_{1-x}Sr

_{x}TiO

_{3}, La-STO) materials are essential for solid oxide fuel cell (SOFC) electrodes and high-temperature gas sensors.[1] In the literature, their electronic structures and optical properties have been investigated intensively by density functional theory (DFT). However, the obtained information is theoretically limited to low temperature because the traditional DFT approach doesn’t include temperature effects. Since many of the applications of these materials for SOFCs and sensors are 400-800°C range, it is very important to know how their properties change when operating at high-temperatures. To better understand the thermodynamic behavior of La-STO with different La-doping levels at high temperatures, the

*ab initio*thermodynamics calculations which combine first-principles DFT with lattice phonon dynamics have been employed in this study to calculate their electronic structures and thermodynamic evolutions versus temperature.[2-5] The obtained results show that with increasing La-doping level, the corresponding structures of La-STO become unstable with an increasing number of soft modes, especially when the La content over Sr is higher than 25%.[6] The La-STOs are conductors even at T=0K due to the electron of La filling in the conduction band of STO, which is consistent with experimental results. The results also reveal that although the GGA+U method could predict the band-gap of STO closer to the experimental measurements, the predicted lattice parameters of La-STO are larger than experimental values and result in more phonon soft modes. These deviations demonstrate the limitations of such U corrections for property extrapolation to high temperatures in comparison with the standard GGA approach. From the calculated optical dielectric tensors of La-STO, one can see that in the optical frequency range, there is a major difference between pure STO and La-doped STO consistent with the dielectric nature of STO and the finite electrical conductivity in La-doped STO associated with electrons in the conduction band, and consistent with expectations from experiments and simple Drude theory arguments. The reason is that STO possesses a band-gap, while La-doped STOs do not have a band-gap, as the extra electrons occupy the conduction band of STO. Due to the reduced symmetry for the La-doped STO systems, the diagonal elements (ε

_{XX}, ε

_{YY}, ε

_{ZZ}) of the dielectric matrix are not equal for some of La-STOs. Related to the DFT energy of pure STO, the calculated thermodynamic properties show that with increasing La-doping levels, the ΔH(T) and ΔG(T) decrease at given temperature T. With increasing T, the ΔH(T) of each La-STO increases while its ΔG(T) decreases because of the effects of TΔS(T) term. These results are useful for understanding the thermodynamic behaviors of La-STO materials at high temperatures and guide further studies of SOFC electrodes and sensor materials.

**References**

[1]^{ }A. M. Schultz, T. D. Brown, and P. R. Ohodnicki, *Optical and Chemi-Resistive Sensing in Extreme Environments: La-Doped SrTiO _{3} Films for Hydrogen Sensing at High Temperature*s,

**Journal of Physical Chemistry C 119**, 6211 (2015).

[2]^{ }Y. Duan, J. Lekse, X. F. Wang, B. Y. Li, B. Alcantar-Vazquez, H. Pfeiffer, and J. W. Halley, *Electronic Structure, Phonon Dynamical Properties, and Capture Capability of Na _{2-x}M_{x}ZrO_{3} (M=Li,K): Density-Functional Calculations and Experimental Validations,*

**Physical Review Applied 3**, 044013 (2015).

[3]^{ }Y. Duan and K. Parlinski, *Density functional theory study of the structural, electronic, lattice dynamical, and thermodynamic properties of Li _{4}SiO_{4} and its capability for CO_{2} capture,*

**Physical Review B 84**, 104113 (2011).

[4]^{ }Y. Duan and D. C. Sorescu, *Density functional theory studies of the structural, electronic, and phonon properties of Li _{2}O and Li_{2}CO_{3}: Application to CO_{2} capture reaction*,

**Physical Review B 79**, 014301 (2009).

[5]^{ }Y. Duan, C. D. Stinespring, and B. Chorpening, *Electronic Structures, Bonding Configurations, and Band-Gap-Opening Properties of Graphene Binding with Low-Concentration Fluorine,* **Chemistryopen 4**, 642 (2015).

[6]^{ }Y. Duan, P. Ohodnicki, B. Chorpening, and G. Hackett, *Electronic structural, optical and phonon lattice dynamical properties of pure- and La-doped SrTiO _{3}: an ab initio thermodynamics study*, to be submitted (2017).