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WagnerJVGR05.pdf

WagnerJVGR05.pdf

M'' [GPa] 0,5 0,4 0,3

M'' [GPa] 0,5 0,4 0,3 0,2 0,1 KWW, β=0.5 Maxwell QUI LIP DYR MIL VUL YEL RAB JAL ATS 0,0 0,0 0,2 0,4 0,6 0,8 1,0 M' [GPa] Fig. 6. Complex Youngs modulus M ⋆ normalised with the unrelaxed Youngs modulus Mα at Tg in the Gaussian-plane. between 60GPa and 100GPa (Wagner (2004)). The obsidians exhibit a relatively constant value of (70 ± 10)GPa. In principle, E is a function of the chemical composition, water-, bubble-, crystal content and temperature prehistory, however, the sensitivity on these influences is much less than those on the relaxation times (Wagner (2004)). There is a positive correlation with the water content and a weak negative correlation with the cooling rate (Fig. 7). In the examined temperature range M ′ (T) decreases continuously for most silicate glasses (Fig. 8). An exception is silica glass with an anomalous increase of Young’s modulus with temperature between 100K and Tg (Brueckner (1970), Brueckner (1971)). Fig. 8 and Tab. 4 clearly indicate that the examined natural glasses have to be assigned to the silica glass with the exception of the LIP-obsidian. The total temperature dependence of Young’s modulus is given by the differential (Brueckner (1971), Askarpour et al. (1993), Rivers and Carmichael (1987), VoThanh et al. (1996), Schilling et al. (2003)).: dM ′ (T) dT = αTV � � ′ ∂M ∂V T + � � ′ ∂M ∂T V (26) with volume V and thermal coefficient of expansion αT = 1 ∂V . The sign of V ∂T dM ′ /dT will be governed by the sign of � ∂M ′ � ∂T V , if αT is negligibly small. In the case of a Born-von-Kármán solid, as in the case of a Debye and Grueneisen solid, it was shown that dM/dT is negative at low temperatures and large αT, 18

MRT [GPa] 90,0 80,0 70,0 60,0 ATS YEL VUL VU DYR JAL RAB MIL QUI LIP 50,0 0,00 0,05 0,10 0,15 0,20 0,25 90,0 80,0 70,0 60,0 50,0 H 2 O [wt %] QU QQU Q I AT AATS T S VUL DYR YEL RAB MIL JALL LIP -2 -1 0 1 EO [mol %] 90,0 80,0 ATS VUL QUI DYR 70,0 MIL 60,0 YEL RAB JAL LIP 50,0 90,0 80,0 70,0 60,0 0,00 0,01 0,02 0,03 0,04 JAL NBO/T ATS YEL LIP MIL QUI VUL RAB DYR 50,0 0,8 1,0 1,2 1,4 1,6 Al 2O 3/(Na 2O+K 2O) Fig. 7. Dependence of the Young’s modulus MRT on the chemical composition (according to NBO/T as well as EO and AI−1 to Tab. 3) as well as the water content for the examined obsidians. Lines are guides to the eye. dM'/dT [MPa/T] 10 5 0 -5 -10 -15 -20 SiO 2 QUI DYR ATS JAL VUL MIL YEL LIP RAB KCS An Na Si O Di 2 3 7 Co NCS JeIIA Di50 Di60 -25 10 15 20 25 30 35 40 45 50 55 60 65 m CCS Obsidian synt. Gläser Schilling et al. '03 Primenko & Galyant '89 Fig. 8. Fragility index m versus the temperature derivative of the storage modulus ∂M ′ (T)/∂T |T

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