Stability of β-Mo₂C Facets from ab Initio Atomistic Thermodynamics

Abstract

The stability of β-Mo2C surfaces has been computed at the level of density functional theory under the consideration of the temperature, pressure, and molar ratios of CH4 /H2 and CO/CO2 gas mixtures by using ab initio atomistic thermodynamic calculations. It was found that the (001) surface is most stable at low temperature, whereas (101) becomes dominant at high temperature with CH4 as carbon source, and the computed surface stability is supported by the experimental X-ray diffraction pattern and intensity. For CO as carbon source, the (101) surface has the smallest surface Gibbs free energy at temperatures up to 1000 K and is most stable. On the basis of the Wulff-type particle shapes from surface Gibbs free energies the (101) facet represents the largest surface area of β-Mo2C. Our findings are in perfect agreement with the results of high-resolution transmission electron microscopy.

Effective and Highly Selective CO Generation from CO2 Using a Polycrystalline α-Mo2C Catalyst

“…26,27 Bulk optimizations carried out using the PBE functional yield lattice parameters (a = 3.04 Å, c = 4.73 Å) in agreement with previous values and those experimentally reported. 27 Note that surface slabs notation follows that of Wang and coworkers and are based on their bulk unit cell definition.…”

Elementary steps of syngas reactions on Mo2C(001): Adsorption thermochemistry and bond dissociation

“…al. [41] found that the Mo 2 C(001) surface is still present when more reactive carbon is present, although to a lesser extent. No previous studies have investigated the effects of hydrogen or oxygen on surface energies.…”

“…No previous studies have investigated the effects of hydrogen or oxygen on surface energies. The Mo 2 C(001) surface is chosen as a starting point to investigate effects of hydrogen and oxygen on Mo 2 C surface stability since it has a simple structure, is the most close-packed surface, and is predicted to have significant presence on nanostructured Mo 2 C [40,41].…”

“…Given a set of n surfaces it is possible to calculate their surface energies γ n and the most stable equilibrium surface can be predicted by min(γ n ). Furthermore, the relative abundance of a surface at equilibrium can be estimated using a Boltzmann distrubution of the surface energies (infinite slab) or a Wulff construction (finite particles) [40,41]. The minimum energy surface and relative abundance of surfaces determined using these methods assumes that the only possible surfaces are the set of n surfaces for which γ is calculated, and assumes that the system is in equilibrium.…”

“…In order to further improve the performance of molybdenum carbide catalysts it is of value to understand the reactivity, selectivity, and stability of molybdenum carbide under various conditions. Numerous theoretical studies have investigated the surface stability [38,39,40,41], adsorption energies [42,43,44,45,46,47,48,49,50,51,40,52], reaction energetics [53,54,46,55,52], and alkali-doping [40,50] on Mo 2 C. The most well-studied surface is the Mo 2 C(001) surface, and both orthorhombic and hexagonal close packed Mo 2 C have been investigated. The results have indicated that the non-polar (011) surface is the most stable regardless of carbon chemical potential, but that the surface energies are sufficiently close that all surfaces are expected to be present on nanoparticles [40,39].…”