Mean-field Modeling Research Articles

A mean-field modeling study of the interaction between hydrogen and a palladium (110) single crystal

A new interpretation of the temperature programmed desorption (TPD) spectra of hydrogen on a Pd(110) single crystal surface is presented. The transient mean-field model developed accounts for both adsorption on the surface and diffusion of hydrogen into the lattice of the crystal. A new approach for modeling TPD spectra is developed, in which both the isothermal exposure as well as the temperature ramp of the TPD experiment are modeled in a consistent way. We demonstrate that for systems with substantial diffusion of the adsorbate into the substrate’s lattice it is not sufficient to report exposure values. For such systems, exposure time has a far more pronounced effect than the exposure pressure has on the TPD spectra, because diffusion is a strongly time-dependent process. The modeling and experimental results for the H2/Pd(110) system are in good agreement and suggest the existence of a distinct subsurface state, in addition to the surface and bulk states of hydrogen. Low frequency factors derived from the model for the processes connecting the subsurface with the surface and bulk state emphasize the restricted nature of the corresponding transition states.

Collapsing cycloidal structures in the magnetic phase diagram of erbium.

The magnetic structure of Er with a magnetic field applied in the hexagonal basal plane has been studied using a combination of experimental techniques and mean-field modeling. From neutron-scattering and magnetization measurements, phase diagrams are constructed. At temperatures above approximately 20 K, the application of a field is found to favor cycloidal structures with modulation wave vectors of ${\mathbf{q}}_{\mathit{c}}$=(6/23)${\mathbf{c}}^{\mathrm{*}}$,(4/15)${\mathbf{c}}^{\mathrm{*}}$, and (2/7)${\mathbf{c}}^{\mathrm{*}}$. For fields above \ensuremath{\approxeq}40 kOe, the (2/7) structure dominates the phase diagram. From a detailed study of this most stable cycloid, we determine how it distorts as the field is increased. In low fields, there is a spin reorientation, so that the plane of the cycloid becomes perpendicular to the applied field, while in larger fields, the cycloid collapses through a series of fanlike structures. At lower temperatures, as the field is increased there is a first-order transition at \ensuremath{\approxeq}20 kOe from a cone to a fan in the a-c plane.

Mechanisms for Dynamo Mode Excitation

Dynamo theory of the solar magnetic field finds itself in a period of reappraisal since about 1980. There are two reasons for this: (1) The required increase of the angular speed Ω, with decreasing r is neither found in numerical simulations nor measured by helioseismology. (2) Mean field modeling shows often little regard for inherent physical restrictions and selfconsistency.