**4. Conclusions**

We have investigated the electrical and structural properties of chosen Ba*Ln*Co2O6−<sup>δ</sup> (*Ln* = La, Pr, and Nd) double perovskites. All measured compositions (BLC, BNC, and BPC) were refined to orthorhombic (*Pmmm*) structure up to 1000 ◦C. Moreover, BLC and BNC showed additional tetragonal (*P*4/*mmm*) and cubic (*Pm*3*m*) minority phases, respectively. The thermal evolution of the unit cells shows that after subtracting expansion from thermal lattice vibrations, partial reduction of cobalt and formation of oxygen vacancies gives positive and negative contributions, respectively, to the chemical expansion. The spectroscopic studies show that cobalt is present only in the intermediate or high-spin state for all compositions at room temperature. The optical bandgap is characterized, showing values of ~3.3 eV, which is not consistent with high electronic conductivity. We ascribe this to partially filled antibonding states at the valence band maximum with high mobility for electrons and electron holes [36,37].

**Supplementary Materials:** The following are available online at http://www.mdpi.com/1996-1944/13/18/4044/s1, Figure S1: The temperature evolution of oxygen stoichiometry in BaGdCo2O6−<sup>δ</sup> with different heating rates, Figure S2: The temperature evolution of unit cell parameters a and b/2, Table S1: BaLaCo2O6−<sup>δ</sup> goodness of fit, Table S2: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At room temperature, Table S3: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At 200 ◦C, Table S4: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At 400◦C, Table S5: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At 600 ◦C, Table S6: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At 800◦C, Table S7: Atomic coordinates and Uiso refined for orthorhombic phase of BaLaCo2O6−δ. At 1000 ◦C, Table S8: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at room temperature, Table S9: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at 200 ◦C, Table S10: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at 400 ◦C, Table S11: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at 600 ◦C, Table S12: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at 800 ◦C, Table S13: Atomic coordinates and Uiso refined for tetragonal phase of BaLaCo2O6−<sup>δ</sup> at 1000 ◦C, Table S14: BaPrCo2O6−<sup>δ</sup> goodness of fit, Table S15: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at room temperature, Table S16: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at 200 ◦C, Table S17: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at 400 ◦C, Table S18: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at 600 ◦C, Table S19: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at 800 ◦C, Table S20: Atomic coordinates and Uiso refined for orthorhombic phase of BaPrCo2O6−<sup>δ</sup> at 1000 ◦C, Table S21: BaNdCo2O6−<sup>δ</sup> goodness of fit, Table S22: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at room temperature, Table S23: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at 200 ◦C, Table S24: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at 400 ◦C, Table S25: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at 600 ◦C, Table S26: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at 800 ◦C, Table S27: Atomic coordinates and Uiso refined for orthorhombic phase of BaNdCo2O6−<sup>δ</sup> at 1000 ◦C.

**Author Contributions:** Conceptualization, R.S., S.L.W., and A.M.-G.; Funding acquisition, R.S., M.H.S., J.M.S., A.M.-G., and T.N.; Investigation, I.S., S.L.W., M.B., A.W., M.G., E.D., and A.M.-G.; Methodology, R.S., M.H.S., S.L.W., and A.M.-G.; Supervision, J.M.S., M.G., E.D., A.M.-G., and T.N.; Writing—original draft, I.S., R.S., S.L.W., and A.M.-G.; Writing—review and editing, I.S., R.S., M.H.S., M.B., M.T., J.M.S., A.W., M.G., E.D., A.M.-G. and T.N. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research has been supported by the National Science Centre Poland (2016/22/Z/ST5/00691), the Spanish Ministry of Science and Innovation (PCIN-2017-125, RTI2018-102161 and IJCI-2017-34110), and the Research Council of Norway (Grant n◦ 272797 "GoPHy MiCO") through the M-ERA.NET Joint Call 2016. We acknowledge the CERIC-ERIC Consortium for the access to MCX beamline at Elettra Sinchrotrone Trieste (proposal no 20187079). We also acknowledge Solaris National Radiation Centre Poland for access to the XAS/PEEM beamline (proposal no 181MS001).

**Conflicts of Interest:** The authors declare no conflict of interest.
