*2.1. X-ray Powder Diffraction (XRPD)*

The X-ray powder diffraction (XRPD) patterns of the three catalysts for LCG (LaCo0.65Ga0.35O3) and LKCG-x (La1−xKxCo0.65Ga0.35O3, x = 0.1 and 0.2, where x is the K content in perovskite) (see 3.2 catalysis synthesis) are shown in Figure 1a. The diffraction peaks at 2θ = 23.2, 33.3, 40.6, 47.4 and 58.8◦ are attributed to the characteristic diffraction peaks of perovskite-type oxide (PTO). For LKCG-0.1 catalyst, with the addition of K ions into LCG, the perovskite diffraction peaks move to lower 2θ values (seen from the illustration of Figure 1a), for that the ion radius of K+ (0.155 nm) is larger than that of La3+ (0.136 nm) [18]. The existence of perovskite structure after calcination is beneficial to the interaction and the even dispersion of all the elements.

For the LKCG-0.2, a new Co3O4 diffraction peak in Figure 1a can be seen. Since the amount of K entering the perovskite is limited, when the K doping amount is more than 0.1, part of potassium cannot incorporate into the perovskite structure and cover the surface of the catalyst in the form of oxide [18]. The presence of K2O disrupted the dispersion of elements in the catalyst precursor, resulting in the formation of Co3O4. It is worth noting that a part of LaCoyGa1−yO3 and La1−zKzCo1−mGamO3 should also exist accompanied by the formation of Co3O4.

Meanwhile, Ga-containing oxides among the three samples cannot be detected, indicating that Ga entered into the structure of perovskite. The uniformly dispersed Co and Ga ions in the LKCG-0.1 catalyst are advantageous for the synergism between them, favoring the catalytic performance.

The XRPD profiles of three catalysts reduced at 750 ◦C (see 3.4 Catalysts' Performance) are presented in Figure 1b. As for LCG, the perovskite structure disappears and transfers to Co and La4Ga2O9. As for the reduction of LKCG-0.1, phases of La2O3, Co, LaGaO3, and a small amount of La4Ga2O9 can be observed. The existence of the characteristic diffraction peak of LaGaO3 and La2O3 indicated that the adding of K weakened the interaction between lanthanum and gallium. In other words, the addition of K in the perovskite modulated the composition of La-Ga-O, resulting in the change of La-Ga-O from La4Ga2O9 to LaGaO3 and La2O3.

Based on the above discussion in Figure 1a, parts of K cannot be doped into perovskite, resulting co-exist of LaCoyGa1−yO3 and La1−zKzCo1−mGamO3 in LKCG-0.2. During reduction, La1−zKzCo1−mGamO3 would be reduced into LaGaO3 while LaCoyGa1−yO3 to La4Ga2O9, as a result, the LKCG-0.2 are reduced to Co/LaGaO3-La4Ga2O9, as can be seen in Figure 1b.

**Figure 1.** X-ray powder diffraction (XRPD) patterns of catalysts after (**a**) calcination, (**b**) reduction and (**c**) reaction.

Figure 1c shows the XRPD profiles of the three catalysts after reaction and LKCG-0.1 after 200 h reaction. After reaction, part of La2O3 transferred to LaCO3OH and La2O2CO3, for that La2O3 and CO2 can react to generate La2O2CO3, and the further reaction between La2O2CO3, H2O and CO2 can generate LaCO3OH [19,20]. Since XRPD in this work was carried out ex situ, the catalysts containing La2O2CO3 could readily absorb H2O and CO2 in air, and then LaCO3OH formed. The co-existence of La2O3 and La2O2CO3 in the catalysts after reaction illustrated the feasibility of reaction of CO2 + La2O3 → La2O2CO3 *C* → 2CO + La2O3, which can help the catalysts eliminate carbon.

For the LCG catalyst after reaction, it should be noted that the catalyst was still Co/La4Ga2O9, which is the same as that after reduction. La2O2CO3 and La2O3 cannot be detected, indicating the above reaction of eliminating carbon deposition may be hard to occur due to a strong interaction existing between lanthanum and gallium.

It should be noted that no Co2C was observed in all the used samples, suggesting that the existence of gallium can prevent the formation of Co2C and stabilize the catalyst composition in the process of reaction. This is in accordance with the literature, which illustrated that the existence of gallium could improve the catalyst's stability [21].
