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

氧化物功能陶瓷被用作导电材料，在工业上的应用得到了扩大。它们的性质由于掺杂和与掺杂有关的氧空位V^&lt；&gt；_O和氧间隙O^&lt；‘’&gt；_i的形成而发生了剧烈的变化。本文测量了固体氧化物燃料电池阴极La_xSR_&lt；1-X&gt；MO_&lt；3-δ&gt；(M=Fe和Co)和透明导电氧化物ITO从近绝对零点到高温的等压热容C_p，并由此研究了相变和晶格振动的变化。根据测得的低于10K的C_p值确定了它们的德拜温度Θ_D，并通过将Θ_D值插入德拜函数，然后计算等容振动熵Δ，T_OS_V来计算等容热容量C_V。此外，通过对Δ^T_OS_V与V^&lt；Δ&lt；T_V&gt；，(V^&lt；&gt；_O)的求积，估计了氧空位的振动熵。在298K时，La_xSR_&lt；1-X&gt；MO_&lt；3-Δ&gt；3-δ&gt；这种大的Δ_FS^&lt；ViB&lt；T_V&gt；(V^&lt；&gt；_O)是形成V^&lt；&gt；_O的重要原因。因此，La_xSR_&lt；1-X&gt；MO_&lt；3-δ&gt；由于在高温下输运氧离子而表现出高的电导率。另一方面，Δ；&lt；Mix&gt；S；298&gt；值小于零，表明Sn^&lt；In&gt；和O^&lt；‘’&gt；_i的短程有序是由热力学自组装补偿电荷引起的。这种自组装使带隙中的Sn^和O^i能级简并，并阻止可见光的吸收，保持了大于3 eV的宽禁带。

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.