Relationship between Thermal Conductivity and Structure of CaO–BO<sub>1.5</sub>–AlO<sub>1.5</sub>–SiO<sub>2</sub> Systems

To understand the relationship between the thermal conductivity of the mold flux and its composition from the perspective of the local structure, the thermal conductivities of CaO–BO1.5–AlO1.5–SiO2 melts were measured using the transient hot-wire method in the range of 1573–1773 K, and structural analyses were conducted using magic-angle spinning nuclear magnetic resonance (MAS-NMR) spectroscopy. Additionally, the covalency of the bonds between each cation in this system and the oxygen atom was evaluated using first-principles calculations to consider the propagation of phonons between each bond. As a result, the degree of polymerization of the network structure, DP, was calculated from the composition and results of the MAS-NMR analysis and confirmed to have a positive effect on thermal conductivity. Some samples exhibited low thermal conductivity despite a high DP below 1673 K, owing to the formation of boroxol ring structures. Using first-principles calculations, the covalency of the B–O, Al–O, and Si–O bonds was evaluated quantitatively as the length between the center of the bonds and the center of the electron distribution, L. The standard deviation of covalency in the entire network of a sample, SL, was obtained and confirmed to have a negative effect on thermal conductivity because a difference in covalency between bonds caused phonon scattering. Finally, by integrating our previous research, the ratio of DP/SL was confirmed to be an effective index for evaluating the thermal conductivities of the CaO–BO1.5, BO1.5–SiO2, CaO–AlO1.5–SiO2, CaO–BO1.5–SiO2, CaO–BO1.5–AlO1.5, and CaO–BO1.5–AlO1.5–SiO2 systems.