008) 203. [17] O. Majerus, L. Cormier, G. Calas, and B. Beuneu: Phys. Rev. B 67 (2003) 024210. [18] C. P. Varsamis, A. Vegiri, and E. I. Kamitsos: Phys. Rev. B 65 (2002) 104203. 12
[19] R. Akagi, N. Ohtori, N. Umesaki: J. Non-Cryst. Solids 293-295 (2001) 471. [20] T. Yano, N. Kunimine, S. Shibata, and M. Yamane: J. Non-Cryst. Solids 321 (2003) 147. [21] S. Sen, Z. Xu, and J. Stebbin: J. Non-Cryst. Solids 226 (1998) 29. [22] M. Kawashima, Y. Matsuda, S. Aramomi, and S. Kojima: Jpn. J. Appl. Phys. 49 (2010) 07HB02. [23] C. A. Angell: J. Non-Cryst. Solids 131-133 (1991) 13. [24] G. D. Chryssikos, E. I. Kamitsos, and Y. D. Yiannopoulos: J. Non-Cryst. Solids 196 (1996) 244. [25] J. Kieffer, J. E. Masnik, B. J. Reardon, and J. D. Bass: J. Non-Cryst. Solids 183 (1995) 51. [26] G. D. Chryssikos, J. A. Duffy, J. M. Hutchinson, M. D. Ingram, E. I. Kamitsos, and A. J. Pappin: J. Non-Cryst. Solids 172-174 (1994) 378. [27] T. A. Vilgis: J. Phys.:Condens. Matter 2 (1990) 3667. [28] T. A. Vilgis: Phys. Rev. B 47 (1993) 2882. [29] Y. Matsuda, Y. Fukawa, M. Kawashima, S. Mamiya, and S. Kojima: Solid State Ionics 179 (2008) 2424 [30] V. K. Michaelis, P. M. Aguiar, and S. Kroeker: J. Non-Cryst. Solids 353 (2007) 2582.
13
Fig. 1
Temperature dependence of Brillouin spectra of 28Cs2O･72B2O3 glass, measured in
backscattering geometry. LA and CP denote the longitudinal acoustic phonon and central peaks, respectively.
Fig. 2
Temperature dependences of (a) Longitudinal sound velocities and (b) Absorption
coefficients of 14M2O･86B2O3 glasses. Inset of (b): fitting curve of the second order.
Fig. 3
Temperature dependences of (a) Longitudinal sound velocities and (b) Absorption
coefficients of 28M2O･72B2O3 glasses. Inset of (b): fitting curve of the second order.
Fig. 4
Scaled Temperature dependence of VL of 14M2O･86B2O3 in such a way that VL and T
are scaled by VL at Tg and Tg.
Fig. 5
Scaled Temperature dependence of VL of 28M2O･72B2O3 in such a way that VL and T
are scaled by VL at Tg and Tg.
Fig. 6 Scaled Temperature dependence of VL of xK2O･(100-x)B2O3 ( x = 4, 10, 14, 20, 28, 34 mol% ) in such a way that VL and T are scaled by VL at Tg and Tg.
14
Fig. 7 Alkali dependence of dVL/dT of xM2O∙ (100-x)B2O3 (M = Li, Na, K, Rb, Cs x = 14, 28) just above Tg. Open symbols denote fragility indices of lithium (square) and sodium (circle) borate glass reported in ref [24]. The increase of fragility means the glasses become “fragile”. On the other hand, the decrease of fragility means the glasses become “strong”.
15
28Rb2O-72B2O3
LA
Scattering intensity (arb. unit)
CP o
900 C o
800 C o
700 C o
450 C o
250 C o
25 C -20
0
20
Brillouin shift (GHz)
Fig. 1
16
5500 14LiB 14NaB 14KB 14RbB 14CsB
Sound velocity VL (m/s)
5000 4500 4000 3500 3000 2500 2000
0
200
400
600
800
1000
1200
o
Temperature ( C)
5x10
6
4x10
6
-1
6x10
6
5x10
6
4x10
6
3x10
6
2x10
6
1x10
6
-1
6
Absorption coefficient L (m )
6x10
Absorption coefficient (m )
Fig. 2 (a)
3x10
6
2x10
6
1x10
6
0 0
200
400
600
800
1000
1200
o
Temperature ( C)
14LiB 14NaB 14KB 14RbB 14CsB
0 0
200
400
600
800
1000
o
Temperature ( C)
Fig. 2 (b)
17
1200
Sound velocity VL (m/s)
7000
28LiB 28NaB 28KB 28RbB 28CsB
6000 5000 4000 3000 2000 0
200
400
600
800
1000
1200
o
Temperature ( C)
7
8.0x10
6
6.0x10
6
4.0x10
6
1.0x10
7
8.0x10
6
6.0x10
6
4.0x10
6
2.0x10
6
-1
1.0x10
Absorption coefficient (m )
-1
Absorption coefficient L (m )
Fig. 3 (a)
0.0 0
200
400
600
800
1000
1200
o
Temperature ( C)
2.0x10
28LiB 28NaB 28KB 28RbB 28CsB
6
0.0 0
200
400
600
800 o
Temperature ( C)
Fig. 3 (b)
18
1000
1200
1.1 14LiB 14NaB 14KB 14RbB 14CsB
1.0
VL/VL
Tg
0.9 0.8 0.7 0.6 0.5
0
1
2
3
4
T/Tg
Fig. 4
1.1 1.0 0.9 0.8
VL/VL
Tg
28LiB 28NaB 28KB 28RbB 28CsB
0.7 0.6 0.5 0.4 0
1
2
3
T/Tg Fig. 5
19
xK2O(100-x)B2O3
1.0 0.9 0.8
x=4 x = 10 x = 14 x = 20 x = 28 x = 34
0.7 0.6 0.5 0
1
2
3
T/Tg
Fig. 6
xM2O(100-x)B2O3
70
[24]
Fragility index of M = Li [24] Fragility index of M = Na M = Li M = Na M=K M = Rb M = Cs
60
50
40
14
28
Alkali composition (mol%)
Fig. 7
20
30
Fragility index m
0.4
dVL/dT
VL scaled by VL at Tg
1.1
