Heat capacity, entropy, configurational entropy, and viscosity of magnesium silicate glasses and liquids

Abstract

AbstractIn this work, five Mg-silicate glasses with compositions between MgSiO$$_3$$ 3 and Mg$$_2$$ 2 SiO$$_4$$ 4 were synthesized by aerodynamic levitation combined with laser melting. Low-temperature heat capacity ($$C_p$$ C p ) was measured (by relaxation calorimetry in the range 2–310 K) for all of them, with the resulting vibrational entropies at T = 298.15 K: sample MG50 with composition Mg$$_{0.996}$$ 0.996 SiO$$_{2.996}$$ 2.996 and entropy 72.88 J mol$$^{-1}$$ - 1 K$$^{-1}$$ - 1 ; MG54 Mg$$_{1.174}$$ 1.174 SiO$$_{3.174}$$ 3.174 78.54; MG58 Mg$$_{1.364}$$ 1.364 SiO$$_{3.364}$$ 3.364 85.05; MG62 Mg$$_{1.611}$$ 1.611 SiO$$_{3.611}$$ 3.611 91.40; and MG67 Mg$$_{1.907}$$ 1.907 SiO$$_{3.907}$$ 3.907 102.75. Heat capacity of the glasses is higher than that of the corresponding crystal mixtures below 200 K but plunges below the C$$_{p,\mathrm{crystal}}$$ p , crystal at higher temperatures. High-temperature $$C_p$$ C p was measured (by differential scanning calorimetry in the range 300–970 K) for MG50 and MG67 up to $$\approx $$ ≈ 1000 K. Using our $$C_p$$ C p data, selected data for entropies of fusion, $$C_p$$ C p of crystals, and fictive temperatures, the configurational entropy ($$S_\mathrm{conf}$$ S conf ) at glass transition temperature ($$T_\mathrm{g}$$ T g ) were calculated. For the near-forsterite glass MG67, the $$S_\mathrm{conf}$$ S conf is 1.9 J mol$$^{-1}$$ - 1 K$$^{-1}$$ - 1 at $$T_\mathrm{g}$$ T g = 1040 K. As this small value is a difference of several large numbers, its uncertainty is relatively high; we consider a conservative estimate of 15 J mol$$^{-1}$$ - 1 K$$^{-1}$$ - 1 . Using the expression $$\log \eta = A + B/[T S_\mathrm{conf}(T)]$$ log η = A + B / [ T S conf ( T ) ] , the available experimental viscosities ($$\eta $$ η ) and the temperature-dependent configurational entropy from our work, we refined the parameters $$A = -2.34$$ A = - 2.34 and $$B = 76,500$$ B = 76 , 500 for this equation, with $$S_\mathrm{conf} (T) = 1.90+(83.7 \ln (T/1040))$$ S conf ( T ) = 1.90 + ( 83.7 ln ( T / 1040 ) ) . The configurational entropy for the enstatitic MG50 glass is 16.8 J mol$$^{-1}$$ - 1 K$$^{-1}$$ - 1 at $$T_\mathrm{g}$$ T g = 1063 K. The presented data can be combined with enthalpies of formation and thermophysical properties of Mg-silicate glasses for models that could elucidate geological and geophysical observations in the crust and mantle of the Earth.