A novel sodium-promoted Fe-Co/NC catalyst prepared by incipient-wet-impregnation method using ZIF-67 as a support was employed to convert CO2 to light olefins through hydrogenation reaction. Properties of the synthesized catalysts calcinated at various temperatures (from 400 to 700 °C) were investigated by XRD, SEM, TEM and Mӧssbauer spectroscopy. Characterization results showed that the support could be fully converted into carbon support above 500 °C, which could anchor metal particles, thus resulting in a uniform dispersion of active components. Furthermore, the Fe-Co alloy was formed during N2 calcination, and was converted into active components, such as Fe3O4, Fe5C2, and Co2C during the reaction. The reaction result indicated that FeCo/NC-600 catalyst exhibited the highest selectivity of light olefins (C2= − C4=, 27%) and CO2 conversion could reach around 37% when this catalyst pyrolyzed at 600 °C in N2. The highest selectivity for light olefins may be related to the combination of suitable particle size and sufficient active sites of iron carbide.

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We give a new unified proof that any simple graph on $n$ vertices with maximum degree at most $\Delta$ has no more than $a\binom{\Delta+1}{t}+\binom{b}{t}$ cliques of size $t \ (t \ge 3)$, where $n = a(\Delta+1)+b \ (0 \le b \le \Delta)$.

For a finite point set P ⊂ R d , denote by diam(P ) the ratio of the largest to the smallest distances between pairs of points in P . Let c d,α (n) be the largest integer c such that any n-point set P ⊂ R d in general position, satisfying diam(P ) < α d √ n, contains an c-point convex independent subset. We determine the asymptotics of c d,α (n) as n → ∞ by showing the existence of positive constants β = β(d, α) and γ = γ(d) such that βn d−1 d+1 ≤ c d,α (n) ≤ γn d−1 d+1 for α ≥ 2.