Surface layer magnetization

Fig. 47. Log-log plot of the surface layer magnetization mi vs. reduced temperature, for various ratios of the exchange 7S in the surface planes to the exchange J in the bulk. Slopes of the straight lines yield effective exponents jS (indicated by the number). Data are from Monte Carlo simulation of 50 x 50 x 40 lattices with two free 50 x 50 surfaces and otherwise periodic boundary conditions. From Binder and Landau (1984).

Fig. 50. Magnetization profiles across thin Ising films [eq. (1) with H — H — 0], upper part, and near the surface of semi-infinite Heisenberg ferromagnels, lower part (where bulk behavior in the Monte Carlo simulation is enforced by an effective field boundary condition at z — 16). Note that in the Ising case (where three film thicknesses L = 5, 10, and 20 are shown) the surface layer magnetization m- — m(z — 0) is independent of L, and for L > 10 already the bulk value of the order parameter is reached in the center of the film. For the Heisenberg model, on the other hand, at a comparable temperature distance from % the free surface produces a Long-range perturbation of the local magnetization m(z). From Binder and Hohenbcrg (1974).

To define the thennodynamic state of a system one must specify fhe values of a minimum number of variables, enough to reproduce the system with all its macroscopic properties. If special forces (surface effecls, external fields—electric, magnetic, gravitational, etc) are absent, or if the bulk properties are insensitive to these forces, e.g. the weak terrestrial magnetic field, it ordinarily suffices—for a one-component system—to specify fliree variables, e.g. fhe femperature T, the pressure p and the number of moles n, or an equivalent set. For example, if the volume of a surface layer is negligible in comparison with the total volume, surface effects usually contribute negligibly to bulk thennodynamic properties. 

Z.S. Wronski, X.Z. Zhou, A.H. Monish, A.M. Stewart, Magnetic microcrystals and surface layers in as-quenched and hydrogenated metaUic glasses, J. Appl. Phys. 57 (1986) 3548-3550. 

Molybdenum oxide - alumina systems have been studied in detail (4-8). Several authors have pointed out that a molybdate surface layer is formed, due to an interaction between molybdenum oxide and the alumina support (9-11). Richardson (12) studied the structural form of cobalt in several oxidic cobalt-molybdenum-alumina catalysts. The presence of an active cobalt-molybdate complex was concluded from magnetic susceptibility measurements. Moreover cobalt aluminate and cobalt oxide were found. Only the active cobalt molybdate complex would contribute to the activity and be characterized by octahedrally coordinated cobalt. Lipsch and Schuit (10) studied a commercial oxidic hydrodesulfurization catalyst, containing 12 wt% M0O3 and 4 wt% CoO. They concluded that a cobalt aluminate phase was present and could not find indications for an active cobalt molybdate complex. Recent magnetic susceptibility studies of the same type of catalyst (13) confirmed the conclusion of Lipsch and Schuit. 

The optimal activity for a cobalt-molybdenum-alumina catalyst is obtained by calcination at the higher temperatures. This means that the cobalt ions, present as a cobalt aluminate phase according to the reflectance spectra and the magnetic susceptibility measurements, still have a pronounced promoting action after this calcination. The assumption of cobalt present in the surface layer of the alumina lattice explains both the high activity due to the cobalt promotion as well as the presence of the second Lewis band. This configuration is shown schematically in Figure lib. 

Scheme 13.1 Reaction of a hydrogen terminated surface with an alkene to generate surface mono-layers (a) monolayer formation by reaction of silicon with H2C=CH(CH2)90Ph(C6H40Me)2, (b, c) monolayer derivatisation to give a surface layer of tethered magnetic TiW5 polyoxometalate clusters.4...

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