Boron coordination change in barium borate melts and glasses and its contribution to configurational heat capacity, entropy, and fragility.

Abstract

High-energy x-ray diffraction from molten and glassy BaB2O4 and BaB4O7 has been performed using aerodynamic levitation and laser heating over a wide range of temperatures. Remarkably, even in the presence of a heavy metal modifier dominating x-ray scattering, it was possible to extract accurate values for the tetrahedral, sp3, boron fraction, N4, which declines with increasing temperature, using bond valence-based mapping from the measured mean B-O bond lengths while accounting for vibrational thermal expansion. These are used within a boron-coordination-change model to extract enthalpies, ΔH, and entropies, ΔS, of isomerization between sp2 and sp3 boron. The results for BaB4O7, ΔH = 22(3) kJ mol-1 boron, ΔS = 19(2) J mol-1 boron K-1, agree quantitatively with those found previously for Na2B4O7. Analytical expressions for N4(J, T) and associated configurational heat capacity, CPconf(J, T), and entropy, Sconf(J, T), contributions are extended to cover a wide composition range 0 ≤ J = BaO/B2O3 ≤ 3 using a model for ΔH(J) and ΔS(J) derived empirically for lithium borates. Maxima in the CPconf(J, Tg) and fragility index contributions are thereby predicted for J ≲ 1, higher than the maximum observed and predicted in N4(J, Tg) at J ≃ 0.6. We discuss the utility of the boron-coordination-change isomerization model in the context of borate liquids containing other modifiers and the prospect of neutron diffraction to aid in empirical determinations of modifier-dependent effects, illustrated by new neutron diffraction data on Ba11B4O7 glass, its well-known α-polymorph, and lesser-known δ-phase.