Magnetic helicity is a conserved quantity of ideal magneto-hydrodynamics characterized by an inverse turbulent cascade. Accordingly, it is often invoked as one of the basic physical quantities driving the generation and structuring of magnetic fields in a variety of astrophysical and laboratory plasmas. We provide here the first systematic comparison of six existing methods for the estimation of the helicity of magnetic fields known in a finite volume. All such methods are reviewed, benchmarked, and compared with each other, and specifically tested for accuracy and sensitivity to errors. To that purpose, we consider four groups of numerical tests, ranging from solutions of the three-dimensional, force-free equilibrium, to magneto-hydrodynamical numerical simulations. Almost all methods are found to produce the same value of magnetic helicity within few percent in all tests. In the more solar-relevant and realistic of the tests employed here, the simulation of an eruptive flux rope, the spread in the computed values obtained by all but one method is only 3 %, indicating the reliability and mutual consistency of such methods in appropriate parameter ranges. However, methods show differences in the sensitivity to numerical resolution and to errors in the solenoidal property of the input fields. In addition to finite volume methods, we also briefly discuss a method that estimates helicity from the field lines' twist, and one that exploits the field's value at one boundary and a coronal minimal connectivity instead of a pre-defined three-dimensional magnetic-field solution.

The surface state and active sites of a fresh Mo2N/Al2O3 were investigated by FTIR, volumetric chemisorption, and TPD-MS techniques. It has been found that adsorption properties of CO on the fresh sample are quite different from those of the reduced passivated one. For reduced passivated Mo2N/Al2O3, the IR spectrum of adsorbed CO shows that a band at ∼2180 cm-1 together with two weak bands at 2100 and 2035 cm-1 appear, suggesting that the Mo4+ cation is predominant on the surface; namely, the surface is in oxynitride form. However, for the fresh sample, adsorbed CO gives two characteristic IR bands at 2045 and 2200 cm-1, respectively, corresponding to the adsorbed CO on the molybdenum and the nitrogen sites, forming linearly adsorbed CO and NCO species. From the band position of adsorbed CO, the surface molybdenum atoms are slightly positively charged, i.e., in a state of Moδ+(0 < δ < 2). The assignment of the band at 2200 cm-1 to NCO species (CO adsorbed on N site) was further confirmed by TPD-MS and volumetric chemisorption. TPD-MS shows two CO desorption peaks at 373 and ca. 473 K, indicating two different CO adsorption sites on the catalyst. The volumetric chemisorption proves that the CO uptake increases significantly when the passivated sample is nitrided at 723 K and above, compared with the case of the reduced sample. These results suggest that not only Mo sites in low valences are present on the surface of fresh Mo nitride, but also nitrogen sites are present and so active that can react with CO to form surface NCO species.

The structure and catalytic properties of binary dispersed oxide structures prepared by sequential deposition of VO x and MoO x or VO x and CrO x on Al 2 O 3 were examined using Raman and UV-visible spectroscopies, the dynamics of stoichiometric reduction in H 2 , and the oxidative dehydrogenation of propane. VO x domains on Al 2 O 3 modified by an equivalent MoO x monolayer led to dispersed binary structures at all surface densities. MoO x layers led to higher reactivity for VO x domains present at low VO x surface densities by replacing V-O-Al structures with more reactive V-O-Mo species. At higher surface densities, V-O-V structures in prevalent polyvanadates were replaced with less reactive V-O-Mo, leading to lower reducibility and oxidative dehydrogenation rates. Raman, reduction, and UV-visible data indicate that polyvanadates predominant on Al 2 O 3 convert to dispersed binary oxide structures when MoO x is deposited before or after VO x deposition; these structures are less reducible and show higher UV-visible absorption energies than polyvanadate structures on Al 2 O 3 . The deposition sequence in binary Mo-V catalysts did not lead to significant differences in structure or catalytic rates, suggesting that the two active oxide components become intimately mixed. The deposition of CrO x on Al 2 O 3 led to more reactive VO x domains than those deposited on pure Al 2 O 3 at similar VO x surface densities. At all surface densities, the replacement of V-O-Al or V-O-V structures with V-O-Cr increased the reducibility and catalytic reactivity of VO x domains; it also led to higher propene selectivities via the selective inhibition of secondary C 3 H 6 combustion pathways, prevalent in VO x -Al 2 O 3 , and of C 3 H 8 combustion routes that lead to low alkene selectivities on CrO x -Al 2 O 3 . VO x and CrO x mix significantly during synthesis or thermal treatment to form CrVO 4 domains. The deposition sequence, however, influences catalytic selectivities and reduction rates, suggesting the retention of some of the component deposited last as unmixed domains exposed at catalyst surfaces. These findings suggest that the reduction and catalytic properties of active VO x domains can be modified significantly by the formation of binary dispersed structures. VO x -CrO x structures, in particular, lead to higher oxidative dehydrogenation rates and selectivities than do VO x domains present at similar surface densities on pure Al 2 O 3 supports.