Entropy of Formation of Oxygen Vacancy in Functional Ceramics Determined by Measuring Heat Capacity from Near Absolute Zero

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Oxide functional ceramics are used as conducting materials, and their application for industries has been expanded. Their characteristics drastically changes resulted from doping and formation of oxygen vacancy, V^<●●>_O, and oxygen interstitial, O^<'''>_i, associated with doping. In the present study, Isobaric heat capacities, C_p, of La_XSr_<1-X>MO_<3-δ> (M = Fe and Co) which is used as cathodes of SOFC, and ITO which is used as transparent conducting oxide have been measured from near absolute zero to high temperatures, and change in phase transitions and lattice vibrations were investigated from such C_p values. Also, their Debye temperatures, Θ_D, were determined from the measured C_p values below 10 K and isochoric heat capacities, C_V, were calculated by inserting the Θ_D values into Debye functions, followed by calculating the isochoric entropies of vibration, Δ^T_OS_V. Furthermore, the entropies of vibration of oxygen vacancy, Δ_fS^<vib>_<T_V>, (V^<●●>_O), were estimated by differentiation of Δ^T_OS_V with the V^<●●>_O content at 298 K. The Δ_fS^<vib>_<T_V> (V^<●●>_O) values of La_XSr_<1-X>MO_<3-δ> were found to be very large. Such large Δ_fS^<vib>_<T_V> (V^<●●>_O) are important reason for forming V^<●●>_O. As a result, La_XSr_<1-X>MO_<3-δ> show high conductivity by transporting oxygen ions at high temperature. On the other hand, the Δ_<mix>S_<298> values of ITO were found to be below zero, indicating that short range orderings of Sn^●_<In> and O^<''>_i are caused by a thermodynamic self-assembly to compensate charges. Such a self-assembly makes Sn^●_<In> and O^<''>_i levels in the band gap degenerate, and the degeneracy prevents absorption of visible light, remaining wide band gap over than 3 eV.